0.10/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.11 % Command : eprover --auto -s --tableau=1 [--tableau-equality=1] --tableau-depth=10 %s 0.10/0.31 % Computer : n018.cluster.edu 0.10/0.31 % Model : x86_64 x86_64 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.31 % Memory : 8042.1875MB 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.31 % CPULimit : 960 0.10/0.31 % WCLimit : 120 0.10/0.31 % DateTime : Thu Jul 2 08:28:07 EDT 2020 0.10/0.31 % CPUTime : 1.16/1.36 % Running in FOF/CNF-non-UEQ mode 6.78/7.00 # No SInE strategy applied 6.78/7.00 # Auto-Mode selected heuristic C07_19_nc_SAT001_MinMin_rr 6.78/7.00 # and selection function SelectMaxLComplexAvoidPosPred. 6.78/7.00 # 6.78/7.00 # Presaturation interreduction done 6.78/7.00 # Number of axioms: 7353 Number of unprocessed: 5978 6.78/7.00 # Tableaux proof search. 6.78/7.00 # 5978 beginning clauses after preprocessing and clausification 6.78/7.00 # Creating start rules for all conjectures. 6.78/7.00 # 1423 unit axioms, 1 start rules, and 4555 other extension candidates. 6.78/7.00 ## Beginning tableaux proof search with 1 start rule applications. 6.97/7.19 # Beginning deep saturation check 6.97/7.19 # Saturate returned empty clause 0x494bb40. 6.97/7.19 # Success 6.97/7.19 # SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p 6.97/7.19 # SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 6.97/7.19 # Begin clausification derivation 6.97/7.19 fof(fact_succ__Bit0, axiom, ![X19]:c_Int_OBit1(X19)=c_Int_Osucc(c_Int_OBit0(X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_succ__Bit0)). 6.97/7.19 fof(fact_Bit0__def, axiom, ![X19]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19),X19)=c_Int_OBit0(X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Bit0__def)). 6.97/7.19 fof(fact_diff__bin__simps_I2_J, axiom, ![X19]:c_Int_Osucc(X19)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19),c_Int_OMin), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I2_J)). 6.97/7.19 fof(fact_add__Pls, axiom, ![X19]:X19=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Pls)). 6.97/7.19 fof(fact_zmult__eq__1__iff, axiom, ![X32, X34]:(((X34=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)&hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=X32)|(c_Groups_Oone__class_Oone(tc_Int_Oint)=X32&c_Groups_Oone__class_Oone(tc_Int_Oint)=X34))<=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34),X32)=c_Groups_Oone__class_Oone(tc_Int_Oint)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult__eq__1__iff)). 6.97/7.19 fof(fact_number__of__is__id, axiom, ![X19]:hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19)=X19, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__is__id)). 6.97/7.19 fof(fact_mult__Min, axiom, ![X19]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X19)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__Min)). 6.97/7.19 fof(fact_minus__Min, axiom, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)=c_Int_OBit1(c_Int_OPls), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__Min)). 6.97/7.19 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)). 6.97/7.19 fof(fact_succ__def, axiom, ![X19]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Int_Osucc(X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_succ__def)). 6.97/7.19 fof(fact_vimage__Collect__eq, axiom, ![X17, X18, X12, X5]:hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(X12,tc_HOL_Obool,X5),X17),X18))=hAPP(c_Set_Ovimage(X5,X12,X18),hAPP(c_Set_OCollect(X12),X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__Collect__eq)). 6.97/7.19 fof(fact_Collect__def, axiom, ![X17, X5]:X17=hAPP(c_Set_OCollect(X5),X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__def)). 6.97/7.19 fof(fact_upt__0, axiom, ![X28]:c_List_Oupt(X28,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_List_Olist_ONil(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upt__0)). 6.97/7.19 fof(fact_sorted__list__of__set__range, axiom, ![X32, X34]:c_List_Oupt(X34,X32)=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__list__of__set__range)). 6.97/7.19 fof(fact_Collect__mem__eq, axiom, ![X4, X5]:hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X4))=X4, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__mem__eq)). 6.97/7.19 fof(fact_Collect__split, axiom, ![X104, X17, X12, X5]:hAPP(c_Set_OCollect(tc_prod(X5,X12)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X12,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X12)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),X17))),X104)))=hAPP(hAPP(c_Product__Type_OSigma(X5,X12),hAPP(c_Set_OCollect(X5),X17)),hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X5),hAPP(c_Set_OCollect(X12),X104))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__split)). 6.97/7.19 fof(fact_Collect__conj__eq, axiom, ![X104, X17, X5]:hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),X17)),X104))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X17)),hAPP(c_Set_OCollect(X5),X104)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__conj__eq)). 6.97/7.19 fof(fact_nat__number__of, axiom, ![X39]:hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X39)=hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X39)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__number__of)). 6.97/7.19 fof(fact_power2__eq__1__iff, axiom, ![X2, X5]:((hAPP(hAPP(c_Power_Opower__class_Opower(X5),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Oone__class_Oone(X5)<=>(X2=c_Groups_Oone__class_Oone(X5)|hAPP(c_Groups_Ouminus__class_Ouminus(X5),c_Groups_Oone__class_Oone(X5))=X2))<=class_Rings_Oring__1__no__zero__divisors(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power2__eq__1__iff)). 6.97/7.19 fof(fact_less__2__cases, axiom, ![X25]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=>(X25=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__2__cases)). 6.97/7.19 fof(fact_zero__less__power2, axiom, ![X2, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),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(X5)!=X2)<=class_Rings_Olinordered__idom(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__power2)). 6.97/7.19 fof(fact_power2__less__0, axiom, ![X30, X8]:(class_Rings_Olinordered__idom(X8)=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X8))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power2__less__0)). 6.97/7.19 fof(fact_pred__def, axiom, ![X19]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Int_Opred(X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pred__def)). 6.97/7.19 fof(fact_add__Min__right, axiom, ![X19]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19),c_Int_OMin)=c_Int_Opred(X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Min__right)). 6.97/7.19 fof(fact_removeAll__filter__not, axiom, ![X23, X5, X35, X17]:(hAPP(c_List_Ofilter(X5,X17),X23)=hAPP(c_List_OremoveAll(X5,X35),hAPP(c_List_Ofilter(X5,X17),X23))<=~(hBOOL(hAPP(X17,X35)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_removeAll__filter__not)). 6.97/7.19 fof(fact_removeAll__filter__not__eq, axiom, ![X35, X5]:c_List_Ofilter(X5,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(c_fequal,X35)))=c_List_OremoveAll(X5,X35), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_removeAll__filter__not__eq)). 6.97/7.19 fof(fact_Collect__neg__eq, axiom, ![X17, X5]:hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X17))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__neg__eq)). 6.97/7.19 fof(fact_not__iszero__Numeral1, axiom, ![X8]:(class_Int_Onumber__ring(X8)=>~(c_Int_Oiszero(X8,hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OBit1(c_Int_OPls))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__iszero__Numeral1)). 6.97/7.19 fof(fact_length__transpose, axiom, ![X23, X5]:c_List_Ofoldr(tc_List_Olist(X5),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X5)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X5))),X23,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),c_List_Otranspose(X5,X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__transpose)). 6.97/7.19 fof(fact_foldr__foldl, axiom, ![X2, X23, X18, X5, X12]:hAPP(c_List_Ofoldl(X5,X12,hAPP(c_COMBC(X12,X5,X5),X18),X2),hAPP(c_List_Orev(X12),X23))=c_List_Ofoldr(X12,X5,X18,X23,X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldr__foldl)). 6.97/7.19 fof(fact_transpose__aux__filter__head, axiom, ![X77, X5]:hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),X5),c_List_Ohd(X5)),hAPP(c_List_Ofilter(tc_List_Olist(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X5)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(X5),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X5)))),X77))=c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_Olist__case(tc_List_Olist(X5),X5,c_List_Olist_ONil(X5),hAPP(hAPP(c_COMBB(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),X5),c_COMBK(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_COMBC(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_OCons(X5)),c_List_Olist_ONil(X5))))),X77)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__aux__filter__head)). 6.97/7.19 fof(fact_concat__conv__foldl, axiom, ![X77, X5]:c_List_Oconcat(X5,X77)=hAPP(c_List_Ofoldl(tc_List_Olist(X5),tc_List_Olist(X5),c_List_Oappend(X5),c_List_Olist_ONil(X5)),X77), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_concat__conv__foldl)). 6.97/7.19 fof(fact_maps__def, axiom, ![X23, X18, X5, X12]:c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(X12,tc_List_Olist(X5)),X18),X23))=c_List_Omaps(X12,X5,X18,X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_maps__def)). 6.97/7.19 fof(fact_singleton__conv, axiom, ![X2, X5]:hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))=hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_singleton__conv)). 6.97/7.19 fof(fact_singleton__conv2, axiom, ![X2, X5]:hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))=hAPP(c_Set_OCollect(X5),hAPP(c_fequal,X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_singleton__conv2)). 6.97/7.19 fof(fact_transpose__aux__filter__tail, axiom, ![X77, X5]:hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Otl(X5)),hAPP(c_List_Ofilter(tc_List_Olist(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X5)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(X5),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X5)))),X77))=c_List_Oconcat(tc_List_Olist(X5),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X5)),X5,c_List_Olist_ONil(tc_List_Olist(X5)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5))),X5),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5)),tc_List_Olist(tc_List_Olist(X5))),c_List_Olist_OCons(tc_List_Olist(X5))),c_List_Olist_ONil(tc_List_Olist(X5)))))),X77)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__aux__filter__tail)). 6.97/7.19 fof(fact_add__Bit0__Bit1, axiom, ![X93, X19]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X19)),c_Int_OBit1(X93))=c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19),X93)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Bit0__Bit1)). 6.97/7.19 fof(fact_diff__bin__simps_I5_J, axiom, ![X93]:c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X93))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X93)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I5_J)). 6.97/7.19 fof(fact_diff__bin__simps_I7_J, axiom, ![X93, X19]:c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19),X93))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X19)),c_Int_OBit0(X93)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I7_J)). 6.97/7.19 fof(fact_Diff__Int__distrib2, axiom, ![X65, X11, X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11)),X65)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X65)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X65)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__Int__distrib2)). 6.97/7.19 fof(fact_Int__Diff, axiom, ![X65, X11, X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X65))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)),X65), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__Diff)). 6.97/7.19 fof(fact_divmod__int__pdivmod, axiom, ![X52, X33]:((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(X33,X52)<=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X33)&(X33!=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)),X33)=c_Divides_Odivmod__int(X33,X52)<=X52=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(X52!=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,X52))),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)),X52)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X52),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(X33,X52)),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),X52))))),c_Divides_Opdivmod(X33,X52))))=c_Divides_Odivmod__int(X33,X52))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__pdivmod)). 6.97/7.19 fof(fact_apsnd__def, axiom, ![X18, X5, X62, X12]:c_Product__Type_Oapsnd(X12,X62,X5,X18)=c_Product__Type_Omap__pair(X5,X5,X12,X62,c_Fun_Oid(X5),X18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_apsnd__def)). 6.97/7.19 fof(fact_divmod__int__code, axiom, ![X52, X33]:((((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,X52))),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,X33)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X52))),c_Divides_Opdivmod(X33,X52)),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),X52))))),c_Divides_Opdivmod(X33,X52))))=c_Divides_Odivmod__int(X33,X52)<=c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X52)&(hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33)=c_Divides_Odivmod__int(X33,X52)<=X52=c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=X33!=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_Ozero__class_Ozero(tc_Int_Oint))=c_Divides_Odivmod__int(X33,X52)<=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__code)). 6.97/7.19 fof(fact_of__int__num, axiom, ![X33, X5]:(((X33=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=>hAPP(c_Int_Oring__1__class_Oof__int(X5),X33)=c_Groups_Ozero__class_Ozero(X5))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X33=>((hAPP(c_Int_Oring__1__class_Oof__int(X5),X33)=hAPP(c_Groups_Ouminus__class_Ouminus(X5),hAPP(c_Int_Oring__1__class_Oof__int(X5),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X33)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))&(hAPP(c_Int_Oring__1__class_Oof__int(X5),X33)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X5),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X5,X5)),tc_fun(tc_Int_Oint,X5)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,X5),X5),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X5,X5)),tc_fun(tc_Int_Oint,X5)),tc_Int_Oint),c_COMBB(tc_fun(X5,X5),X5,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X5,tc_fun(tc_fun(X5,X5),X5),tc_Int_Oint),c_HOL_OLet(X5,X5)),c_Int_Oring__1__class_Oof__int(X5)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X5,X5),tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,X5)),tc_fun(tc_fun(X5,X5),tc_fun(X5,X5)),tc_Int_Oint),c_COMBS(X5,X5,X5)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X5,X5),tc_fun(X5,tc_fun(X5,X5))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,X5)),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_fun(X5,X5))),tc_Int_Oint),c_COMBB(X5,tc_fun(X5,X5),X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),tc_Int_Oint),c_If(X5)),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(X5,X5,X5),c_Groups_Oplus__class_Oplus(X5)),c_COMBI(X5))))),hAPP(hAPP(c_COMBC(X5,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_Groups_Oplus__class_Oplus(X5)),hAPP(hAPP(c_COMBS(X5,X5,X5),c_Groups_Oplus__class_Oplus(X5)),c_COMBI(X5)))),c_Groups_Oone__class_Oone(X5))))),c_Divides_Odivmod__int(X33,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))))<=class_Rings_Oring__1(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__num)). 6.97/7.19 fof(fact_power2__diff, axiom, ![X7, X6, X8]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),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(X8),X7),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(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X6)),X7))=hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X6),X7)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))<=class_Int_Onumber__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power2__diff)). 6.97/7.19 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)). 6.97/7.19 fof(fact_power2__sum, axiom, ![X7, X6, X8]:(class_Int_Onumber__ring(X8)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),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(X8),X7),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(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X6)),X7))=hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X6),X7)),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__sum)). 6.97/7.19 fof(fact_neg__zmod__mult__2, axiom, ![X29, X30]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X30),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),X29),c_Groups_Oone__class_Oone(tc_Int_Oint)),X30))),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)))),X29)),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)))),X30))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__zmod__mult__2)). 6.97/7.19 fof(fact_pos__zmod__mult__2, axiom, ![X29, X30]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30))=>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)))),X29)),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)))),X30))=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,X29,X30)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__zmod__mult__2)). 6.97/7.19 fof(fact_int__of__code, axiom, ![X19]:((((c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X19,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,X19)=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),X19),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,X19,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),X19),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,X19)))<=X19!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))&(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X19=>c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(c_Code__Numeral_Oint__of,X19))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__of__code)). 6.97/7.19 fof(fact_neg__zdiv__mult__2, axiom, ![X29, X30]:(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X29),c_Groups_Oone__class_Oone(tc_Int_Oint))),X30)=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)))),X29))),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)))),X30))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X30),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__zdiv__mult__2)). 6.97/7.19 fof(fact_zmod__number__of__Bit1, axiom, ![X40, X39]:((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),X39)))=>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),X40),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X39)))),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(X40)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X39))))&(c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X40)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X39)))=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),X40)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X39)))),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),X39)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__number__of__Bit1)). 6.97/7.19 fof(fact_vimage__def, axiom, ![X11, X18, X12, X5]:hAPP(c_Set_Ovimage(X5,X12,X18),X11)=hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBC(X5,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(X12,tc_fun(tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),X5),c_member(X12)),X18)),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__def)). 6.97/7.19 fof(fact_pos__zdiv__mult__2, axiom, ![X29, X30]:(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X29),X30)=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)))),X29))),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)))),X30))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__zdiv__mult__2)). 6.97/7.19 fof(fact_transpose__rectangle, axiom, ![X32, X5, X23]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X32<=c_List_Olist_ONil(tc_List_Olist(X5))=X23)=>(![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X23)))=>hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X5)),X23),X42))=X32)=>c_List_Otranspose(X5,X23)=hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X5)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X5)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X5),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X5)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X5)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X5),hAPP(hAPP(c_COMBB(tc_List_Olist(X5),tc_fun(tc_Nat_Onat,X5),tc_Nat_Onat),c_List_Onth(X5)),hAPP(c_List_Onth(tc_List_Olist(X5)),X23))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X23)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__rectangle)). 6.97/7.19 fof(fact_atLeastLessThan0, axiom, ![X34]:c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThan0)). 6.97/7.19 fof(fact_sum__power2__le__zero__iff, axiom, ![X38, X35, X5]:(class_Rings_Olinordered__idom(X5)=>((X38=c_Groups_Ozero__class_Ozero(X5)&X35=c_Groups_Ozero__class_Ozero(X5))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X35),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(X5),X38),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__power2__le__zero__iff)). 6.97/7.19 fof(fact_sum__power2__gt__zero__iff, axiom, ![X38, X35, X5]:(class_Rings_Olinordered__idom(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X35),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(X5),X38),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))<=>(c_Groups_Ozero__class_Ozero(X5)!=X38|c_Groups_Ozero__class_Ozero(X5)!=X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__power2__gt__zero__iff)). 6.97/7.19 fof(fact_Suc__eq__number__of, axiom, ![X60, X32]:(hAPP(c_Nat_OSuc,X32)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X60)<=>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(X60))),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)),X32)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__eq__number__of)). 6.97/7.19 fof(fact_Collect__imp__eq, axiom, ![X104, X17, X5]:hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fimplies),X17)),X104))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X17))),hAPP(c_Set_OCollect(X5),X104)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__imp__eq)). 6.97/7.19 fof(fact_Compl__Diff__eq, axiom, ![X11, X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X4)),X11)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__Diff__eq)). 6.97/7.19 fof(fact_sum__power2__ge__zero, axiom, ![X7, X6, X8]:(class_Rings_Olinordered__idom(X8)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),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(X8),X7),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)). 6.97/7.19 fof(fact_lists__eq__set, axiom, ![X4, X5]:hAPP(c_Set_OCollect(tc_List_Olist(X5)),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X5)),c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool))),c_List_Oset(X5))),X4))=c_List_Olists(X5,X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists__eq__set)). 6.97/7.19 fof(fact_less__Suc__number__of, axiom, ![X60, X32]:(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(X60))),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),X32)),c_Int_Onat)))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X32)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X60)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__Suc__number__of)). 6.97/7.19 fof(fact_le__Suc__number__of, axiom, ![X60, X32]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X32)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X60)))<=>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(X60))),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),X32)),c_Int_Onat)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__Suc__number__of)). 6.97/7.19 fof(fact_negDivAlg_Opinduct, axiom, ![X17, X103, X109]:(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),X109),X103)))=>(![X13, X96]:(((hBOOL(hAPP(hAPP(X17,X13),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)))),X96)))<=~((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),X13),X96)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X96),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))=>hBOOL(hAPP(hAPP(X17,X13),X96)))<=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),X13),X96))))=>hBOOL(hAPP(hAPP(X17,X109),X103)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negDivAlg_Opinduct)). 6.97/7.19 fof(fact_sum__power2__eq__zero__iff, axiom, ![X38, X35, X5]:(class_Rings_Olinordered__idom(X5)=>(c_Groups_Ozero__class_Ozero(X5)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X35),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(X5),X38),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))<=>(c_Groups_Ozero__class_Ozero(X5)=X35&c_Groups_Ozero__class_Ozero(X5)=X38))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__power2__eq__zero__iff)). 6.97/7.19 fof(fact_Sup__Inf, axiom, ![X4, X5]:(c_Complete__Lattice_OInf__class_OInf(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OAll(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fimplies),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X4)))),hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X5))))))=c_Complete__Lattice_OSup__class_OSup(X5,X4)<=class_Complete__Lattice_Ocomplete__lattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__Inf)). 6.97/7.19 fof(fact_Collect__ball__eq, axiom, ![X17, X4, X12, X5]:hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OAll(X12)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool),X5),hAPP(c_COMBS(X12,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X12),c_fimplies),hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X4)))),X17)))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X12),c_Set_OCollect(X5)),hAPP(c_COMBC(X5,X12,tc_HOL_Obool),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__ball__eq)). 6.97/7.19 fof(fact_Inf__Sup, axiom, ![X4, X5]:(c_Complete__Lattice_OInf__class_OInf(X5,X4)=c_Complete__Lattice_OSup__class_OSup(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OAll(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fimplies),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X4)))),c_Orderings_Oord__class_Oless__eq(X5)))))<=class_Complete__Lattice_Ocomplete__lattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__Sup)). 6.97/7.19 fof(fact_posDivAlg_Opinduct, axiom, ![X17, X103, X109]:((![X13, X96]:((hBOOL(hAPP(hAPP(X17,X13),X96))<=(~((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13),X96))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X96),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))=>hBOOL(hAPP(hAPP(X17,X13),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)))),X96)))))<=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),X13),X96))))=>hBOOL(hAPP(hAPP(X17,X109),X103)))<=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),X109),X103)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_posDivAlg_Opinduct)). 6.97/7.19 fof(fact_Nitpick_Oprod__def, axiom, ![X11, X4, X12, X5]:hAPP(c_Set_OCollect(tc_prod(X5,X12)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X12,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X12)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X4)))),hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X11))))=c_Nitpick_Oprod(X5,X12,X4,X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Oprod__def)). 6.97/7.19 fof(fact_power__odd__eq, axiom, ![X25, X30, X8]:(class_Groups_Omonoid__mult(X8)=>hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),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)))),X25)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25)),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)). 6.97/7.19 fof(fact_power__minus__even, axiom, ![X25, X30, X8]:(class_Rings_Oring__1(X8)=>hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X30)),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)))),X25))=hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),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)))),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__minus__even)). 6.97/7.19 fof(fact_power__even__eq, axiom, ![X25, X30, X8]:(hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25)),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(X8),X30),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)))),X25))<=class_Groups_Omonoid__mult(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__even__eq)). 6.97/7.19 fof(fact_dropWhile__neq__rev, axiom, ![X35, X23, X5]:(hBOOL(hAPP(c_List_Odistinct(X5),X23))=>(hAPP(hAPP(c_List_Olist_OCons(X5),X35),hAPP(c_List_Orev(X5),c_List_OtakeWhile(X5,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X35)),X23)))=c_List_OdropWhile(X5,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X35)),hAPP(c_List_Orev(X5),X23))<=hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dropWhile__neq__rev)). 6.97/7.19 fof(fact_dropWhile__eq__drop, axiom, ![X23, X17, X5]:c_List_OdropWhile(X5,X17,X23)=hAPP(hAPP(c_List_Odrop(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X17,X23))),X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dropWhile__eq__drop)). 6.97/7.19 fof(fact_inv__into__def, axiom, ![X35, X18, X4, X12, X5]:hAPP(c_Hilbert__Choice_Oinv__into(X5,X12,X4,X18),X35)=c_Hilbert__Choice_OEps(X5,hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X4))),hAPP(hAPP(c_COMBC(X5,X12,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X12,tc_fun(X12,tc_HOL_Obool),X5),c_fequal),X18)),X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inv__into__def)). 6.97/7.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J, axiom, ![X25, X6, X8]:(class_Rings_Ocomm__semiring__1(X8)=>hAPP(hAPP(c_Power_Opower__class_Opower(X8),X6),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)))),X25)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X6),X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X6),X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J)). 6.97/7.19 fof(fact_zminus__zadd__distrib, axiom, ![X39, X26]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26),X39))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X39)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zminus__zadd__distrib)). 6.97/7.19 fof(fact_diff__int__def__symmetric, axiom, ![X39, X26]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26),X39)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X39)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__int__def__symmetric)). 6.97/7.19 fof(fact_less__number__of__Suc, axiom, ![X32, X60]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X60)),hAPP(c_Nat_OSuc,X32)))<=>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(X60))),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)),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__number__of__Suc)). 6.97/7.19 fof(fact_le__number__of__Suc, axiom, ![X32, X60]:(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(X60))),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)),X32))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X60)),hAPP(c_Nat_OSuc,X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__number__of__Suc)). 6.97/7.19 fof(fact_refl__on__def_H, axiom, ![X3, X4, X5]:((![X22]:(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X4)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X4))),X22))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X22),X3)))&![X22]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X22),X22)),X3))<=hBOOL(hAPP(hAPP(c_member(X5),X22),X4))))<=>c_Relation_Orefl__on(X5,X4,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__on__def_H)). 6.97/7.19 fof(fact_abs__power2, axiom, ![X30, X8]:(class_Rings_Olinordered__idom(X8)=>hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),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(X8),X30),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_abs__power2)). 6.97/7.19 fof(fact_power2__abs, axiom, ![X30, X8]:(class_Rings_Olinordered__idom(X8)=>hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),X30)),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(X8),X30),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__abs)). 6.97/7.19 fof(fact_power2__minus, axiom, ![X30, X8]:(class_Rings_Oring__1(X8)=>hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),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(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X30)),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)). 6.97/7.19 fof(fact_of__nat__double, axiom, ![X6, X8]:((hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),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)))),X6)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),hAPP(c_Int_Onat,X6))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),hAPP(c_Int_Onat,X6)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)))<=class_Rings_Osemiring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__double)). 6.97/7.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J, axiom, ![X25, X6, X8]:(class_Rings_Ocomm__semiring__1(X8)=>hAPP(hAPP(c_Power_Opower__class_Opower(X8),X6),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)))),X25))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X6),X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X6),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J)). 6.97/7.19 fof(fact_negDivAlg_Osimps, axiom, ![X29, X30]:(((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),X30),X29)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))=>c_Divides_OnegDivAlg(X30,X29)=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),X30),X29)))&(~((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29),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),X30),X29)))))=>c_Divides_OnegDivAlg(X30,X29)=hAPP(c_Divides_Oadjust(X29),c_Divides_OnegDivAlg(X30,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)))),X29))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negDivAlg_Osimps)). 6.97/7.19 fof(fact_mod2__gr__0, axiom, ![X34]:(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,X34,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,X34,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)). 6.97/7.19 fof(fact_takeWhile__neq__rev, axiom, ![X35, X23, X5]:((hAPP(c_List_Orev(X5),hAPP(c_List_Otl(X5),c_List_OdropWhile(X5,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X35)),X23)))=c_List_OtakeWhile(X5,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X35)),hAPP(c_List_Orev(X5),X23))<=hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23))))<=hBOOL(hAPP(c_List_Odistinct(X5),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__neq__rev)). 6.97/7.19 fof(fact_drop__tl, axiom, ![X41, X25, X8]:hAPP(hAPP(c_List_Odrop(X8),X25),hAPP(c_List_Otl(X8),X41))=hAPP(c_List_Otl(X8),hAPP(hAPP(c_List_Odrop(X8),X25),X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__tl)). 6.97/7.19 fof(fact_drop__Suc, axiom, ![X41, X25, X8]:hAPP(hAPP(c_List_Odrop(X8),hAPP(c_Nat_OSuc,X25)),X41)=hAPP(hAPP(c_List_Odrop(X8),X25),hAPP(c_List_Otl(X8),X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__Suc)). 6.97/7.19 fof(fact_negDivAlg__eqn, axiom, ![X30, X29]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X29))=>((~(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),X30),X29))))=>c_Divides_OnegDivAlg(X30,X29)=hAPP(c_Divides_Oadjust(X29),c_Divides_OnegDivAlg(X30,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)))),X29))))&(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),X30),X29)))=>c_Divides_OnegDivAlg(X30,X29)=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),X30),X29))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negDivAlg__eqn)). 6.97/7.19 fof(fact_odd__power__less__zero, axiom, ![X25, X30, X8]:(class_Rings_Olinordered__idom(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),c_Groups_Ozero__class_Ozero(X8)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),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)))),X25)))),c_Groups_Ozero__class_Ozero(X8))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_odd__power__less__zero)). 6.97/7.19 fof(fact_power__number__of__odd, axiom, ![X14, X9, X5]:(class_Int_Onumber__ring(X5)=>((~(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),X9))))=>c_Groups_Oone__class_Oone(X5)=hAPP(hAPP(c_Power_Opower__class_Opower(X5),X14),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X9))))&(hAPP(hAPP(c_HOL_OLet(X5,X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X14),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X9))),hAPP(hAPP(c_COMBS(X5,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_Groups_Otimes__class_Otimes(X5)),hAPP(c_Groups_Otimes__class_Otimes(X5),X14))),c_COMBI(X5)))=hAPP(hAPP(c_Power_Opower__class_Opower(X5),X14),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X9)))<=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),X9)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__number__of__odd)). 6.97/7.19 fof(fact_zpower__number__of__odd, axiom, ![X14, X9]:((c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X14),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X9)))<=~(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),X9)))))&(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X14),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X9))),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),X14))),c_COMBI(tc_Int_Oint)))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X14),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X9)))<=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),X9))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zpower__number__of__odd)). 6.97/7.19 fof(fact_posDivAlg_Osimps, axiom, ![X29, X30]:((c_Divides_OposDivAlg(X30,X29)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30)<=(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),X29))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))&(c_Divides_OposDivAlg(X30,X29)=hAPP(c_Divides_Oadjust(X29),c_Divides_OposDivAlg(X30,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)))),X29)))<=~((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),X29))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_posDivAlg_Osimps)). 6.97/7.19 fof(fact_power3__eq__cube, axiom, ![X30, X8]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X30)),X30)=hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))<=class_Groups_Omonoid__mult(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power3__eq__cube)). 6.97/7.19 fof(fact_numeral__3__eq__3, axiom, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))=hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_numeral__3__eq__3)). 6.97/7.19 fof(fact_Suc__n__div__2__gt__zero, axiom, ![X25]:(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),X25),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)),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__n__div__2__gt__zero)). 6.97/7.19 fof(fact_length__take, axiom, ![X41, X25, X8]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),hAPP(hAPP(c_List_Otake(X8),X25),X41))=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)),X25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__take)). 6.97/7.19 fof(fact_posDivAlg__eqn, axiom, ![X30, X29]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X29))=>((c_Divides_OposDivAlg(X30,X29)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),X29)))&(hAPP(c_Divides_Oadjust(X29),c_Divides_OposDivAlg(X30,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)))),X29)))=c_Divides_OposDivAlg(X30,X29)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),X29)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_posDivAlg__eqn)). 6.97/7.19 fof(fact_power__minus1__odd, axiom, ![X25, X8]:(hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),c_Groups_Oone__class_Oone(X8))),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)))),X25)))=hAPP(c_Groups_Ouminus__class_Ouminus(X8),c_Groups_Oone__class_Oone(X8))<=class_Rings_Oring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__minus1__odd)). 6.97/7.19 fof(fact_not__sum__power2__lt__zero, axiom, ![X7, X6, X8]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),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(X8),X7),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X8))))<=class_Rings_Olinordered__idom(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__sum__power2__lt__zero)). 6.97/7.19 fof(fact_map__removeAll__inj__on, axiom, ![X23, X35, X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,hAPP(hAPP(c_Set_Oinsert(X5),X35),hAPP(c_List_Oset(X5),X23)))=>hAPP(hAPP(c_List_Omap(X5,X12),X18),hAPP(c_List_OremoveAll(X5,X35),X23))=hAPP(c_List_OremoveAll(X12,hAPP(X18,X35)),hAPP(hAPP(c_List_Omap(X5,X12),X18),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__removeAll__inj__on)). 6.97/7.19 fof(fact_power__m1__odd, axiom, ![X25, X8]:(class_Int_Onumber__ring(X8)=>hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),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)))),X25)))=hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OMin)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__m1__odd)). 6.97/7.19 fof(fact_zero__le__even__power_H, axiom, ![X25, X30, X8]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),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)))),X25))))<=class_Rings_Olinordered__idom(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__even__power_H)). 6.97/7.19 fof(fact_half__gt__zero, axiom, ![X70, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X70),hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X70)))<=(class_Int_Onumber__ring(X8)&class_Fields_Olinordered__field__inverse__zero(X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_half__gt__zero)). 6.97/7.19 fof(fact_zdiv__number__of__Bit1, axiom, ![X40, X39]:((hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X40))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X39)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X40)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X39))<=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),X39))))&(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),X40)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X39))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X40))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X39)))<=~(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),X39)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__number__of__Bit1)). 6.97/7.19 fof(fact_map__removeAll__inj, axiom, ![X23, X35, X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))=>hAPP(hAPP(c_List_Omap(X5,X12),X18),hAPP(c_List_OremoveAll(X5,X35),X23))=hAPP(c_List_OremoveAll(X12,hAPP(X18,X35)),hAPP(hAPP(c_List_Omap(X5,X12),X18),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__removeAll__inj)). 6.97/7.19 fof(fact_power__minus1__even, axiom, ![X25, X8]:(class_Rings_Oring__1(X8)=>c_Groups_Oone__class_Oone(X8)=hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),c_Groups_Oone__class_Oone(X8))),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)))),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__minus1__even)). 6.97/7.19 fof(fact_div__2__gt__zero, axiom, ![X25]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X25))=>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),X25),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_div__2__gt__zero)). 6.97/7.19 fof(fact_power__m1__even, axiom, ![X25, X8]:(hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),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)))),X25))=c_Groups_Oone__class_Oone(X8)<=class_Int_Onumber__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__m1__even)). 6.97/7.19 fof(fact_nat__number__of__Bit1, axiom, ![X9]:((~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X9))))=>hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X9)),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(X9)))&(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X9))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<=hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X9))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__number__of__Bit1)). 6.97/7.19 fof(fact_Nitpick_Oof__frac__def, axiom, ![X53, X8, X5]:((class_Rings_Oring__1(X5)&class_Rings_Oinverse(X5))=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(c_Int_Oring__1__class_Oof__int(X5),hAPP(c_Nitpick_Onum(X8),X53))),hAPP(c_Int_Oring__1__class_Oof__int(X5),hAPP(c_Nitpick_Odenom(X8),X53)))=c_Nitpick_Oof__frac(X8,X5,X53)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Oof__frac__def)). 6.97/7.19 fof(fact_Nitpick_Odenom__def, axiom, ![X5]:c_Nitpick_Odenom(X5)=hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X5,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Odenom__def)). 6.97/7.19 fof(fact_Nitpick_Onum__def, axiom, ![X5]:hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X5,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X5))=c_Nitpick_Onum(X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Onum__def)). 6.97/7.19 fof(fact_zero__le__power2, axiom, ![X30, X8]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))<=class_Rings_Olinordered__idom(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__power2)). 6.97/7.19 fof(fact_mult__2, axiom, ![X26, X8]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X26),X26)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26)<=class_Int_Onumber__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__2)). 6.97/7.19 fof(fact_mult__2__right, axiom, ![X26, X8]:(class_Int_Onumber__ring(X8)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X26),X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__2__right)). 6.97/7.19 fof(fact_power2__eq__square, axiom, ![X30, X8]:(hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),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(X8),X30),X30)<=class_Groups_Omonoid__mult(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power2__eq__square)). 6.97/7.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, axiom, ![X6, X8]:(class_Rings_Ocomm__semiring__1(X8)=>hAPP(hAPP(c_Power_Opower__class_Opower(X8),X6),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(X8),X6),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J)). 6.97/7.19 fof(fact_removeAll_Osimps_I2_J, axiom, ![X41, X8, X7, X6]:((hAPP(c_List_OremoveAll(X8,X6),hAPP(hAPP(c_List_Olist_OCons(X8),X7),X41))=hAPP(hAPP(c_List_Olist_OCons(X8),X7),hAPP(c_List_OremoveAll(X8,X6),X41))<=X7!=X6)&(hAPP(c_List_OremoveAll(X8,X6),hAPP(hAPP(c_List_Olist_OCons(X8),X7),X41))=hAPP(c_List_OremoveAll(X8,X6),X41)<=X7=X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_removeAll_Osimps_I2_J)). 6.97/7.19 fof(fact_one__add__one__is__two, axiom, ![X8]:(class_Int_Onumber__ring(X8)=>hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),c_Groups_Oone__class_Oone(X8)),c_Groups_Oone__class_Oone(X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__add__one__is__two)). 6.97/7.19 fof(fact_zero__eq__power2, axiom, ![X2, X5]:((c_Groups_Ozero__class_Ozero(X5)=hAPP(hAPP(c_Power_Opower__class_Opower(X5),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))<=>X2=c_Groups_Ozero__class_Ozero(X5))<=class_Rings_Oring__1__no__zero__divisors(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__eq__power2)). 6.97/7.19 fof(fact_one__power2, axiom, ![X8]:(class_Rings_Osemiring__1(X8)=>c_Groups_Oone__class_Oone(X8)=hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Groups_Oone__class_Oone(X8)),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_one__power2)). 6.97/7.19 fof(fact_zero__power2, axiom, ![X8]:(class_Rings_Osemiring__1(X8)=>c_Groups_Ozero__class_Ozero(X8)=hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Groups_Ozero__class_Ozero(X8)),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__power2)). 6.97/7.19 fof(fact_nat__minus__add__max, axiom, ![X36, X25]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X36)),X36)=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X25),X36), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__minus__add__max)). 6.97/7.19 fof(fact_nat__add__commute, axiom, ![X25, X36]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X25)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X36), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__add__commute)). 6.97/7.19 fof(fact_odd__0__le__power__imp__0__le, axiom, ![X25, X30, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),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)))),X25)))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X30)))<=class_Rings_Olinordered__idom(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_odd__0__le__power__imp__0__le)). 6.97/7.19 fof(fact_Collect__disj__eq, axiom, ![X104, X17, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X17)),hAPP(c_Set_OCollect(X5),X104))=hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fdisj),X17)),X104)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__disj__eq)). 6.97/7.19 fof(fact_Suc__diff__eq__diff__pred, axiom, ![X36, X25]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X36)),X25)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__diff__eq__diff__pred)). 6.97/7.19 fof(fact_dropWhile__nth, axiom, ![X23, X17, X5, X46]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OdropWhile(X5,X17,X23))))=>hAPP(hAPP(c_List_Onth(X5),c_List_OdropWhile(X5,X17,X23)),X46)=hAPP(hAPP(c_List_Onth(X5),X23),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X17,X23))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dropWhile__nth)). 6.97/7.19 fof(fact_diff__special_I2_J, axiom, ![X40, X8]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),X40)),c_Groups_Oone__class_Oone(X8))=hAPP(c_Int_Onumber__class_Onumber__of(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X40),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))<=class_Int_Onumber__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__special_I2_J)). 6.97/7.19 fof(fact_diff__special_I1_J, axiom, ![X39, X8]:(class_Int_Onumber__ring(X8)=>hAPP(c_Int_Onumber__class_Onumber__of(X8),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),X39)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),c_Groups_Oone__class_Oone(X8)),hAPP(c_Int_Onumber__class_Onumber__of(X8),X39))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__special_I1_J)). 6.97/7.19 fof(fact_half__gt__zero__iff, axiom, ![X3, X5]:((class_Int_Onumber__ring(X5)&class_Fields_Olinordered__field__inverse__zero(X5))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X3),hAPP(c_Int_Onumber__class_Onumber__of(X5),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_half__gt__zero__iff)). 6.97/7.19 fof(fact_negDivAlg__minus1, axiom, ![X29]:c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X29)=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),X29),c_Groups_Oone__class_Oone(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negDivAlg__minus1)). 6.97/7.19 fof(fact_fst__eqD, axiom, ![X30, X7, X6, X5, X8]:(hAPP(c_Product__Type_Ofst(X8,X5),hAPP(hAPP(c_Product__Type_OPair(X8,X5),X6),X7))=X30=>X30=X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fst__eqD)). 6.97/7.19 fof(fact_add__special_I2_J, axiom, ![X39, X8]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),c_Groups_Oone__class_Oone(X8)),hAPP(c_Int_Onumber__class_Onumber__of(X8),X39))=hAPP(c_Int_Onumber__class_Onumber__of(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X39))<=class_Int_Onumber__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__special_I2_J)). 6.97/7.19 fof(fact_add__special_I3_J, axiom, ![X40, X8]:(class_Int_Onumber__ring(X8)=>hAPP(c_Int_Onumber__class_Onumber__of(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X40),c_Int_OBit1(c_Int_OPls)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),X40)),c_Groups_Oone__class_Oone(X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__special_I3_J)). 6.97/7.19 fof(fact_psubset__insert__iff, axiom, ![X11, X35, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),X11)))<=>((((hBOOL(hAPP(hAPP(c_member(X5),X35),X4))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X11)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))<=~(hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))))<=~(hBOOL(hAPP(hAPP(c_member(X5),X35),X11))))&(hBOOL(hAPP(hAPP(c_member(X5),X35),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X4),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_psubset__insert__iff)). 6.97/7.19 fof(fact_psubset__eq, axiom, ![X11, X4, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))&X11!=X4)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X4),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_psubset__eq)). 6.97/7.19 fof(fact_snd__eqD, axiom, ![X30, X7, X6, X8, X5]:(X7=X30<=X30=hAPP(c_Product__Type_Osnd(X5,X8),hAPP(hAPP(c_Product__Type_OPair(X5,X8),X6),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_snd__eqD)). 6.97/7.19 fof(fact_filter__filter, axiom, ![X23, X104, X17, X5]:hAPP(c_List_Ofilter(X5,X17),hAPP(c_List_Ofilter(X5,X104),X23))=hAPP(c_List_Ofilter(X5,hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),X104)),X17)),X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__filter)). 6.97/7.19 fof(fact_Collect__conv__if2, axiom, ![X5, X2, X17]:((hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))=hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(c_fequal,X2))),X17))<=hBOOL(hAPP(X17,X2)))&(~(hBOOL(hAPP(X17,X2)))=>c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(c_fequal,X2))),X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__conv__if2)). 6.97/7.19 fof(fact_list__ex1__simps_I2_J, axiom, ![X23, X35, X17, X5]:(c_List_Olist__ex1(X5,X17,hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23))<=>((c_List_Olist__ex1(X5,X17,X23)<=~(hBOOL(hAPP(X17,X35))))&(c_List_Olist__all(X5,hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X17))),hAPP(c_fequal,X35)),X23)<=hBOOL(hAPP(X17,X35))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex1__simps_I2_J)). 6.97/7.19 fof(fact_Suc__nat__number__of__add, axiom, ![X25, X40]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X25)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)),X25))<=hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X40))))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X40))),X25)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)),X25))<=~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X40)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__nat__number__of__add)). 6.97/7.19 fof(fact_Nitpick_Oless__frac__def, axiom, ![X3, X124, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X5),c_Nitpick_Oplus__frac(X5,X124,c_Nitpick_Ouminus__frac(X5,X3)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=>c_Nitpick_Oless__frac(X5,X124,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Oless__frac__def)). 6.97/7.19 fof(fact_Nitpick_Oless__eq__frac__def, axiom, ![X3, X124, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X5),c_Nitpick_Oplus__frac(X5,X124,c_Nitpick_Ouminus__frac(X5,X3)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=>c_Nitpick_Oless__eq__frac(X5,X124,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Oless__eq__frac__def)). 6.97/7.19 fof(fact_eq__special_I2_J, axiom, ![X38, X5]:(class_Int_Onumber__ring(X5)=>(c_Groups_Oone__class_Oone(X5)=hAPP(c_Int_Onumber__class_Onumber__of(X5),X38)<=>c_Int_Oiszero(X5,hAPP(c_Int_Onumber__class_Onumber__of(X5),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),X38)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__special_I2_J)). 6.97/7.19 fof(fact_eq__special_I4_J, axiom, ![X35, X5]:(class_Int_Onumber__ring(X5)=>(c_Int_Oiszero(X5,hAPP(c_Int_Onumber__class_Onumber__of(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X35),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))<=>hAPP(c_Int_Onumber__class_Onumber__of(X5),X35)=c_Groups_Oone__class_Oone(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__special_I4_J)). 6.97/7.19 fof(fact_interv__listsum__conv__setsum__set__nat, axiom, ![X32, X34, X18, X5]:(hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X5),X18),c_List_Oupt(X34,X32)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X34,X32)))<=class_Groups_Ocomm__monoid__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_interv__listsum__conv__setsum__set__nat)). 6.97/7.19 fof(fact_set__upt, axiom, ![X46, X47]:hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X47,X46))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X47),X46), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__upt)). 6.97/7.19 fof(fact_upt__Suc__append, axiom, ![X27, X28]:(c_List_Oupt(X28,hAPP(c_Nat_OSuc,X27))=hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X28,X27)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X27),c_List_Olist_ONil(tc_Nat_Onat)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28),X27))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upt__Suc__append)). 6.97/7.19 fof(fact_less__special_I2_J, axiom, ![X38, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X38))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Oone__class_Oone(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X38))))<=(class_Rings_Olinordered__idom(X5)&class_Int_Onumber__ring(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__special_I2_J)). 6.97/7.19 fof(fact_le__special_I2_J, axiom, ![X38, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X38))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Oone__class_Oone(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X38))))<=(class_Int_Onumber__ring(X5)&class_Rings_Olinordered__idom(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__special_I2_J)). 6.97/7.19 fof(fact_less__special_I4_J, axiom, ![X35, X5]:((class_Int_Onumber__ring(X5)&class_Rings_Olinordered__idom(X5))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X35),c_Int_OBit1(c_Int_OPls)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X35)),c_Groups_Oone__class_Oone(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__special_I4_J)). 6.97/7.19 fof(fact_le__special_I4_J, axiom, ![X35, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X35)),c_Groups_Oone__class_Oone(X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X35),c_Int_OBit1(c_Int_OPls))))<=(class_Rings_Olinordered__idom(X5)&class_Int_Onumber__ring(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__special_I4_J)). 6.97/7.19 fof(fact_Suc__diff__number__of, axiom, ![X36, X40]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X40))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X36)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X40)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__diff__number__of)). 6.97/7.19 fof(fact_irrefl__tranclI, axiom, ![X35, X3, X5]:(~(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X35)),c_Transitive__Closure_Otrancl(X5,X3))))<=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X5,X5),X3)),c_Transitive__Closure_Ortrancl(X5,X3))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_irrefl__tranclI)). 6.97/7.19 fof(fact_trancl__unfold__left, axiom, ![X3, X5]:c_Transitive__Closure_Otrancl(X5,X3)=hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X3),c_Transitive__Closure_Ortrancl(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__unfold__left)). 6.97/7.19 fof(fact_upt__eq__Cons__conv, axiom, ![X23, X35, X46, X47]:(hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X35),X23)=c_List_Oupt(X47,X46)<=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X47),X46))&X35=X47)&X23=c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X47),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X46))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upt__eq__Cons__conv)). 6.97/7.19 fof(fact_nat__of__aux__code, axiom, ![X25, X28]:((c_Code__Numeral_Onat__of__aux(X28,X25)=c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X28),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,X25))<=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X28)&(X25=c_Code__Numeral_Onat__of__aux(X28,X25)<=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__of__aux__code)). 6.97/7.19 fof(fact_nat__of__aux__def, axiom, ![X25, X28]:c_Code__Numeral_Onat__of__aux(X28,X25)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X28)),X25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__of__aux__def)). 6.97/7.19 fof(fact_add__Suc, axiom, ![X25, X36]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X36)),X25)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Suc)). 6.97/7.19 fof(fact_add__Suc__shift, axiom, ![X25, X36]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X36)),X25)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),hAPP(c_Nat_OSuc,X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Suc__shift)). 6.97/7.19 fof(fact_divide__Numeral1, axiom, ![X6, X8]:(X6=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X6),hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OBit1(c_Int_OPls)))<=(class_Fields_Ofield(X8)&class_Int_Onumber__ring(X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__Numeral1)). 6.97/7.19 fof(fact_removeAll__id, axiom, ![X23, X35, X5]:(~(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23))))=>hAPP(c_List_OremoveAll(X5,X35),X23)=X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_removeAll__id)). 6.97/7.19 fof(fact_mult__numeral__1, axiom, ![X30, X8]:(class_Int_Onumber__ring(X8)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OBit1(c_Int_OPls))),X30)=X30), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__numeral__1)). 6.97/7.19 fof(fact_mult__numeral__1__right, axiom, ![X30, X8]:(X30=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OBit1(c_Int_OPls)))<=class_Int_Onumber__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__numeral__1__right)). 6.97/7.19 fof(fact_rel__simps_I12_J, axiom, ![X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X33)),c_Int_OPls))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33),c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I12_J)). 6.97/7.19 fof(fact_rel__simps_I29_J, axiom, ![X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X33)),c_Int_OPls))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33),c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I29_J)). 6.97/7.19 fof(fact_neg__number__of__Bit1, axiom, ![X9]:(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X9)))<=>hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X9))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__number__of__Bit1)). 6.97/7.19 fof(fact_rel__simps_I5_J, axiom, ![X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X33))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X33)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I5_J)). 6.97/7.19 fof(fact_rel__simps_I22_J, axiom, ![X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X33)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X33))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I22_J)). 6.97/7.19 fof(fact_nat__number__of__diff__1, axiom, ![X40]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X40))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X40),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),X40)),c_Groups_Oone__class_Oone(tc_Nat_Onat))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X40),c_Int_OPls)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__number__of__diff__1)). 6.97/7.19 fof(fact_nat__1__add__number__of, axiom, ![X40]:((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),X40))=c_Groups_Oone__class_Oone(tc_Nat_Onat)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X40),c_Int_OPls)))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X40),c_Int_OPls)))=>hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X40))=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),X40)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__1__add__number__of)). 6.97/7.19 fof(fact_distinct__remove1__removeAll, axiom, ![X6, X41, X8]:(hBOOL(hAPP(c_List_Odistinct(X8),X41))=>c_List_Oremove1(X8,X6,X41)=hAPP(c_List_OremoveAll(X8,X6),X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__remove1__removeAll)). 6.97/7.19 fof(fact_add__Pls__right, axiom, ![X19]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19),c_Int_OPls)=X19, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Pls__right)). 6.97/7.19 fof(fact_semiring__norm_I110_J, axiom, ![X8]:(class_Int_Onumber__ring(X8)=>c_Groups_Oone__class_Oone(X8)=hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OBit1(c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_semiring__norm_I110_J)). 6.97/7.19 fof(fact_Suc__nat__number__of, axiom, ![X40]:((hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X40))<=~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X40)))))&(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40))=c_Groups_Oone__class_Oone(tc_Nat_Onat)<=hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X40))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__nat__number__of)). 6.97/7.19 fof(fact_rel__simps_I10_J, axiom, ![X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X33)),c_Int_OPls))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33),c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I10_J)). 6.97/7.19 fof(fact_rel__simps_I27_J, axiom, ![X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X33)),c_Int_OPls))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X33),c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I27_J)). 6.97/7.19 fof(fact_neg__number__of__Bit0, axiom, ![X9]:(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X9))))<=>hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X9)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__number__of__Bit0)). 6.97/7.19 fof(fact_rel__simps_I4_J, axiom, ![X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X33))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X33)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I4_J)). 6.97/7.19 fof(fact_rel__simps_I21_J, axiom, ![X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X33)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X33))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I21_J)). 6.97/7.19 fof(fact_upt__Suc, axiom, ![X27, X28]:((c_List_Olist_ONil(tc_Nat_Onat)=c_List_Oupt(X28,hAPP(c_Nat_OSuc,X27))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28),X27))))&(c_List_Oupt(X28,hAPP(c_Nat_OSuc,X27))=hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X28,X27)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X27),c_List_Olist_ONil(tc_Nat_Onat)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28),X27)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upt__Suc)). 6.97/7.19 fof(fact_neg__number__of__pred__iff__0, axiom, ![X60]:(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X60))))<=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X60)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__number__of__pred__iff__0)). 6.97/7.19 fof(fact_code__numeral_Oinject, axiom, ![X267, X222]:(c_Code__Numeral_OSuc__code__numeral(X267)=c_Code__Numeral_OSuc__code__numeral(X222)<=>X267=X222), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral_Oinject)). 6.97/7.19 fof(fact_Suc__code__numeral__def, axiom, ![X19]:hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X19)))=c_Code__Numeral_OSuc__code__numeral(X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__code__numeral__def)). 6.97/7.19 fof(fact_rel__simps_I38_J, axiom, ![X52]:(c_Int_OPls=X52<=>c_Int_OPls=c_Int_OBit0(X52)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I38_J)). 6.97/7.19 fof(fact_rel__simps_I39_J, axiom, ![X93]:c_Int_OPls!=c_Int_OBit1(X93), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I39_J)). 6.97/7.19 fof(fact_code__numeral_Osimps_I3_J, axiom, ![X167]:c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=c_Code__Numeral_OSuc__code__numeral(X167), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral_Osimps_I3_J)). 6.97/7.19 fof(fact_trancl__insert, axiom, ![X3, X35, X38, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X5,X3)),hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5))),hAPP(hAPP(c_COMBC(X5,X5,tc_prod(X5,X5)),c_Product__Type_OPair(X5,X5)),X38))),c_Transitive__Closure_Ortrancl(X5,X3))))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5))),hAPP(c_Product__Type_OPair(X5,X5),X35))),c_Transitive__Closure_Ortrancl(X5,X3))))))=c_Transitive__Closure_Otrancl(X5,hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X38),X35)),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__insert)). 6.97/7.19 fof(fact_sublist__shift__lemma, axiom, ![X47, X23, X4, X5]:hAPP(hAPP(c_List_Omap(tc_prod(X5,tc_Nat_Onat),X5),c_Product__Type_Ofst(X5,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X5,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(X5,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X5,tc_Nat_Onat))),X4)),hAPP(hAPP(c_List_Ozip(X5,tc_Nat_Onat),X23),c_List_Oupt(X47,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X47),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23))))))=hAPP(hAPP(c_List_Omap(tc_prod(X5,tc_Nat_Onat),X5),c_Product__Type_Ofst(X5,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X5,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(X5,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X5,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(X5,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(X5,tc_Nat_Onat))),X47))),X4)),hAPP(hAPP(c_List_Ozip(X5,tc_Nat_Onat),X23),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublist__shift__lemma)). 6.97/7.19 fof(fact_arith__series__int, axiom, ![X32, X97, 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)))),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),X2)),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))),X97))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X32)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X32)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),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),X32),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X97)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_arith__series__int)). 6.97/7.19 fof(fact_zmod__number__of__Bit0, axiom, ![X39, X40]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X40)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X39)))=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),X40),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X39))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__number__of__Bit0)). 6.97/7.19 fof(fact_transpose__max__length, axiom, ![X23, X5]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),hAPP(c_List_Ofilter(tc_List_Olist(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X5)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(X5),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X5)))),X23))=c_List_Ofoldr(tc_List_Olist(X5),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X5)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X5))),c_List_Otranspose(X5,X23),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__max__length)). 6.97/7.19 fof(fact_nat__mult__2, axiom, ![X26]: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)))),X26)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26),X26), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__2)). 6.97/7.19 fof(fact_nat__mult__2__right, axiom, ![X26]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26),X26)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),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)). 6.97/7.19 fof(fact_map__concat, axiom, ![X23, X18, X5, X12]:c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(tc_List_Olist(X12),tc_List_Olist(X5)),hAPP(c_List_Omap(X12,X5),X18)),X23))=hAPP(hAPP(c_List_Omap(X12,X5),X18),c_List_Oconcat(X12,X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__concat)). 6.97/7.19 fof(fact_mult__Bit1, axiom, ![X93, X19]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19),X93))),X93)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(X19)),X93), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__Bit1)). 6.97/7.19 fof(fact_diff__bin__simps_I9_J, axiom, ![X93, X19]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X19)),c_Int_OBit0(X93))=c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19),X93)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I9_J)). 6.97/7.19 fof(fact_mult__Bit0, axiom, ![X93, X19]:c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19),X93))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(X19)),X93), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__Bit0)). 6.97/7.19 fof(fact_code__numeral_Orecs_I2_J, axiom, ![X222, X120, X85, X5]:c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X5,X85,X120,c_Code__Numeral_OSuc__code__numeral(X222))=hAPP(hAPP(X120,X222),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X5,X85,X120,X222)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral_Orecs_I2_J)). 6.97/7.19 fof(fact_adjust__def, axiom, ![X1]: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), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_adjust__def)). 6.97/7.19 fof(fact_Nitpick_Oplus__frac__def, axiom, ![X3, X124, X5]:c_Nitpick_Oplus__frac(X5,X124,X3)=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X5),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(X5),X124),hAPP(c_Nitpick_Odenom(X5),X3))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,X5),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,X5),tc_Int_Oint),c_Nitpick_Ofrac(X5)),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(X5),X124))),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(X5),X124))))),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(X5),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(X5),X3)))))),c_COMBI(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Oplus__frac__def)). 6.97/7.19 fof(fact_adjust__eq, axiom, ![X3, X124, X1]: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)))),X124)),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)))),X124)),X3)))=hAPP(c_Divides_Oadjust(X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X124),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_adjust__eq)). 6.97/7.19 fof(fact_transpose_Osimps_I3_J, axiom, ![X77, X23, X35, X5]:hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X35),c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_Olist__case(tc_List_Olist(X5),X5,c_List_Olist_ONil(X5),hAPP(hAPP(c_COMBB(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),X5),c_COMBK(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_COMBC(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_OCons(X5)),c_List_Olist_ONil(X5))))),X77)))),c_List_Otranspose(X5,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),X23),c_List_Oconcat(tc_List_Olist(X5),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X5)),X5,c_List_Olist_ONil(tc_List_Olist(X5)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5))),X5),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5)),tc_List_Olist(tc_List_Olist(X5))),c_List_Olist_OCons(tc_List_Olist(X5))),c_List_Olist_ONil(tc_List_Olist(X5)))))),X77)))))=c_List_Otranspose(X5,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23)),X77)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose_Osimps_I3_J)). 6.97/7.19 fof(fact_nat__rec__add__eq__if, axiom, ![X32, X60, X18, X2, X5]:hAPP(c_Nat_Onat_Onat__rec(X5,X2,X18),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X60)),X32))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X5),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X60))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X5,X5),hAPP(hAPP(c_COMBC(tc_Int_Oint,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),tc_Int_Oint),c_If(X5)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(X5,X2,X18),X32))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X5,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X5,X5),tc_Int_Oint),X18),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)),X32))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Int_Oint),c_Nat_Onat_Onat__rec(X5,X2,X18)),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)),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__rec__add__eq__if)). 6.97/7.19 fof(fact_transpose__aux__max, axiom, ![X77, X12, X23, X5]:hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)),c_List_Ofoldr(tc_List_Olist(X12),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X12)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X12),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X12)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X12)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(X12),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X12)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X12),tc_List_Olist(X12),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X12)))),X77),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23))),c_List_Ofoldr(tc_List_Olist(X12),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X12)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X12))),X77,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__aux__max)). 6.97/7.19 fof(fact_nat__case__add__eq__if, axiom, ![X32, X60, X18, X2, X5]:hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X5),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X60))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X5,X5),hAPP(hAPP(c_COMBC(tc_Int_Oint,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),tc_Int_Oint),c_If(X5)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(X5,X2,X18,X32))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Int_Oint),X18),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)),X32))))=c_Nat_Onat_Onat__case(X5,X2,X18,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X60)),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__case__add__eq__if)). 6.97/7.19 fof(fact_max__Suc__number__of, axiom, ![X32, X60]:hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X60)),hAPP(c_Nat_OSuc,X32))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X60))),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,X32))),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)),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__Suc__number__of)). 6.97/7.19 fof(fact_Inter__eq, axiom, ![X4, X5]:hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OAll(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),X5),hAPP(c_COMBS(tc_fun(X5,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(X5,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X5,tc_HOL_Obool))),X4)))),c_member(X5))))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__eq)). 6.97/7.19 fof(fact_min__Suc__number__of, axiom, ![X32, X60]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X60)),hAPP(c_Nat_OSuc,X32))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X60))),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)),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__Suc__number__of)). 6.97/7.19 fof(fact_Id__def, axiom, ![X5]:c_Relation_OId(X5)=hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X5,X5)),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBC(tc_prod(X5,X5),tc_fun(X5,tc_prod(X5,X5)),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_prod(X5,X5)),tc_fun(X5,tc_HOL_Obool)),tc_prod(X5,X5)),c_COMBB(tc_prod(X5,X5),tc_HOL_Obool,X5)),c_fequal)),hAPP(hAPP(c_COMBS(X5,X5,tc_prod(X5,X5)),c_Product__Type_OPair(X5,X5)),c_COMBI(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Id__def)). 6.97/7.19 fof(fact_rtrancl__empty, axiom, ![X5]:c_Transitive__Closure_Ortrancl(X5,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)))=c_Relation_OId(X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__empty)). 6.97/7.19 fof(fact_nat__rec__number__of, axiom, ![X60, X18, X2, X5]:hAPP(c_Nat_Onat_Onat__rec(X5,X2,X18),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X60))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X5),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X60))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X5,X5),hAPP(hAPP(c_COMBC(tc_Int_Oint,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),tc_Int_Oint),c_If(X5)),c_Nat__Numeral_Oneg)),X2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X5,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X5,X5),tc_Int_Oint),X18),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Int_Oint),c_Nat_Onat_Onat__rec(X5,X2,X18)),c_Int_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__rec__number__of)). 6.97/7.19 fof(fact_Nitpick_Otimes__frac__def, axiom, ![X70, X53, X8]:c_Nitpick_Otimes__frac(X8,X53,X70)=hAPP(hAPP(c_Nitpick_Ofrac(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X8),X53)),hAPP(c_Nitpick_Onum(X8),X70))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(X8),X53)),hAPP(c_Nitpick_Odenom(X8),X70))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Otimes__frac__def)). 6.97/7.19 fof(fact_max__number__of__Suc, axiom, ![X60, X32]:hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X60))),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,X32))),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),X32)),c_Int_Onat))))=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X32)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X60)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__number__of__Suc)). 6.97/7.19 fof(fact_n__lists_Osimps_I2_J, axiom, ![X23, X32, X5]:c_Enum_On__lists(X5,hAPP(c_Nat_OSuc,X32),X23)=c_List_Oconcat(tc_List_Olist(X5),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_List_Olist(X5)),tc_fun(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5))),tc_List_Olist(X5)),c_List_Omap(X5,tc_List_Olist(X5))),hAPP(c_COMBC(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_OCons(X5)))),X23)),c_Enum_On__lists(X5,X32,X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_n__lists_Osimps_I2_J)). 6.97/7.19 fof(fact_min__number__of__Suc, axiom, ![X60, X32]:hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X60))),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),X32)),c_Int_Onat))))=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X32)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X60)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__number__of__Suc)). 6.97/7.19 fof(fact_int__ge__less__than__def, axiom, ![X97]:c_Int_Oint__ge__less__than(X97)=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),X97)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__ge__less__than__def)). 6.97/7.19 fof(fact_SetCompr__Sigma__eq, axiom, ![X104, X17, X12, X5]:hAPP(c_Set_OCollect(tc_prod(X5,X12)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X12,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X5,tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X12)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),X17))),X104)))=hAPP(hAPP(c_Product__Type_OSigma(X5,X12),hAPP(c_Set_OCollect(X5),X17)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool),X5),c_Set_OCollect(X12)),X104)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SetCompr__Sigma__eq)). 6.97/7.19 fof(fact_sublist__def, axiom, ![X4, X23, X5]:hAPP(hAPP(c_List_Omap(tc_prod(X5,tc_Nat_Onat),X5),c_Product__Type_Ofst(X5,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X5,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(X5,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X5,tc_Nat_Onat))),X4)),hAPP(hAPP(c_List_Ozip(X5,tc_Nat_Onat),X23),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)))))=c_List_Osublist(X5,X23,X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublist__def)). 6.97/7.19 fof(fact_div2__Suc__Suc, axiom, ![X36]:hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X36),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X36))),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)). 6.97/7.19 fof(fact_mod2__Suc__Suc, axiom, ![X36]:c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X36)),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,X36,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)). 6.97/7.19 fof(fact_nat__case__number__of, axiom, ![X60, X18, X2, X5]:c_Nat_Onat_Onat__case(X5,X2,X18,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X60))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X5),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X60))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X5,X5),hAPP(hAPP(c_COMBC(tc_Int_Oint,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),tc_Int_Oint),c_If(X5)),c_Nat__Numeral_Oneg)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Int_Oint),X18),c_Int_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__case__number__of)). 6.97/7.19 fof(fact_add__Bit1__Bit1, axiom, ![X93, X19]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X19)),c_Int_OBit1(X93))=c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19),c_Int_Osucc(X93))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Bit1__Bit1)). 6.97/7.19 fof(fact_diff__bin__simps_I8_J, axiom, ![X93, X19]:c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(X19)),X93))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X19)),c_Int_OBit1(X93)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I8_J)). 6.97/7.19 fof(fact_New__DSequence_Opos__not__seq__def, axiom, ![X47, X64]:hAPP(c_New__DSequence_Opos__not__seq(X64),X47)=c_Lazy__Sequence_Ohb__not__seq(hAPP(X64,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)))),X47))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Opos__not__seq__def)). 6.97/7.19 fof(fact_concat__map__singleton, axiom, ![X23, X18, X12, X5]:c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(X12,tc_List_Olist(X5)),hAPP(hAPP(c_COMBC(X12,tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_COMBB(X5,tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),X12),c_List_Olist_OCons(X5)),X18)),c_List_Olist_ONil(X5))),X23))=hAPP(hAPP(c_List_Omap(X12,X5),X18),X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_concat__map__singleton)). 6.97/7.19 fof(fact_trancl__reflcl, axiom, ![X3, X5]:c_Transitive__Closure_Ortrancl(X5,X3)=c_Transitive__Closure_Otrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),c_Relation_OId(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__reflcl)). 6.97/7.19 fof(fact_rtrancl__reflcl, axiom, ![X67, X5]:c_Transitive__Closure_Ortrancl(X5,X67)=c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X67),c_Relation_OId(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__reflcl)). 6.97/7.19 fof(fact_add__Bit1__Bit0, axiom, ![X93, X19]:c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19),X93))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X19)),c_Int_OBit0(X93)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Bit1__Bit0)). 6.97/7.19 fof(fact_zadd__assoc, axiom, ![X265, X182, X183]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X183),X182)),X265)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X183),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X182),X265)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__assoc)). 6.97/7.19 fof(fact_Nitpick_Ouminus__frac__def, axiom, ![X53, X8]:c_Nitpick_OAbs__Frac(X8,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(X8),X53))),hAPP(c_Nitpick_Odenom(X8),X53)))=c_Nitpick_Ouminus__frac(X8,X53), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Ouminus__frac__def)). 6.97/7.19 fof(fact_add__self__div__2, axiom, ![X36]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X36)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=X36, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__self__div__2)). 6.97/7.19 fof(fact_Nitpick_Oint__lcm__def, axiom, ![X7, X6]:c_Nitpick_Oint__lcm(X6,X7)=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),X6)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Oint__lcm__def)). 6.97/7.19 fof(fact_Nitpick_Onat__lcm__def, axiom, ![X7, X6]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),X7)),c_Nitpick_Onat__gcd(X6,X7))=c_Nitpick_Onat__lcm(X6,X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Onat__lcm__def)). 6.97/7.19 fof(fact_nat__abs__mult__distrib, axiom, ![X26, X39]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X39))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X26)))=hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X39),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__abs__mult__distrib)). 6.97/7.19 fof(fact_add__2__eq__Suc_H, axiom, ![X25]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),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,X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__2__eq__Suc_H)). 6.97/7.19 fof(fact_diff__bin__simps_I10_J, axiom, ![X93, X19]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X19)),c_Int_OBit1(X93))=c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19),X93)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I10_J)). 6.97/7.19 fof(fact_minus__Bit1, axiom, ![X19]:c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19)))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__Bit1)). 6.97/7.19 fof(fact_rev__concat, axiom, ![X23, X5]:c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Orev(X5)),hAPP(c_List_Orev(tc_List_Olist(X5)),X23)))=hAPP(c_List_Orev(X5),c_List_Oconcat(X5,X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__concat)). 6.97/7.19 fof(fact_trancl__unfold, axiom, ![X3, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),c_Transitive__Closure_Otrancl(X5,X3)),X3))=c_Transitive__Closure_Otrancl(X5,X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__unfold)). 6.97/7.19 fof(fact_Diff__Int2, axiom, ![X11, X65, X4, X5]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X65)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X65))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X65)),X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__Int2)). 6.97/7.19 fof(fact_diff__bin__simps_I4_J, axiom, ![X93]:c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X93))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X93)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I4_J)). 6.97/7.19 fof(fact_filter__concat, axiom, ![X23, X24, X5]:c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Ofilter(X5,X24)),X23))=hAPP(c_List_Ofilter(X5,X24),c_List_Oconcat(X5,X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__concat)). 6.97/7.19 fof(fact_transfer__nat__int__list__functions_I1_J, axiom, ![X36, X93]:hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),X93),X36)=c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(X93)),c_List_Oembed__list(X36))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__list__functions_I1_J)). 6.97/7.19 fof(fact_return__list__def, axiom, ![X52]:c_List_Oreturn__list(X52)=hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X52), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_return__list__def)). 6.97/7.19 fof(fact_embed__list__def, axiom, ![X52]:hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X52)=c_List_Oembed__list(X52), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_embed__list__def)). 6.97/7.19 fof(fact_zdiv__number__of__Bit0, axiom, ![X39, X40]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X40)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X39))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X40))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X39))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__number__of__Bit0)). 6.97/7.19 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J, axiom, ![X17]: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)))),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J)). 6.97/7.19 fof(fact_rtrancl__unfold, axiom, ![X3, X5]:c_Transitive__Closure_Ortrancl(X5,X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Relation_OId(X5)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),c_Transitive__Closure_Ortrancl(X5,X3)),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__unfold)). 6.97/7.19 fof(fact_foldl__foldr, axiom, ![X23, X2, X18, X12, X5]:c_List_Ofoldr(X12,X5,hAPP(c_COMBC(X5,X12,X5),X18),hAPP(c_List_Orev(X12),X23),X2)=hAPP(c_List_Ofoldl(X5,X12,X18,X2),X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__foldr)). 6.97/7.19 fof(fact_succ__Bit1, axiom, ![X19]:c_Int_Osucc(c_Int_OBit1(X19))=c_Int_OBit0(c_Int_Osucc(X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_succ__Bit1)). 6.97/7.19 fof(fact_diff__bin__simps_I6_J, axiom, ![X93]:c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X93))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X93)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I6_J)). 6.97/7.19 fof(fact_card__eq__0__iff, axiom, ![X4, X5]:((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=X4|~(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))))<=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(X5),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__eq__0__iff)). 6.97/7.19 fof(fact_map__Suc__upt, axiom, ![X32, X34]:hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(X34,X32))=c_List_Oupt(hAPP(c_Nat_OSuc,X34),hAPP(c_Nat_OSuc,X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__Suc__upt)). 6.97/7.19 fof(fact_pred__Bit1, axiom, ![X19]:c_Int_Opred(c_Int_OBit1(X19))=c_Int_OBit0(X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pred__Bit1)). 6.97/7.19 fof(fact_Bit1__def, axiom, ![X19]:c_Int_OBit1(X19)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X19)),X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Bit1__def)). 6.97/7.19 fof(fact_image__Suc__atLeastLessThan, axiom, ![X46, X47]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X47)),hAPP(c_Nat_OSuc,X46))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X47),X46)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__Suc__atLeastLessThan)). 6.97/7.19 fof(fact_atLeastLessThanSuc__atLeastAtMost, axiom, ![X51, X52]:c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X52,X51)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X52),hAPP(c_Nat_OSuc,X51)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThanSuc__atLeastAtMost)). 6.97/7.19 fof(fact_code__numeral_Osize_I4_J, axiom, ![X260]:hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X260))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),X260)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral_Osize_I4_J)). 6.97/7.19 fof(fact_card__greaterThanAtMost__int, axiom, ![X51, X52]:hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X52,X51))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X51),X52)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__greaterThanAtMost__int)). 6.97/7.19 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int, axiom, ![X51, X52]:c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X52,X51)=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X52),c_Groups_Oone__class_Oone(tc_Int_Oint)),X51), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastPlusOneAtMost__greaterThanAtMost__int)). 6.97/7.19 fof(fact_card__atLeastAtMost__int, axiom, ![X51, X52]:hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X51),X52)),c_Groups_Oone__class_Oone(tc_Int_Oint)))=hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X52,X51)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__atLeastAtMost__int)). 6.97/7.19 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)). 6.97/7.19 fof(fact_rotate__is__Nil__conv, axiom, ![X23, X32, X5]:(hAPP(c_List_Orotate(X5,X32),X23)=c_List_Olist_ONil(X5)<=>c_List_Olist_ONil(X5)=X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__is__Nil__conv)). 6.97/7.19 fof(fact_rotate__def, axiom, ![X32, X5]:hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X5),tc_List_Olist(X5)),X32),c_List_Orotate1(X5))=c_List_Orotate(X5,X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__def)). 6.97/7.19 fof(fact_atLeastAtMost__upt, axiom, ![X34, X32]:hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X32,hAPP(c_Nat_OSuc,X34)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X32,X34), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastAtMost__upt)). 6.97/7.19 fof(fact_code__numeral_Osize_I2_J, axiom, ![X260]:c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(X260))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X260)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral_Osize_I2_J)). 6.97/7.19 fof(fact_atLeastLessThan__singleton, axiom, ![X34]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34),hAPP(c_Nat_OSuc,X34))=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X34),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThan__singleton)). 6.97/7.19 fof(fact_Suc__code__numeral__minus__one, axiom, ![X25]:X25=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X25)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__code__numeral__minus__one)). 6.97/7.19 fof(fact_empty__def, axiom, ![X5]:hAPP(c_Set_OCollect(X5),hAPP(c_COMBK(tc_HOL_Obool,X5),c_fFalse))=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__def)). 6.97/7.19 fof(fact_code__numeral_Osimps_I5_J, axiom, ![X222, X120, X85, X5]:c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X5,X85,X120,c_Code__Numeral_OSuc__code__numeral(X222))=hAPP(X120,X222), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral_Osimps_I5_J)). 6.97/7.19 fof(fact_zadd__zminus__inverse2, axiom, ![X26]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26)),X26)=c_Groups_Ozero__class_Ozero(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__zminus__inverse2)). 6.97/7.19 fof(fact_zadd__commute, axiom, ![X39, X26]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X39),X26)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26),X39), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__commute)). 6.97/7.19 fof(fact_card__greaterThanAtMost, axiom, ![X51, X52]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X51),X52)=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X52,X51)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__greaterThanAtMost)). 6.97/7.19 fof(fact_atLeastSucAtMost__greaterThanAtMost, axiom, ![X51, X52]:c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X52),X51)=c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X52,X51), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastSucAtMost__greaterThanAtMost)). 6.97/7.19 fof(fact_UNIV__def, axiom, ![X5]:c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))=hAPP(c_Set_OCollect(X5),hAPP(c_COMBK(tc_HOL_Obool,X5),c_fTrue)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UNIV__def)). 6.97/7.19 fof(fact_setsum__mult__setsum__if__inj, axiom, ![X11, X4, X50, X18, X12, X5, X62]:(class_Rings_Osemiring__0(X62)=>(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X62),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X62),X18),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X62),X50),X11))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X62,X62),c_Fun_Oid(X62)),hAPP(c_Set_OCollect(X62),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X62),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X12,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool),X62),hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X12))),hAPP(hAPP(c_COMBC(X62,tc_fun(X5,tc_fun(X12,tc_HOL_Obool)),tc_fun(X5,tc_fun(X12,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool))),tc_fun(tc_fun(X5,tc_fun(X12,tc_HOL_Obool)),tc_fun(X5,tc_fun(X12,tc_HOL_Obool))),X62),c_COMBS(X5,tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X12,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X5,tc_fun(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool))),X62),hAPP(c_COMBB(tc_fun(X12,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_COMBS(X12,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X12,tc_HOL_Obool)),tc_fun(X5,tc_fun(X12,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X62),hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X12),c_fconj))),hAPP(hAPP(c_COMBC(X62,tc_fun(X5,tc_fun(X12,X62)),tc_fun(X5,tc_fun(X12,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X12,X62),tc_fun(X12,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_fun(X12,X62)),tc_fun(X5,tc_fun(X12,tc_HOL_Obool))),X62),c_COMBB(tc_fun(X12,X62),tc_fun(X12,tc_HOL_Obool),X5)),hAPP(hAPP(c_COMBB(tc_fun(X62,tc_HOL_Obool),tc_fun(tc_fun(X12,X62),tc_fun(X12,tc_HOL_Obool)),X62),c_COMBB(X62,tc_HOL_Obool,X12)),c_fequal))),hAPP(hAPP(c_COMBC(X5,tc_fun(X12,X62),tc_fun(X12,X62)),hAPP(hAPP(c_COMBB(tc_fun(X62,X62),tc_fun(tc_fun(X12,X62),tc_fun(X12,X62)),X5),c_COMBB(X62,X62,X12)),hAPP(hAPP(c_COMBB(X62,tc_fun(X62,X62),X5),c_Groups_Otimes__class_Otimes(X62)),X18))),X50)))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X12)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X4)))),hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X11)))))))<=c_Fun_Oinj__on(tc_prod(X5,X12),X62,hAPP(c_Product__Type_Oprod_Oprod__case(X5,X12,X62),hAPP(hAPP(c_COMBC(X5,tc_fun(X12,X62),tc_fun(X12,X62)),hAPP(hAPP(c_COMBB(tc_fun(X62,X62),tc_fun(tc_fun(X12,X62),tc_fun(X12,X62)),X5),c_COMBB(X62,X62,X12)),hAPP(hAPP(c_COMBB(X62,tc_fun(X62,X62),X5),c_Groups_Otimes__class_Otimes(X62)),X18))),X50)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X4),hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X5),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__mult__setsum__if__inj)). 6.97/7.19 fof(fact_min__max_Oinf__Sup2__distrib, axiom, ![X11, X4, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))=>(c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),tc_fun(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X5),c_COMBS(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),X5),hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X5),hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_fun(X5,X5)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_fun(X5,X5)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X5),c_COMBB(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool),X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal))),c_Orderings_Oord__class_Omin(X5)))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X4)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X11)))))))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X4)),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X11))<=X11!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__Sup2__distrib)). 6.97/7.19 fof(fact_min__max_Osup__Inf2__distrib, axiom, ![X11, X4, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))=>(X11!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X4)),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X11))=c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),tc_fun(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X5),c_COMBS(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),X5),hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X5),hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_fun(X5,X5)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_fun(X5,X5)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X5),c_COMBB(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool),X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal))),c_Orderings_Oord__class_Omax(X5)))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X4)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X11)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__Inf2__distrib)). 6.97/7.19 fof(fact_sup__Inf2__distrib, axiom, ![X11, X4, X5]:(class_Lattices_Odistrib__lattice(X5)=>((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))=>(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X11=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),c_Big__Operators_Olattice__class_OInf__fin(X5,X4)),c_Big__Operators_Olattice__class_OInf__fin(X5,X11))=c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),tc_fun(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X5),c_COMBS(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),X5),hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X5),hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_fun(X5,X5)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_fun(X5,X5)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X5),c_COMBB(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool),X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(X5)))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X4)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X11))))))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__Inf2__distrib)). 6.97/7.19 fof(fact_inf__Sup2__distrib, axiom, ![X11, X4, X5]:((((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))=>(c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),tc_fun(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X5),c_COMBS(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),X5),hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X5),hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_fun(X5,X5)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_fun(X5,X5)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X5),c_COMBB(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool),X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(X5)))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X4)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X11)))))))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Big__Operators_Olattice__class_OSup__fin(X5,X4)),c_Big__Operators_Olattice__class_OSup__fin(X5,X11))<=X11!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Lattices_Odistrib__lattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__Sup2__distrib)). 6.97/7.19 fof(fact_setsum__setsum__restrict, axiom, ![X67, X18, X108, X12, X44, X5, X62]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X44))=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X62),hAPP(hAPP(c_COMBS(X5,tc_fun(X12,tc_HOL_Obool),X62),hAPP(hAPP(c_COMBB(tc_fun(X12,X62),tc_fun(tc_fun(X12,tc_HOL_Obool),X62),X5),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X62)),X18)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool),X5),c_Set_OCollect(X12)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool),X5),hAPP(c_COMBS(X12,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X12),c_fconj),hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X108)))),X67)))),X44)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X62),hAPP(hAPP(c_COMBS(X12,tc_fun(X5,tc_HOL_Obool),X62),hAPP(hAPP(c_COMBB(tc_fun(X5,X62),tc_fun(tc_fun(X5,tc_HOL_Obool),X62),X12),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X62)),hAPP(c_COMBC(X5,X12,X62),X18))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X12),c_Set_OCollect(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X12),hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X44)))),hAPP(c_COMBC(X5,X12,tc_HOL_Obool),X67))))),X108)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X108))))<=class_Groups_Ocomm__monoid__add(X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__setsum__restrict)). 6.97/7.19 fof(fact_One__nat__def, axiom, hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_One__nat__def)). 6.97/7.19 fof(fact_Sup__apply, axiom, ![X35, X4, X12, X5]:(class_Complete__Lattice_Ocomplete__lattice(X5)=>hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X12,X5),X4),X35)=c_Complete__Lattice_OSup__class_OSup(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X12,X5),tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(tc_fun(X12,X5))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X12,X5),tc_HOL_Obool),tc_fun(tc_fun(X12,X5),tc_HOL_Obool),X5),hAPP(c_COMBS(tc_fun(X12,X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X12,X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X12,X5),tc_fun(tc_fun(X12,X5),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X12,X5))),X4)))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_fun(X12,X5),X5),tc_fun(tc_fun(X12,X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X12,X5),X5),tc_fun(tc_fun(X12,X5),tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,tc_fun(X12,X5))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X12,X5),X12,X5),c_COMBI(tc_fun(X12,X5))),X35))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__apply)). 6.97/7.19 fof(fact_Inf__apply, axiom, ![X35, X4, X12, X5]:(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X12,X5),X4),X35)=c_Complete__Lattice_OInf__class_OInf(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X12,X5),tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(tc_fun(X12,X5))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X12,X5),tc_HOL_Obool),tc_fun(tc_fun(X12,X5),tc_HOL_Obool),X5),hAPP(c_COMBS(tc_fun(X12,X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X12,X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X12,X5),tc_fun(tc_fun(X12,X5),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X12,X5))),X4)))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_fun(X12,X5),X5),tc_fun(tc_fun(X12,X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X12,X5),X5),tc_fun(tc_fun(X12,X5),tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,tc_fun(X12,X5))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X12,X5),X12,X5),c_COMBI(tc_fun(X12,X5))),X35))))))<=class_Complete__Lattice_Ocomplete__lattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__apply)). 6.97/7.19 fof(fact_min__max_Osup__Inf1__distrib, axiom, ![X35, X4, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4=>c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(X5),X35))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X4)))))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X35),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__Inf1__distrib)). 6.97/7.19 fof(fact_min__max_Oinf__Sup1__distrib, axiom, ![X35, X4, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X35),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X4))=c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(X5),X35))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X4)))))<=X4!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__Sup1__distrib)). 6.97/7.19 fof(fact_add__Min__commute, axiom, ![X33, X20, X5]:(class_Groups_Olinordered__ab__semigroup__add(X5)=>((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X20=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X33),c_Big__Operators_Olinorder__class_OMin(X5,X20))=c_Big__Operators_Olinorder__class_OMin(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X5),X33))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X20))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Min__commute)). 6.97/7.19 fof(fact_sup__Inf1__distrib, axiom, ![X35, X4, X5]:(class_Lattices_Odistrib__lattice(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X35),c_Big__Operators_Olattice__class_OInf__fin(X5,X4))=c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X35))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X4)))))<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__Inf1__distrib)). 6.97/7.19 fof(fact_add__Max__commute, axiom, ![X33, X20, X5]:(((X20!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>c_Big__Operators_Olinorder__class_OMax(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X5),X33))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X20)))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X33),c_Big__Operators_Olinorder__class_OMax(X5,X20)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X20)))<=class_Groups_Olinordered__ab__semigroup__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Max__commute)). 6.97/7.19 fof(fact_inf__Sup1__distrib, axiom, ![X35, X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(X4!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X35),c_Big__Operators_Olattice__class_OSup__fin(X5,X4))=c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X35))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X4)))))))<=class_Lattices_Odistrib__lattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__Sup1__distrib)). 6.97/7.19 fof(fact_reflcl__set__eq, axiom, ![X38, X35, X3, X5]:(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X5,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5)))),c_Product__Type_OPair(X5,X5)))),X3)),c_fequal),X35),X38))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),c_Relation_OId(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_reflcl__set__eq)). 6.97/7.19 fof(fact_setsum__multicount__gen, axiom, ![X33, X67, X82, X12, X66, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X66))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X82))=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_Nat_Onat,X5),c_Finite__Set_Ocard(X12)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool),X5),c_Set_OCollect(X12)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool),X5),hAPP(c_COMBS(X12,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X12),c_fconj),hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X82)))),X67)))),X66)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,tc_Nat_Onat),X33),X82)<=![X22]:(hBOOL(hAPP(hAPP(c_member(X12),X22),X82))=>hAPP(c_Finite__Set_Ocard(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X66))),hAPP(hAPP(c_COMBC(X5,X12,tc_HOL_Obool),X67),X22))))=hAPP(X33,X22))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__multicount__gen)). 6.97/7.19 fof(fact_finite__image__set, axiom, ![X18, X12, X17, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X12),hAPP(c_Set_OCollect(X12),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X12),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBC(X12,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X12),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X12),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj)),hAPP(hAPP(c_COMBC(X12,tc_fun(X5,X12),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(tc_fun(X5,X12),tc_fun(X5,tc_HOL_Obool)),X12),c_COMBB(X12,tc_HOL_Obool,X5)),c_fequal)),X18)))),X17)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__image__set)). 6.97/7.19 fof(fact_setsum__multicount, axiom, ![X33, X67, X108, X12, X44, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X108))=>(![X22]:(hBOOL(hAPP(hAPP(c_member(X12),X22),X108))=>X33=hAPP(c_Finite__Set_Ocard(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X44))),hAPP(hAPP(c_COMBC(X5,X12,tc_HOL_Obool),X67),X22)))))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_Nat_Onat,X5),c_Finite__Set_Ocard(X12)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool),X5),c_Set_OCollect(X12)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool),X5),hAPP(c_COMBS(X12,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X12),c_fconj),hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X108)))),X67)))),X44)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),hAPP(c_Finite__Set_Ocard(X12),X108))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X44))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__multicount)). 6.97/7.19 fof(fact_small__lazy__list_Osimps, axiom, ![X97, X5]:(c_Lazy__Sequence_Oappend(tc_List_Olist(X5),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X5))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X97)),hAPP(c_Lazy__Sequence_Obind(tc_prod(X5,tc_List_Olist(X5)),tc_List_Olist(X5),c_Lazy__Sequence_Oproduct(X5,tc_List_Olist(X5),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X97),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X97),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(X5,tc_List_Olist(X5),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_List_Olist(X5),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X5))),X5),hAPP(c_COMBB(tc_List_Olist(X5),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X5)),tc_List_Olist(X5)),c_Lazy__Sequence_Osingle(tc_List_Olist(X5)))),c_List_Olist_OCons(X5))))),c_Lazy__Sequence_Oempty(tc_List_Olist(X5))))=c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X5),X97)<=class_Lazy__Sequence_Osmall__lazy(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_small__lazy__list_Osimps)). 6.97/7.19 fof(fact_setsum__image__gen, axiom, ![X18, X62, X50, X44, X5, X12]:((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X62,X12),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),X12,X62),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X50)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X62),c_Set_OCollect(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X62),hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X44)))),hAPP(c_COMBC(X5,X62,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X62,tc_fun(X62,tc_HOL_Obool),X5),c_fequal),X18)))))),hAPP(c_Set_Oimage(X5,X62,X18),X44))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X50),X44)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X44)))<=class_Groups_Ocomm__monoid__add(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__image__gen)). 6.97/7.19 fof(fact_min__ext__compat, axiom, ![X44, X67, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Wellfounded_Omin__ext(X5,X67)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(X5,X44)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(X5,X67)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X67),X44)),X67))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__ext__compat)). 6.97/7.19 fof(fact_max__ext__compat, axiom, ![X44, X67, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X67),X44)),X67))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Wellfounded_Omax__ext(X5,X67)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(X5,X44)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(X5,X67)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__ext__compat)). 6.97/7.19 fof(fact_card__less__Suc2, axiom, ![X47, X94]:(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)),X94))),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,X47)))))=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)),X94))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X47))))<=~(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X94)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__less__Suc2)). 6.97/7.19 fof(fact_card__less__Suc, axiom, ![X47, X94]:(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X94))=>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)),X94))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X47)))))=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)),X94))),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,X47)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__less__Suc)). 6.97/7.19 fof(fact_map_Osimps_I1_J, axiom, ![X18, X5, X12]:hAPP(hAPP(c_List_Omap(X12,X5),X18),c_List_Olist_ONil(X12))=c_List_Olist_ONil(X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map_Osimps_I1_J)). 6.97/7.19 fof(fact_arith__series__general, axiom, ![X32, X97, X2, X5]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X32)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X32),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X97))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oone__class_Oone(X5)),c_Groups_Oone__class_Oone(X5))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBB(X5,X5,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(X5),X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(X5)),c_Nat_Osemiring__1__class_Oof__nat(X5))),X97))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X32)))<=class_Rings_Ocomm__semiring__1(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_arith__series__general)). 6.97/7.19 fof(fact_atLeast0LessThan, axiom, ![X32]:hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X32)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeast0LessThan)). 6.97/7.19 fof(fact_Diff__eq, axiom, ![X11, X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X11))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__eq)). 6.97/7.19 fof(fact_finite__lists__length__le, axiom, ![X32, X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X5)),hAPP(c_Set_OCollect(tc_List_Olist(X5)),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X5)),c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool))),c_List_Oset(X5))),X4))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X5)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),X32)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__lists__length__le)). 6.97/7.19 fof(fact_finite__lists__length__eq, axiom, ![X32, X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X5)),hAPP(c_Set_OCollect(tc_List_Olist(X5)),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X5)),c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool))),c_List_Oset(X5))),X4))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),X32)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__lists__length__eq)). 6.97/7.19 fof(fact_setsum__cases, axiom, ![X50, X18, X17, X4, X5, X12]:(class_Groups_Ocomm__monoid__add(X12)=>(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Set_OCollect(X5),X17)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X50),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X17)))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),hAPP(hAPP(c_COMBS(X5,X12,X12),hAPP(hAPP(c_COMBS(X5,X12,tc_fun(X12,X12)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X12,tc_fun(X12,X12)),X5),c_If(X12)),X17)),X18)),X50)),X4)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__cases)). 6.97/7.19 fof(fact_wf__if__measure, axiom, ![X5, X50, X18, X17]:(![X22]:(hBOOL(hAPP(X17,X22))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X18,hAPP(X50,X22))),hAPP(X18,X22))))=>c_Wellfounded_Owf(X5,hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),X17))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal)),X50)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__if__measure)). 6.97/7.19 fof(fact_less__eq__Suc__le__raw, axiom, ![X32]:hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X32))=hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__eq__Suc__le__raw)). 6.97/7.19 fof(fact_less, axiom, ![X60, X51, X38, X35]:(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),X35),X38)),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),X51),X60)),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),X35),X60)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X51),X38)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less)). 6.97/7.19 fof(fact_le, axiom, ![X60, X51, X38, X35]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X35),X60)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X51),X38)))<=>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),X35),X38)),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),X51),X60)),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)). 6.97/7.19 fof(fact_listrel__subset, axiom, ![X4, X3, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X4),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X4))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool)),c_List_Olistrel(X5,X3)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olists(X5,X4)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_List_Olist(X5)),c_List_Olists(X5,X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__subset)). 6.97/7.19 fof(fact_lfp__induct2, axiom, ![X17, X18, X1, X2, X12, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X2),X1)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),X18)))=>(c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(tc_prod(X5,X12),tc_HOL_Obool),X18)=>(hBOOL(hAPP(hAPP(X17,X2),X1))<=![X13, X96]:(hBOOL(hAPP(hAPP(X17,X13),X96))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X13),X96)),hAPP(X18,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),X18)),hAPP(c_Set_OCollect(tc_prod(X5,X12)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X12,tc_HOL_Obool),X17)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lfp__induct2)). 6.97/7.19 fof(fact_finite__Collect__bex, axiom, ![X104, X12, X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X12),hAPP(c_Set_OCollect(X12),hAPP(hAPP(c_COMBC(X12,X5,tc_HOL_Obool),X104),X22)))))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(X12),hAPP(c_Set_OCollect(X12),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X12),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X12),hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X4)))),X104))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Collect__bex)). 6.97/7.19 fof(fact_Nitpick_Osetsum_H__def, axiom, ![X18, X4, X5, X12]:(class_Groups_Ocomm__monoid__add(X12)=>((~(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))=>c_Nitpick_Osetsum_H(X5,X12,X18,X4)=c_Groups_Ozero__class_Ozero(X12))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>c_Nitpick_Osetsum_H(X5,X12,X18,X4)=hAPP(c_List_Omonoid__add__class_Olistsum(X12),hAPP(hAPP(c_List_Omap(X5,X12),X18),c_Hilbert__Choice_OEps(tc_List_Olist(X5),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_List_Oset(X5))),X4))),c_List_Odistinct(X5)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Osetsum_H__def)). 6.97/7.19 fof(fact_Int__commute, axiom, ![X11, X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X4)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__commute)). 6.97/7.19 fof(fact_zminus1__lemma, axiom, ![X3, X124, X1, X2]:(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2),X1),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),X124)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X124)),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),X1),X3)))))<=hBOOL(hAPP(c_Divides_Odivmod__int__rel(X2,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X124),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zminus1__lemma)). 6.97/7.19 fof(fact_minus__fold__remove, axiom, ![X11, X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X4)=hAPP(hAPP(c_Finite__Set_Ofold(X5,tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_Oinsert(X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X11),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__fold__remove)). 6.97/7.19 fof(fact_fold__image__def, axiom, ![X50, X18, X12, X5]:c_Finite__Set_Ofold(X12,X5,hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X12),X18),X50))=hAPP(c_Finite__Set_Ofold__image(X5,X12,X18),X50), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__def)). 6.97/7.19 fof(fact_def__coinduct3, axiom, ![X56, X2, X18, X5, X4]:((c_Orderings_Oorder__class_Omono(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X18)=>(hBOOL(hAPP(hAPP(c_member(X5),X2),X56))=>(hBOOL(hAPP(hAPP(c_member(X5),X2),X4))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X56),hAPP(X18,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),X18)),X56))),X4))))))))<=c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X5,tc_HOL_Obool),X18)=X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_def__coinduct3)). 6.97/7.19 fof(fact_divmod__nat__rel__add1__eq, axiom, ![X229, X230, X29, X231, X232, X31, X30]:(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X30,X31),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X232),X231)))=>(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X29,X31),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X230),X229)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X31))=>hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X29),X31),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),X232),X230)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X231),X229)),X31))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X231),X229),X31))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__rel__add1__eq)). 6.97/7.19 fof(fact_nat__add__assoc, axiom, ![X19, X25, X36]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X25)),X19)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__add__assoc)). 6.97/7.19 fof(fact_diff__nat__number__of, axiom, ![X60, X61]:((hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X60)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X60)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X61))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X61),c_Int_OPls)))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X61),c_Int_OPls)))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X60)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X61))=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),X60),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X61)))),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)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__nat__number__of)). 6.97/7.19 fof(fact_setprod__gen__delta, axiom, ![X10, X1, X2, X44, X5, X12]:(class_Groups_Ocomm__monoid__mult(X12)=>(((hAPP(hAPP(c_Power_Opower__class_Opower(X12),X10),hAPP(c_Finite__Set_Ocard(X5),X44))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),hAPP(hAPP(c_COMBC(X5,X12,X12),hAPP(hAPP(c_COMBS(X5,X12,tc_fun(X12,X12)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X12,tc_fun(X12,X12)),X5),c_If(X12)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X2))),X1)),X10)),X44)<=~(hBOOL(hAPP(hAPP(c_member(X5),X2),X44))))&(hBOOL(hAPP(hAPP(c_member(X5),X2),X44))=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12),hAPP(X1,X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X12),X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X44)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),hAPP(hAPP(c_COMBC(X5,X12,X12),hAPP(hAPP(c_COMBS(X5,X12,tc_fun(X12,X12)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X12,tc_fun(X12,X12)),X5),c_If(X12)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X2))),X1)),X10)),X44)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X44)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__gen__delta)). 6.97/7.19 fof(fact_finite__Collect__bounded__ex, axiom, ![X104, X12, X17, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),X17)))=>(![X72]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X12),hAPP(c_Set_OCollect(X12),hAPP(hAPP(c_COMBC(X12,X5,tc_HOL_Obool),X104),X72))))<=hBOOL(hAPP(X17,X72)))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(X12),hAPP(c_Set_OCollect(X12),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X12),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X12),hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),X17))),X104))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Collect__bounded__ex)). 6.97/7.19 fof(fact_transfer__nat__int__set__cong, axiom, ![X221, X17]:(![X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22))=>(hBOOL(hAPP(X17,X22))<=>hBOOL(hAPP(X221,X22))))=>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)))),X17))=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)))),X221))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__set__cong)). 6.97/7.19 fof(fact_zadd1__lemma, axiom, ![X229, X230, X29, X231, X232, X31, X30]:(((X31!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=>hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X30),X29),X31),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),X232),X230)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X231),X229)),X31))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X231),X229),X31)))))<=hBOOL(hAPP(c_Divides_Odivmod__int__rel(X29,X31),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X230),X229))))<=hBOOL(hAPP(c_Divides_Odivmod__int__rel(X30,X31),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X232),X231)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd1__lemma)). 6.97/7.19 fof(fact_setsum__natinterval__difff, axiom, ![X18, X32, X34, X5]:(class_Groups_Oab__group__add(X5)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),X32))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(X18,X34)),hAPP(X18,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X5)),X18)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Nat_Onat),X18),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,X34,X32)))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),X32)))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X5)),X18)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Nat_Onat),X18),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,X34,X32))=c_Groups_Ozero__class_Ozero(X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__natinterval__difff)). 6.97/7.19 fof(fact_Suc__eq__plus1, axiom, ![X25]:hAPP(c_Nat_OSuc,X25)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),c_Groups_Oone__class_Oone(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__eq__plus1)). 6.97/7.19 fof(fact_Nitpick_Ocard_H__def, axiom, ![X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>c_Nitpick_Ocard_H(X5,X4)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_Hilbert__Choice_OEps(tc_List_Olist(X5),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_List_Oset(X5))),X4))),c_List_Odistinct(X5)))))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Nitpick_Ocard_H(X5,X4)<=~(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Ocard_H__def)). 6.97/7.19 fof(fact_setsum__restrict__set, axiom, ![X11, X18, X4, X5, X12]:(class_Groups_Ocomm__monoid__add(X12)=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),hAPP(hAPP(c_COMBC(X5,X12,X12),hAPP(hAPP(c_COMBS(X5,X12,tc_fun(X12,X12)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X12,tc_fun(X12,X12)),X5),c_If(X12)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X11))),X18)),c_Groups_Ozero__class_Ozero(X12))),X4)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__restrict__set)). 6.97/7.19 fof(fact_vimage__if, axiom, ![X11, X12, X97, X4, X10, X5]:((((hBOOL(hAPP(hAPP(c_member(X5),X97),X4))=>hAPP(c_Set_Ovimage(X12,X5,hAPP(hAPP(c_COMBC(X12,X5,X5),hAPP(hAPP(c_COMBC(X12,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X12),c_If(X5)),hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X11))),X10)),X97)),X4)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X12,tc_HOL_Obool)),X11))&(c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool))=hAPP(c_Set_Ovimage(X12,X5,hAPP(hAPP(c_COMBC(X12,X5,X5),hAPP(hAPP(c_COMBC(X12,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X12),c_If(X5)),hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X11))),X10)),X97)),X4)<=~(hBOOL(hAPP(hAPP(c_member(X5),X97),X4)))))<=~(hBOOL(hAPP(hAPP(c_member(X5),X10),X4))))&(((hBOOL(hAPP(hAPP(c_member(X5),X97),X4))=>c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))=hAPP(c_Set_Ovimage(X12,X5,hAPP(hAPP(c_COMBC(X12,X5,X5),hAPP(hAPP(c_COMBC(X12,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X12),c_If(X5)),hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X11))),X10)),X97)),X4))&(hAPP(c_Set_Ovimage(X12,X5,hAPP(hAPP(c_COMBC(X12,X5,X5),hAPP(hAPP(c_COMBC(X12,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X12),c_If(X5)),hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X11))),X10)),X97)),X4)=X11<=~(hBOOL(hAPP(hAPP(c_member(X5),X97),X4)))))<=hBOOL(hAPP(hAPP(c_member(X5),X10),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__if)). 6.97/7.19 fof(fact_equiv__intrel__iff, axiom, ![X38, X35]:(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)),X35),X38)),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)),X35),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)),X38),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)). 6.97/7.19 fof(fact_sum__diff__distrib, axiom, ![X32, X17, X104]:(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)),X17)),X104)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X32))=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),X17),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X32))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X104),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X32)))<=![X22]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X104,X22)),hAPP(X17,X22)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__diff__distrib)). 6.97/7.19 fof(fact_setprod__delta, axiom, ![X1, X2, X44, X5, X12]:((((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),hAPP(hAPP(c_COMBC(X5,X12,X12),hAPP(hAPP(c_COMBS(X5,X12,tc_fun(X12,X12)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X12,tc_fun(X12,X12)),X5),c_If(X12)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X2))),X1)),c_Groups_Oone__class_Oone(X12))),X44)=hAPP(X1,X2)<=hBOOL(hAPP(hAPP(c_member(X5),X2),X44)))&(~(hBOOL(hAPP(hAPP(c_member(X5),X2),X44)))=>c_Groups_Oone__class_Oone(X12)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),hAPP(hAPP(c_COMBC(X5,X12,X12),hAPP(hAPP(c_COMBS(X5,X12,tc_fun(X12,X12)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X12,tc_fun(X12,X12)),X5),c_If(X12)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X2))),X1)),c_Groups_Oone__class_Oone(X12))),X44)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X44)))<=class_Groups_Ocomm__monoid__mult(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__delta)). 6.97/7.19 fof(fact_setprod_OF__eq, axiom, ![X50, X4, X5, X12]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X12,X5,c_Groups_Otimes__class_Otimes(X12)),X50),c_Groups_Oone__class_Oone(X12)),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X50),X4))&(c_Groups_Oone__class_Oone(X12)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X50),X4)<=~(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))))<=class_Groups_Ocomm__monoid__mult(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod_OF__eq)). 6.97/7.19 fof(fact_setsum__delta, axiom, ![X1, X2, X44, X5, X12]:((((~(hBOOL(hAPP(hAPP(c_member(X5),X2),X44)))=>c_Groups_Ozero__class_Ozero(X12)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),hAPP(hAPP(c_COMBC(X5,X12,X12),hAPP(hAPP(c_COMBS(X5,X12,tc_fun(X12,X12)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X12,tc_fun(X12,X12)),X5),c_If(X12)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X2))),X1)),c_Groups_Ozero__class_Ozero(X12))),X44))&(hBOOL(hAPP(hAPP(c_member(X5),X2),X44))=>hAPP(X1,X2)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),hAPP(hAPP(c_COMBC(X5,X12,X12),hAPP(hAPP(c_COMBS(X5,X12,tc_fun(X12,X12)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X12,tc_fun(X12,X12)),X5),c_If(X12)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X2))),X1)),c_Groups_Ozero__class_Ozero(X12))),X44)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X44)))<=class_Groups_Ocomm__monoid__add(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__delta)). 6.97/7.19 fof(fact_setsum_OF__eq, axiom, ![X50, X4, X5, X12]:(class_Groups_Ocomm__monoid__add(X12)=>((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X12,X5,c_Groups_Oplus__class_Oplus(X12)),X50),c_Groups_Ozero__class_Ozero(X12)),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X50),X4))&(c_Groups_Ozero__class_Ozero(X12)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X50),X4)<=~(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum_OF__eq)). 6.97/7.19 fof(fact_Least__mono, axiom, ![X44, X18, X5, X12]:(((c_Orderings_Oord__class_OLeast(X12,hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),hAPP(c_Set_Oimage(X5,X12,X18),X44)))=hAPP(X18,c_Orderings_Oord__class_OLeast(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X44)))<=?[X22]:(![X115]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X22),X115))<=hBOOL(hAPP(hAPP(c_member(X5),X115),X44)))&hBOOL(hAPP(hAPP(c_member(X5),X22),X44))))<=c_Orderings_Oorder__class_Omono(X5,X12,X18))<=(class_Orderings_Oorder(X5)&class_Orderings_Oorder(X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Least__mono)). 6.97/7.19 fof(fact_UN__finite2__subset, axiom, ![X11, X33, X4, X5]:(![X48]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X48)),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,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),X48),X33))),X11)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,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(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__finite2__subset)). 6.97/7.19 fof(fact_inj__vimage__singleton, axiom, ![X2, X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X12,X18),hAPP(hAPP(c_Set_Oinsert(X12),X2),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X5),c_HOL_OThe(X5,hAPP(hAPP(c_COMBC(X5,X12,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X12,tc_fun(X12,tc_HOL_Obool),X5),c_fequal),X18)),X2))),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__vimage__singleton)). 6.97/7.19 fof(fact_card__Diff2__less, axiom, ![X38, X35, X4, X5]:((hBOOL(hAPP(hAPP(c_member(X5),X35),X4))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X5),X38),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X5),X4)))<=hBOOL(hAPP(hAPP(c_member(X5),X38),X4))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Diff2__less)). 6.97/7.19 fof(fact_Diff__insert2, axiom, ![X11, X2, X4, X5]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X2),X11))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__insert2)). 6.97/7.19 fof(fact_concat__eq__concat__iff, axiom, ![X84, X23, X5]:(![X22]:(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X5),tc_List_Olist(X5),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_Nat_Onat),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X5),tc_Nat_Onat),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_List_Olist(X5)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X5))))),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),X22))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),X22),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X5),tc_List_Olist(X5)),X23),X84)))))=>(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X23)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X84)=>(X23=X84<=>c_List_Oconcat(X5,X84)=c_List_Oconcat(X5,X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_concat__eq__concat__iff)). 6.97/7.19 fof(fact_concat__injective, axiom, ![X84, X23, X5]:(c_List_Oconcat(X5,X84)=c_List_Oconcat(X5,X23)=>(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X84)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X23)=>(X23=X84<=![X22]:(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X5),tc_List_Olist(X5),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_Nat_Onat),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X5),tc_Nat_Onat),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_List_Olist(X5)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X5))))),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),X22))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),X22),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X5),tc_List_Olist(X5)),X23),X84)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_concat__injective)). 6.97/7.19 fof(fact_diff__nat__eq__if, axiom, ![X14, X135]:((hBOOL(hAPP(c_Nat__Numeral_Oneg,X135))=>hAPP(c_Int_Onat,X14)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X14)),hAPP(c_Int_Onat,X135)))&(~(hBOOL(hAPP(c_Nat__Numeral_Oneg,X135)))=>hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X14),X135)),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,X14)),hAPP(c_Int_Onat,X135)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__nat__eq__if)). 6.97/7.19 fof(fact_zip__obtain__same__length, axiom, ![X17, X84, X12, X23, X5]:((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(hAPP(c_List_Otake(X5),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12)),X84))),X23))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12)),hAPP(hAPP(c_List_Otake(X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12)),X84))),X84))=>hBOOL(hAPP(X17,hAPP(hAPP(c_List_Ozip(X5,X12),hAPP(hAPP(c_List_Otake(X5),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12)),X84))),X23)),hAPP(hAPP(c_List_Otake(X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12)),X84))),X84)))))=>hBOOL(hAPP(X17,hAPP(hAPP(c_List_Ozip(X5,X12),X23),X84)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__obtain__same__length)). 6.97/7.19 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)). 6.97/7.19 fof(fact_trancl__trans, axiom, ![X10, X3, X1, X2, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),c_Transitive__Closure_Otrancl(X5,X3)))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X10)),c_Transitive__Closure_Otrancl(X5,X3)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X1),X10)),c_Transitive__Closure_Otrancl(X5,X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__trans)). 6.97/7.19 fof(fact_eq__equiv__class__iff2, axiom, ![X38, X35, X3, X4, X5]:(c_Equiv__Relations_Oequiv(X5,X4,X3)=>(hBOOL(hAPP(hAPP(c_member(X5),X35),X4))=>(hBOOL(hAPP(hAPP(c_member(X5),X38),X4))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),X3))<=>hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X3)=hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),hAPP(hAPP(c_Set_Oinsert(X5),X38),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__equiv__class__iff2)). 6.97/7.19 fof(fact_equiv__class__eq__iff, axiom, ![X38, X35, X3, X4, X5]:(c_Equiv__Relations_Oequiv(X5,X4,X3)=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),X3))<=>((hAPP(c_Relation_OImage(X5,X5,X3),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))=hAPP(c_Relation_OImage(X5,X5,X3),hAPP(hAPP(c_Set_Oinsert(X5),X38),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))&hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))&hBOOL(hAPP(hAPP(c_member(X5),X38),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__class__eq__iff)). 6.97/7.19 fof(fact_lexord__take__index__conv, axiom, ![X3, X38, X35, X5]:(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)),X35),X38)),c_List_Olexord(X5,X3)))<=>(?[X42]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X35)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X38))))&hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(hAPP(c_List_Onth(X5),X35),X42)),hAPP(hAPP(c_List_Onth(X5),X38),X42))),X3)))&hAPP(hAPP(c_List_Otake(X5),X42),X35)=hAPP(hAPP(c_List_Otake(X5),X42),X38))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X35)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X38)))&X35=hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X35)),X38)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__take__index__conv)). 6.97/7.19 fof(fact_setsum__ub__add__nat, axiom, ![X24, X18, X32, X34, X5]:(class_Groups_Ocomm__monoid__add(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),c_Groups_Oone__class_Oone(tc_Nat_Onat))))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X34,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X24)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X34,X32))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X24)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__ub__add__nat)). 6.97/7.19 fof(fact_setprod__delta_H, axiom, ![X1, X2, X44, X5, X12]:(class_Groups_Ocomm__monoid__mult(X12)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X44))=>((~(hBOOL(hAPP(hAPP(c_member(X5),X2),X44)))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),hAPP(hAPP(c_COMBC(X5,X12,X12),hAPP(hAPP(c_COMBS(X5,X12,tc_fun(X12,X12)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X12,tc_fun(X12,X12)),X5),c_If(X12)),hAPP(c_fequal,X2))),X1)),c_Groups_Oone__class_Oone(X12))),X44)=c_Groups_Oone__class_Oone(X12))&(hBOOL(hAPP(hAPP(c_member(X5),X2),X44))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),hAPP(hAPP(c_COMBC(X5,X12,X12),hAPP(hAPP(c_COMBS(X5,X12,tc_fun(X12,X12)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X12,tc_fun(X12,X12)),X5),c_If(X12)),hAPP(c_fequal,X2))),X1)),c_Groups_Oone__class_Oone(X12))),X44)=hAPP(X1,X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__delta_H)). 6.97/7.19 fof(fact_setsum__delta_H, axiom, ![X1, X2, X44, X5, X12]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X44))=>((c_Groups_Ozero__class_Ozero(X12)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),hAPP(hAPP(c_COMBC(X5,X12,X12),hAPP(hAPP(c_COMBS(X5,X12,tc_fun(X12,X12)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X12,tc_fun(X12,X12)),X5),c_If(X12)),hAPP(c_fequal,X2))),X1)),c_Groups_Ozero__class_Ozero(X12))),X44)<=~(hBOOL(hAPP(hAPP(c_member(X5),X2),X44))))&(hBOOL(hAPP(hAPP(c_member(X5),X2),X44))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),hAPP(hAPP(c_COMBC(X5,X12,X12),hAPP(hAPP(c_COMBS(X5,X12,tc_fun(X12,X12)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X12,tc_fun(X12,X12)),X5),c_If(X12)),hAPP(c_fequal,X2))),X1)),c_Groups_Ozero__class_Ozero(X12))),X44)=hAPP(X1,X2))))<=class_Groups_Ocomm__monoid__add(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__delta_H)). 6.97/7.19 fof(fact_in__lex__prod, axiom, ![X66, X3, X259, X165, X1, X2, X12, X5]:(((hBOOL(hAPP(hAPP(c_member(tc_prod(X12,X12)),hAPP(hAPP(c_Product__Type_OPair(X12,X12),X1),X259)),X66))&X165=X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X165)),X3)))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X12),tc_prod(X5,X12))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X12),tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X2),X1)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X165),X259))),c_Wellfounded_Olex__prod(X5,X12,X3,X66)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__lex__prod)). 6.97/7.19 fof(fact_of__int, axiom, ![X46, X47, X5]:(class_Rings_Oring__1(X5)=>hAPP(c_Int_Oring__1__class_Oof__int(X5),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),X47),X46)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X47)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X46))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int)). 6.97/7.19 fof(fact_rtrancl__trancl__trancl, axiom, ![X14, X3, X38, X35, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),c_Transitive__Closure_Ortrancl(X5,X3)))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X38),X14)),c_Transitive__Closure_Otrancl(X5,X3)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X14)),c_Transitive__Closure_Otrancl(X5,X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__trancl__trancl)). 6.97/7.19 fof(fact_trancl__rtrancl__trancl, axiom, ![X10, X3, X1, X2, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),c_Transitive__Closure_Otrancl(X5,X3)))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X1),X10)),c_Transitive__Closure_Ortrancl(X5,X3)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X10)),c_Transitive__Closure_Otrancl(X5,X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__rtrancl__trancl)). 6.97/7.19 fof(fact_divmod__nat__if, axiom, ![X34, X32]:((~((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X32|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34),X32))))=>c_Divides_Odivmod__nat(X34,X32)=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),X34),X32),X32)))&((X32=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34),X32)))=>hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X34)=c_Divides_Odivmod__nat(X34,X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__if)). 6.97/7.19 fof(fact_divmod__nat__def, axiom, ![X32, X34]:c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X34,X32))=c_Divides_Odivmod__nat(X34,X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__def)). 6.97/7.19 fof(fact_Int__Collect__mono, axiom, ![X104, X17, X11, X4, X5]:((![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))=>(hBOOL(hAPP(X17,X22))=>hBOOL(hAPP(X104,X22))))=>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),X17))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(c_Set_OCollect(X5),X104)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__Collect__mono)). 6.97/7.19 fof(fact_trancl__into__trancl2, axiom, ![X10, X3, X1, X2, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),X3))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X1),X10)),c_Transitive__Closure_Otrancl(X5,X3)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X10)),c_Transitive__Closure_Otrancl(X5,X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__into__trancl2)). 6.97/7.19 fof(fact_Transitive__Closure_Otrancl__into__trancl, axiom, ![X10, X3, X1, X2, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),c_Transitive__Closure_Otrancl(X5,X3)))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X1),X10)),X3))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X10)),c_Transitive__Closure_Otrancl(X5,X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Transitive__Closure_Otrancl__into__trancl)). 6.97/7.19 fof(fact_dropWhile__append1, axiom, ![X84, X17, X23, X35, X5]:((~(hBOOL(hAPP(X17,X35)))=>hAPP(hAPP(c_List_Oappend(X5),c_List_OdropWhile(X5,X17,X23)),X84)=c_List_OdropWhile(X5,X17,hAPP(hAPP(c_List_Oappend(X5),X23),X84)))<=hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dropWhile__append1)). 6.97/7.19 fof(fact_listrel1I, axiom, ![X84, X217, X218, X23, X3, X38, X35, X5]:(((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)),X23),X84)),c_List_Olistrel1(X5,X3)))<=X84=hAPP(hAPP(c_List_Oappend(X5),X218),hAPP(hAPP(c_List_Olist_OCons(X5),X38),X217)))<=hAPP(hAPP(c_List_Oappend(X5),X218),hAPP(hAPP(c_List_Olist_OCons(X5),X35),X217))=X23)<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1I)). 6.97/7.19 fof(fact_def__Collect__coinduct, axiom, ![X56, X2, X17, X5, X4]:(c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_OCollect(X5)),X17))=X4=>(c_Orderings_Oorder__class_Omono(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_OCollect(X5)),X17))=>(hBOOL(hAPP(hAPP(c_member(X5),X2),X56))=>(![X116]:(hBOOL(hAPP(hAPP(X17,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X56),X4)),X116))<=hBOOL(hAPP(hAPP(c_member(X5),X116),X56)))=>hBOOL(hAPP(hAPP(c_member(X5),X2),X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_def__Collect__coinduct)). 6.97/7.19 fof(fact_o__def, axiom, ![X35, X50, X18, X62, X5, X12]:hAPP(X18,hAPP(X50,X35))=hAPP(hAPP(c_Fun_Ocomp(X12,X5,X62,X18),X50),X35), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_o__def)). 6.97/7.19 fof(fact_lists__IntI, axiom, ![X11, X4, X52, X5]:(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X52),c_List_Olists(X5,X4)))=>(hBOOL(hAPP(c_List_Olistsp(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X4)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X11))),X52))<=hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X52),c_List_Olists(X5,X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists__IntI)). 6.97/7.19 fof(fact_UN__finite2__eq, axiom, ![X11, X33, X4, X5]:(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,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(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X11)<=![X48]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X48)),X4)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,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),X48),X33))),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__finite2__eq)). 6.97/7.19 fof(fact_flat__lub__def, axiom, ![X1, X4, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X1),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))=>c_Partial__Function_Oflat__lub(X5,X1,X4)=X1)&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X1),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))=>c_HOL_OThe(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X1),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))=c_Partial__Function_Oflat__lub(X5,X1,X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_flat__lub__def)). 6.97/7.19 fof(fact_trancl__subset__Sigma, axiom, ![X4, X3, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X5,X3)),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X4),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X4))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X4),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__subset__Sigma)). 6.97/7.19 fof(fact_append__listrel1I, axiom, ![X217, X218, X3, X84, X23, X5]:(((X84=X23&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)),X218),X217)),c_List_Olistrel1(X5,X3))))|(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)),X23),X84)),c_List_Olistrel1(X5,X3)))&X217=X218))=>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),X23),X218)),hAPP(hAPP(c_List_Oappend(X5),X84),X217))),c_List_Olistrel1(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__listrel1I)). 6.97/7.19 fof(fact_lexord__cons__cons, axiom, ![X3, X38, X1, X35, X2, X5]:(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),X2),X35)),hAPP(hAPP(c_List_Olist_OCons(X5),X1),X38))),c_List_Olexord(X5,X3)))<=>((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)),X35),X38)),c_List_Olexord(X5,X3)))&X1=X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__cons__cons)). 6.97/7.19 fof(fact_listrel1__iff__update, axiom, ![X3, X84, X23, X5]:(?[X72, X48]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(hAPP(c_List_Onth(X5),X23),X48)),X72)),X3))&X84=hAPP(hAPP(c_List_Olist__update(X5,X23),X48),X72))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X48),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23))))<=>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)),X23),X84)),c_List_Olistrel1(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1__iff__update)). 6.97/7.19 fof(fact_Cons__in__lex, axiom, ![X3, X84, X38, X23, X35, X5]:(((X38=X35&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)),X23),X84)),c_List_Olex(X5,X3))))|(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),X3))&hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X84)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)))<=>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),X35),X23)),hAPP(hAPP(c_List_Olist_OCons(X5),X38),X84))),c_List_Olex(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Cons__in__lex)). 6.97/7.19 fof(fact_distinct__concat, axiom, ![X23, X5]:((![X155]:(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X155),hAPP(c_List_Oset(tc_List_Olist(X5)),X23)))=>hBOOL(hAPP(c_List_Odistinct(X5),X155)))=>(hBOOL(hAPP(c_List_Odistinct(X5),c_List_Oconcat(X5,X23)))<=![X155]:(![X194]:(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X194),hAPP(c_List_Oset(tc_List_Olist(X5)),X23)))=>(X194!=X155=>c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X155)),hAPP(c_List_Oset(X5),X194))))<=hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X155),hAPP(c_List_Oset(tc_List_Olist(X5)),X23))))))<=hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X5)),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__concat)). 6.97/7.19 fof(fact_rtrancl__into__trancl1, axiom, ![X10, X3, X1, X2, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),c_Transitive__Closure_Ortrancl(X5,X3)))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X1),X10)),X3))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X10)),c_Transitive__Closure_Otrancl(X5,X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__into__trancl1)). 6.97/7.19 fof(fact_divmod__nat__step, axiom, ![X36, X25]:((c_Divides_Odivmod__nat(X36,X25)=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),X36),X25)),X25))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),X25),X25))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X36)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__step)). 6.97/7.19 fof(fact_wf__union__merge, axiom, ![X44, X67, X5]:(c_Wellfounded_Owf(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X67),X44))<=>c_Wellfounded_Owf(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X67),X67)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X44),X67))),X44))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__union__merge)). 6.97/7.19 fof(fact_Un__assoc, axiom, ![X65, X11, X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X65))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11)),X65), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__assoc)). 6.97/7.19 fof(fact_Un__commute, axiom, ![X11, X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X4)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__commute)). 6.97/7.19 fof(fact_dropWhile__append2, axiom, ![X84, X17, X23, X5]:(![X22]:(hBOOL(hAPP(X17,X22))<=hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X23))))=>c_List_OdropWhile(X5,X17,hAPP(hAPP(c_List_Oappend(X5),X23),X84))=c_List_OdropWhile(X5,X17,X84)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dropWhile__append2)). 6.97/7.19 fof(fact_quotient__eq__iff, axiom, ![X38, X35, X95, X56, X3, X4, X5]:((hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X56),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X4),X3)))=>(((hBOOL(hAPP(hAPP(c_member(X5),X38),X95))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),X3))<=>X95=X56))<=hBOOL(hAPP(hAPP(c_member(X5),X35),X56)))<=hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X95),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X4),X3)))))<=c_Equiv__Relations_Oequiv(X5,X4,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_quotient__eq__iff)). 6.97/7.19 fof(fact_r__r__into__trancl, axiom, ![X10, X67, X1, X2, X5]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X1),X10)),X67))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X10)),c_Transitive__Closure_Otrancl(X5,X67))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),X67))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_r__r__into__trancl)). 6.97/7.19 fof(fact_card__partition, axiom, ![X33, X65, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X65)))=>(![X78]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X78),X65))=>hAPP(c_Finite__Set_Ocard(X5),X78)=X33)=>(![X79]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X79),X65))=>![X80]:((X80!=X79=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X79),X80)=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))<=hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X80),X65))))=>hAPP(c_Finite__Set_Ocard(X5),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X65))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),hAPP(c_Finite__Set_Ocard(tc_fun(X5,tc_HOL_Obool)),X65)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,tc_HOL_Obool)),X65))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__partition)). 6.97/7.19 fof(fact_finite__UnionD, axiom, ![X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X4)))=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,tc_HOL_Obool)),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__UnionD)). 6.97/7.19 fof(fact_periodic__finite__ex, axiom, ![X17, X97]:(((?[X76]:hBOOL(hAPP(X17,X76))<=>?[X22]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X22),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X97)))&hBOOL(hAPP(X17,X22))))<=![X22, X145]:(hBOOL(hAPP(X17,X22))<=>hBOOL(hAPP(X17,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X145),X97))))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X97))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_periodic__finite__ex)). 6.97/7.19 fof(fact_zmult__commute, axiom, ![X39, X26]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X39),X26)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),X39), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult__commute)). 6.97/7.19 fof(fact_lexord__lex, axiom, ![X3, X38, X35, X5]:(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)),X35),X38)),c_List_Olex(X5,X3)))<=>(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X35)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X38)&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)),X35),X38)),c_List_Olexord(X5,X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__lex)). 6.97/7.19 fof(fact_divmod__nat__rel__def, axiom, ![X204, X32, X34]:(((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),X204)),X32)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X204))=X34&(X32!=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)),X32)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X204)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X204)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32))=>(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),X204)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X204)),X32)))))))&(X32=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X204)))<=>hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X34,X32),X204))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__rel__def)). 6.97/7.19 fof(fact_le0, axiom, ![X25]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le0)). 6.97/7.19 fof(fact_append__eq__append__conv__if, axiom, ![X199, X200, X201, X202, X5]:(hAPP(hAPP(c_List_Oappend(X5),X200),X199)=hAPP(hAPP(c_List_Oappend(X5),X202),X201)<=>((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X202)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X200))))=>(X199=hAPP(hAPP(c_List_Oappend(X5),hAPP(hAPP(c_List_Odrop(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X200)),X202)),X201)&X200=hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X200)),X202)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X202)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X200)))=>(X201=hAPP(hAPP(c_List_Oappend(X5),hAPP(hAPP(c_List_Odrop(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X202)),X200)),X199)&X202=hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X202)),X200))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__eq__append__conv__if)). 6.97/7.19 fof(fact_the__inv__into__comp, axiom, ![X35, X4, X50, X62, X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,hAPP(c_Set_Oimage(X62,X5,X50),X4))=>((hAPP(hAPP(c_Fun_Ocomp(X5,X62,X12,c_Fun_Othe__inv__into(X62,X5,X4,X50)),c_Fun_Othe__inv__into(X5,X12,hAPP(c_Set_Oimage(X62,X5,X50),X4),X18)),X35)=hAPP(c_Fun_Othe__inv__into(X62,X12,X4,hAPP(c_Fun_Ocomp(X5,X12,X62,X18),X50)),X35)<=hBOOL(hAPP(hAPP(c_member(X12),X35),hAPP(c_Set_Oimage(X5,X12,X18),hAPP(c_Set_Oimage(X62,X5,X50),X4)))))<=c_Fun_Oinj__on(X62,X5,X50,X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__inv__into__comp)). 6.97/7.19 fof(fact_inv__into__comp, axiom, ![X35, X4, X50, X62, X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,hAPP(c_Set_Oimage(X62,X5,X50),X4))=>(c_Fun_Oinj__on(X62,X5,X50,X4)=>(hAPP(c_Hilbert__Choice_Oinv__into(X62,X12,X4,hAPP(c_Fun_Ocomp(X5,X12,X62,X18),X50)),X35)=hAPP(hAPP(c_Fun_Ocomp(X5,X62,X12,c_Hilbert__Choice_Oinv__into(X62,X5,X4,X50)),c_Hilbert__Choice_Oinv__into(X5,X12,hAPP(c_Set_Oimage(X62,X5,X50),X4),X18)),X35)<=hBOOL(hAPP(hAPP(c_member(X12),X35),hAPP(c_Set_Oimage(X5,X12,X18),hAPP(c_Set_Oimage(X62,X5,X50),X4))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inv__into__comp)). 6.97/7.19 fof(fact_lfp__induct__set, axiom, ![X17, X18, X2, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X2),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X5,tc_HOL_Obool),X18)))=>((hBOOL(hAPP(X17,X2))<=![X22]:(hBOOL(hAPP(X17,X22))<=hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(X18,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X5,tc_HOL_Obool),X18)),hAPP(c_Set_OCollect(X5),X17)))))))<=c_Orderings_Oorder__class_Omono(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lfp__induct__set)). 6.97/7.19 fof(fact_pigeonhole__infinite, axiom, ![X18, X12, X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X12),hAPP(c_Set_Oimage(X5,X12,X18),X4)))=>?[X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))&~(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X4))),hAPP(hAPP(c_COMBC(X5,X12,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X12,tc_fun(X12,tc_HOL_Obool),X5),c_fequal),X18)),hAPP(X18,X22)))))))))<=~(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pigeonhole__infinite)). 6.97/7.19 fof(fact_split__zdiv, axiom, ![X33, X32, X17]:(hBOOL(hAPP(X17,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X32),X33)))<=>(((![X42]:(?[X43]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X43))&hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X42)),X43)=X32)&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X43),X33)))=>hBOOL(hAPP(X17,X42)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33)))&(![X42]:(?[X43]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X43),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))&X32=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X42)),X43))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33),X43)))=>hBOOL(hAPP(X17,X42)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))&(hBOOL(hAPP(X17,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=X33=c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__zdiv)). 6.97/7.19 fof(fact_trancl__Int__subset, axiom, ![X66, X3, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X5,X3)),X66)),X3)),X66))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X5,X3)),X66)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),X66))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__Int__subset)). 6.97/7.19 fof(fact_small__lazy_H_Opinduct, axiom, ![X17, X103, X109]:(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),X109),X103)))=>(![X254, X42]:(((hBOOL(hAPP(hAPP(X17,X254),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X42),c_Groups_Oone__class_Oone(tc_Int_Oint))))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X254),X42))))=>hBOOL(hAPP(hAPP(X17,X254),X42)))<=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),X254),X42))))=>hBOOL(hAPP(hAPP(X17,X109),X103)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_small__lazy_H_Opinduct)). 6.97/7.19 fof(fact_vimage__inter__cong, axiom, ![X38, X12, X50, X18, X44, X5]:(![X273]:(hBOOL(hAPP(hAPP(c_member(X5),X273),X44))=>hAPP(X18,X273)=hAPP(X50,X273))=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X12,X18),X38)),X44)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X12,X50),X38)),X44)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__inter__cong)). 6.97/7.19 fof(fact_setsum__ivl__cong, axiom, ![X50, X18, X97, X1, X10, X2, X5, X12]:(((X1=X97=>(![X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X10),X22))=>(hAPP(X18,X22)=hAPP(X50,X22)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X22),X97))))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X50),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X10),X97))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X2),X1))))<=X2=X10)<=(class_Groups_Ocomm__monoid__add(X12)&class_Orderings_Oord(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__ivl__cong)). 6.97/7.19 fof(fact_nat__intermed__int__val, axiom, ![X33, X18, X32, X34]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X18,X34)),X33))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X33),hAPP(X18,X32)))=>?[X42]:((X33=hAPP(X18,X42)&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X32)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),X42)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34),X32)))<=![X42]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),X42))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),X32)))=>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(X18,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X18,X42)))),c_Groups_Oone__class_Oone(tc_Int_Oint))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__intermed__int__val)). 6.97/7.19 fof(fact_rev__update, axiom, ![X7, X41, X8, X19]:(hAPP(hAPP(c_List_Olist__update(X8,hAPP(c_List_Orev(X8),X41)),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(X8)),X41)),X19)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X7)=hAPP(c_List_Orev(X8),hAPP(hAPP(c_List_Olist__update(X8,X41),X19),X7))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__update)). 6.97/7.19 fof(fact_diff__diff__left, axiom, ![X19, X27, X28]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X28),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27),X19))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X28),X27)),X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__diff__left)). 6.97/7.19 fof(fact_nat__eq__add__iff2, axiom, ![X32, X34, X51, X46, X47]:((X34=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),X46),X47)),X51)),X32)<=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X46),X51)),X32)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X47),X51)),X34))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X47),X46))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__eq__add__iff2)). 6.97/7.19 fof(fact_left__add__mult__distrib, axiom, ![X19, X27, X139, X28]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X139)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),X139)),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_Oplus__class_Oplus(tc_Nat_Onat),X28),X27)),X139)),X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_left__add__mult__distrib)). 6.97/7.19 fof(fact_sup__nat__def, axiom, c_Orderings_Oord__class_Omax(tc_Nat_Onat)=c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__nat__def)). 6.97/7.19 fof(fact_def__lfp__induct__set, axiom, ![X17, X2, X18, X5, X4]:((c_Orderings_Oorder__class_Omono(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X18)=>(hBOOL(hAPP(hAPP(c_member(X5),X2),X4))=>(![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(X18,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Set_OCollect(X5),X17)))))=>hBOOL(hAPP(X17,X22)))=>hBOOL(hAPP(X17,X2)))))<=c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X5,tc_HOL_Obool),X18)=X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_def__lfp__induct__set)). 6.97/7.19 fof(fact_split__zmod, axiom, ![X33, X32, X17]:((((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X33=>hBOOL(hAPP(X17,X32)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33))=>![X42, X43]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X43),X33))&X32=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X42)),X43))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X43)))=>hBOOL(hAPP(X17,X43)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>![X42, X43]:(hBOOL(hAPP(X17,X43))<=((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X42)),X43)=X32&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X43),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33),X43))))))<=>hBOOL(hAPP(X17,c_Divides_Odiv__class_Omod(tc_Int_Oint,X32,X33)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__zmod)). 6.97/7.19 fof(fact_aset_I6_J, axiom, ![X4, X82, X73]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X82),c_Groups_Oone__class_Oone(tc_Int_Oint))),X4))=>![X22]:(![X115]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X115),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X73)))=>![X158]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X158),X4))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X158),X115)!=X22))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22),X73)),X82))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22),X82)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_aset_I6_J)). 6.97/7.19 fof(fact_bset_I8_J, axiom, ![X11, X82, X73]:((![X22]:(![X115]:(![X158]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X158),X11))=>X22!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X158),X115))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X115),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X73))))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X82),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X22),X73)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X82),X22))))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X82),c_Groups_Oone__class_Oone(tc_Int_Oint))),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bset_I8_J)). 6.97/7.19 fof(fact_wf__weak__decr__stable, axiom, ![X3, X18, X5]:(![X42]:hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(X18,hAPP(c_Nat_OSuc,X42))),hAPP(X18,X42))),c_Transitive__Closure_Ortrancl(X5,X3)))=>(c_Wellfounded_Owf(X5,c_Transitive__Closure_Otrancl(X5,X3))=>?[X42]:![X145]:hAPP(X18,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),X145))=hAPP(X18,X42))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__weak__decr__stable)). 6.97/7.19 fof(fact_power__number__of__even, axiom, ![X9, X14, X5]:(class_Int_Onumber__ring(X5)=>hAPP(hAPP(c_Power_Opower__class_Opower(X5),X14),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X9)))=hAPP(hAPP(c_HOL_OLet(X5,X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X14),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X9))),hAPP(hAPP(c_COMBS(X5,X5,X5),c_Groups_Otimes__class_Otimes(X5)),c_COMBI(X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__number__of__even)). 6.97/7.19 fof(fact_Collect__conv__if, axiom, ![X5, X2, X17]:((hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X2))),X17))=hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))<=hBOOL(hAPP(X17,X2)))&(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X2))),X17))<=~(hBOOL(hAPP(X17,X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__conv__if)). 6.97/7.19 fof(fact_eq__add__iff1, axiom, ![X97, X1, X10, X136, X2, X5]:(class_Rings_Oring(X5)=>(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X136)),X97)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X136)),X10)<=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X2),X1)),X136)),X10)=X97)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__add__iff1)). 6.97/7.19 fof(fact_decr__lemma, axiom, ![X26, X6, X74]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X6),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),X6),X26))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X74))),X26))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X74))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_decr__lemma)). 6.97/7.19 fof(fact_tranclD, axiom, ![X67, X38, X35, X5]:(?[X116]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X116)),X67))&hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X116),X38)),c_Transitive__Closure_Ortrancl(X5,X67))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),c_Transitive__Closure_Otrancl(X5,X67)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tranclD)). 6.97/7.19 fof(fact_tranclD2, axiom, ![X67, X38, X35, X5]:(?[X116]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X116),X38)),X67))&hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X116)),c_Transitive__Closure_Ortrancl(X5,X67))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),c_Transitive__Closure_Otrancl(X5,X67)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tranclD2)). 6.97/7.19 fof(fact_trancl__mono, axiom, ![X66, X3, X24, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),X66))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X24),c_Transitive__Closure_Otrancl(X5,X66))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X24),c_Transitive__Closure_Otrancl(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__mono)). 6.97/7.19 fof(fact_incr__lemma, axiom, ![X6, X26, X74]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X74))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6),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),X6),X26))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X74))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_incr__lemma)). 6.97/7.19 fof(fact_gr0I, axiom, ![X25]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_gr0I)). 6.97/7.19 fof(fact_Cons__eq__filter__iff, axiom, ![X84, X17, X23, X35, X5]:(?[X140, X141]:(((X23=hAPP(c_List_Ofilter(X5,X17),X141)&hBOOL(hAPP(X17,X35)))&![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X140)))=>~(hBOOL(hAPP(X17,X22)))))&hAPP(hAPP(c_List_Oappend(X5),X140),hAPP(hAPP(c_List_Olist_OCons(X5),X35),X141))=X84)<=>hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23)=hAPP(c_List_Ofilter(X5,X17),X84)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Cons__eq__filter__iff)). 6.97/7.19 fof(fact_filter__eq__Cons__iff, axiom, ![X23, X35, X84, X17, X5]:(?[X140, X141]:(((X84=hAPP(hAPP(c_List_Oappend(X5),X140),hAPP(hAPP(c_List_Olist_OCons(X5),X35),X141))&![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X140)))=>~(hBOOL(hAPP(X17,X22)))))&hBOOL(hAPP(X17,X35)))&X23=hAPP(c_List_Ofilter(X5,X17),X141))<=>hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23)=hAPP(c_List_Ofilter(X5,X17),X84)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__eq__Cons__iff)). 6.97/7.19 fof(fact_upto_Opinduct, axiom, ![X17, X103, X109]:((hBOOL(hAPP(hAPP(X17,X109),X103))<=![X42, X43]:(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),X42),X43)))=>((hBOOL(hAPP(hAPP(X17,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X42),c_Groups_Oone__class_Oone(tc_Int_Oint))),X43))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X42),X43)))=>hBOOL(hAPP(hAPP(X17,X42),X43)))))<=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),X109),X103)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upto_Opinduct)). 6.97/7.19 fof(fact_upt__add__eq__append, axiom, ![X19, X27, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28),X27))=>hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X28,X27)),c_List_Oupt(X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27),X19)))=c_List_Oupt(X28,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27),X19))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upt__add__eq__append)). 6.97/7.19 fof(fact_order__fun_I2_J, axiom, ![X50, X18, X5, X12]:(((hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBS(X5,X12,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X12,tc_fun(X12,tc_HOL_Obool),X5),c_fequal),X18)),X50))))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X12)),X18),X50)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,X12)),X18),X50)))<=(class_Orderings_Oorder(X12)&class_Enum_Oenum(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__fun_I2_J)). 6.97/7.19 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)). 6.97/7.19 fof(fact_semiring__norm_I113_J, axiom, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_semiring__norm_I113_J)). 6.97/7.19 fof(fact_dropWhile_Osimps_I2_J, axiom, ![X23, X5, X35, X17]:((c_List_OdropWhile(X5,X17,hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23))=hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23)<=~(hBOOL(hAPP(X17,X35))))&(c_List_OdropWhile(X5,X17,X23)=c_List_OdropWhile(X5,X17,hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23))<=hBOOL(hAPP(X17,X35)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dropWhile_Osimps_I2_J)). 6.97/7.19 fof(fact_nat0__intermed__int__val, axiom, ![X33, X18, X32]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X18,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X33))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X33),hAPP(X18,X32)))=>?[X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X32))&X33=hAPP(X18,X42))))<=![X42]:(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(X18,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X18,X42)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat0__intermed__int__val)). 6.97/7.19 fof(fact_int__val__lemma, axiom, ![X33, X18, X32]:(![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),X32))=>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(X18,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X18,X42)))),c_Groups_Oone__class_Oone(tc_Int_Oint))))=>((?[X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X32))&X33=hAPP(X18,X42))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X33),hAPP(X18,X32))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X18,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X33)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__val__lemma)). 6.97/7.19 fof(fact_take__zip, axiom, ![X45, X41, X25, X5, X8]:hAPP(hAPP(c_List_Otake(tc_prod(X8,X5)),X25),hAPP(hAPP(c_List_Ozip(X8,X5),X41),X45))=hAPP(hAPP(c_List_Ozip(X8,X5),hAPP(hAPP(c_List_Otake(X8),X25),X41)),hAPP(hAPP(c_List_Otake(X5),X25),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__zip)). 6.97/7.19 fof(fact_transpose__transpose, axiom, ![X23, X5]:(c_List_OtakeWhile(tc_List_Olist(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X5)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(X5),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X5))),X23)=c_List_Otranspose(X5,c_List_Otranspose(X5,X23))<=c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X5))),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__transpose)). 6.97/7.19 fof(fact_rtranclD, axiom, ![X67, X1, X2, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),c_Transitive__Closure_Ortrancl(X5,X67)))=>((hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),c_Transitive__Closure_Otrancl(X5,X67)))&X2!=X1)|X2=X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtranclD)). 6.97/7.19 fof(fact_length__drop, axiom, ![X41, X25, X8]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)),X25)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),hAPP(hAPP(c_List_Odrop(X8),X25),X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__drop)). 6.97/7.19 fof(fact_add__number__of__diff2, axiom, ![X39, X31, X40, X8]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X40),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X39)))),X31)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),X40)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X31),hAPP(c_Int_Onumber__class_Onumber__of(X8),X39)))<=class_Int_Onumber__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__number__of__diff2)). 6.97/7.19 fof(fact_image__minus__const__atLeastLessThan__nat, axiom, ![X35, X38, X10]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10),X38)))=>((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)),X10)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X35),X38))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X35),X38)))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X35),X38)))=>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)),X10)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X35),X38)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10),X38))=>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)),X10)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X35),X38))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X35),X10)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X38),X10)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__minus__const__atLeastLessThan__nat)). 6.97/7.19 fof(fact_rtrancl__Int__subset, axiom, ![X3, X66, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X3)),X66))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X3)),X66)),X3)),X66)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Relation_OId(X5)),X66))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__Int__subset)). 6.97/7.19 fof(fact_map__sorted__distinct__set__unique, axiom, ![X84, X23, X18, X5, X12]:((c_Fun_Oinj__on(X5,X12,X18,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X23)),hAPP(c_List_Oset(X5),X84)))=>(c_List_Olinorder__class_Osorted(X12,hAPP(hAPP(c_List_Omap(X5,X12),X18),X23))=>(hBOOL(hAPP(c_List_Odistinct(X12),hAPP(hAPP(c_List_Omap(X5,X12),X18),X23)))=>(((X23=X84<=hAPP(c_List_Oset(X5),X23)=hAPP(c_List_Oset(X5),X84))<=hBOOL(hAPP(c_List_Odistinct(X12),hAPP(hAPP(c_List_Omap(X5,X12),X18),X84))))<=c_List_Olinorder__class_Osorted(X12,hAPP(hAPP(c_List_Omap(X5,X12),X18),X84))))))<=class_Orderings_Olinorder(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__sorted__distinct__set__unique)). 6.97/7.19 fof(fact_set__append, axiom, ![X84, X23, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X23)),hAPP(c_List_Oset(X5),X84))=hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Oappend(X5),X23),X84)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__append)). 6.97/7.19 fof(fact_setsum__op__ivl__Suc, axiom, ![X18, X34, X32, X5]:(((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32),X34)))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34),hAPP(c_Nat_OSuc,X32)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34),X32))),hAPP(X18,X32)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32),X34))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34),hAPP(c_Nat_OSuc,X32)))=c_Groups_Ozero__class_Ozero(X5)))<=class_Groups_Ocomm__monoid__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__op__ivl__Suc)). 6.97/7.19 fof(fact_nat__number__of__add__left, axiom, ![X19, X99, X40]:((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X40)))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99)),X19))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99)),X19))&(((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X99)))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)),X19)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99)),X19)))&(~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X99))))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99)),X19))=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),X40),X99))),X19)))<=~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X40)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__number__of__add__left)). 6.97/7.19 fof(fact_zmod__zmult2__eq, axiom, ![X29, X30, X31]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X31))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X29),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),X29),X31))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X29))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X29),X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zmult2__eq)). 6.97/7.19 fof(fact_trancl__power, axiom, ![X67, X24, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X24),c_Transitive__Closure_Otrancl(X5,X67)))<=>?[X48]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X48))&hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X24),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X48),X67))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__power)). 6.97/7.19 fof(fact_dropWhile__eq__Cons__conv, axiom, ![X84, X38, X23, X17, X5]:((X23=hAPP(hAPP(c_List_Oappend(X5),c_List_OtakeWhile(X5,X17,X23)),hAPP(hAPP(c_List_Olist_OCons(X5),X38),X84))&~(hBOOL(hAPP(X17,X38))))<=>hAPP(hAPP(c_List_Olist_OCons(X5),X38),X84)=c_List_OdropWhile(X5,X17,X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dropWhile__eq__Cons__conv)). 6.97/7.19 fof(fact_zip__same, axiom, ![X23, X1, X2, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),hAPP(c_List_Oset(tc_prod(X5,X5)),hAPP(hAPP(c_List_Ozip(X5,X5),X23),X23))))<=>(X1=X2&hBOOL(hAPP(hAPP(c_member(X5),X2),hAPP(c_List_Oset(X5),X23))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__same)). 6.97/7.19 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J, axiom, ![X11, X4]:(c_Nat__Transfer_Onat__set(X4)=>(c_Nat__Transfer_Onat__set(X11)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X4),X11)=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),X4)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J)). 6.97/7.19 fof(fact_image__Un, axiom, ![X11, X4, X18, X5, X12]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X12,X5,X18),X4)),hAPP(c_Set_Oimage(X12,X5,X18),X11))=hAPP(c_Set_Oimage(X12,X5,X18),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),X4),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__Un)). 6.97/7.19 fof(fact_image__image, axiom, ![X4, X50, X62, X18, X5, X12]:hAPP(c_Set_Oimage(X12,X5,X18),hAPP(c_Set_Oimage(X62,X12,X50),X4))=hAPP(c_Set_Oimage(X62,X5,hAPP(hAPP(c_COMBB(X12,X5,X62),X18),X50)),X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__image)). 6.97/7.19 fof(fact_card__less, axiom, ![X47, X94]:(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X94))=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=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)),X94))),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,X47)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__less)). 6.97/7.19 fof(fact_split__pos__lemma, axiom, ![X32, X17, X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33))=>(![X42, X43]:(hBOOL(hAPP(hAPP(X17,X42),X43))<=((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X43),X33))&X32=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X42)),X43))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X43))))<=>hBOOL(hAPP(hAPP(X17,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X32),X33)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X32,X33))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__pos__lemma)). 6.97/7.19 fof(fact_split__neg__lemma, axiom, ![X32, X17, X33]:((hBOOL(hAPP(hAPP(X17,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X32),X33)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X32,X33)))<=>![X42, X43]:(hBOOL(hAPP(hAPP(X17,X42),X43))<=((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33),X43))&hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X42)),X43)=X32)&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X43),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__neg__lemma)). 6.97/7.19 fof(fact_div__pos__neg__1__number__of, axiom, ![X39]:(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),X39))=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),X39)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X39)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__pos__neg__1__number__of)). 6.97/7.19 fof(fact_negateSnd__eq, axiom, ![X70, X53]:hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X53),X70))=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X53),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X70)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negateSnd__eq)). 6.97/7.19 fof(fact_less__int__code_I16_J, axiom, ![X122, X123]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X123),X122))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X123)),c_Int_OBit1(X122)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__int__code_I16_J)). 6.97/7.19 fof(fact_incr__mult__lemma, axiom, ![X33, X17, X97]:((![X22]:(hBOOL(hAPP(X17,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22),X97)))<=hBOOL(hAPP(X17,X22)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33))=>![X22]:(hBOOL(hAPP(X17,X22))=>hBOOL(hAPP(X17,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X97)))))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X97))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_incr__mult__lemma)). 6.97/7.19 fof(fact_nat__number__of__mult__left, axiom, ![X19, X99, X40]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X40),c_Int_OPls))=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99)),X19)))&(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),X40),X99))),X19)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99)),X19))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X40),c_Int_OPls))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__number__of__mult__left)). 6.97/7.19 fof(fact_rel__simps_I34_J, axiom, ![X52, X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X33),X52))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X33)),c_Int_OBit1(X52)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I34_J)). 6.97/7.19 fof(fact_acyclic__def, axiom, ![X3, X5]:(c_Wellfounded_Oacyclic(X5,X3)<=>![X22]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X22),X22)),c_Transitive__Closure_Otrancl(X5,X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acyclic__def)). 6.97/7.19 fof(fact_acyclicI, axiom, ![X3, X5]:(c_Wellfounded_Oacyclic(X5,X3)<=![X22]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X22),X22)),c_Transitive__Closure_Otrancl(X5,X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acyclicI)). 6.97/7.19 fof(fact_takeWhile__eq__filter, axiom, ![X23, X17, X5]:(hAPP(c_List_Ofilter(X5,X17),X23)=c_List_OtakeWhile(X5,X17,X23)<=![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),c_List_OdropWhile(X5,X17,X23))))=>~(hBOOL(hAPP(X17,X22))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__eq__filter)). 6.97/7.19 fof(fact_divmod__int__relI, axiom, ![X70, X53, X29, X30]:((hBOOL(hAPP(c_Divides_Odivmod__int__rel(X30,X29),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X53),X70)))<=((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X29))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X70))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X70),X29))))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X29)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X70),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X29),X70))))))<=X30=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X29),X53)),X70)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__relI)). 6.97/7.19 fof(fact_divmod__int__rel__div__eq, axiom, ![X87, X7, X88, X89]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X88),X7)),X87)=X89=>(((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X88)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X88),X87))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X87),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),X88))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X87)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X88))))=>(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X89),X88)=X7<=X88!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__rel__div__eq)). 6.97/7.19 fof(fact_int__power__div__base, axiom, ![X19, X36]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X36))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19))=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X19),X36)),X19)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X19),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__power__div__base)). 6.97/7.19 fof(fact_strong__setprod__reindex__cong, axiom, ![X71, X50, X11, X4, X18, X12, X5, X62]:(class_Groups_Ocomm__monoid__mult(X62)=>(c_Fun_Oinj__on(X5,X12,X18,X4)=>((![X22]:(hAPP(hAPP(c_Fun_Ocomp(X12,X62,X5,X71),X18),X22)=hAPP(X50,X22)<=hBOOL(hAPP(hAPP(c_member(X5),X22),X4)))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X62),X50),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12,X62),X71),X11))<=X11=hAPP(c_Set_Oimage(X5,X12,X18),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_strong__setprod__reindex__cong)). 6.97/7.19 fof(fact_hd__rotate__conv__nth, axiom, ![X25, X8, X41]:(X41!=c_List_Olist_ONil(X8)=>hAPP(hAPP(c_List_Onth(X8),X41),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X25,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)))=hAPP(c_List_Ohd(X8),hAPP(c_List_Orotate(X8,X25),X41))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__rotate__conv__nth)). 6.97/7.19 fof(fact_setsum__reindex__cong, axiom, ![X71, X50, X11, X4, X18, X12, X5, X62]:(class_Groups_Ocomm__monoid__add(X62)=>(c_Fun_Oinj__on(X5,X12,X18,X4)=>(X11=hAPP(c_Set_Oimage(X5,X12,X18),X4)=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X62),X50),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X62),X71),X11)<=![X13]:(hAPP(X50,X13)=hAPP(X71,hAPP(X18,X13))<=hBOOL(hAPP(hAPP(c_member(X5),X13),X4))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__reindex__cong)). 6.97/7.19 fof(fact_take__upt, axiom, ![X25, X36, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),X36)),X25))=>c_List_Oupt(X28,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),X36))=hAPP(hAPP(c_List_Otake(tc_Nat_Onat),X36),c_List_Oupt(X28,X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__upt)). 6.97/7.19 fof(fact_def__coinduct__set, axiom, ![X56, X2, X18, X5, X4]:(X4=c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X5,tc_HOL_Obool),X18)=>(c_Orderings_Oorder__class_Omono(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X18)=>(hBOOL(hAPP(hAPP(c_member(X5),X2),X56))=>(hBOOL(hAPP(hAPP(c_member(X5),X2),X4))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X56),hAPP(X18,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X56),X4)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_def__coinduct__set)). 6.97/7.19 fof(fact_mod__pos__neg__1__number__of, axiom, ![X39]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X39)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>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),X39)))))=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),X39))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__pos__neg__1__number__of)). 6.97/7.19 fof(fact_pick__same, axiom, ![X23, X5, X52]:(hAPP(c_Random_Opick(X5,hAPP(hAPP(c_List_Omap(X5,tc_prod(tc_Code__Numeral_Ocode__numeral,X5)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X5),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X23)),hAPP(c_Code__Numeral_Oof__nat,X52))=hAPP(hAPP(c_List_Onth(X5),X23),X52)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X52),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pick__same)). 6.97/7.19 fof(fact_vimage__subset__eq, axiom, ![X4, X11, X18, X12, X5]:(c_Fun_Obij__betw(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X12,X18),X11)),X4))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),X11),hAPP(c_Set_Oimage(X5,X12,X18),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__subset__eq)). 6.97/7.19 fof(fact_setsum__shift__bounds__Suc__ivl, axiom, ![X32, X34, X18, X5]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Nat_Onat),X18),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34),X32))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X34)),hAPP(c_Nat_OSuc,X32)))<=class_Groups_Ocomm__monoid__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__shift__bounds__Suc__ivl)). 6.97/7.19 fof(fact_bij__image__Collect__eq, axiom, ![X17, X18, X12, X5]:(hAPP(c_Set_Oimage(X5,X12,X18),hAPP(c_Set_OCollect(X5),X17))=hAPP(c_Set_OCollect(X12),hAPP(hAPP(c_COMBB(X5,tc_HOL_Obool,X12),X17),c_Hilbert__Choice_Oinv__into(X5,X12,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X18)))<=c_Fun_Obij__betw(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bij__image__Collect__eq)). 6.97/7.19 fof(fact_listsp__conj__eq, axiom, ![X35, X11, X4, X5]:(hBOOL(hAPP(c_List_Olistsp(X5,hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),X4)),X11)),X35))<=>(hBOOL(hAPP(c_List_Olistsp(X5,X4),X35))&hBOOL(hAPP(c_List_Olistsp(X5,X11),X35)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsp__conj__eq)). 6.97/7.19 fof(fact_foldr__max__sorted, axiom, ![X38, X23, X5]:((c_List_Olinorder__class_Osorted(X5,hAPP(c_List_Orev(X5),X23))=>((hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_List_Onth(X5),X23),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X38)=c_List_Ofoldr(X5,X5,c_Orderings_Oord__class_Omax(X5),X23,X38)<=c_List_Olist_ONil(X5)!=X23)&(X38=c_List_Ofoldr(X5,X5,c_Orderings_Oord__class_Omax(X5),X23,X38)<=X23=c_List_Olist_ONil(X5))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldr__max__sorted)). 6.97/7.19 fof(fact_crossproduct__eq, axiom, ![X14, X35, X38, X9, X5]:(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)=>((X14=X38|X35=X9)<=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X14)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X35),X38))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X38)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X35),X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_crossproduct__eq)). 6.97/7.19 fof(fact_nth__map__upt, axiom, ![X18, X5, X34, X32, X47]:(hAPP(hAPP(c_List_Onth(X5),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X5),X18),c_List_Oupt(X34,X32))),X47)=hAPP(X18,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34),X47))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X47),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X32),X34)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__map__upt)). 6.97/7.19 fof(fact_in__measure, axiom, ![X18, X38, X35, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X18,X35)),hAPP(X18,X38)))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),hAPP(c_Wellfounded_Omeasure(X5),X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__measure)). 6.97/7.19 fof(fact_measure__def, axiom, ![X5]:hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X5),c_Wellfounded_Oless__than)=c_Wellfounded_Omeasure(X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_measure__def)). 6.97/7.19 fof(fact_finite__Collect__subsets, axiom, ![X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool))),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Collect__subsets)). 6.97/7.19 fof(fact_foldl__foldr1__lemma, axiom, ![X23, X2, X5]:(class_Groups_Omonoid__add(X5)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X2),c_List_Ofoldr(X5,X5,c_Groups_Oplus__class_Oplus(X5),X23,c_Groups_Ozero__class_Ozero(X5)))=hAPP(c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),X2),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__foldr1__lemma)). 6.97/7.19 fof(fact_setsum__lessThan__Suc, axiom, ![X32, X18, X5]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X32)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X32))),hAPP(X18,X32))<=class_Groups_Ocomm__monoid__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__lessThan__Suc)). 6.97/7.19 fof(fact_number__of__Bit1, axiom, ![X39, X8]:(class_Int_Onumber__ring(X8)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),c_Groups_Oone__class_Oone(X8)),hAPP(c_Int_Onumber__class_Onumber__of(X8),X39))),hAPP(c_Int_Onumber__class_Onumber__of(X8),X39))=hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OBit1(X39))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__Bit1)). 6.97/7.19 fof(fact_bset_I3_J, axiom, ![X11, X82, X73]:(((X82=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X82),X73)<=![X22]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X22),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X73)))=>![X115]:(X82!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X115),X22)<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X115),X11)))))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X82),c_Groups_Oone__class_Oone(tc_Int_Oint))),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bset_I3_J)). 6.97/7.19 fof(fact_aset_I3_J, axiom, ![X4, X82, X73]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73))=>((![X22]:(![X115]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X115),X4))=>X82!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X115),X22))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X22),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X73))))=>X82=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X82),X73))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X82),c_Groups_Oone__class_Oone(tc_Int_Oint))),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_aset_I3_J)). 6.97/7.19 fof(fact_setsum__atMost__Suc, axiom, ![X32, X18, X5]:(class_Groups_Ocomm__monoid__add(X5)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X32))),hAPP(X18,hAPP(c_Nat_OSuc,X32)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__atMost__Suc)). 6.97/7.19 fof(fact_atLeast0AtMost, axiom, ![X32]:hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X32)=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeast0AtMost)). 6.97/7.19 fof(fact_inf__INFI__fold__inf, axiom, ![X18, X11, X4, X5, X12]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X12),X11),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X12),X4),X18))=hAPP(hAPP(c_Finite__Set_Ofold(X5,X12,hAPP(hAPP(c_COMBB(X12,tc_fun(X12,X12),X5),c_Lattices_Osemilattice__inf__class_Oinf(X12)),X18)),X11),X4))<=class_Complete__Lattice_Ocomplete__lattice(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__INFI__fold__inf)). 6.97/7.19 fof(fact_sup__SUPR__fold__sup, axiom, ![X18, X11, X4, X5, X12]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X12),X11),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X12),X4),X18))=hAPP(hAPP(c_Finite__Set_Ofold(X5,X12,hAPP(hAPP(c_COMBB(X12,tc_fun(X12,X12),X5),c_Lattices_Osemilattice__sup__class_Osup(X12)),X18)),X11),X4))<=class_Complete__Lattice_Ocomplete__lattice(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__SUPR__fold__sup)). 6.97/7.19 fof(fact_setsum__head, axiom, ![X17, X32, X34, X5]:(class_Groups_Ocomm__monoid__add(X5)=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X17),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X34,X32))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(X17,X34)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X17),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X34,X32)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__head)). 6.97/7.19 fof(fact_setsum__nonneg__leq__bound, axiom, ![X47, X11, X18, X66, X5, X12]:(class_Groups_Oordered__ab__group__add(X12)=>((![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),c_Groups_Ozero__class_Ozero(X12)),hAPP(X18,X42)))<=hBOOL(hAPP(hAPP(c_member(X5),X42),X66)))=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),X66)=X11=>(hBOOL(hAPP(hAPP(c_member(X5),X47),X66))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),hAPP(X18,X47)),X11)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X66)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__nonneg__leq__bound)). 6.97/7.19 fof(fact_set__mp, axiom, ![X35, X11, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))=>(hBOOL(hAPP(hAPP(c_member(X5),X35),X4))=>hBOOL(hAPP(hAPP(c_member(X5),X35),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__mp)). 6.97/7.19 fof(fact_apsnd__eq__conv, axiom, ![X50, X35, X18, X5, X12, X62]:(hAPP(X50,hAPP(c_Product__Type_Osnd(X5,X62),X35))=hAPP(X18,hAPP(c_Product__Type_Osnd(X5,X62),X35))<=>hAPP(c_Product__Type_Oapsnd(X62,X12,X5,X50),X35)=hAPP(c_Product__Type_Oapsnd(X62,X12,X5,X18),X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_apsnd__eq__conv)). 6.97/7.19 fof(fact_apfst__eq__conv, axiom, ![X50, X35, X18, X12, X5, X62]:(hAPP(X18,hAPP(c_Product__Type_Ofst(X62,X12),X35))=hAPP(X50,hAPP(c_Product__Type_Ofst(X62,X12),X35))<=>hAPP(c_Product__Type_Oapfst(X62,X5,X12,X18),X35)=hAPP(c_Product__Type_Oapfst(X62,X5,X12,X50),X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_apfst__eq__conv)). 6.97/7.19 fof(fact_apfst__def, axiom, ![X18, X12, X62, X5]:c_Product__Type_Oapfst(X5,X62,X12,X18)=c_Product__Type_Omap__pair(X5,X62,X12,X12,X18,c_Fun_Oid(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_apfst__def)). 6.97/7.19 fof(fact_divmod__int__rel__mod__eq, axiom, ![X7, X191, X88, X89]:(((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X88=>c_Divides_Odiv__class_Omod(tc_Int_Oint,X89,X88)=X7)<=(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X88),X7)))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X88))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7),X88))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X88)))))<=X89=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X88),X191)),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__rel__mod__eq)). 6.97/7.19 fof(fact_sum__squares__le__zero__iff, axiom, ![X38, X35, X5]:(((c_Groups_Ozero__class_Ozero(X5)=X35&c_Groups_Ozero__class_Ozero(X5)=X38)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X35),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X38),X38))),c_Groups_Ozero__class_Ozero(X5))))<=class_Rings_Olinordered__ring__strict(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__squares__le__zero__iff)). 6.97/7.19 fof(fact_vimage__subsetD, axiom, ![X4, X11, X18, X5, X12]:(c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))=hAPP(c_Set_Oimage(X12,X5,X18),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X12,X5,X18),X11)),X4))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(c_Set_Oimage(X12,X5,X18),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__subsetD)). 6.97/7.19 fof(fact_atLeastatMost__psubset__iff, axiom, ![X97, X10, X1, X2, X5]:(class_Orderings_Oorder(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X10,X97)))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X10),X97))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X2),X1)))|((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X1),X97))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X1),X97))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),X2))))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X10),X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastatMost__psubset__iff)). 6.97/7.19 fof(fact_order__le__less, axiom, ![X38, X35, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),X38))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X35),X38))|X35=X38))<=class_Orderings_Oorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__le__less)). 6.97/7.19 fof(fact_ivl__disj__un_I6_J, axiom, ![X51, X52, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X52),X51))=>c_SetInterval_Oord__class_OatLeastAtMost(X5,X52,X51)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X52),X51)),hAPP(hAPP(c_Set_Oinsert(X5),X51),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I6_J)). 6.97/7.19 fof(fact_Un__insert__right, axiom, ![X11, X2, X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X2),X11))=hAPP(hAPP(c_Set_Oinsert(X5),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__insert__right)). 6.97/7.19 fof(fact_Un__empty__right, axiom, ![X4, X5]:X4=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__empty__right)). 6.97/7.19 fof(fact_INFI__fold__inf, axiom, ![X18, X4, X5, X12]:(class_Complete__Lattice_Ocomplete__lattice(X12)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hAPP(hAPP(c_Finite__Set_Ofold(X5,X12,hAPP(hAPP(c_COMBB(X12,tc_fun(X12,X12),X5),c_Lattices_Osemilattice__inf__class_Oinf(X12)),X18)),c_Orderings_Otop__class_Otop(X12)),X4)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X12),X4),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INFI__fold__inf)). 6.97/7.19 fof(fact_SUPR__fold__sup, axiom, ![X18, X4, X5, X12]:(class_Complete__Lattice_Ocomplete__lattice(X12)=>(hAPP(hAPP(c_Finite__Set_Ofold(X5,X12,hAPP(hAPP(c_COMBB(X12,tc_fun(X12,X12),X5),c_Lattices_Osemilattice__sup__class_Osup(X12)),X18)),c_Orderings_Obot__class_Obot(X12)),X4)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X12),X4),X18)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUPR__fold__sup)). 6.97/7.19 fof(fact_ivl__disj__un_I3_J, axiom, ![X51, X52, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X52),X51))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X52),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X52,X51))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X52),X51))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I3_J)). 6.97/7.19 fof(fact_Un__insert__left, axiom, ![X65, X11, X2, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X2),X11)),X65)=hAPP(hAPP(c_Set_Oinsert(X5),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X65)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__insert__left)). 6.97/7.19 fof(fact_Un__empty__left, axiom, ![X11, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X11)=X11, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__empty__left)). 6.97/7.19 fof(fact_setprod__reindex__cong, axiom, ![X71, X50, X11, X4, X18, X12, X5, X62]:((c_Fun_Oinj__on(X5,X12,X18,X4)=>(hAPP(c_Set_Oimage(X5,X12,X18),X4)=X11=>(hAPP(c_Fun_Ocomp(X12,X62,X5,X71),X18)=X50=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X62),X50),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12,X62),X71),X11))))<=class_Groups_Ocomm__monoid__mult(X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__reindex__cong)). 6.97/7.19 fof(fact_aset_I4_J, axiom, ![X4, X82, X73]:((![X22]:(![X115]:(![X158]:(X22!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X158),X115)<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X158),X4)))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X115),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X73))))=>(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22),X73)!=X82<=X22!=X82))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X82),X4)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_aset_I4_J)). 6.97/7.19 fof(fact_Nat_Odiff__diff__eq, axiom, ![X25, X36, X19]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19),X25))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),X19)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X19))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),X25))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19),X36))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat_Odiff__diff__eq)). 6.97/7.19 fof(fact_uminus__listsum__map, axiom, ![X23, X18, X12, X5]:(class_Groups_Oab__group__add(X5)=>hAPP(c_Groups_Ouminus__class_Ouminus(X5),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X12,X5),X18),X23)))=hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X12,X5),hAPP(c_Fun_Ocomp(X5,X5,X12,c_Groups_Ouminus__class_Ouminus(X5)),X18)),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_uminus__listsum__map)). 6.97/7.19 fof(fact_List_Omap_Ocompositionality, axiom, ![X253, X50, X62, X18, X5, X12]:hAPP(hAPP(c_List_Omap(X62,X5),hAPP(c_Fun_Ocomp(X12,X5,X62,X18),X50)),X253)=hAPP(hAPP(c_List_Omap(X12,X5),X18),hAPP(hAPP(c_List_Omap(X62,X12),X50),X253)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_List_Omap_Ocompositionality)). 6.97/7.19 fof(fact_bset_I4_J, axiom, ![X11, X82, X73]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73))=>(![X22]:((X82!=X22=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X22),X73)!=X82)<=![X115]:(![X158]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X158),X11))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X158),X115)!=X22)<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X115),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X73)))))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X82),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bset_I4_J)). 6.97/7.19 fof(fact_takeWhile__not__last, axiom, ![X5, X23]:((c_List_OtakeWhile(X5,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),c_List_Olast(X5,X23))),X23)=c_List_Obutlast(X5,X23)<=hBOOL(hAPP(c_List_Odistinct(X5),X23)))<=c_List_Olist_ONil(X5)!=X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__not__last)). 6.97/7.19 fof(fact_inj__on__iff__surj, axiom, ![X107, X12, X5, X4]:((?[X185]:(c_Fun_Oinj__on(X5,X12,X185,X4)&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X12,X185),X4)),X107)))<=>?[X268]:hAPP(c_Set_Oimage(X12,X5,X268),X107)=X4)<=X4!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__iff__surj)). 6.97/7.19 fof(fact_concat__eq__Nil__conv, axiom, ![X77, X5]:(c_List_Oconcat(X5,X77)=c_List_Olist_ONil(X5)<=>![X22]:(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X22),hAPP(c_List_Oset(tc_List_Olist(X5)),X77)))=>X22=c_List_Olist_ONil(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_concat__eq__Nil__conv)). 6.97/7.19 fof(fact_Nil__eq__concat__conv, axiom, ![X77, X5]:(![X22]:(c_List_Olist_ONil(X5)=X22<=hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X22),hAPP(c_List_Oset(tc_List_Olist(X5)),X77))))<=>c_List_Oconcat(X5,X77)=c_List_Olist_ONil(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nil__eq__concat__conv)). 6.97/7.19 fof(fact_transfer__nat__int__sum__prod__cong_I2_J, axiom, ![X50, X18, X11, X4, X5]:((((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),X18),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),X50),X11)<=![X22]:(hAPP(X18,X22)=hAPP(X50,X22)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22))))<=c_Nat__Transfer_Onat__set(X11))<=X11=X4)<=(class_Groups_Ocomm__monoid__add(X5)&class_Groups_Ocomm__monoid__mult(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__sum__prod__cong_I2_J)). 6.97/7.19 fof(fact_vimage__subsetI, axiom, ![X4, X11, X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X12,X18),X11)),X4))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),X11),hAPP(c_Set_Oimage(X5,X12,X18),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__subsetI)). 6.97/7.19 fof(fact_transfer__nat__int__sum__prod__cong_I1_J, axiom, ![X50, X18, X11, X4, X5]:((class_Groups_Ocomm__monoid__mult(X5)&class_Groups_Ocomm__monoid__add(X5))=>(X4=X11=>((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X50),X11)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X18),X4)<=![X22]:(hAPP(X50,X22)=hAPP(X18,X22)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22))))<=c_Nat__Transfer_Onat__set(X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__sum__prod__cong_I1_J)). 6.97/7.19 fof(fact_setsum__eq__Suc0__iff, axiom, ![X18, X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X18),X4)<=>?[X22]:((hBOOL(hAPP(hAPP(c_member(X5),X22),X4))&hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(X18,X22))&![X115]:((X115!=X22=>hAPP(X18,X115)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<=hBOOL(hAPP(hAPP(c_member(X5),X115),X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__eq__Suc0__iff)). 6.97/7.19 fof(fact_split__div, axiom, ![X33, X32, X17]:(((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X33=>hBOOL(hAPP(X17,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))&(X33!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>![X42, X43]:((hBOOL(hAPP(X17,X42))<=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X42)),X43)=X32)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),X33)))))<=>hBOOL(hAPP(X17,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X32),X33)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__div)). 6.97/7.19 fof(fact_INT__cong, axiom, ![X12, X73, X65, X5, X11, X4]:(X4=X11=>(![X22]:(hAPP(X65,X22)=hAPP(X73,X22)<=hBOOL(hAPP(hAPP(c_member(X5),X22),X11)))=>hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),X11),X73)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),X4),X65))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__cong)). 6.97/7.19 fof(fact_filter__in__sublist, axiom, ![X66, X23, X5]:(c_List_Osublist(X5,X23,X66)=hAPP(c_List_Ofilter(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),hAPP(c_List_Oset(X5),c_List_Osublist(X5,X23,X66)))),X23)<=hBOOL(hAPP(c_List_Odistinct(X5),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__in__sublist)). 6.97/7.19 fof(fact_ivl__disj__un_I5_J, axiom, ![X51, X52, X5]:((hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X52),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X52,X51))=c_SetInterval_Oord__class_OatLeastAtMost(X5,X52,X51)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X52),X51)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I5_J)). 6.97/7.19 fof(fact_ivl__disj__un_I4_J, axiom, ![X51, X52, X5]:(class_Orderings_Olinorder(X5)=>(c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X52,X51)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X52,X51)),hAPP(hAPP(c_Set_Oinsert(X5),X51),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X52),X51)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I4_J)). 6.97/7.19 fof(fact_n__less__n__mult__m, axiom, ![X36, X25]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X25))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X36))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X36))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_n__less__n__mult__m)). 6.97/7.19 fof(fact_n__less__m__mult__n, axiom, ![X36, X25]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X36))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X25))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_n__less__m__mult__n)). 6.97/7.19 fof(fact_finite__less__ub, axiom, ![X51, X18]:(![X48]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X48),hAPP(X18,X48)))=>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)),X18)),X51))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__less__ub)). 6.97/7.19 fof(fact_less__int__code_I15_J, axiom, ![X122, X123]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X123)),c_Int_OBit0(X122)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X123),X122))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__int__code_I15_J)). 6.97/7.19 fof(fact_less__eq__int__code_I15_J, axiom, ![X122, X123]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X123)),c_Int_OBit0(X122)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X123),X122))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__eq__int__code_I15_J)). 6.97/7.19 fof(fact_rel__simps_I15_J, axiom, ![X52, X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X33),X52))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X33)),c_Int_OBit1(X52)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I15_J)). 6.97/7.19 fof(fact_less__eq__int__code_I14_J, axiom, ![X122, X123]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X123)),c_Int_OBit1(X122)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X123),X122))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__eq__int__code_I14_J)). 6.97/7.19 fof(fact_snd__image__times, axiom, ![X11, X12, X5, X4]:((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4=>hAPP(c_Set_Oimage(tc_prod(X5,X12),X12,c_Product__Type_Osnd(X5,X12)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X4),hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X5),X11)))=X11)&(hAPP(c_Set_Oimage(tc_prod(X5,X12),X12,c_Product__Type_Osnd(X5,X12)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X4),hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X5),X11)))=c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool))<=X4=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_snd__image__times)). 6.97/7.19 fof(fact_snd__eq__Range, axiom, ![X67, X5, X12]:hAPP(c_Relation_ORange(X12,X5),X67)=hAPP(c_Set_Oimage(tc_prod(X12,X5),X5,c_Product__Type_Osnd(X12,X5)),X67), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_snd__eq__Range)). 6.97/7.19 fof(fact_zdiv__zminus2__eq__if, axiom, ![X30, X29]:(((hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),X29))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X29))<=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X29))&(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),X30),X29))),c_Groups_Oone__class_Oone(tc_Int_Oint))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X29))<=c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X29)))<=X29!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__zminus2__eq__if)). 6.97/7.19 fof(fact_fst__image__times, axiom, ![X4, X12, X5, X11]:((X11!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>hAPP(c_Set_Oimage(tc_prod(X12,X5),X12,c_Product__Type_Ofst(X12,X5)),hAPP(hAPP(c_Product__Type_OSigma(X12,X5),X4),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X12),X11)))=X4)&(X11=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool))=hAPP(c_Set_Oimage(tc_prod(X12,X5),X12,c_Product__Type_Ofst(X12,X5)),hAPP(hAPP(c_Product__Type_OSigma(X12,X5),X4),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X12),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fst__image__times)). 6.97/7.19 fof(fact_fst__eq__Domain, axiom, ![X67, X12, X5]:hAPP(c_Relation_ODomain(X5,X12),X67)=hAPP(c_Set_Oimage(tc_prod(X5,X12),X5,c_Product__Type_Ofst(X5,X12)),X67), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fst__eq__Domain)). 6.97/7.19 fof(fact_partition__set, axiom, ![X171, X172, X23, X17, X5]:(c_List_Opartition(X5,X17,X23)=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X172),X171)=>hAPP(c_List_Oset(X5),X23)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X172)),hAPP(c_List_Oset(X5),X171))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_partition__set)). 6.97/7.19 fof(fact_ivl__disj__un_I2_J, axiom, ![X51, X5]:(class_Orderings_Olinorder(X5)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X51)),hAPP(hAPP(c_Set_Oinsert(X5),X51),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))=hAPP(c_SetInterval_Oord__class_OatMost(X5),X51)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I2_J)). 6.97/7.19 fof(fact_nat__mult__distrib__neg, axiom, ![X112, X26]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X112)))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),X112))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__distrib__neg)). 6.97/7.19 fof(fact_trancl__into__rtrancl, axiom, ![X3, X1, X2, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),c_Transitive__Closure_Otrancl(X5,X3)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),c_Transitive__Closure_Ortrancl(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__into__rtrancl)). 6.97/7.19 fof(fact_number__of__Bit0, axiom, ![X39, X8]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(c_Int_Onumber__class_Onumber__of(X8),X39))),hAPP(c_Int_Onumber__class_Onumber__of(X8),X39))=hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OBit0(X39))<=class_Int_Onumber__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__Bit0)). 6.97/7.19 fof(fact_mod__nat__number__of, axiom, ![X99, X40]:((~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X40))))=>((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X99)))=>hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99)))&(~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X99))))=>hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X40),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X99)))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99)))))&(c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<=hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X40))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__nat__number__of)). 6.97/7.19 fof(fact_image__inv__into__cancel, axiom, ![X106, X107, X4, X18, X5, X12]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X106),X107))=>X106=hAPP(c_Set_Oimage(X12,X5,X18),hAPP(c_Set_Oimage(X5,X12,c_Hilbert__Choice_Oinv__into(X12,X5,X4,X18)),X106)))<=hAPP(c_Set_Oimage(X12,X5,X18),X4)=X107), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__inv__into__cancel)). 6.97/7.19 fof(fact_div__nat__number__of, axiom, ![X99, X40]:((hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99))=hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X40)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X99)))<=~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X40)))))&(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X40)))=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__nat__number__of)). 6.97/7.19 fof(fact_split__mod, axiom, ![X33, X32, X17]:(((hBOOL(hAPP(X17,X32))<=X33=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(![X42, X43]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X42)),X43)=X32=>hBOOL(hAPP(X17,X43)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),X33)))<=X33!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))<=>hBOOL(hAPP(X17,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X32,X33)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__mod)). 6.97/7.19 fof(fact_one__less__mult, axiom, ![X36, X25]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X25))=>(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),X36),X25)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X36)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__less__mult)). 6.97/7.19 fof(fact_one__le__mult__iff, axiom, ![X32, X34]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X34))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X32)))<=>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),X34),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__le__mult__iff)). 6.97/7.19 fof(fact_finite__conv__nat__seg__image, axiom, ![X4, X5]:(?[X48, X185]:X4=hAPP(c_Set_Oimage(tc_Nat_Onat,X5,X185),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)),X48)))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__conv__nat__seg__image)). 6.97/7.19 fof(fact_foldl__foldr1, axiom, ![X23, X5]:(class_Groups_Omonoid__add(X5)=>hAPP(c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),c_Groups_Ozero__class_Ozero(X5)),X23)=c_List_Ofoldr(X5,X5,c_Groups_Oplus__class_Oplus(X5),X23,c_Groups_Ozero__class_Ozero(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__foldr1)). 6.97/7.19 fof(fact_double__number__of__Bit0, axiom, ![X39, X8]:(class_Int_Onumber__ring(X8)=>hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OBit0(X39))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),c_Groups_Oone__class_Oone(X8)),c_Groups_Oone__class_Oone(X8))),hAPP(c_Int_Onumber__class_Onumber__of(X8),X39))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_double__number__of__Bit0)). 6.97/7.19 fof(fact_setsum__shift__lb__Suc0__0__upt, axiom, ![X33, X18, X5]:(class_Groups_Ocomm__monoid__add(X5)=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X33))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))<=hAPP(X18,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__shift__lb__Suc0__0__upt)). 6.97/7.19 fof(fact_transfer__nat__int__set__return__embed, axiom, ![X4]:(X4=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),X4))<=c_Nat__Transfer_Onat__set(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__set__return__embed)). 6.97/7.19 fof(fact_vimage__mono, axiom, ![X18, X12, X11, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X12,X5,X18),X4)),hAPP(c_Set_Ovimage(X12,X5,X18),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__mono)). 6.97/7.19 fof(fact_finite__fun__UNIVD1, axiom, ![X12, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))<=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(c_Finite__Set_Ocard(X12),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,X12)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X5,X12),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__fun__UNIVD1)). 6.97/7.19 fof(fact_add__nat__number__of, axiom, ![X99, X40]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X40),c_Int_OPls)))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X99),c_Int_OPls))=>hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99)))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X99),c_Int_OPls)))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X40),X99)))))&(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X40),c_Int_OPls)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__nat__number__of)). 6.97/7.19 fof(fact_setsum__shift__lb__Suc0__0, axiom, ![X33, X18]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X18),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X18),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X33))<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(X18,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__shift__lb__Suc0__0)). 6.97/7.19 fof(fact_mult__0__right, axiom, ![X36]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__0__right)). 6.97/7.19 fof(fact_Nat_Oadd__0__right, axiom, ![X36]:X36=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat_Oadd__0__right)). 6.97/7.19 fof(fact_div__pos__pos__1__number__of, axiom, ![X39]:(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),X39)))=>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),X39)))=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),X39))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__pos__pos__1__number__of)). 6.97/7.19 fof(fact_nat__add__distrib, axiom, ![X112, X26]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X112))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X26)),hAPP(c_Int_Onat,X112))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26),X112)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__add__distrib)). 6.97/7.19 fof(fact_ivl__disj__un_I1_J, axiom, ![X52, X5]:(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X52),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X52))=hAPP(c_SetInterval_Oord__class_OatLeast(X5),X52)<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I1_J)). 6.97/7.19 fof(fact_r__into__trancl_H, axiom, ![X3, X24, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X24),c_Transitive__Closure_Otrancl(X5,X3)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X24),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_r__into__trancl_H)). 6.97/7.19 fof(fact_nat__diff__distrib, axiom, ![X26, X112]:((hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26),X112))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X26)),hAPP(c_Int_Onat,X112))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X112),X26)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X112))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__diff__distrib)). 6.97/7.19 fof(fact_Int__Collect, axiom, ![X17, X4, X35, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Set_OCollect(X5),X17))))<=>(hBOOL(hAPP(hAPP(c_member(X5),X35),X4))&hBOOL(hAPP(X17,X35)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__Collect)). 6.97/7.19 fof(fact_bij__vimage__eq__inv__image, axiom, ![X4, X18, X12, X5]:(hAPP(c_Set_Oimage(X12,X5,c_Hilbert__Choice_Oinv__into(X5,X12,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X18)),X4)=hAPP(c_Set_Ovimage(X5,X12,X18),X4)<=c_Fun_Obij__betw(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bij__vimage__eq__inv__image)). 6.97/7.19 fof(fact_acyclicP__converse, axiom, ![X3, X5]:(c_Wellfounded_Oacyclic(X5,hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),X3)))<=>c_Wellfounded_Oacyclic(X5,hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),c_Predicate_Oconversep(X5,X5,X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acyclicP__converse)). 6.97/7.19 fof(fact_total__on__diff__Id, axiom, ![X3, X4, X5]:(c_Relation_Ototal__on(X5,X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),c_Relation_OId(X5)))<=>c_Relation_Ototal__on(X5,X4,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_total__on__diff__Id)). 6.97/7.19 fof(fact_foldr__conv__foldl, axiom, ![X2, X23, X5]:(class_Groups_Oab__semigroup__add(X5)=>c_List_Ofoldr(X5,X5,c_Groups_Oplus__class_Oplus(X5),X23,X2)=hAPP(c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),X2),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldr__conv__foldl)). 6.97/7.19 fof(fact_upt__rec, axiom, ![X27, X28]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28),X27))=>c_List_Oupt(X28,X27)=hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X28),c_List_Oupt(hAPP(c_Nat_OSuc,X28),X27)))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28),X27)))=>c_List_Olist_ONil(tc_Nat_Onat)=c_List_Oupt(X28,X27))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upt__rec)). 6.97/7.19 fof(fact_dropWhile__eq__Nil__conv, axiom, ![X23, X17, X5]:(![X22]:(hBOOL(hAPP(X17,X22))<=hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X23))))<=>c_List_Olist_ONil(X5)=c_List_OdropWhile(X5,X17,X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dropWhile__eq__Nil__conv)). 6.97/7.19 fof(fact_trans__diff__Id, axiom, ![X3, X5]:(c_Relation_Otrans(X5,X3)=>(c_Relation_Oantisym(X5,X3)=>c_Relation_Otrans(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),c_Relation_OId(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trans__diff__Id)). 6.97/7.19 fof(fact_IdE, axiom, ![X24, X5]:(~(![X22]:hAPP(hAPP(c_Product__Type_OPair(X5,X5),X22),X22)!=X24)<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X24),c_Relation_OId(X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_IdE)). 6.97/7.19 fof(fact_code__numeral__decr, axiom, ![X19]:(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,X19)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,X19)))<=hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral__decr)). 6.97/7.19 fof(fact_zero__code__numeral__def, axiom, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__code__numeral__def)). 6.97/7.19 fof(fact_Code__Numeral_Oof__nat__code, axiom, c_Code__Numeral_Oof__nat=c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Code__Numeral_Oof__nat__code)). 6.97/7.19 fof(fact_simp__from__to, axiom, ![X47, X46]:((c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X47,X46)=c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X46),X47)))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X46),X47)))=>c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X47,X46)=hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X47),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X47),c_Groups_Oone__class_Oone(tc_Int_Oint)),X46)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_simp__from__to)). 6.97/7.19 fof(fact_rev__eq__Cons__iff, axiom, ![X84, X38, X23, X5]:(hAPP(hAPP(c_List_Olist_OCons(X5),X38),X84)=hAPP(c_List_Orev(X5),X23)<=>hAPP(hAPP(c_List_Oappend(X5),hAPP(c_List_Orev(X5),X84)),hAPP(hAPP(c_List_Olist_OCons(X5),X38),c_List_Olist_ONil(X5)))=X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__eq__Cons__iff)). 6.97/7.19 fof(fact_rev_Osimps_I2_J, axiom, ![X41, X6, X8]:hAPP(hAPP(c_List_Oappend(X8),hAPP(c_List_Orev(X8),X41)),hAPP(hAPP(c_List_Olist_OCons(X8),X6),c_List_Olist_ONil(X8)))=hAPP(c_List_Orev(X8),hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev_Osimps_I2_J)). 6.97/7.19 fof(fact_zip__eq__conv, axiom, ![X83, X84, X12, X23, X5]:(((hAPP(hAPP(c_List_Omap(tc_prod(X5,X12),X5),c_Product__Type_Ofst(X5,X12)),X83)=X23&hAPP(hAPP(c_List_Omap(tc_prod(X5,X12),X12),c_Product__Type_Osnd(X5,X12)),X83)=X84)<=>X83=hAPP(hAPP(c_List_Ozip(X5,X12),X23),X84))<=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12)),X84)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__eq__conv)). 6.97/7.19 fof(fact_Powp__Pow__eq, axiom, ![X35, X4, X5]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X35),hAPP(c_Set_OPow(X5),X4)))<=>hBOOL(hAPP(c_Predicate_OPowp(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X4)),X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Powp__Pow__eq)). 6.97/7.19 fof(fact_inj__on__mapI, axiom, ![X4, X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool),c_List_Oset(X5)),X4)))=>c_Fun_Oinj__on(tc_List_Olist(X5),tc_List_Olist(X12),hAPP(c_List_Omap(X5,X12),X18),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__mapI)). 6.97/7.19 fof(fact_UNION__eq__Union__image, axiom, ![X11, X4, X5, X12]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X4),X11)=c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(X12,tc_fun(X5,tc_HOL_Obool),X11),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UNION__eq__Union__image)). 6.97/7.19 fof(fact_sum__squares__eq__zero__iff, axiom, ![X38, X35, X5]:(class_Rings_Olinordered__ring__strict(X5)=>(c_Groups_Ozero__class_Ozero(X5)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X35),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X38),X38))<=>(X35=c_Groups_Ozero__class_Ozero(X5)&X38=c_Groups_Ozero__class_Ozero(X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__squares__eq__zero__iff)). 6.97/7.19 fof(fact_sorted_Osimps, axiom, ![X2, X5]:(class_Orderings_Olinorder(X5)=>(c_List_Olinorder__class_Osorted(X5,X2)<=>(X2=c_List_Olist_ONil(X5)|?[X86, X22]:((![X115]:(hBOOL(hAPP(hAPP(c_member(X5),X115),hAPP(c_List_Oset(X5),X86)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X22),X115)))&c_List_Olinorder__class_Osorted(X5,X86))&hAPP(hAPP(c_List_Olist_OCons(X5),X22),X86)=X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted_Osimps)). 6.97/7.19 fof(fact_nth__upt, axiom, ![X27, X19, X28]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),X19)=hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(X28,X27)),X19)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),X19)),X27))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__upt)). 6.97/7.19 fof(fact_power__nat__number__of, axiom, ![X25, X40]:((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X40)))=>hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)),X25)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))&(hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X40)),X25))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)),X25)<=~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X40)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__nat__number__of)). 6.97/7.19 fof(fact_small__lazy_H_Osimps, axiom, ![X28, X74]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X74),X28))=>c_Lazy__Sequence_Oempty(tc_Int_Oint)=c_Lazy__Sequence_Osmall__lazy_H(X74,X28))&(c_Lazy__Sequence_Osmall__lazy_H(X74,X28)=c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X28),c_Lazy__Sequence_Osmall__lazy_H(X74,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X28),c_Groups_Oone__class_Oone(tc_Int_Oint))))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X74),X28))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_small__lazy_H_Osimps)). 6.97/7.19 fof(fact_mod__pos__pos__1__number__of, axiom, ![X39]:(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),X39)))=>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),X39))=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),X39)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__pos__pos__1__number__of)). 6.97/7.19 fof(fact_hd__dropWhile, axiom, ![X23, X17, X5]:(c_List_OdropWhile(X5,X17,X23)!=c_List_Olist_ONil(X5)=>~(hBOOL(hAPP(X17,hAPP(c_List_Ohd(X5),c_List_OdropWhile(X5,X17,X23)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__dropWhile)). 6.97/7.19 fof(fact_mult__nat__number__of, axiom, ![X99, X40]:((hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X40),X99))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X40),c_Int_OPls))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X40),c_Int_OPls))=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X99))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__nat__number__of)). 6.97/7.19 fof(fact_eq__nat__number__of, axiom, ![X61, X60]:(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X60)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X61)<=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X61)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X60))))&(((~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X61))))=>X61=X60)&(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X61)))=>hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X60)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X60))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__nat__number__of)). 6.97/7.19 fof(fact_Id__on__eqI, axiom, ![X4, X5, X1, X2]:(X1=X2=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),c_Relation_OId__on(X5,X4)))<=hBOOL(hAPP(hAPP(c_member(X5),X2),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Id__on__eqI)). 6.97/7.19 fof(fact_split__div__lemma, axiom, ![X34, X124, X32]:((X124=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X34),X32)<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),hAPP(c_Nat_OSuc,X124))))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X124)),X34))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__div__lemma)). 6.97/7.19 fof(fact_divide__eq__eq__number__of, axiom, ![X9, X10, X1, X5]:((class_Fields_Ofield__inverse__zero(X5)&class_Int_Onumber(X5))=>(((X10=c_Groups_Ozero__class_Ozero(X5)=>c_Groups_Ozero__class_Ozero(X5)=hAPP(c_Int_Onumber__class_Onumber__of(X5),X9))&(X1=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X9)),X10)<=X10!=c_Groups_Ozero__class_Ozero(X5)))<=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X1),X10)=hAPP(c_Int_Onumber__class_Onumber__of(X5),X9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__eq__eq__number__of)). 6.97/7.19 fof(fact_add__nonneg__eq__0__iff, axiom, ![X38, X35, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X35))=>((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X35),X38)=c_Groups_Ozero__class_Ozero(X5)<=>(X35=c_Groups_Ozero__class_Ozero(X5)&c_Groups_Ozero__class_Ozero(X5)=X38))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X38))))<=class_Groups_Oordered__comm__monoid__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__nonneg__eq__0__iff)). 6.97/7.19 fof(fact_card__Pow, axiom, ![X4, X5]:(hAPP(c_Finite__Set_Ocard(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OPow(X5),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_Finite__Set_Ocard(X5),X4))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Pow)). 6.97/7.19 fof(fact_setsum__set__upto__conv__listsum__int, axiom, ![X46, X47, X18, X5]:(class_Groups_Ocomm__monoid__add(X5)=>hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X5),X18),c_List_Oupto(X47,X46)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X18),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X47,X46)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__set__upto__conv__listsum__int)). 6.97/7.19 fof(fact_atLeastAtMost__upto, axiom, ![X46, X47]:hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X47,X46))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X47,X46), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastAtMost__upto)). 6.97/7.19 fof(fact_le__diff__conv2, axiom, ![X47, X46, X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X46))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X47),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X46),X33)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X47),X33)),X46)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__diff__conv2)). 6.97/7.19 fof(fact_add__leD2, axiom, ![X25, X19, X36]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19),X25))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X19)),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__leD2)). 6.97/7.19 fof(fact_listsp__lists__eq, axiom, ![X35, X4, X5]:(hBOOL(hAPP(c_List_Olistsp(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X4)),X35))<=>hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X35),c_List_Olists(X5,X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsp__lists__eq)). 6.97/7.19 fof(fact_one__mod__nat__number__of, axiom, ![X99]:((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),X99)))=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),X99))<=~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X99)))))&(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=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),X99))<=hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X99))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__mod__nat__number__of)). 6.97/7.19 fof(fact_antisym__reflcl, axiom, ![X3, X5]:(c_Relation_Oantisym(X5,X3)<=>c_Relation_Oantisym(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),c_Relation_OId(X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_antisym__reflcl)). 6.97/7.19 fof(fact_trans__reflclI, axiom, ![X3, X5]:(c_Relation_Otrans(X5,X3)=>c_Relation_Otrans(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),c_Relation_OId(X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trans__reflclI)). 6.97/7.19 fof(fact_Suc__eq__plus1__left, axiom, ![X25]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X25)=hAPP(c_Nat_OSuc,X25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__eq__plus1__left)). 6.97/7.19 fof(fact_append__eq__conv__conj, axiom, ![X83, X84, X23, X5]:(X83=hAPP(hAPP(c_List_Oappend(X5),X23),X84)<=>(X23=hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)),X83)&X84=hAPP(hAPP(c_List_Odrop(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)),X83))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__eq__conv__conj)). 6.97/7.19 fof(fact_rel__simps_I13_J, axiom, ![X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33),c_Int_OMin))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X33)),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I13_J)). 6.97/7.19 fof(fact_rel__simps_I30_J, axiom, ![X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X33),c_Int_OMin))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X33)),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I30_J)). 6.97/7.19 fof(fact_rel__simps_I9_J, axiom, ![X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X33))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X33)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I9_J)). 6.97/7.19 fof(fact_rel__simps_I26_J, axiom, ![X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X33)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X33))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I26_J)). 6.97/7.19 fof(fact_less__int__code_I13_J, axiom, ![X122, X123]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X123),X122))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X123)),c_Int_OBit0(X122)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__int__code_I13_J)). 6.97/7.19 fof(fact_rel__simps_I31_J, axiom, ![X52, X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X33)),c_Int_OBit0(X52)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X33),X52))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I31_J)). 6.97/7.19 fof(fact_div__mult__mult1__if, axiom, ![X29, X30, X31, X8]:(class_Divides_Osemiring__div(X8)=>((hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X30)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X29))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),X30),X29)<=c_Groups_Ozero__class_Ozero(X8)!=X31)&(hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X30)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X29))=c_Groups_Ozero__class_Ozero(X8)<=c_Groups_Ozero__class_Ozero(X8)=X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__mult1__if)). 6.97/7.19 fof(fact_dvd__mult__cancel__left, axiom, ![X1, X2, X10, X5]:(class_Rings_Oidom(X5)=>(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X1)))<=>(c_Groups_Ozero__class_Ozero(X5)=X10|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X2),X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dvd__mult__cancel__left)). 6.97/7.19 fof(fact_number__of__pred, axiom, ![X39, X8]:(class_Int_Onumber__ring(X8)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),c_Groups_Oone__class_Oone(X8))),hAPP(c_Int_Onumber__class_Onumber__of(X8),X39))=hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_Opred(X39))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__pred)). 6.97/7.19 fof(fact_dvd__mult__cancel__right, axiom, ![X1, X10, X2, X5]:((hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X10)))<=>(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X2),X1))|c_Groups_Ozero__class_Ozero(X5)=X10))<=class_Rings_Oidom(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dvd__mult__cancel__right)). 6.97/7.19 fof(fact_range__ex1__eq, axiom, ![X1, X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))=>(?[X22]:(X1=hAPP(X18,X22)&![X72]:(hAPP(X18,X72)=X1=>X22=X72))<=>hBOOL(hAPP(hAPP(c_member(X12),X1),hAPP(c_Set_Oimage(X5,X12,X18),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_range__ex1__eq)). 6.97/7.19 fof(fact_rangeI, axiom, ![X12, X35, X18, X5]:hBOOL(hAPP(hAPP(c_member(X5),hAPP(X18,X35)),hAPP(c_Set_Oimage(X12,X5,X18),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rangeI)). 6.97/7.19 fof(fact_sum__eq__0__conv, axiom, ![X186, X34]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X34&![X22]:(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X22),hAPP(c_List_Oset(tc_Nat_Onat),X186)))=>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),X34),X186)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__eq__0__conv)). 6.97/7.19 fof(fact_surj__image__vimage__eq, axiom, ![X4, X18, X5, X12]:(hAPP(c_Set_Oimage(X12,X5,X18),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))=>X4=hAPP(c_Set_Oimage(X12,X5,X18),hAPP(c_Set_Ovimage(X12,X5,X18),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_surj__image__vimage__eq)). 6.97/7.19 fof(fact_finite__vimageI, axiom, ![X71, X12, X55, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X55))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X12),hAPP(c_Set_Ovimage(X12,X5,X71),X55)))<=c_Fun_Oinj__on(X12,X5,X71,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__vimageI)). 6.97/7.19 fof(fact_finite__vimage__iff, axiom, ![X55, X71, X12, X5]:(c_Fun_Obij__betw(X5,X12,X71,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_Ovimage(X5,X12,X71),X55)))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X55)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__vimage__iff)). 6.97/7.19 fof(fact_finite__vimageD, axiom, ![X55, X71, X12, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_Ovimage(X5,X12,X71),X55)))=>(hAPP(c_Set_Oimage(X5,X12,X71),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X55)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__vimageD)). 6.97/7.19 fof(fact_vimage__const, axiom, ![X12, X4, X10, X5]:((hAPP(c_Set_Ovimage(X12,X5,hAPP(c_COMBK(X5,X12),X10)),X4)=c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool))<=~(hBOOL(hAPP(hAPP(c_member(X5),X10),X4))))&(hBOOL(hAPP(hAPP(c_member(X5),X10),X4))=>hAPP(c_Set_Ovimage(X12,X5,hAPP(c_COMBK(X5,X12),X10)),X4)=c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__const)). 6.97/7.19 fof(fact_inj__vimage__image__eq, axiom, ![X4, X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))=>X4=hAPP(c_Set_Ovimage(X5,X12,X18),hAPP(c_Set_Oimage(X5,X12,X18),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__vimage__image__eq)). 6.97/7.19 fof(fact_vimageI2, axiom, ![X12, X4, X2, X18, X5]:(hBOOL(hAPP(hAPP(c_member(X12),X2),hAPP(c_Set_Ovimage(X12,X5,X18),X4)))<=hBOOL(hAPP(hAPP(c_member(X5),hAPP(X18,X2)),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimageI2)). 6.97/7.19 fof(fact_vimage__singleton__eq, axiom, ![X1, X18, X12, X2, X5]:(X1=hAPP(X18,X2)<=>hBOOL(hAPP(hAPP(c_member(X5),X2),hAPP(c_Set_Ovimage(X5,X12,X18),hAPP(hAPP(c_Set_Oinsert(X12),X1),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__singleton__eq)). 6.97/7.19 fof(fact_vimageD, axiom, ![X4, X18, X12, X2, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X2),hAPP(c_Set_Ovimage(X5,X12,X18),X4)))=>hBOOL(hAPP(hAPP(c_member(X12),hAPP(X18,X2)),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimageD)). 6.97/7.19 fof(fact_image__atLeastZeroLessThan__int, axiom, ![X51]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X51))=>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,X51)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X51)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__atLeastZeroLessThan__int)). 6.97/7.19 fof(fact_nat__one__le__power, axiom, ![X25, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X28))=>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),X28),X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__one__le__power)). 6.97/7.19 fof(fact_hoare__derivs_Oinsert, axiom, ![X174, X82, X117, X5]:((c_Hoare__Mirabelle_Ohoare__derivs(X5,X117,X174)=>c_Hoare__Mirabelle_Ohoare__derivs(X5,X117,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),X82),X174)))<=c_Hoare__Mirabelle_Ohoare__derivs(X5,X117,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),X82),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hoare__derivs_Oinsert)). 6.97/7.19 fof(fact_inj__on__map__eq__map, axiom, ![X84, X23, X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X23)),hAPP(c_List_Oset(X5),X84)))=>(hAPP(hAPP(c_List_Omap(X5,X12),X18),X84)=hAPP(hAPP(c_List_Omap(X5,X12),X18),X23)<=>X84=X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__map__eq__map)). 6.97/7.19 fof(fact_finite__trancl, axiom, ![X3, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X5)),X3))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X5)),c_Transitive__Closure_Otrancl(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__trancl)). 6.97/7.19 fof(fact_wf__converse__trancl, axiom, ![X3, X5]:(c_Wellfounded_Owf(X5,hAPP(c_Relation_Oconverse(X5,X5),X3))=>c_Wellfounded_Owf(X5,hAPP(c_Relation_Oconverse(X5,X5),c_Transitive__Closure_Otrancl(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__converse__trancl)). 6.97/7.19 fof(fact_Divides_Otransfer__nat__int__functions_I2_J, axiom, ![X7, X6]:((hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X6,X7))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X6),hAPP(c_Int_Onat,X7))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7)))<=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_Divides_Otransfer__nat__int__functions_I2_J)). 6.97/7.19 fof(fact_of__int__of__nat, axiom, ![X19, X8]:(((hAPP(c_Int_Oring__1__class_Oof__int(X8),X19)=hAPP(c_Groups_Ouminus__class_Ouminus(X8),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))=>hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),hAPP(c_Int_Onat,X19))=hAPP(c_Int_Oring__1__class_Oof__int(X8),X19)))<=class_Rings_Oring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__of__nat)). 6.97/7.19 fof(fact_upto_Osimps, axiom, ![X27, X28]:((c_List_Oupto(X28,X27)=hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X28),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X28),c_Groups_Oone__class_Oone(tc_Int_Oint)),X27))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X28),X27)))&(c_List_Oupto(X28,X27)=c_List_Olist_ONil(tc_Int_Oint)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X28),X27))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upto_Osimps)). 6.97/7.19 fof(fact_min__max_OInf__fin__set__fold, axiom, ![X23, X35, X5]:(c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23)))=hAPP(c_List_Ofoldl(X5,X5,c_Orderings_Oord__class_Omin(X5),X35),X23)<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin__set__fold)). 6.97/7.19 fof(fact_List_Oset_Osimps_I2_J, axiom, ![X23, X35, X5]:hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23))=hAPP(hAPP(c_Set_Oinsert(X5),X35),hAPP(c_List_Oset(X5),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_List_Oset_Osimps_I2_J)). 6.97/7.19 fof(fact_min__max_OSup__fin__set__fold, axiom, ![X23, X35, X5]:(class_Orderings_Olinorder(X5)=>hAPP(c_List_Ofoldl(X5,X5,c_Orderings_Oord__class_Omax(X5),X35),X23)=c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin__set__fold)). 6.97/7.19 fof(fact_transfer__int__nat__set__relations_I2_J, axiom, ![X4, X35]:(c_Nat__Transfer_Ois__nat(X35)=>(c_Nat__Transfer_Onat__set(X4)=>(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X35),X4))<=>hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X35)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__set__relations_I2_J)). 6.97/7.19 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J, axiom, ![X35, X4]:(c_Nat__Transfer_Onat__set(X4)=>(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X35),X4))=>c_Nat__Transfer_Ois__nat(X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J)). 6.97/7.19 fof(fact_nat__div__distrib, axiom, ![X7, X6]:(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X6)),hAPP(c_Int_Onat,X7))=hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6),X7))<=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__div__distrib)). 6.97/7.19 fof(fact_nat__mult__distrib, axiom, ![X112, X26]:(hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),X112))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X26)),hAPP(c_Int_Onat,X112))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__distrib)). 6.97/7.19 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J, axiom, ![X7, X6]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X6)),hAPP(c_Int_Onat,X7))=hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(X6,X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J)). 6.97/7.19 fof(fact_Union__disjoint, axiom, ![X4, X65, X5]:(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X65)),X4)<=>![X22]:(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X22),X4)<=hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X22),X65)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__disjoint)). 6.97/7.19 fof(fact_eq__number__of__eq, axiom, ![X38, X35, X5]:(class_Int_Onumber__ring(X5)=>(hAPP(c_Int_Onumber__class_Onumber__of(X5),X38)=hAPP(c_Int_Onumber__class_Onumber__of(X5),X35)<=>c_Int_Oiszero(X5,hAPP(c_Int_Onumber__class_Onumber__of(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X35),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X38)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__number__of__eq)). 6.97/7.19 fof(fact_SetInterval_Otransfer__int__nat__set__functions, axiom, ![X32, X34]:(c_Nat__Transfer_Ois__nat(X34)=>(c_Nat__Transfer_Ois__nat(X32)=>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,X34),hAPP(c_Int_Onat,X32)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X34,X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SetInterval_Otransfer__int__nat__set__functions)). 6.97/7.19 fof(fact_list__eq__iff__zip__eq, axiom, ![X5, X84, X23]:(X23=X84<=>(![X22]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X22),hAPP(c_List_Oset(tc_prod(X5,X5)),hAPP(hAPP(c_List_Ozip(X5,X5),X23),X84))))=>hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),c_fequal),X22)))&hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X84)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__eq__iff__zip__eq)). 6.97/7.19 fof(fact_reflp__def, axiom, ![X3, X5]:(c_Predicate_Oreflp(X5,X3)<=>c_Relation_Orefl__on(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_reflp__def)). 6.97/7.19 fof(fact_distinct__rotate, axiom, ![X23, X32, X5]:(hBOOL(hAPP(c_List_Odistinct(X5),X23))<=>hBOOL(hAPP(c_List_Odistinct(X5),hAPP(c_List_Orotate(X5,X32),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__rotate)). 6.97/7.19 fof(fact_le__nat__number__of, axiom, ![X61, X60]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X60),c_Int_OPls))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X60),X61))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X60)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X61)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__nat__number__of)). 6.97/7.19 fof(fact_add__scale__eq__noteq, axiom, ![X74, X31, X29, X30, X70, X8]:((X70!=c_Groups_Ozero__class_Ozero(X8)=>(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X70),X31))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X70),X74))<=(X31!=X74&X29=X30)))<=class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__scale__eq__noteq)). 6.97/7.19 fof(fact_rotate__length01, axiom, ![X25, X41, X8]:(X41=hAPP(c_List_Orotate(X8,X25),X41)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__length01)). 6.97/7.19 fof(fact_atLeastLessThanSuc, axiom, ![X32, X34]:((hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34),hAPP(c_Nat_OSuc,X32))=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),X34),X32))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),X32))=>hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34),hAPP(c_Nat_OSuc,X32))=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X32),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThanSuc)). 6.97/7.19 fof(fact_nat__less__eq__zless, axiom, ![X14, X9]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X9)),hAPP(c_Int_Onat,X14)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9),X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__less__eq__zless)). 6.97/7.19 fof(fact_div__pos__neg__trivial, axiom, ![X29, X30]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30))=>(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),X29)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X30),X29)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__pos__neg__trivial)). 6.97/7.19 fof(fact_zless__nat__conj, axiom, ![X14, X9]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X9)),hAPP(c_Int_Onat,X14)))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9),X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zless__nat__conj)). 6.97/7.19 fof(fact_card__Suc__eq, axiom, ![X33, X4, X5]:(hAPP(c_Finite__Set_Ocard(X5),X4)=hAPP(c_Nat_OSuc,X33)<=>?[X96, X132]:(((hAPP(hAPP(c_Set_Oinsert(X5),X96),X132)=X4&~(hBOOL(hAPP(hAPP(c_member(X5),X96),X132))))&(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=X132<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X33))&hAPP(c_Finite__Set_Ocard(X5),X132)=X33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Suc__eq)). 6.97/7.19 fof(fact_eq__special_I1_J, axiom, ![X38, X5]:(class_Int_Onumber__ring(X5)=>(c_Groups_Ozero__class_Ozero(X5)=hAPP(c_Int_Onumber__class_Onumber__of(X5),X38)<=>c_Int_Oiszero(X5,hAPP(c_Int_Onumber__class_Onumber__of(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X38)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__special_I1_J)). 6.97/7.19 fof(fact_eq__special_I3_J, axiom, ![X35, X5]:((c_Groups_Ozero__class_Ozero(X5)=hAPP(c_Int_Onumber__class_Onumber__of(X5),X35)<=>c_Int_Oiszero(X5,hAPP(c_Int_Onumber__class_Onumber__of(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X35),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))))<=class_Int_Onumber__ring(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__special_I3_J)). 6.97/7.19 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)). 6.97/7.19 fof(fact_Sup__fin__set__fold, axiom, ![X23, X35, X5]:(class_Lattices_Olattice(X5)=>c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23)))=hAPP(c_List_Ofoldl(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5),X35),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin__set__fold)). 6.97/7.19 fof(fact_Inf__fin__set__fold, axiom, ![X23, X35, X5]:(class_Lattices_Olattice(X5)=>c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23)))=hAPP(c_List_Ofoldl(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5),X35),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin__set__fold)). 6.97/7.19 fof(fact_Max__fin__set__fold, axiom, ![X23, X35, X5]:(class_Orderings_Olinorder(X5)=>hAPP(c_List_Ofoldl(X5,X5,c_Orderings_Oord__class_Omax(X5),X35),X23)=c_Big__Operators_Olinorder__class_OMax(X5,hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max__fin__set__fold)). 6.97/7.19 fof(fact_Min__fin__set__fold, axiom, ![X23, X35, X5]:(hAPP(c_List_Ofoldl(X5,X5,c_Orderings_Oord__class_Omin(X5),X35),X23)=c_Big__Operators_Olinorder__class_OMin(X5,hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min__fin__set__fold)). 6.97/7.19 fof(fact_ex__least__nat__less, axiom, ![X32, X17]:(~(hBOOL(hAPP(X17,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=>(hBOOL(hAPP(X17,X32))=>?[X145]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X145),X32))&hBOOL(hAPP(X17,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X145),c_Groups_Oone__class_Oone(tc_Nat_Onat)))))&![X42]:(~(hBOOL(hAPP(X17,X42)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X145)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ex__least__nat__less)). 6.97/7.19 fof(fact_nat__less__iff, axiom, ![X34, X9]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X9)),X34))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X34))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__less__iff)). 6.97/7.19 fof(fact_of__nat__number__of__lemma, axiom, ![X40, X8]:(class_Int_Onumber__ring(X8)=>((hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40))=hAPP(c_Int_Onumber__class_Onumber__of(X8),X40)<=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),X40))))&(hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40))=c_Groups_Ozero__class_Ozero(X8)<=~(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),X40))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__number__of__lemma)). 6.97/7.19 fof(fact_last__list__update, axiom, ![X6, X19, X8, X41]:(((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X19=>X6=c_List_Olast(X8,hAPP(hAPP(c_List_Olist__update(X8,X41),X19),X6)))&(X19!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=>c_List_Olast(X8,X41)=c_List_Olast(X8,hAPP(hAPP(c_List_Olist__update(X8,X41),X19),X6))))<=c_List_Olist_ONil(X8)!=X41), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__list__update)). 6.97/7.19 fof(fact_sorted__same, axiom, ![X23, X50, X5]:(c_List_Olinorder__class_Osorted(X5,hAPP(c_List_Ofilter(X5,hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),hAPP(X50,X23))),X23))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__same)). 6.97/7.19 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J, axiom, ![X25, X6]:(hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),X25))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X6)),X25)<=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__functions_I4_J)). 6.97/7.19 fof(fact_rotate__id, axiom, ![X41, X8, X25]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X25,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41))=>hAPP(c_List_Orotate(X8,X25),X41)=X41), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__id)). 6.97/7.19 fof(fact_last__upt, axiom, ![X27, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28),X27))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X27),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_List_Olast(tc_Nat_Onat,c_List_Oupt(X28,X27))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__upt)). 6.97/7.19 fof(fact_list__ex__iff__not__all__inverval__nat, axiom, ![X46, X47, X17]:(c_List_Olist__ex(tc_Nat_Onat,X17,c_List_Oupt(X47,X46))<=>~(c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),X17),X47,X46))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex__iff__not__all__inverval__nat)). 6.97/7.19 fof(fact_less__special_I3_J, axiom, ![X35, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X35),c_Int_OPls))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X35)),c_Groups_Ozero__class_Ozero(X5))))<=(class_Int_Onumber__ring(X5)&class_Rings_Olinordered__idom(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__special_I3_J)). 6.97/7.19 fof(fact_le__special_I3_J, axiom, ![X35, X5]:((class_Rings_Olinordered__idom(X5)&class_Int_Onumber__ring(X5))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X35)),c_Groups_Ozero__class_Ozero(X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X35),c_Int_OPls)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__special_I3_J)). 6.97/7.19 fof(fact_less__special_I1_J, axiom, ![X38, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X38)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X38)))<=(class_Int_Onumber__ring(X5)&class_Rings_Olinordered__idom(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__special_I1_J)). 6.97/7.19 fof(fact_le__special_I1_J, axiom, ![X38, X5]:((class_Rings_Olinordered__idom(X5)&class_Int_Onumber__ring(X5))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X38)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X38)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__special_I1_J)). 6.97/7.19 fof(fact_add1__zle__eq, axiom, ![X14, X9]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X9),c_Groups_Oone__class_Oone(tc_Int_Oint))),X14))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9),X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add1__zle__eq)). 6.97/7.19 fof(fact_sum__squares__gt__zero__iff, axiom, ![X38, X35, X5]:(((c_Groups_Ozero__class_Ozero(X5)!=X38|X35!=c_Groups_Ozero__class_Ozero(X5))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X35),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X38),X38)))))<=class_Rings_Olinordered__ring__strict(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__squares__gt__zero__iff)). 6.97/7.19 fof(fact_zless__add1__eq, axiom, ![X14, X9]:((X14=X9|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9),X14)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X14),c_Groups_Oone__class_Oone(tc_Int_Oint))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zless__add1__eq)). 6.97/7.19 fof(fact_zle__add1__eq__le, axiom, ![X14, X9]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X14),c_Groups_Oone__class_Oone(tc_Int_Oint))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9),X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zle__add1__eq__le)). 6.97/7.19 fof(fact_zle__diff1__eq, axiom, ![X14, X9]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X14),c_Groups_Oone__class_Oone(tc_Int_Oint))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9),X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zle__diff1__eq)). 6.97/7.19 fof(fact_snoc__eq__iff__butlast, axiom, ![X84, X35, X23, X5]:(hAPP(hAPP(c_List_Oappend(X5),X23),hAPP(hAPP(c_List_Olist_OCons(X5),X35),c_List_Olist_ONil(X5)))=X84<=>((X84!=c_List_Olist_ONil(X5)&c_List_Olast(X5,X84)=X35)&c_List_Obutlast(X5,X84)=X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_snoc__eq__iff__butlast)). 6.97/7.19 fof(fact_number__of__succ, axiom, ![X19, X8]:(class_Int_Onumber__ring(X8)=>hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_Osucc(X19))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),c_Groups_Oone__class_Oone(X8)),hAPP(c_Int_Onumber__class_Onumber__of(X8),X19))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__succ)). 6.97/7.19 fof(fact_bij__betw__subset, axiom, ![X106, X11, X107, X4, X18, X12, X5]:(c_Fun_Obij__betw(X5,X12,X18,X4,X107)=>((hAPP(c_Set_Oimage(X5,X12,X18),X11)=X106=>c_Fun_Obij__betw(X5,X12,X18,X11,X106))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bij__betw__subset)). 6.97/7.19 fof(fact_split__nat, axiom, ![X47, X17]:((![X48]:(hBOOL(hAPP(X17,X48))<=X47=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X48))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X47),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>hBOOL(hAPP(X17,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))<=>hBOOL(hAPP(X17,hAPP(c_Int_Onat,X47)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__nat)). 6.97/7.19 fof(fact_in__set__replicate, axiom, ![X38, X32, X35, X5]:((X32!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&X35=X38)<=>hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),c_List_Oreplicate(X5,X32,X38))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__replicate)). 6.97/7.19 fof(fact_Suc__nat__eq__nat__zadd1, axiom, ![X26]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))=>hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,X26))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__nat__eq__nat__zadd1)). 6.97/7.19 fof(fact_norm__frac_Osimps, axiom, ![X2, X1]:((~(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|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=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))=c_Nitpick_Onorm__frac(X2,X1))&(~((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)))=>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))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_norm__frac_Osimps)). 6.97/7.19 fof(fact_one__less__nat__eq, axiom, ![X14]:(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,X14)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__less__nat__eq)). 6.97/7.19 fof(fact_iszero__number__of__Bit0, axiom, ![X9, X5]:((c_Int_Oiszero(X5,hAPP(c_Int_Onumber__class_Onumber__of(X5),X9))<=>c_Int_Oiszero(X5,hAPP(c_Int_Onumber__class_Onumber__of(X5),c_Int_OBit0(X9))))<=(class_Int_Oring__char__0(X5)&class_Int_Onumber__ring(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_iszero__number__of__Bit0)). 6.97/7.19 fof(fact_transfer__nat__int__list__return__embed, axiom, ![X93]:(c_List_Oembed__list(c_List_Oreturn__list(X93))=X93<=c_List_Onat__list(X93)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__list__return__embed)). 6.97/7.19 fof(fact_nat__le__eq__zle, axiom, ![X14, X9]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X9)),hAPP(c_Int_Onat,X14)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9),X14)))<=(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__le__eq__zle)). 6.97/7.19 fof(fact_zmod__minus1, axiom, ![X29]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X29))=>c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X29)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X29),c_Groups_Oone__class_Oone(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__minus1)). 6.97/7.19 fof(fact_div__eq__minus1, axiom, ![X29]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X29))=>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)),X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__eq__minus1)). 6.97/7.19 fof(fact_rel__simps_I11_J, axiom, ![X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X33),c_Int_OMin))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X33)),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I11_J)). 6.97/7.19 fof(fact_rel__simps_I28_J, axiom, ![X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X33)),c_Int_OMin))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X33),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I28_J)). 6.97/7.19 fof(fact_le__iff__pred__less, axiom, ![X52, X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X33),X52))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X33)),X52))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__iff__pred__less)). 6.97/7.19 fof(fact_rel__simps_I51_J, axiom, ![X52, X33]:(c_Int_OBit1(X52)=c_Int_OBit1(X33)<=>X52=X33), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I51_J)). 6.97/7.19 fof(fact_rel__simps_I8_J, axiom, ![X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X33)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X33))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I8_J)). 6.97/7.19 fof(fact_rel__simps_I25_J, axiom, ![X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X33)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X33))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I25_J)). 6.97/7.19 fof(fact_Nats__number__of, axiom, ![X9, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X9))=>hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X9)),c_Nat_Osemiring__1__class_ONats(X5))))<=class_Int_Onumber__ring(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nats__number__of)). 6.97/7.19 fof(fact_wf, axiom, ![X5]:(c_Wellfounded_Owf(X5,hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),c_Orderings_Oord__class_Oless(X5))))<=class_Orderings_Owellorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf)). 6.97/7.19 fof(fact_disjoint__iff__not__equal, axiom, ![X11, X4, X5]:(![X22]:(![X115]:(X22!=X115<=hBOOL(hAPP(hAPP(c_member(X5),X115),X11)))<=hBOOL(hAPP(hAPP(c_member(X5),X22),X4)))<=>c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_disjoint__iff__not__equal)). 6.97/7.19 fof(fact_of__nat__number__of__eq, axiom, ![X40, X8]:(((hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40))=c_Groups_Ozero__class_Ozero(X8)<=hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X40))))&(hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40))=hAPP(c_Int_Onumber__class_Onumber__of(X8),X40)<=~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X40))))))<=class_Int_Onumber__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__number__of__eq)). 6.97/7.19 fof(fact_card_Oneutral, axiom, ![X4, X5]:(((?[X22]:hBOOL(hAPP(hAPP(c_member(X5),X22),X4))=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Groups_Oone__class_Oone(tc_Nat_Onat))=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(X5),X4))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card_Oneutral)). 6.97/7.19 fof(fact_card__def, axiom, ![X4, X5]:((hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X5,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X5),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4)=hAPP(c_Finite__Set_Ocard(X5),X4)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))&(~(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__def)). 6.97/7.19 fof(fact_le__imp__diff__is__add, axiom, ![X33, X46, X47]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X47),X46))=>(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X47)=X46<=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X46),X47)=X33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__imp__diff__is__add)). 6.97/7.19 fof(fact_Ints__double__eq__0__iff, axiom, ![X2, X5]:(((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X2),X2)=c_Groups_Ozero__class_Ozero(X5)<=>c_Groups_Ozero__class_Ozero(X5)=X2)<=hBOOL(hAPP(hAPP(c_member(X5),X2),c_Int_Oring__1__class_OInts(X5))))<=class_Int_Oring__char__0(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__double__eq__0__iff)). 6.97/7.19 fof(fact_wfP__acyclicP, axiom, ![X3, X5]:(c_Wellfounded_Oacyclic(X5,hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),X3)))<=c_Wellfounded_OwfP(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wfP__acyclicP)). 6.97/7.19 fof(fact_transp__def, axiom, ![X3, X5]:(c_Relation_Otrans(X5,hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),X3)))<=>c_Predicate_Otransp(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transp__def)). 6.97/7.19 fof(fact_symp__def, axiom, ![X3, X5]:(c_Relation_Osym(X5,hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),X3)))<=>c_Predicate_Osymp(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_symp__def)). 6.97/7.19 fof(fact_wfP__def, axiom, ![X3, X5]:(c_Wellfounded_OwfP(X5,X3)<=>c_Wellfounded_Owf(X5,hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wfP__def)). 6.97/7.19 fof(fact_divide__eq__eq, axiom, ![X2, X10, X1, X5]:(class_Fields_Ofield__inverse__zero(X5)=>(((X10=c_Groups_Ozero__class_Ozero(X5)=>c_Groups_Ozero__class_Ozero(X5)=X2)&(X1=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X10)<=c_Groups_Ozero__class_Ozero(X5)!=X10))<=>X2=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X1),X10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__eq__eq)). 6.97/7.19 fof(fact_nonzero__eq__divide__eq, axiom, ![X1, X2, X10, X5]:(class_Rings_Odivision__ring(X5)=>(c_Groups_Ozero__class_Ozero(X5)!=X10=>(X2=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X1),X10)<=>X1=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X10)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nonzero__eq__divide__eq)). 6.97/7.19 fof(fact_comp__equivI, axiom, ![X4, X3, X5]:(hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(c_Relation_Oconverse(X5,X5),X3)),X3)=X3=>(c_Equiv__Relations_Oequiv(X5,X4,X3)<=hAPP(c_Relation_ODomain(X5,X5),X3)=X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comp__equivI)). 6.97/7.19 fof(fact_less__code__numeral__code, axiom, ![X34, X32]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32),X34))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X32)),hAPP(c_Code__Numeral_Oof__nat,X34)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__code__numeral__code)). 6.97/7.19 fof(fact_less__eq__code__numeral__code, axiom, ![X34, X32]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X32)),hAPP(c_Code__Numeral_Oof__nat,X34)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32),X34))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__eq__code__numeral__code)). 6.97/7.19 fof(fact_eq__divide__eq, axiom, ![X10, X1, X2, X5]:(class_Fields_Ofield__inverse__zero(X5)=>(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X1),X10)=X2<=>((X10=c_Groups_Ozero__class_Ozero(X5)=>c_Groups_Ozero__class_Ozero(X5)=X2)&(X10!=c_Groups_Ozero__class_Ozero(X5)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X10)=X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__divide__eq)). 6.97/7.19 fof(fact_pair__in__Id__conv, axiom, ![X1, X2, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),c_Relation_OId(X5)))<=>X2=X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__in__Id__conv)). 6.97/7.19 fof(fact_zero__less__zpower__abs__iff, axiom, ![X32, X35]:(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),X35)),X32)))<=>(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X35|X32=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__zpower__abs__iff)). 6.97/7.19 fof(fact_divide__eq__imp, axiom, ![X30, X29, X31, X8]:(class_Rings_Odivision__ring(X8)=>((X30=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X29),X31)<=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X31)=X29)<=X31!=c_Groups_Ozero__class_Ozero(X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__eq__imp)). 6.97/7.19 fof(fact_hd__upt, axiom, ![X27, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28),X27))=>hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(X28,X27))=X28), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__upt)). 6.97/7.19 fof(fact_abs__le__zero__iff, axiom, ![X2, X5]:(class_Groups_Oordered__ab__group__add__abs(X5)=>(X2=c_Groups_Ozero__class_Ozero(X5)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Oabs__class_Oabs(X5),X2)),c_Groups_Ozero__class_Ozero(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__le__zero__iff)). 6.97/7.19 fof(fact_zero__less__nat__eq, axiom, ![X14]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__nat__eq)). 6.97/7.19 fof(fact_zless__nat__eq__int__zless, axiom, ![X14, X34]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34),hAPP(c_Int_Onat,X14)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X34)),X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zless__nat__eq__int__zless)). 6.97/7.19 fof(fact_not__less__eq__eq, axiom, ![X32, X34]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X32)),X34))<=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__less__eq__eq)). 6.97/7.19 fof(fact_bex__UNIV, axiom, ![X17, X5]:(?[X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))&hBOOL(hAPP(X17,X22)))<=>?[X76]:hBOOL(hAPP(X17,X76))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bex__UNIV)). 6.97/7.19 fof(fact_UNIV__I, axiom, ![X35, X5]:hBOOL(hAPP(hAPP(c_member(X5),X35),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UNIV__I)). 6.97/7.19 fof(fact_remove1__filter__not, axiom, ![X23, X5, X35, X17]:(c_List_Oremove1(X5,X35,hAPP(c_List_Ofilter(X5,X17),X23))=hAPP(c_List_Ofilter(X5,X17),X23)<=~(hBOOL(hAPP(X17,X35)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remove1__filter__not)). 6.97/7.19 fof(fact_filter__remove1, axiom, ![X23, X35, X104, X5]:hAPP(c_List_Ofilter(X5,X104),c_List_Oremove1(X5,X35,X23))=c_List_Oremove1(X5,X35,hAPP(c_List_Ofilter(X5,X104),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__remove1)). 6.97/7.19 fof(fact_sym__trancl, axiom, ![X3, X5]:(c_Relation_Osym(X5,c_Transitive__Closure_Otrancl(X5,X3))<=c_Relation_Osym(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sym__trancl)). 6.97/7.19 fof(fact_dvd_OatLeastAtMost__singleton__iff, axiom, ![X10, X1, X2]:((X1=X2&X1=X10)<=>c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2,X1)=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X10),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dvd_OatLeastAtMost__singleton__iff)). 6.97/7.19 fof(fact_wf__trancl, axiom, ![X3, X5]:(c_Wellfounded_Owf(X5,c_Transitive__Closure_Otrancl(X5,X3))<=c_Wellfounded_Owf(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__trancl)). 6.97/7.19 fof(fact_finite__sorted__distinct__unique, axiom, ![X4, X5]:(class_Orderings_Olinorder(X5)=>(?[X22]:(((c_List_Olinorder__class_Osorted(X5,X22)&hBOOL(hAPP(c_List_Odistinct(X5),X22)))&![X72]:(((X4=hAPP(c_List_Oset(X5),X72)&hBOOL(hAPP(c_List_Odistinct(X5),X72)))&c_List_Olinorder__class_Osorted(X5,X72))=>X22=X72))&X4=hAPP(c_List_Oset(X5),X22))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__sorted__distinct__unique)). 6.97/7.19 fof(fact_finite__set, axiom, ![X23, X5]:hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_List_Oset(X5),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__set)). 6.97/7.19 fof(fact_square__eq__iff, axiom, ![X1, X2, X5]:(class_Rings_Oidom(X5)=>(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X1)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X2)<=>(X2=hAPP(c_Groups_Ouminus__class_Ouminus(X5),X1)|X1=X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_square__eq__iff)). 6.97/7.19 fof(fact_zsgn__def, axiom, ![X28]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X28=>c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Groups_Osgn__class_Osgn(tc_Int_Oint,X28))&(((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X28)))=>c_Groups_Osgn__class_Osgn(tc_Int_Oint,X28)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))&(c_Groups_Oone__class_Oone(tc_Int_Oint)=c_Groups_Osgn__class_Osgn(tc_Int_Oint,X28)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X28))))<=c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zsgn__def)). 6.97/7.19 fof(fact_one__is__add, axiom, ![X32, X34]:(((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X34&X32=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X34&X32=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))<=>hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__is__add)). 6.97/7.19 fof(fact_less__eq__nat_Osimps_I2_J, axiom, ![X32, X34]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X34)),X32))<=>hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__eq__nat_Osimps_I2_J)). 6.97/7.19 fof(fact_all__nat, axiom, ![X17]:(![X22]:(hBOOL(hAPP(X17,hAPP(c_Int_Onat,X22)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22)))<=>![X76]:hBOOL(hAPP(X17,X76))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_all__nat)). 6.97/7.19 fof(fact_dvdI, axiom, ![X19, X29, X30, X8]:((X30=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X19)=>hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X8),X29),X30)))<=class_Rings_Odvd(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dvdI)). 6.97/7.19 fof(fact_of__nat__nat, axiom, ![X26, X8]:(class_Rings_Oring__1(X8)=>(hAPP(c_Int_Oring__1__class_Oof__int(X8),X26)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),hAPP(c_Int_Onat,X26))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__nat)). 6.97/7.19 fof(fact_code__numeral__not__eq__zero, axiom, ![X47]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X47))<=>hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=X47), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral__not__eq__zero)). 6.97/7.19 fof(fact_square__eq__1__iff, axiom, ![X35, X5]:(class_Rings_Oring__1__no__zero__divisors(X5)=>(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X35),X35)=c_Groups_Oone__class_Oone(X5)<=>(X35=hAPP(c_Groups_Ouminus__class_Ouminus(X5),c_Groups_Oone__class_Oone(X5))|X35=c_Groups_Oone__class_Oone(X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_square__eq__1__iff)). 6.97/7.19 fof(fact_divide__Numeral0, axiom, ![X6, X8]:(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X6),hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OPls))=c_Groups_Ozero__class_Ozero(X8)<=(class_Int_Onumber__ring(X8)&class_Fields_Ofield__inverse__zero(X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__Numeral0)). 6.97/7.19 fof(fact_int__nat__eq, axiom, ![X26]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))=>hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X26))=X26)&(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X26))=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)),X26))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__nat__eq)). 6.97/7.19 fof(fact_upt__eq__Nil__conv, axiom, ![X46, X47]:(c_List_Oupt(X47,X46)=c_List_Olist_ONil(tc_Nat_Onat)<=>(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X46|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X46),X47)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upt__eq__Nil__conv)). 6.97/7.19 fof(fact_power__eq__0__iff, axiom, ![X32, X2, X5]:((hAPP(hAPP(c_Power_Opower__class_Opower(X5),X2),X32)=c_Groups_Ozero__class_Ozero(X5)<=>(X2=c_Groups_Ozero__class_Ozero(X5)&X32!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))<=(((class_Rings_Omult__zero(X5)&class_Rings_Ono__zero__divisors(X5))&class_Rings_Ozero__neq__one(X5))&class_Power_Opower(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__eq__0__iff)). 6.97/7.19 fof(fact_ex__nat, axiom, ![X17]:(?[X76]:hBOOL(hAPP(X17,X76))<=>?[X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22))&hBOOL(hAPP(X17,hAPP(c_Int_Onat,X22))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ex__nat)). 6.97/7.19 fof(fact_divmod__nat__eq, axiom, ![X119, X25, X36]:(X119=c_Divides_Odivmod__nat(X36,X25)<=hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X36,X25),X119))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__eq)). 6.97/7.19 fof(fact_trancl__id, axiom, ![X3, X5]:(c_Relation_Otrans(X5,X3)=>X3=c_Transitive__Closure_Otrancl(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__id)). 6.97/7.19 fof(fact_add__is__1, axiom, ![X32, X34]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34),X32)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<=>((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X32&hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X34)|(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X32&X34=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__is__1)). 6.97/7.19 fof(fact_list__all__iff__all__interval__nat, axiom, ![X46, X47, X17]:(c_List_Olist__all(tc_Nat_Onat,X17,c_List_Oupt(X47,X46))<=>c_List_Oall__interval__nat(X17,X47,X46)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all__iff__all__interval__nat)). 6.97/7.19 fof(fact_eq__nat__nat__iff, axiom, ![X135, X14]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X135))=>(X135=X14<=>hAPP(c_Int_Onat,X14)=hAPP(c_Int_Onat,X135)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__nat__nat__iff)). 6.97/7.19 fof(fact_eq__divide__eq__number__of1, axiom, ![X9, X1, X2, X5]:((((c_Groups_Ozero__class_Ozero(X5)=X2<=hAPP(c_Int_Onumber__class_Onumber__of(X5),X9)=c_Groups_Ozero__class_Ozero(X5))&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),hAPP(c_Int_Onumber__class_Onumber__of(X5),X9))=X1<=hAPP(c_Int_Onumber__class_Onumber__of(X5),X9)!=c_Groups_Ozero__class_Ozero(X5)))<=>X2=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X1),hAPP(c_Int_Onumber__class_Onumber__of(X5),X9)))<=(class_Fields_Ofield__inverse__zero(X5)&class_Int_Onumber(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__divide__eq__number__of1)). 6.97/7.19 fof(fact_nat__of__induct, axiom, ![X17, X38]:(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X38),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))=>(![X22]:hBOOL(hAPP(X17,hAPP(c_Code__Numeral_Onat__of,X22)))=>hBOOL(hAPP(X17,X38)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__of__induct)). 6.97/7.19 fof(fact_Collect__empty__eq, axiom, ![X17, X5]:(![X22]:~(hBOOL(hAPP(X17,X22)))<=>c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(c_Set_OCollect(X5),X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__empty__eq)). 6.97/7.19 fof(fact_empty__Collect__eq, axiom, ![X17, X5]:(![X22]:~(hBOOL(hAPP(X17,X22)))<=>hAPP(c_Set_OCollect(X5),X17)=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__Collect__eq)). 6.97/7.19 fof(fact_nat__power__eq__Suc__0__iff, axiom, ![X34, X35]:((hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X35|X34=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<=>hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X35),X34)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__power__eq__Suc__0__iff)). 6.97/7.19 fof(fact_add__numeral__0, axiom, ![X30, X8]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OPls)),X30)=X30<=class_Int_Onumber__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__numeral__0)). 6.97/7.19 fof(fact_add__numeral__0__right, axiom, ![X30, X8]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OPls))=X30<=class_Int_Onumber__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__numeral__0__right)). 6.97/7.19 fof(fact_iszero__number__of__Bit1, axiom, ![X39, X8]:(~(c_Int_Oiszero(X8,hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OBit1(X39))))<=(class_Int_Onumber__ring(X8)&class_Int_Oring__char__0(X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_iszero__number__of__Bit1)). 6.97/7.19 fof(fact_length__remdups__eq, axiom, ![X23, X5]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oremdups(X5,X23))<=>X23=c_List_Oremdups(X5,X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__remdups__eq)). 6.97/7.19 fof(fact_length__remdups__card__conv, axiom, ![X23, X5]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oremdups(X5,X23))=hAPP(c_Finite__Set_Ocard(X5),hAPP(c_List_Oset(X5),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__remdups__card__conv)). 6.97/7.19 fof(fact_diff__eq__diff__eq, axiom, ![X97, X10, X1, X2, X5]:(class_Groups_Oab__group__add(X5)=>(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X2),X1)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X10),X97)=>(X1=X2<=>X10=X97))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__eq__diff__eq)). 6.97/7.19 fof(fact_int__nat__number__of, axiom, ![X40]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40))<=hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X40))))&(~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X40))))=>hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X40)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__nat__number__of)). 6.97/7.19 fof(fact_nat__0__le, axiom, ![X26]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))=>hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X26))=X26), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__0__le)). 6.97/7.19 fof(fact_nat__eq__iff, axiom, ![X34, X9]:(hAPP(c_Int_Onat,X9)=X34<=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9))=>X9=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X34))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9)))=>X34=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__eq__iff)). 6.97/7.19 fof(fact_bij__betw__def, axiom, ![X11, X4, X18, X12, X5]:((c_Fun_Oinj__on(X5,X12,X18,X4)&hAPP(c_Set_Oimage(X5,X12,X18),X4)=X11)<=>c_Fun_Obij__betw(X5,X12,X18,X4,X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bij__betw__def)). 6.97/7.19 fof(fact_double__zero__sym, axiom, ![X2, X5]:(class_Groups_Olinordered__ab__group__add(X5)=>(c_Groups_Ozero__class_Ozero(X5)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X2),X2)<=>c_Groups_Ozero__class_Ozero(X5)=X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_double__zero__sym)). 6.97/7.19 fof(fact_mult__eq__0__iff, axiom, ![X1, X2, X5]:(class_Rings_Oring__no__zero__divisors(X5)=>((c_Groups_Ozero__class_Ozero(X5)=X2|X1=c_Groups_Ozero__class_Ozero(X5))<=>c_Groups_Ozero__class_Ozero(X5)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__eq__0__iff)). 6.97/7.19 fof(fact_eq__iff__diff__eq__0, axiom, ![X1, X2, X5]:(class_Groups_Oab__group__add(X5)=>(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X2),X1)=c_Groups_Ozero__class_Ozero(X5)<=>X2=X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__iff__diff__eq__0)). 6.97/7.19 fof(fact_add__0__iff, axiom, ![X2, X1, X5]:(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)=>(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X1),X2)=X1<=>c_Groups_Ozero__class_Ozero(X5)=X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__0__iff)). 6.97/7.19 fof(fact_not__neg__nat, axiom, ![X26]:(X26=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X26))<=~(hBOOL(hAPP(c_Nat__Numeral_Oneg,X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__neg__nat)). 6.97/7.19 fof(fact_rel__simps_I43_J, axiom, ![X52]:(c_Int_OBit1(X52)=c_Int_OMin<=>X52=c_Int_OMin), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I43_J)). 6.97/7.19 fof(fact_def__lfp__unfold, axiom, ![X18, X71, X5]:(((c_Orderings_Oorder__class_Omono(X5,X5,X18)=>hAPP(X18,X71)=X71)<=X71=c_Inductive_Ocomplete__lattice__class_Olfp(X5,X18))<=class_Complete__Lattice_Ocomplete__lattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_def__lfp__unfold)). 6.97/7.19 fof(fact_def__gfp__unfold, axiom, ![X18, X4, X5]:(class_Complete__Lattice_Ocomplete__lattice(X5)=>(X4=c_Inductive_Ocomplete__lattice__class_Ogfp(X5,X18)=>(hAPP(X18,X4)=X4<=c_Orderings_Oorder__class_Omono(X5,X5,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_def__gfp__unfold)). 6.97/7.19 fof(fact_rel__simps_I48_J, axiom, ![X52, X33]:(c_Int_OBit0(X52)=c_Int_OBit0(X33)<=>X33=X52), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I48_J)). 6.97/7.19 fof(fact_equation__minus__iff, axiom, ![X1, X2, X5]:(class_Groups_Ogroup__add(X5)=>(X1=hAPP(c_Groups_Ouminus__class_Ouminus(X5),X2)<=>X2=hAPP(c_Groups_Ouminus__class_Ouminus(X5),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equation__minus__iff)). 6.97/7.19 fof(fact_less__Suc0, axiom, ![X32]:(X32=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__Suc0)). 6.97/7.19 fof(fact_zero__less__abs__iff, axiom, ![X2, X5]:((c_Groups_Ozero__class_Ozero(X5)!=X2<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Groups_Oabs__class_Oabs(X5),X2))))<=class_Groups_Oordered__ab__group__add__abs(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__abs__iff)). 6.97/7.19 fof(fact_eq__0__number__of, axiom, ![X60]:(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X60)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X60),c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__0__number__of)). 6.97/7.19 fof(fact_nat__0__iff, axiom, ![X47]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X47),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=>hAPP(c_Int_Onat,X47)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__0__iff)). 6.97/7.19 fof(fact_neg__nat, axiom, ![X26]:(hBOOL(hAPP(c_Nat__Numeral_Oneg,X26))=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onat,X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__nat)). 6.97/7.19 fof(fact_of__nat__induct, axiom, ![X35, X17]:(![X72]:(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X72),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))=>hBOOL(hAPP(X17,hAPP(c_Code__Numeral_Oof__nat,X72))))=>hBOOL(hAPP(X17,X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__induct)). 6.97/7.19 fof(fact_of__int__eq__0__iff, axiom, ![X14, X5]:(class_Int_Oring__char__0(X5)=>(c_Groups_Ozero__class_Ozero(X5)=hAPP(c_Int_Oring__1__class_Oof__int(X5),X14)<=>X14=c_Groups_Ozero__class_Ozero(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__eq__0__iff)). 6.97/7.19 fof(fact_iszero__Numeral0, axiom, ![X8]:(class_Int_Onumber__ring(X8)=>c_Int_Oiszero(X8,hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_iszero__Numeral0)). 6.97/7.19 fof(fact_equal__neg__zero, axiom, ![X2, X5]:(class_Groups_Olinordered__ab__group__add(X5)=>(hAPP(c_Groups_Ouminus__class_Ouminus(X5),X2)=X2<=>c_Groups_Ozero__class_Ozero(X5)=X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equal__neg__zero)). 6.97/7.19 fof(fact_sgn__0__0, axiom, ![X2, X5]:(class_Rings_Olinordered__idom(X5)=>(c_Groups_Ozero__class_Ozero(X5)=c_Groups_Osgn__class_Osgn(X5,X2)<=>c_Groups_Ozero__class_Ozero(X5)=X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__0__0)). 6.97/7.19 fof(fact_order__less__imp__not__eq2, axiom, ![X7, X6, X8]:(class_Orderings_Oorder(X8)=>(X7!=X6<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X6),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__less__imp__not__eq2)). 6.97/7.19 fof(fact_linorder__neq__iff, axiom, ![X38, X35, X5]:((X38!=X35<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X38),X35))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X35),X38))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_linorder__neq__iff)). 6.97/7.19 fof(fact_Code__Numeral_Oof__nat__inject, axiom, ![X34, X32]:(X32=X34<=>hAPP(c_Code__Numeral_Oof__nat,X32)=hAPP(c_Code__Numeral_Oof__nat,X34)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Code__Numeral_Oof__nat__inject)). 6.97/7.19 fof(fact_semiring__norm_I112_J, axiom, ![X8]:(c_Groups_Ozero__class_Ozero(X8)=hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OPls)<=class_Int_Onumber__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_semiring__norm_I112_J)). 6.97/7.19 fof(fact_max__ext_Osimps, axiom, ![X67, X125, X103, X5]:((((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X103))&![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X103))=>?[X115]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X22),X115)),X67))&hBOOL(hAPP(hAPP(c_member(X5),X115),X125)))))&X125!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))&hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X125)))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X103),X125)),c_Wellfounded_Omax__ext(X5,X67)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__ext_Osimps)). 6.97/7.19 fof(fact_conversep__noteq, axiom, ![X38, X35, X5]:(X38!=X35<=>hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X5,X5,hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot)),c_fequal)),X35),X38))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_conversep__noteq)). 6.97/7.19 fof(fact_rel__simps_I49_J, axiom, ![X93, X19]:c_Int_OBit1(X93)!=c_Int_OBit0(X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I49_J)). 6.97/7.19 fof(fact_zless__le, axiom, ![X9, X14]:((X14!=X9&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X14),X9)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14),X9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zless__le)). 6.97/7.19 fof(fact_max__extp_Oequations, axiom, ![X125, X103, X67, X5]:((((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X103))&X125!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))&![X22]:(?[X115]:(hBOOL(hAPP(hAPP(X67,X22),X115))&hBOOL(hAPP(hAPP(c_member(X5),X115),X125)))<=hBOOL(hAPP(hAPP(c_member(X5),X22),X103))))&hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X125)))<=>c_Wellfounded_Omax__extp(X5,X67,X103,X125)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__extp_Oequations)). 6.97/7.19 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)). 6.97/7.19 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)). 6.97/7.19 fof(fact_rel__simps_I42_J, axiom, ![X93]:c_Int_OMin!=c_Int_OBit0(X93), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I42_J)). 6.97/7.19 fof(conj_2, conjecture, c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', conj_2)). 6.97/7.19 fof(fact_fun__lub__def, axiom, ![X35, X4, X210, X62, X5, X12]:hAPP(X210,hAPP(c_Set_OCollect(X12),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X62,X12),tc_HOL_Obool),tc_HOL_Obool,X12),c_HOL_OEx(tc_fun(X62,X12))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X62,X12),tc_HOL_Obool),tc_fun(tc_fun(X62,X12),tc_HOL_Obool),X12),hAPP(c_COMBS(tc_fun(X62,X12),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X62,X12)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X62,X12),tc_fun(tc_fun(X62,X12),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X62,X12))),X4)))),hAPP(hAPP(c_COMBC(X12,tc_fun(tc_fun(X62,X12),X12),tc_fun(tc_fun(X62,X12),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X62,X12),X12),tc_fun(tc_fun(X62,X12),tc_HOL_Obool)),X12),c_COMBB(X12,tc_HOL_Obool,tc_fun(X62,X12))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X62,X12),X62,X12),c_COMBI(tc_fun(X62,X12))),X35))))))=c_Partial__Function_Ofun__lub(X12,X5,X62,X210,X4,X35), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__lub__def)). 6.97/7.19 fof(fact_mult, axiom, ![X60, X51, X38, X35]: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),X35),X38)),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),X51),X60)),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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X35),X51)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X60))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X35),X60)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X51)))),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)). 6.97/7.19 fof(fact_if__image__distrib, axiom, ![X44, X50, X18, X17, X5, X12]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X12,X5,X18),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),X44),hAPP(c_Set_OCollect(X12),X17)))),hAPP(c_Set_Oimage(X12,X5,X50),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),X44),hAPP(c_Set_OCollect(X12),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X12),c_fNot),X17)))))=hAPP(c_Set_Oimage(X12,X5,hAPP(hAPP(c_COMBS(X12,X5,X5),hAPP(hAPP(c_COMBS(X12,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X12),c_If(X5)),X17)),X18)),X50)),X44), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_if__image__distrib)). 6.97/7.19 fof(fact_arith__series__nat, axiom, ![X32, X97, X2]: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)),X97))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X32)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),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),X32),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X97)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_arith__series__nat)). 6.97/7.19 fof(fact_length__sublist, axiom, ![X15, X23, X5]: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(X5)),X23)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X15))))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Osublist(X5,X23,X15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__sublist)). 6.97/7.19 fof(fact_map__pair__surj__on, axiom, ![X106, X11, X50, X62, X92, X107, X4, X18, X5, X12]:(hAPP(c_Set_Oimage(X12,X5,X18),X4)=X107=>(X106=hAPP(c_Set_Oimage(X92,X62,X50),X11)=>hAPP(hAPP(c_Product__Type_OSigma(X5,X62),X107),hAPP(c_COMBK(tc_fun(X62,tc_HOL_Obool),X5),X106))=hAPP(c_Set_Oimage(tc_prod(X12,X92),tc_prod(X5,X62),c_Product__Type_Omap__pair(X12,X5,X92,X62,X18,X50)),hAPP(hAPP(c_Product__Type_OSigma(X12,X92),X4),hAPP(c_COMBK(tc_fun(X92,tc_HOL_Obool),X12),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair__surj__on)). 6.97/7.19 fof(fact_dropWhile__map, axiom, ![X23, X18, X12, X17, X5]:hAPP(hAPP(c_List_Omap(X12,X5),X18),c_List_OdropWhile(X12,hAPP(c_Fun_Ocomp(X5,tc_HOL_Obool,X12,X17),X18),X23))=c_List_OdropWhile(X5,X17,hAPP(hAPP(c_List_Omap(X12,X5),X18),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dropWhile__map)). 6.97/7.19 fof(fact_Image__singleton, axiom, ![X2, X3, X5, X12]:hAPP(c_Relation_OImage(X12,X5,X3),hAPP(hAPP(c_Set_Oinsert(X12),X2),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool))))=hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X12,X5),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X12,X5),tc_fun(tc_fun(tc_prod(X12,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X12,X5))),hAPP(c_Product__Type_OPair(X12,X5),X2))),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__singleton)). 6.97/7.19 fof(fact_UN__le__add__shift, axiom, ![X33, X94, X32, X5]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X32)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool),tc_Nat_Onat),X94),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X33)))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X33,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X33))),X94), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__le__add__shift)). 6.97/7.19 fof(fact_foldr__map, axiom, ![X2, X23, X18, X62, X50, X5, X12]:c_List_Ofoldr(X62,X5,hAPP(c_Fun_Ocomp(X12,tc_fun(X5,X5),X62,X50),X18),X23,X2)=c_List_Ofoldr(X12,X5,X50,hAPP(hAPP(c_List_Omap(X62,X12),X18),X23),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldr__map)). 6.97/7.19 fof(fact_foldr_Osimps_I2_J, axiom, ![X2, X23, X35, X18, X5, X12]:c_List_Ofoldr(X12,X5,X18,hAPP(hAPP(c_List_Olist_OCons(X12),X35),X23),X2)=hAPP(hAPP(X18,X35),c_List_Ofoldr(X12,X5,X18,X23,X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldr_Osimps_I2_J)). 6.97/7.19 fof(fact_apsnd__apfst, axiom, ![X35, X50, X92, X18, X5, X12, X62]:hAPP(hAPP(c_Product__Type_OPair(X5,X12),hAPP(X50,hAPP(c_Product__Type_Ofst(X92,X62),X35))),hAPP(X18,hAPP(c_Product__Type_Osnd(X92,X62),X35)))=hAPP(c_Product__Type_Oapsnd(X62,X12,X5,X18),hAPP(c_Product__Type_Oapfst(X92,X5,X62,X50),X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_apsnd__apfst)). 6.97/7.19 fof(fact_apfst__apsnd, axiom, ![X35, X50, X92, X18, X12, X5, X62]:hAPP(hAPP(c_Product__Type_OPair(X5,X12),hAPP(X18,hAPP(c_Product__Type_Ofst(X62,X92),X35))),hAPP(X50,hAPP(c_Product__Type_Osnd(X62,X92),X35)))=hAPP(c_Product__Type_Oapfst(X62,X5,X12,X18),hAPP(c_Product__Type_Oapsnd(X92,X12,X62,X50),X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_apfst__apsnd)). 6.97/7.19 fof(fact_apsnd__apfst__commute, axiom, ![X24, X50, X92, X18, X5, X12, X62]:hAPP(c_Product__Type_Oapsnd(X62,X12,X5,X18),hAPP(c_Product__Type_Oapfst(X92,X5,X62,X50),X24))=hAPP(c_Product__Type_Oapfst(X92,X5,X12,X50),hAPP(c_Product__Type_Oapsnd(X62,X12,X92,X18),X24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_apsnd__apfst__commute)). 6.97/7.19 fof(fact_zadd__zmult__distrib2, axiom, ![X182, X183, X39]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X39),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X183),X182))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X39),X183)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X39),X182)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__zmult__distrib2)). 6.97/7.19 fof(fact_rotate__map, axiom, ![X23, X18, X12, X32, X5]:hAPP(hAPP(c_List_Omap(X12,X5),X18),hAPP(c_List_Orotate(X12,X32),X23))=hAPP(c_List_Orotate(X5,X32),hAPP(hAPP(c_List_Omap(X12,X5),X18),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__map)). 6.97/7.19 fof(fact_apsnd__compose, axiom, ![X35, X50, X92, X18, X5, X12, X62]:hAPP(c_Product__Type_Oapsnd(X62,X12,X5,X18),hAPP(c_Product__Type_Oapsnd(X92,X62,X5,X50),X35))=hAPP(c_Product__Type_Oapsnd(X92,X12,X5,hAPP(c_Fun_Ocomp(X62,X12,X92,X18),X50)),X35), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_apsnd__compose)). 6.97/7.19 fof(fact_apfst__compose, axiom, ![X35, X50, X92, X18, X12, X5, X62]:hAPP(c_Product__Type_Oapfst(X92,X5,X12,hAPP(c_Fun_Ocomp(X62,X5,X92,X18),X50)),X35)=hAPP(c_Product__Type_Oapfst(X62,X5,X12,X18),hAPP(c_Product__Type_Oapfst(X92,X62,X12,X50),X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_apfst__compose)). 6.97/7.19 fof(fact_zpower__number__of__even, axiom, ![X9, X14]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X14),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X9)))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X14),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X9))),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)). 6.97/7.19 fof(fact_set__Cons__sing__Nil, axiom, ![X4, X5]:hAPP(c_Set_Oimage(X5,tc_List_Olist(X5),hAPP(hAPP(c_COMBC(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_OCons(X5)),c_List_Olist_ONil(X5))),X4)=c_List_Oset__Cons(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__Cons__sing__Nil)). 6.97/7.19 fof(fact_length__concat, axiom, ![X77, X5]:hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X5))),X77))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oconcat(X5,X77)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__concat)). 6.97/7.19 fof(fact_list_Osize_I2_J, axiom, ![X253, X2, X131, X5]:c_List_Olist_Olist__size(X5,X131,hAPP(hAPP(c_List_Olist_OCons(X5),X2),X253))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X131,X2)),c_List_Olist_Olist__size(X5,X131,X253))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list_Osize_I2_J)). 6.97/7.19 fof(fact_lazy__sequence_Osize_I2_J, axiom, ![X166, X2, X131, X5]:hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X5,X131),c_Lazy__Sequence_Olazy__sequence_OInsert(X5,X2,X166))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X131,X2)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X5,X131),X166))),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)). 6.97/7.19 fof(fact_nat__number__of__Bit0, axiom, ![X9]:hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X9)),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(X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__number__of__Bit0)). 6.97/7.19 fof(fact_Range__Collect__split, axiom, ![X17, X5, X12]:hAPP(c_Relation_ORange(X12,X5),hAPP(c_Set_OCollect(tc_prod(X12,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X12,X5,tc_HOL_Obool),X17)))=hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X12)),hAPP(c_COMBC(X12,X5,tc_HOL_Obool),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__Collect__split)). 6.97/7.19 fof(fact_Field__Union, axiom, ![X67, X5]:hAPP(c_Relation_OField(X5),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),X67))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),c_Relation_OField(X5)),X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Field__Union)). 6.97/7.19 fof(fact_vimage__compose, axiom, ![X35, X18, X50, X62, X12, X5]:hAPP(c_Set_Ovimage(X5,X62,X18),hAPP(c_Set_Ovimage(X62,X12,X50),X35))=hAPP(c_Set_Ovimage(X5,X12,hAPP(c_Fun_Ocomp(X62,X12,X5,X50),X18)),X35), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__compose)). 6.97/7.19 fof(fact_Pow__def, axiom, ![X4, X5]:hAPP(c_Set_OPow(X5),X4)=hAPP(c_Set_OCollect(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool))),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__def)). 6.97/7.19 fof(fact_vimage__Compl, axiom, ![X4, X18, X12, X5]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X12,X18),X4))=hAPP(c_Set_Ovimage(X5,X12,X18),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X12,tc_HOL_Obool)),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__Compl)). 6.97/7.19 fof(fact_divmod__nat__div__mod, axiom, ![X25, X36]:hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X36),X25)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X36,X25))=c_Divides_Odivmod__nat(X36,X25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__div__mod)). 6.97/7.19 fof(fact_image__vimage__eq, axiom, ![X4, X18, X5, X12]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X12,X5,X18),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))))=hAPP(c_Set_Oimage(X12,X5,X18),hAPP(c_Set_Ovimage(X12,X5,X18),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__vimage__eq)). 6.97/7.19 fof(fact_anamorph_Osimps, axiom, ![X35, X18, X5, X12, X33]:((X33=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=>hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X12,X5,X18),X33),X35)=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),X12),c_List_Olist_ONil(X5)),X35))&(X33!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=>c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(X5),X12),tc_prod(X5,X12),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),X12),c_List_Olist_ONil(X5)),X35),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X12,tc_prod(tc_List_Olist(X5),X12)),hAPP(hAPP(c_COMBC(X5,tc_fun(X12,tc_prod(tc_List_Olist(X5),X12)),tc_fun(X12,tc_prod(tc_List_Olist(X5),X12))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(X5),X12),tc_prod(tc_List_Olist(X5),X12)),tc_fun(tc_fun(X12,tc_prod(tc_List_Olist(X5),X12)),tc_fun(X12,tc_prod(tc_List_Olist(X5),X12))),X5),c_COMBB(tc_prod(tc_List_Olist(X5),X12),tc_prod(tc_List_Olist(X5),X12),X12)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_fun(X12,tc_prod(tc_List_Olist(X5),X12))),tc_fun(tc_prod(tc_List_Olist(X5),X12),tc_prod(tc_List_Olist(X5),X12)),X5),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X5),X12,tc_prod(tc_List_Olist(X5),X12))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_List_Olist(X5),tc_fun(X12,tc_prod(tc_List_Olist(X5),X12))),X5),hAPP(c_COMBB(tc_List_Olist(X5),tc_fun(X12,tc_prod(tc_List_Olist(X5),X12)),tc_List_Olist(X5)),c_Product__Type_OPair(tc_List_Olist(X5),X12))),c_List_Olist_OCons(X5))))),hAPP(c_Lazy__Sequence_Oanamorph(X12,X5,X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X33),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))),hAPP(X18,X35))=hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X12,X5,X18),X33),X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_anamorph_Osimps)). 6.97/7.19 fof(fact_relpow_Osimps_I1_J, axiom, ![X67, X5]:c_Relation_OId(X5)=hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X67), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_relpow_Osimps_I1_J)). 6.97/7.19 fof(fact_lenlex__conv, axiom, ![X3, X5]:hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X5),tc_List_Olist(X5),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_List_Olist(X5)),c_COMBS(tc_List_Olist(X5),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X5)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_Nat_Onat),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X5),tc_Nat_Onat),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_List_Olist(X5)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X5)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X5))))),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_List_Olist(X5)),c_COMBS(tc_List_Olist(X5),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X5)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_Nat_Onat),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X5),tc_Nat_Onat),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_List_Olist(X5)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X5))))),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_fun(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_List_Olist(X5)),c_COMBC(tc_List_Olist(X5),tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),tc_fun(tc_List_Olist(X5),tc_fun(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(X5)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X5)),c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))))),c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5))))),c_List_Olex(X5,X3))))))=c_List_Olenlex(X5,X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lenlex__conv)). 6.97/7.19 fof(fact_set__Cons__def, axiom, ![X142, X4, X5]:hAPP(c_Set_OCollect(tc_List_Olist(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(X5)),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool),tc_List_Olist(X5)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(tc_List_Olist(X5)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool))),tc_fun(tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool))),tc_List_Olist(X5)),c_COMBS(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X5,tc_fun(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool))),tc_List_Olist(X5)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),X5),c_COMBS(tc_List_Olist(X5),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(X5)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_List_Olist(X5))),tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_List_Olist(X5))),tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool))),tc_List_Olist(X5)),c_COMBB(tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_List_Olist(X5),tc_HOL_Obool),X5)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_List_Olist(X5)),c_COMBB(tc_List_Olist(X5),tc_HOL_Obool,tc_List_Olist(X5))),c_fequal))),c_List_Olist_OCons(X5)))))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X4)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X5))),X142))))))=c_List_Oset__Cons(X5,X4,X142), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__Cons__def)). 6.97/7.19 fof(fact_rel__comp__def, axiom, ![X66, X3, X12, X62, X5]:hAPP(hAPP(c_Relation_Orel__comp(X5,X62,X12),X3),X66)=hAPP(c_Set_OCollect(tc_prod(X5,X12)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X12,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_fun(X62,tc_HOL_Obool)),tc_fun(X12,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_fun(X62,tc_HOL_Obool),tc_HOL_Obool,X12),c_HOL_OEx(X62))),hAPP(hAPP(c_COMBC(X5,tc_fun(X12,tc_fun(X62,tc_HOL_Obool)),tc_fun(X12,tc_fun(X62,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X62,tc_HOL_Obool),tc_fun(X62,tc_HOL_Obool)),tc_fun(tc_fun(X12,tc_fun(X62,tc_HOL_Obool)),tc_fun(X12,tc_fun(X62,tc_HOL_Obool))),X5),c_COMBB(tc_fun(X62,tc_HOL_Obool),tc_fun(X62,tc_HOL_Obool),X12)),hAPP(hAPP(c_COMBB(tc_fun(X62,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X62,tc_HOL_Obool),tc_fun(X62,tc_HOL_Obool)),X5),c_COMBS(X62,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X62,tc_HOL_Obool),tc_fun(X62,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X62),c_fconj)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X62),tc_HOL_Obool),tc_fun(X62,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X62,tc_fun(tc_fun(tc_prod(X5,X62),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X62),tc_HOL_Obool),tc_fun(X62,tc_HOL_Obool)),X5),c_COMBC(X62,tc_fun(tc_prod(X5,X62),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X62,tc_prod(X5,X62)),tc_fun(X62,tc_fun(tc_fun(tc_prod(X5,X62),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X62),tc_fun(tc_fun(tc_prod(X5,X62),tc_HOL_Obool),tc_HOL_Obool),X62),c_member(tc_prod(X5,X62)))),c_Product__Type_OPair(X5,X62)))),X3))))),hAPP(hAPP(c_COMBC(X12,tc_fun(tc_prod(X62,X12),tc_HOL_Obool),tc_fun(X62,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X62,tc_fun(tc_fun(tc_prod(X62,X12),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X62,X12),tc_HOL_Obool),tc_fun(X62,tc_HOL_Obool)),X12),c_COMBC(X62,tc_fun(tc_prod(X62,X12),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X62,tc_prod(X62,X12)),tc_fun(X62,tc_fun(tc_fun(tc_prod(X62,X12),tc_HOL_Obool),tc_HOL_Obool)),X12),hAPP(c_COMBB(tc_prod(X62,X12),tc_fun(tc_fun(tc_prod(X62,X12),tc_HOL_Obool),tc_HOL_Obool),X62),c_member(tc_prod(X62,X12)))),hAPP(c_COMBC(X62,X12,tc_prod(X62,X12)),c_Product__Type_OPair(X62,X12))))),X66))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__comp__def)). 6.97/7.19 fof(fact_lexn_Osimps_I2_J, axiom, ![X32, X3, X5]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(X5,tc_List_Olist(X5)),tc_prod(X5,tc_List_Olist(X5))),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),c_Product__Type_Omap__pair(tc_prod(X5,tc_List_Olist(X5)),tc_List_Olist(X5),tc_prod(X5,tc_List_Olist(X5)),tc_List_Olist(X5),hAPP(c_Product__Type_Oprod_Oprod__case(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_OCons(X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_OCons(X5)))),c_Wellfounded_Olex__prod(X5,tc_List_Olist(X5),X3,hAPP(c_List_Olexn(X5,X3),X32)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X5),tc_List_Olist(X5),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_List_Olist(X5)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),hAPP(c_Nat_OSuc,X32))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),hAPP(c_Nat_OSuc,X32))))))=hAPP(c_List_Olexn(X5,X3),hAPP(c_Nat_OSuc,X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexn_Osimps_I2_J)). 6.97/7.19 fof(fact_Pow__Compl, axiom, ![X4, X5]:hAPP(c_Set_OPow(X5),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X4))=hAPP(c_Set_OCollect(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool)),c_HOL_OEx(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_COMBS(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool)),hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X4)),c_Set_OPow(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__Compl)). 6.97/7.19 fof(fact_set__zip, axiom, ![X84, X23, X12, X5]:hAPP(c_List_Oset(tc_prod(X5,X12)),hAPP(hAPP(c_List_Ozip(X5,X12),X23),X84))=hAPP(c_Set_OCollect(tc_prod(X5,X12)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X5,X12)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X5,X12),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(X5,X12)),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(X5,X12)),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(X5,X12),tc_fun(tc_Nat_Onat,tc_prod(X5,X12)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(X5,X12)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X5,X12)),c_COMBB(tc_prod(X5,X12),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X12,tc_prod(X5,X12)),hAPP(hAPP(c_COMBB(X5,tc_fun(X12,tc_prod(X5,X12)),tc_Nat_Onat),c_Product__Type_OPair(X5,X12)),hAPP(c_List_Onth(X5),X23))),hAPP(c_List_Onth(X12),X84)))))),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(X5)),X23)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12)),X84)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__zip)). 6.97/7.19 fof(fact_divmod__int__rel__def, axiom, ![X1, X2]: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,X2))),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),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),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),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(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)),X1))))),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)),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(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1))),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(X2,X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__rel__def)). 6.97/7.19 fof(fact_set__sublist, axiom, ![X15, X23, X5]:hAPP(c_List_Oset(X5),c_List_Osublist(X5,X23,X15))=hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X5,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)),X5),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)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_Nat_Onat,X5),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X5),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X5),X23))))),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(X5)),X23)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X15))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__sublist)). 6.97/7.19 fof(fact_inv__image__def, axiom, ![X18, X3, X5, X12]:hAPP(hAPP(c_Relation_Oinv__image(X12,X5),X3),X18)=hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X12,X12),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X12,X12),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X12,X12),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_fun(tc_prod(X12,X12),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X12,X12)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X12,X12),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X12,X12),tc_fun(tc_fun(tc_prod(X12,X12),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X12,X12)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X12),tc_fun(X5,tc_prod(X12,X12))),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_prod(X12,X12)),tc_fun(tc_fun(X5,X12),tc_fun(X5,tc_prod(X12,X12))),X5),c_COMBB(X12,tc_prod(X12,X12),X5)),hAPP(hAPP(c_COMBB(X12,tc_fun(X12,tc_prod(X12,X12)),X5),c_Product__Type_OPair(X12,X12)),X18))),X18)))),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inv__image__def)). 6.97/7.19 fof(fact_set__conv__nth, axiom, ![X23, X5]:hAPP(c_List_Oset(X5),X23)=hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X5,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)),X5),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)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_Nat_Onat,X5),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X5),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X5),X23))))),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(X5)),X23))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__conv__nth)). 6.97/7.19 fof(fact_INT__eq, axiom, ![X11, X4, X5, X12]:c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool)),c_HOL_OEx(X12)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(c_COMBS(X12,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X12),c_fconj),hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X4)))),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X12,tc_fun(X5,tc_HOL_Obool)),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X12,tc_fun(X5,tc_HOL_Obool)),tc_fun(X12,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X12)),c_fequal)),X11)))))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),X4),X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__eq)). 6.97/7.19 fof(fact_UN__eq, axiom, ![X11, X4, X5, X12]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X4),X11)=c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool)),c_HOL_OEx(X12)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(c_COMBS(X12,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X12),c_fconj),hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X4)))),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X12,tc_fun(X5,tc_HOL_Obool)),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X12,tc_fun(X5,tc_HOL_Obool)),tc_fun(X12,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X12)),c_fequal)),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__eq)). 6.97/7.19 fof(fact_converse__def, axiom, ![X3, X5, X12]:hAPP(c_Set_OCollect(tc_prod(X5,X12)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X12,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X12,X5),tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_fun(tc_fun(tc_prod(X12,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X12,X5),tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_COMBC(X12,tc_fun(tc_prod(X12,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_prod(X12,X5)),tc_fun(X12,tc_fun(tc_fun(tc_prod(X12,X5),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X12,X5),tc_fun(tc_fun(tc_prod(X12,X5),tc_HOL_Obool),tc_HOL_Obool),X12),c_member(tc_prod(X12,X5)))),hAPP(c_COMBC(X12,X5,tc_prod(X12,X5)),c_Product__Type_OPair(X12,X5))))),X3)))=hAPP(c_Relation_Oconverse(X12,X5),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__def)). 6.97/7.19 fof(fact_nat__def, axiom, ![X14]: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,X14)),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,X14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__def)). 6.97/7.19 fof(fact_finite__psubset__def, axiom, ![X5]:hAPP(c_Set_OCollect(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_COMBS(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool))))),c_Finite__Set_Ofinite(X5))))=c_Wellfounded_Ofinite__psubset(X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__psubset__def)). 6.97/7.19 fof(fact_INTER__def, axiom, ![X11, X4, X5, X12]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),X4),X11)=hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OAll(X12)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool),X5),hAPP(c_COMBS(X12,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X12),c_fimplies),hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X4)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X12,tc_fun(X5,tc_HOL_Obool)),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X12,tc_fun(X5,tc_HOL_Obool)),tc_fun(X12,tc_HOL_Obool)),X5),c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X12)),c_member(X5))),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INTER__def)). 6.97/7.19 fof(fact_quotient__def, axiom, ![X3, X4, X5]:hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X4),X3)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X5),c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X5),c_Relation_OImage(X5,X5,X3)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_Oinsert(X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_quotient__def)). 6.97/7.19 fof(fact_image__eq__UN, axiom, ![X4, X18, X5, X12]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBC(X12,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X12),c_Set_Oinsert(X5)),X18)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))=hAPP(c_Set_Oimage(X12,X5,X18),X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__eq__UN)). 6.97/7.19 fof(fact_set__n__lists, axiom, ![X23, X32, X5]:hAPP(c_List_Oset(tc_List_Olist(X5)),c_Enum_On__lists(X5,X32,X23))=hAPP(c_Set_OCollect(tc_List_Olist(X5)),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),X32))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X5)),c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool))),c_List_Oset(X5))),hAPP(c_List_Oset(X5),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__n__lists)). 6.97/7.19 fof(fact_zip__map__map, axiom, ![X84, X50, X92, X23, X18, X62, X12, X5]:hAPP(hAPP(c_List_Ozip(X5,X12),hAPP(hAPP(c_List_Omap(X62,X5),X18),X23)),hAPP(hAPP(c_List_Omap(X92,X12),X50),X84))=hAPP(hAPP(c_List_Omap(tc_prod(X62,X92),tc_prod(X5,X12)),hAPP(c_Product__Type_Oprod_Oprod__case(X62,X92,tc_prod(X5,X12)),hAPP(hAPP(c_COMBC(X62,tc_fun(X92,X12),tc_fun(X92,tc_prod(X5,X12))),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_prod(X5,X12)),tc_fun(tc_fun(X92,X12),tc_fun(X92,tc_prod(X5,X12))),X62),c_COMBB(X12,tc_prod(X5,X12),X92)),hAPP(hAPP(c_COMBB(X5,tc_fun(X12,tc_prod(X5,X12)),X62),c_Product__Type_OPair(X5,X12)),X18))),X50))),hAPP(hAPP(c_List_Ozip(X62,X92),X23),X84)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__map__map)). 6.97/7.19 fof(fact_map__pair__def, axiom, ![X50, X18, X92, X12, X62, X5]:hAPP(c_Product__Type_Oprod_Oprod__case(X5,X12,tc_prod(X62,X92)),hAPP(hAPP(c_COMBC(X5,tc_fun(X12,X92),tc_fun(X12,tc_prod(X62,X92))),hAPP(hAPP(c_COMBB(tc_fun(X92,tc_prod(X62,X92)),tc_fun(tc_fun(X12,X92),tc_fun(X12,tc_prod(X62,X92))),X5),c_COMBB(X92,tc_prod(X62,X92),X12)),hAPP(hAPP(c_COMBB(X62,tc_fun(X92,tc_prod(X62,X92)),X5),c_Product__Type_OPair(X62,X92)),X18))),X50))=c_Product__Type_Omap__pair(X5,X62,X12,X92,X18,X50), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair__def)). 6.97/7.19 fof(fact_add, axiom, ![X60, X51, X38, X35]: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),X35),X38)),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),X51),X60)),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),X35),X51)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X38),X60))),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)). 6.97/7.19 fof(fact_Union__eq, axiom, ![X4, X5]:c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X4)=hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),X5),hAPP(c_COMBS(tc_fun(X5,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(X5,tc_HOL_Obool)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X5,tc_HOL_Obool))),X4)))),c_member(X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__eq)). 6.97/7.19 fof(fact_Id__on__def, axiom, ![X4, X5]:c_Relation_OId__on(X5,X4)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X5),c_Set_Oinsert(tc_prod(X5,X5))),hAPP(hAPP(c_COMBS(X5,X5,tc_prod(X5,X5)),c_Product__Type_OPair(X5,X5)),c_COMBI(X5)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Id__on__def)). 6.97/7.19 fof(fact_Image__Collect__split, axiom, ![X4, X17, X5, X12]:hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X12)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool),X5),hAPP(c_COMBS(X12,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X12),c_fconj),hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X4)))),hAPP(c_COMBC(X12,X5,tc_HOL_Obool),X17))))=hAPP(c_Relation_OImage(X12,X5,hAPP(c_Set_OCollect(tc_prod(X12,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X12,X5,tc_HOL_Obool),X17))),X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__Collect__split)). 6.97/7.19 fof(fact_Eps__split__eq, axiom, ![X38, X35, X12, X5]:hAPP(hAPP(c_Product__Type_OPair(X5,X12),X35),X38)=c_Hilbert__Choice_OEps(tc_prod(X5,X12),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X12,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X12)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(c_fequal,X35)))),hAPP(c_fequal,X38)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Eps__split__eq)). 6.97/7.19 fof(fact_The__split__eq, axiom, ![X38, X35, X12, X5]:hAPP(hAPP(c_Product__Type_OPair(X5,X12),X35),X38)=c_HOL_OThe(tc_prod(X5,X12),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X12,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X12)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(c_fequal,X35)))),hAPP(c_fequal,X38)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_The__split__eq)). 6.97/7.19 fof(fact_sublist__Cons, axiom, ![X4, X52, X35, X5]:hAPP(hAPP(c_List_Oappend(X5),hAPP(hAPP(hAPP(c_If(tc_List_Olist(X5)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4)),hAPP(hAPP(c_List_Olist_OCons(X5),X35),c_List_Olist_ONil(X5))),c_List_Olist_ONil(X5))),c_List_Osublist(X5,X52,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)),X4))))=c_List_Osublist(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X35),X52),X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublist__Cons)). 6.97/7.19 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)). 6.97/7.19 fof(fact_lists__Int__eq, axiom, ![X11, X4, X5]:c_List_Olistsp(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X4)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X11)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X5))),c_List_Olists(X5,X4))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X5))),c_List_Olists(X5,X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists__Int__eq)). 6.97/7.19 fof(fact_Un__Int__crazy, axiom, ![X65, X11, X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X65))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X65),X4))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X65))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X65),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Int__crazy)). 6.97/7.19 fof(fact_Int__assoc, axiom, ![X65, X11, X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)),X65)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X65)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__assoc)). 6.97/7.19 fof(fact_UN__UN__finite__eq, axiom, ![X4, X5]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,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(X5,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(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__UN__finite__eq)). 6.97/7.19 fof(fact_UN__simps_I9_J, axiom, ![X65, X11, X4, X62, X5, X12]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X62,tc_fun(X12,tc_HOL_Obool)),X4),X11)),X65)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X62,tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBC(X62,tc_fun(X12,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(tc_fun(X12,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),X62),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool))),X11)),X65)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__simps_I9_J)). 6.97/7.19 fof(fact_sublist__append, axiom, ![X4, X242, X52, X5]:c_List_Osublist(X5,hAPP(hAPP(c_List_Oappend(X5),X52),X242),X4)=hAPP(hAPP(c_List_Oappend(X5),c_List_Osublist(X5,X52,X4)),c_List_Osublist(X5,X242,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(X5)),X52)))),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublist__append)). 6.97/7.19 fof(fact_lenlex__def, axiom, ![X3, X5]:hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(X5)),tc_List_Olist(X5)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(X5),c_Wellfounded_Oless__than,c_List_Olex(X5,X3))),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_List_Olist(X5),tc_prod(tc_Nat_Onat,tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(X5),tc_prod(tc_Nat_Onat,tc_List_Olist(X5))),tc_List_Olist(X5)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(X5))),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),c_COMBI(tc_List_Olist(X5))))=c_List_Olenlex(X5,X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lenlex__def)). 6.97/7.19 fof(fact_mlex__prod__def, axiom, ![X67, X18, X5]:hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X5),X5),c_Wellfounded_Olex__prod(tc_Nat_Onat,X5,c_Wellfounded_Oless__than,X67)),hAPP(hAPP(c_COMBS(X5,X5,tc_prod(tc_Nat_Onat,X5)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X5,tc_prod(tc_Nat_Onat,X5)),X5),c_Product__Type_OPair(tc_Nat_Onat,X5)),X18)),c_COMBI(X5)))=c_Wellfounded_Omlex__prod(X5,X18,X67), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mlex__prod__def)). 6.97/7.19 fof(fact_select__def, axiom, ![X23, X5]:c_Random_Oselect(X5,X23)=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(X5,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(X5)),X23)))),hAPP(hAPP(c_COMBB(X5,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X5,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X5,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(X5),X23)),c_Code__Numeral_Onat__of))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_select__def)). 6.97/7.19 fof(fact_minus, axiom, ![X38, X35]: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),X35),X38)),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),X38),X35)),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)). 6.97/7.19 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)). 6.97/7.19 fof(fact_length__filter__conv__card, axiom, ![X23, X24, X5]: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(X5)),X23)))),hAPP(hAPP(c_COMBB(X5,tc_HOL_Obool,tc_Nat_Onat),X24),hAPP(c_List_Onth(X5),X23)))))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,X24),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__filter__conv__card)). 6.97/7.19 fof(fact_vimage__Times, axiom, ![X11, X4, X18, X62, X12, X5]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X12,hAPP(c_Fun_Ocomp(tc_prod(X12,X62),X12,X5,c_Product__Type_Ofst(X12,X62)),X18)),X4)),hAPP(c_Set_Ovimage(X5,X62,hAPP(c_Fun_Ocomp(tc_prod(X12,X62),X62,X5,c_Product__Type_Osnd(X12,X62)),X18)),X11))=hAPP(c_Set_Ovimage(X5,tc_prod(X12,X62),X18),hAPP(hAPP(c_Product__Type_OSigma(X12,X62),X4),hAPP(c_COMBK(tc_fun(X62,tc_HOL_Obool),X12),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__Times)). 6.97/7.19 fof(fact_the__inv__into__def, axiom, ![X35, X18, X4, X12, X5]:hAPP(c_Fun_Othe__inv__into(X5,X12,X4,X18),X35)=c_HOL_OThe(X5,hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X4))),hAPP(hAPP(c_COMBC(X5,X12,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X12,tc_fun(X12,tc_HOL_Obool),X5),c_fequal),X18)),X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__inv__into__def)). 6.97/7.19 fof(fact_listrel__Cons, axiom, ![X23, X35, X3, X5]:c_List_Oset__Cons(X5,hAPP(c_Relation_OImage(X5,X5,X3),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(X5),tc_List_Olist(X5),c_List_Olistrel(X5,X3)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X5)),X23),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)))))=hAPP(c_Relation_OImage(tc_List_Olist(X5),tc_List_Olist(X5),c_List_Olistrel(X5,X3)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__Cons)). 6.97/7.19 fof(fact_zdiv__zadd1__eq, axiom, ![X31, X29, X30]: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),X30),X31)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X29),X31))),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,X30,X31)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X29,X31))),X31))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X30),X29)),X31), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__zadd1__eq)). 6.97/7.19 fof(fact_div__add1__eq, axiom, ![X31, X29, X30]: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),X30),X31)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X29),X31))),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,X30,X31)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X29,X31))),X31))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X29)),X31), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__add1__eq)). 6.97/7.19 fof(fact_UN__simps_I2_J, axiom, ![X11, X4, X12, X5, X65]:((X65!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X65),hAPP(hAPP(c_COMBC(X5,tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool))),X4)),X11))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X65),X4)),X11))&(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=X65=>hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X65),hAPP(hAPP(c_COMBC(X5,tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool))),X4)),X11))=c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__simps_I2_J)). 6.97/7.19 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)). 6.97/7.19 fof(fact_int__ge__less__than2__def, axiom, ![X97]: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),X97)))),c_Orderings_Oord__class_Oless(tc_Int_Oint))))=c_Int_Oint__ge__less__than2(X97), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__ge__less__than2__def)). 6.97/7.19 fof(fact_rotate__rev, axiom, ![X41, X25, X8]:hAPP(c_List_Orotate(X8,X25),hAPP(c_List_Orev(X8),X41))=hAPP(c_List_Orev(X8),hAPP(c_List_Orotate(X8,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X25,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)))),X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__rev)). 6.97/7.19 fof(fact_insert__Collect, axiom, ![X17, X2, X5]:hAPP(hAPP(c_Set_Oinsert(X5),X2),hAPP(c_Set_OCollect(X5),X17))=hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X2)))),X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__Collect)). 6.97/7.19 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J, axiom, ![X17]:hAPP(c_Set_OCollect(tc_Nat_Onat),X17)=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),X17),c_Int_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J)). 6.97/7.19 fof(fact_set__filter, axiom, ![X23, X17, X5]:hAPP(c_List_Oset(X5),hAPP(c_List_Ofilter(X5,X17),X23))=hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),hAPP(c_List_Oset(X5),X23)))),X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__filter)). 6.97/7.19 fof(fact_trancl__subset__Field2, axiom, ![X3, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X5,X3)),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),hAPP(c_Relation_OField(X5),X3)),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_Relation_OField(X5),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__subset__Field2)). 6.97/7.19 fof(fact_rotate__drop__take, axiom, ![X41, X25, X8]:hAPP(hAPP(c_List_Oappend(X8),hAPP(hAPP(c_List_Odrop(X8),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X25,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41))),X41)),hAPP(hAPP(c_List_Otake(X8),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X25,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41))),X41))=hAPP(c_List_Orotate(X8,X25),X41), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__drop__take)). 6.97/7.19 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)). 6.97/7.19 fof(fact_nat, axiom, ![X38, X35]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X35),X38)=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),X35),X38)),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)). 6.97/7.19 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J, axiom, ![X17]: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),X17),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))))=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)))),X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J)). 6.97/7.19 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)). 6.97/7.19 fof(fact_Field__insert, axiom, ![X3, X1, X2, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X2),hAPP(hAPP(c_Set_Oinsert(X5),X1),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),hAPP(c_Relation_OField(X5),X3))=hAPP(c_Relation_OField(X5),hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Field__insert)). 6.97/7.19 fof(fact_singleton__quotient, axiom, ![X3, X35, X5]:hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X3),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)))=hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_singleton__quotient)). 6.97/7.19 fof(fact_rotate__rotate, axiom, ![X41, X25, X36, X8]:hAPP(c_List_Orotate(X8,X36),hAPP(c_List_Orotate(X8,X25),X41))=hAPP(c_List_Orotate(X8,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X25)),X41), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__rotate)). 6.97/7.19 fof(fact_int__def, axiom, ![X34]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X34)=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),X34),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))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__def)). 6.97/7.19 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)). 6.97/7.19 fof(fact_rev__map, axiom, ![X23, X18, X12, X5]:hAPP(c_List_Orev(X5),hAPP(hAPP(c_List_Omap(X12,X5),X18),X23))=hAPP(hAPP(c_List_Omap(X12,X5),X18),hAPP(c_List_Orev(X12),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__map)). 6.97/7.19 fof(fact_O__assoc, axiom, ![X108, X44, X67, X92, X12, X62, X5]:hAPP(hAPP(c_Relation_Orel__comp(X5,X62,X12),hAPP(hAPP(c_Relation_Orel__comp(X5,X92,X62),X67),X44)),X108)=hAPP(hAPP(c_Relation_Orel__comp(X5,X92,X12),X67),hAPP(hAPP(c_Relation_Orel__comp(X92,X62,X12),X44),X108)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_O__assoc)). 6.97/7.19 fof(fact_r__comp__rtrancl__eq, axiom, ![X3, X5]:hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X3),c_Transitive__Closure_Ortrancl(X5,X3))=hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),c_Transitive__Closure_Ortrancl(X5,X3)),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_r__comp__rtrancl__eq)). 6.97/7.19 fof(fact_eq__Abs__Integ, axiom, ![X14]:~(![X22, X72]:X14!=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),X72)),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_eq__Abs__Integ)). 6.97/7.19 fof(fact_sum__length__filter__compl, axiom, ![X23, X17, X5]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,X17),X23))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X17)),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__length__filter__compl)). 6.97/7.19 fof(fact_length__append, axiom, ![X45, X41, X8]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),hAPP(hAPP(c_List_Oappend(X8),X41),X45))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__append)). 6.97/7.19 fof(fact_vimage__INT, axiom, ![X11, X4, X62, X18, X12, X5]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X62,tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X62),c_Set_Ovimage(X5,X12,X18)),X11))=hAPP(c_Set_Ovimage(X5,X12,X18),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X62,tc_fun(X12,tc_HOL_Obool)),X4),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__INT)). 6.97/7.19 fof(fact_vimage__UN, axiom, ![X11, X4, X62, X18, X12, X5]:hAPP(c_Set_Ovimage(X5,X12,X18),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X62,tc_fun(X12,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X62,tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X62),c_Set_Ovimage(X5,X12,X18)),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__UN)). 6.97/7.19 fof(fact_finite__M__bounded__by__nat, axiom, ![X47, X17]: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),X17)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X47))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__M__bounded__by__nat)). 6.97/7.19 fof(fact_Diff__Un, axiom, ![X65, X11, X4, X5]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X65))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X65)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__Un)). 6.97/7.19 fof(fact_Diff__Int__distrib, axiom, ![X11, X4, X65, X5]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X65),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X65),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X65),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__Int__distrib)). 6.97/7.19 fof(fact_lexord__append__rightI, axiom, ![X3, X35, X5, X38]:(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)),X35),hAPP(hAPP(c_List_Oappend(X5),X35),X38))),c_List_Olexord(X5,X3)))<=?[X96, X116]:hAPP(hAPP(c_List_Olist_OCons(X5),X96),X116)=X38), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__append__rightI)). 6.97/7.19 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)). 6.97/7.19 fof(fact_UN__simps_I3_J, axiom, ![X11, X4, X12, X5, X65]:((X65!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X65),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool),X5),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),X4)),X11))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X65),X11)))&(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=X65=>c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X65),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool),X5),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),X4)),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__simps_I3_J)). 6.97/7.19 fof(fact_prod__size__simp, axiom, ![X24, X50, X18, X12, X5]:c_Product__Type_Oprod_Oprod__size(X5,X12,X18,X50,X24)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X18,hAPP(c_Product__Type_Ofst(X5,X12),X24))),hAPP(X50,hAPP(c_Product__Type_Osnd(X5,X12),X24)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_prod__size__simp)). 6.97/7.19 fof(fact_map__append, axiom, ![X84, X23, X18, X5, X12]:hAPP(hAPP(c_List_Omap(X12,X5),X18),hAPP(hAPP(c_List_Oappend(X12),X23),X84))=hAPP(hAPP(c_List_Oappend(X5),hAPP(hAPP(c_List_Omap(X12,X5),X18),X23)),hAPP(hAPP(c_List_Omap(X12,X5),X18),X84)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__append)). 6.97/7.19 fof(fact_Int__eq__Inter, axiom, ![X11, X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)=c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X11),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__eq__Inter)). 6.97/7.19 fof(fact_Un__eq__Union, axiom, ![X11, X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11)=c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X11),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__eq__Union)). 6.97/7.19 fof(fact_pdivmod__def, axiom, ![X93, X19]:c_Divides_Opdivmod(X19,X93)=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),X19)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X93))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X19),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X93))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pdivmod__def)). 6.97/7.19 fof(fact_divmod__int__mod__div, axiom, ![X53, X81]:c_Divides_Odivmod__int(X81,X53)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X81),X53)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X81,X53)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__mod__div)). 6.97/7.19 fof(fact_UN__simps_I1_J, axiom, ![X11, X2, X12, X5, X65]:((hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X65),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool),X5),hAPP(c_Set_Oinsert(X12),X2)),X11))=hAPP(hAPP(c_Set_Oinsert(X12),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X65),X11))<=X65!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))&(X65=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X65),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool),X5),hAPP(c_Set_Oinsert(X12),X2)),X11))=c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__simps_I1_J)). 6.97/7.19 fof(fact_listrel__Nil, axiom, ![X3, X5]:hAPP(c_Relation_OImage(tc_List_Olist(X5),tc_List_Olist(X5),c_List_Olistrel(X5,X3)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X5),tc_HOL_Obool))))=hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X5),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__Nil)). 6.97/7.19 fof(fact_mod__mult2__eq, axiom, ![X31, X29, X30]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X30),X29),X31))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X30,X29))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X30,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult2__eq)). 6.97/7.19 fof(fact_rev__rev__ident, axiom, ![X41, X8]:hAPP(c_List_Orev(X8),hAPP(c_List_Orev(X8),X41))=X41, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__rev__ident)). 6.97/7.19 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)). 6.97/7.19 fof(fact_lexord__Nil__left, axiom, ![X3, X38, X5]:(?[X13, X22]:hAPP(hAPP(c_List_Olist_OCons(X5),X13),X22)=X38<=>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)),c_List_Olist_ONil(X5)),X38)),c_List_Olexord(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__Nil__left)). 6.97/7.19 fof(fact_max__Suc2, axiom, ![X32, X34]:c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X32),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)),X32)),X34)=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X34),hAPP(c_Nat_OSuc,X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__Suc2)). 6.97/7.19 fof(fact_rotate__conv__mod, axiom, ![X41, X25, X8]:hAPP(c_List_Orotate(X8,X25),X41)=hAPP(c_List_Orotate(X8,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X25,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41))),X41), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__conv__mod)). 6.97/7.19 fof(fact_vimage__Un, axiom, ![X11, X4, X18, X12, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X12,X18),X4)),hAPP(c_Set_Ovimage(X5,X12,X18),X11))=hAPP(c_Set_Ovimage(X5,X12,X18),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),X4),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__Un)). 6.97/7.19 fof(fact_vimage__Diff, axiom, ![X11, X4, X18, X12, X5]:hAPP(c_Set_Ovimage(X5,X12,X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X12,X18),X4)),hAPP(c_Set_Ovimage(X5,X12,X18),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__Diff)). 6.97/7.19 fof(fact_vimage__Int, axiom, ![X11, X4, X18, X12, X5]:hAPP(c_Set_Ovimage(X5,X12,X18),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X12,X18),X4)),hAPP(c_Set_Ovimage(X5,X12,X18),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__Int)). 6.97/7.19 fof(fact_rel__pow__commute, axiom, ![X32, X67, X5]:hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X32),X67)),X67)=hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X67),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X32),X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__commute)). 6.97/7.19 fof(fact_relpow_Osimps_I2_J, axiom, ![X67, X32, X5]:hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X32)),X67)=hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X32),X67)),X67), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_relpow_Osimps_I2_J)). 6.97/7.19 fof(fact_Compl__Un, axiom, ![X11, X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X4)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X11))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__Un)). 6.97/7.19 fof(fact_length__map, axiom, ![X23, X18, X12, X5]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12)),X23)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(hAPP(c_List_Omap(X12,X5),X18),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__map)). 6.97/7.19 fof(fact_min__Suc2, axiom, ![X32, X34]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X34),hAPP(c_Nat_OSuc,X32))=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)),X32)),X34), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__Suc2)). 6.97/7.19 fof(fact_length__zip, axiom, ![X45, X41, X5, X8]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X45))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(X8,X5))),hAPP(hAPP(c_List_Ozip(X8,X5),X41),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__zip)). 6.97/7.19 fof(fact_Inter__Un__distrib, axiom, ![X11, X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X4)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X11))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X4),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__Un__distrib)). 6.97/7.19 fof(fact_Inter__insert, axiom, ![X11, X2, X5]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X11))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X2),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__insert)). 6.97/7.19 fof(fact_Union__Un__distrib, axiom, ![X11, X4, X5]:c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X4)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__Un__distrib)). 6.97/7.19 fof(fact_Union__insert, axiom, ![X11, X2, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X11))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X2),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__insert)). 6.97/7.19 fof(fact_image__Pow__surj, axiom, ![X11, X4, X18, X5, X12]:(hAPP(c_Set_Oimage(tc_fun(X12,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),c_Set_Oimage(X12,X5,X18)),hAPP(c_Set_OPow(X12),X4))=hAPP(c_Set_OPow(X5),X11)<=hAPP(c_Set_Oimage(X12,X5,X18),X4)=X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__Pow__surj)). 6.97/7.19 fof(fact_lazy__sequence_Osimps_I5_J, axiom, ![X166, X2, X120, X85, X12, X5]:hAPP(hAPP(X120,X2),X166)=c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X5,X12,X85,X120,c_Lazy__Sequence_Olazy__sequence_OInsert(X12,X2,X166)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lazy__sequence_Osimps_I5_J)). 6.97/7.19 fof(fact_seq__case, axiom, ![X64, X50, X18, X12, X5]:c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X5,X12,X18,X50,X64)=c_Option_Ooption_Ooption__case(X5,tc_prod(X12,tc_Lazy__Sequence_Olazy__sequence(X12)),X18,hAPP(c_Product__Type_Oprod_Oprod__case(X12,tc_Lazy__Sequence_Olazy__sequence(X12),X5),X50),hAPP(c_Lazy__Sequence_Oyield(X12),X64)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_seq__case)). 6.97/7.19 fof(fact_Domain__Collect__split, axiom, ![X17, X12, X5]:hAPP(c_Relation_ODomain(X5,X12),hAPP(c_Set_OCollect(tc_prod(X5,X12)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X12,tc_HOL_Obool),X17)))=hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X12)),X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__Collect__split)). 6.97/7.19 fof(fact_greaterThan__Suc, axiom, ![X33]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X33)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X33)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))=hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_greaterThan__Suc)). 6.97/7.19 fof(fact_rotate__Suc, axiom, ![X41, X25, X8]:hAPP(c_List_Orotate1(X8),hAPP(c_List_Orotate(X8,X25),X41))=hAPP(c_List_Orotate(X8,hAPP(c_Nat_OSuc,X25)),X41), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__Suc)). 6.97/7.19 fof(fact_transfer__int__nat__set__return__embed, axiom, ![X4]:X4=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)),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__set__return__embed)). 6.97/7.19 fof(fact_set__concat, axiom, ![X23, X5]:hAPP(c_List_Oset(X5),c_List_Oconcat(X5,X23))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X5)),X23)),c_List_Oset(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__concat)). 6.97/7.19 fof(fact_vimage__Union, axiom, ![X4, X18, X12, X5]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X12,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X4),c_Set_Ovimage(X5,X12,X18))=hAPP(c_Set_Ovimage(X5,X12,X18),c_Complete__Lattice_OSup__class_OSup(tc_fun(X12,tc_HOL_Obool),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__Union)). 6.97/7.19 fof(fact_zip__replicate, axiom, ![X7, X27, X6, X28, X5, X8]:hAPP(hAPP(c_List_Ozip(X8,X5),c_List_Oreplicate(X8,X28,X6)),c_List_Oreplicate(X5,X27,X7))=c_List_Oreplicate(tc_prod(X8,X5),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X28),X27),hAPP(hAPP(c_Product__Type_OPair(X8,X5),X6),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__replicate)). 6.97/7.19 fof(fact_refl__reflcl, axiom, ![X3, X5]:c_Relation_Orefl__on(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),c_Relation_OId(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__reflcl)). 6.97/7.19 fof(fact_min__diff, axiom, ![X25, X28, X36]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),X28)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X28))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X36),X25)),X28), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__diff)). 6.97/7.19 fof(fact_UN__extend__simps_I1_J, axiom, ![X11, X2, X12, X5, X65]:((hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X65),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool),X5),hAPP(c_Set_Oinsert(X12),X2)),X11))=hAPP(hAPP(c_Set_Oinsert(X12),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X65),X11))<=X65!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))&(hAPP(hAPP(c_Set_Oinsert(X12),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X65),X11))=hAPP(hAPP(c_Set_Oinsert(X12),X2),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool)))<=X65=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__extend__simps_I1_J)). 6.97/7.19 fof(fact_Pow__empty, axiom, ![X5]:hAPP(c_Set_OPow(X5),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))=hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__empty)). 6.97/7.19 fof(fact_atLeast__Suc, axiom, ![X33]:hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X33))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),X33)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X33),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeast__Suc)). 6.97/7.19 fof(fact_atLeast__Suc__greaterThan, axiom, ![X33]:hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X33))=hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X33), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeast__Suc__greaterThan)). 6.97/7.19 fof(fact_foldl__conv__concat, axiom, ![X77, X23, X5]:hAPP(c_List_Ofoldl(tc_List_Olist(X5),tc_List_Olist(X5),c_List_Oappend(X5),X23),X77)=hAPP(hAPP(c_List_Oappend(X5),X23),c_List_Oconcat(X5,X77)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__conv__concat)). 6.97/7.19 fof(fact_max__Suc1, axiom, ![X34, X32]:hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X32)),X34)=c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X32),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),X32)),X34), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__Suc1)). 6.97/7.19 fof(fact_Suc__diff__diff, axiom, ![X19, X25, X36]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),X25)),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,X36)),X25)),hAPP(c_Nat_OSuc,X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__diff__diff)). 6.97/7.19 fof(fact_takeWhile__dropWhile__id, axiom, ![X23, X17, X5]:hAPP(hAPP(c_List_Oappend(X5),c_List_OtakeWhile(X5,X17,X23)),c_List_OdropWhile(X5,X17,X23))=X23, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__dropWhile__id)). 6.97/7.19 fof(fact_list__size__conv__listsum, axiom, ![X23, X18, X5]: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(X5,tc_Nat_Onat),X18),X23))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23))=c_List_Olist_Olist__size(X5,X18,X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__size__conv__listsum)). 6.97/7.19 fof(fact_list_Osize_I4_J, axiom, ![X149, X30, X8]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),hAPP(hAPP(c_List_Olist_OCons(X8),X30),X149))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X149)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list_Osize_I4_J)). 6.97/7.19 fof(fact_map__nth, axiom, ![X23, X5]:hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X5),hAPP(c_List_Onth(X5),X23)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)))=X23, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__nth)). 6.97/7.19 fof(fact_pair__box_Osize_I1_J, axiom, ![X1, X2, X276, X131, X12, X5]:c_Nitpick_Opair__box_Opair__box__size(X5,X12,X131,X276,c_Nitpick_Opair__box_OPairBox(X5,X12,X2,X1))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X131,X2)),hAPP(X276,X1))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__box_Osize_I1_J)). 6.97/7.19 fof(fact_min__Suc1, axiom, ![X34, X32]: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),X32)),X34)=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X32)),X34), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__Suc1)). 6.97/7.19 fof(fact_rtrancl__r__diff__Id, axiom, ![X3, X5]:c_Transitive__Closure_Ortrancl(X5,X3)=c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),c_Relation_OId(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__r__diff__Id)). 6.97/7.19 fof(fact_rtrancl__reflcl__absorb, axiom, ![X67, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X67)),c_Relation_OId(X5))=c_Transitive__Closure_Ortrancl(X5,X67), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__reflcl__absorb)). 6.97/7.19 fof(fact_map__replicate__trivial, axiom, ![X47, X35, X5]:c_List_Oreplicate(X5,X47,X35)=hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X5),hAPP(c_COMBK(X5,tc_Nat_Onat),X35)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__replicate__trivial)). 6.97/7.19 fof(fact_empty__iff, axiom, ![X10, X5]:~(hBOOL(hAPP(hAPP(c_member(X5),X10),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__iff)). 6.97/7.19 fof(fact_length__splice, axiom, ![X45, X41, X8]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),c_List_Osplice(X8,X41,X45))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__splice)). 6.97/7.19 fof(fact_UN__constant, axiom, ![X10, X12, X5, X4]:((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=X4=>c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X4),hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X5),X10)))&(X4!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>X10=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X4),hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X5),X10)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__constant)). 6.97/7.19 fof(fact_image__vimage__subset, axiom, ![X4, X18, X12, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X12,X5,X18),hAPP(c_Set_Ovimage(X12,X5,X18),X4))),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__vimage__subset)). 6.97/7.19 fof(fact_vimage__UNIV, axiom, ![X18, X12, X5]:hAPP(c_Set_Ovimage(X5,X12,X18),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__UNIV)). 6.97/7.19 fof(fact_vimage__empty, axiom, ![X18, X12, X5]:hAPP(c_Set_Ovimage(X5,X12,X18),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__empty)). 6.97/7.19 fof(fact_vimage__ident, axiom, ![X95, X5]:hAPP(c_Set_Ovimage(X5,X5,c_COMBI(X5)),X95)=X95, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__ident)). 6.97/7.19 fof(fact_vimage__id, axiom, ![X4, X5]:hAPP(c_Set_Ovimage(X5,X5,c_Fun_Oid(X5)),X4)=X4, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__id)). 6.97/7.19 fof(fact_drop__upt, axiom, ![X27, X28, X36]:hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),X36),c_List_Oupt(X28,X27))=c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),X36),X27), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__upt)). 6.97/7.19 fof(fact_one__div__nat__number__of, axiom, ![X99]: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),X99)))=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),X99)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__div__nat__number__of)). 6.97/7.19 fof(fact_Times__empty, axiom, ![X11, X4, X12, X5]:(hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X4),hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X5),X11))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X12),tc_HOL_Obool))<=>(X4=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool))=X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Times__empty)). 6.97/7.19 fof(fact_lazy__sequence_Osimps_I4_J, axiom, ![X120, X85, X12, X5]:X85=c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X5,X12,X85,X120,c_Lazy__Sequence_Olazy__sequence_OEmpty(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lazy__sequence_Osimps_I4_J)). 6.97/7.19 fof(fact_zmod__zdiv__equality, axiom, ![X29, X30]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X29),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),X29))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X29))=X30, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zdiv__equality)). 6.97/7.19 fof(fact_UN__extend__simps_I2_J, axiom, ![X11, X4, X12, X5, X65]:((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=X65=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X65),X4)),X11)=X11)&(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X65=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X65),X4)),X11)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X65),hAPP(hAPP(c_COMBC(X5,tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool))),X4)),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__extend__simps_I2_J)). 6.97/7.19 fof(fact_UN__extend__simps_I3_J, axiom, ![X11, X4, X12, X5, X65]:((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=X65=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X65),X11))=X4)&(X65!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X65),X11))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X65),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool),X5),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),X4)),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__extend__simps_I3_J)). 6.97/7.19 fof(fact_irrefl__diff__Id, axiom, ![X3, X5]:c_Relation_Oirrefl(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),c_Relation_OId(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_irrefl__diff__Id)). 6.97/7.19 fof(fact_INT__extend__simps_I4_J, axiom, ![X11, X4, X12, X5, X65]:((hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),X65),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool),X5),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12,tc_HOL_Obool)),X4)),X11))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X65),X11))<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X65)&(X4=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X65),X11))<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=X65)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__extend__simps_I4_J)). 6.97/7.19 fof(fact_length__rotate, axiom, ![X41, X25, X8]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),hAPP(c_List_Orotate(X8,X25),X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__rotate)). 6.97/7.19 fof(fact_Nitpick_Oint__gcd__def, axiom, ![X7, X6]: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),X6)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X7))))=hAPP(hAPP(c_Nitpick_Oint__gcd,X6),X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Oint__gcd__def)). 6.97/7.19 fof(fact_nat__mult__div__cancel__disj, axiom, ![X25, X36, X19]:((X19=c_Groups_Ozero__class_Ozero(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_Otimes__class_Otimes(tc_Nat_Onat),X19),X36)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X25)))&(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X36)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X25))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X36),X25)<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__div__cancel__disj)). 6.97/7.19 fof(fact_mult__0, axiom, ![X25]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__0)). 6.97/7.19 fof(fact_lessThan__Suc__eq__insert__0, axiom, ![X32]: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),X32)))=hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lessThan__Suc__eq__insert__0)). 6.97/7.19 fof(fact_Divides_Omod__div__equality_H, axiom, ![X25, X36]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X36),X25)),X25))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X36,X25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Divides_Omod__div__equality_H)). 6.97/7.19 fof(fact_nat__mult__commute, axiom, ![X25, X36]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X36)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__commute)). 6.97/7.19 fof(fact_zmod__zdiv__equality_H, axiom, ![X25, X36]:c_Divides_Odiv__class_Omod(tc_Int_Oint,X36,X25)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X36),X25)),X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zdiv__equality_H)). 6.97/7.19 fof(fact_take__take, axiom, ![X41, X36, X25, X8]:hAPP(hAPP(c_List_Otake(X8),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X25),X36)),X41)=hAPP(hAPP(c_List_Otake(X8),X25),hAPP(hAPP(c_List_Otake(X8),X36),X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__take)). 6.97/7.19 fof(fact_Cons__eq__append__conv, axiom, ![X83, X84, X23, X35, X5]:(hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23)=hAPP(hAPP(c_List_Oappend(X5),X84),X83)<=>((c_List_Olist_ONil(X5)=X84&hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23)=X83)|?[X203]:(X23=hAPP(hAPP(c_List_Oappend(X5),X203),X83)&X84=hAPP(hAPP(c_List_Olist_OCons(X5),X35),X203)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Cons__eq__append__conv)). 6.97/7.19 fof(fact_in__set__conv__decomp, axiom, ![X23, X35, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23)))<=>?[X155, X194]:X23=hAPP(hAPP(c_List_Oappend(X5),X155),hAPP(hAPP(c_List_Olist_OCons(X5),X35),X194))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__conv__decomp)). 6.97/7.19 fof(fact_length__sublists, axiom, ![X41, X8]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X8))),c_Enum_Osublists(X8,X41))=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(X8)),X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__sublists)). 6.97/7.19 fof(fact_set__rotate, axiom, ![X23, X32, X5]:hAPP(c_List_Oset(X5),X23)=hAPP(c_List_Oset(X5),hAPP(c_List_Orotate(X5,X32),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__rotate)). 6.97/7.19 fof(fact_concat__replicate__trivial, axiom, ![X28, X8]:c_List_Oconcat(X8,c_List_Oreplicate(tc_List_Olist(X8),X28,c_List_Olist_ONil(X8)))=c_List_Olist_ONil(X8), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_concat__replicate__trivial)). 6.97/7.19 fof(fact_trancl__domain, axiom, ![X3, X5]:hAPP(c_Relation_ODomain(X5,X5),X3)=hAPP(c_Relation_ODomain(X5,X5),c_Transitive__Closure_Otrancl(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__domain)). 6.97/7.19 fof(fact_trancl__range, axiom, ![X3, X5]:hAPP(c_Relation_ORange(X5,X5),X3)=hAPP(c_Relation_ORange(X5,X5),c_Transitive__Closure_Otrancl(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__range)). 6.97/7.19 fof(fact_listset_Osimps_I1_J, axiom, ![X5]:c_List_Olistset(X5,c_List_Olist_ONil(tc_fun(X5,tc_HOL_Obool)))=hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X5),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listset_Osimps_I1_J)). 6.97/7.19 fof(fact_converse__Id, axiom, ![X5]:c_Relation_OId(X5)=hAPP(c_Relation_Oconverse(X5,X5),c_Relation_OId(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__Id)). 6.97/7.19 fof(fact_lists__empty, axiom, ![X5]:c_List_Olists(X5,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))=hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X5),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists__empty)). 6.97/7.19 fof(fact_internal__split__conv, axiom, ![X1, X2, X10, X5, X62, X12]:hAPP(hAPP(X10,X2),X1)=hAPP(hAPP(c_Product__Type_Ointernal__split(X12,X62,X5),X10),hAPP(hAPP(c_Product__Type_OPair(X12,X62),X2),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_internal__split__conv)). 6.97/7.19 fof(fact_internal__split__def, axiom, ![X62, X12, X5]:c_Product__Type_Ointernal__split(X5,X12,X62)=c_Product__Type_Oprod_Oprod__case(X5,X12,X62), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_internal__split__def)). 6.97/7.19 fof(fact_some__eq__trivial, axiom, ![X35, X5]:c_Hilbert__Choice_OEps(X5,hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X35))=X35, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_some__eq__trivial)). 6.97/7.19 fof(fact_the__eq__trivial, axiom, ![X2, X5]:c_HOL_OThe(X5,hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X2))=X2, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__eq__trivial)). 6.97/7.19 fof(fact_butlast__list__update, axiom, ![X6, X41, X8, X19]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)),c_Groups_Oone__class_Oone(tc_Nat_Onat))!=X19=>c_List_Obutlast(X8,hAPP(hAPP(c_List_Olist__update(X8,X41),X19),X6))=hAPP(hAPP(c_List_Olist__update(X8,c_List_Obutlast(X8,X41)),X19),X6))&(c_List_Obutlast(X8,hAPP(hAPP(c_List_Olist__update(X8,X41),X19),X6))=c_List_Obutlast(X8,X41)<=X19=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_butlast__list__update)). 6.97/7.19 fof(fact_lazy__sequence_Osize_I4_J, axiom, ![X187, X30, X8]:hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X8)),c_Lazy__Sequence_Olazy__sequence_OInsert(X8,X30,X187))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X8)),X187)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lazy__sequence_Osize_I4_J)). 6.97/7.19 fof(fact_finite__Collect__less__nat, axiom, ![X33]: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)),X33)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Collect__less__nat)). 6.97/7.19 fof(fact_finite__Collect__le__nat, axiom, ![X33]: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)),X33)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Collect__le__nat)). 6.97/7.19 fof(fact_fold1Set__sing, axiom, ![X1, X2, X18, X5]:(hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X18,hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X1))<=>X1=X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1Set__sing)). 6.97/7.19 fof(fact_minus__code__numeral__def, axiom, ![X36, X25]:hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X25)),hAPP(c_Code__Numeral_Onat__of,X36)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X25),X36), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__code__numeral__def)). 6.97/7.19 fof(fact_plus__code__numeral__def, axiom, ![X36, X25]:hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X25)),hAPP(c_Code__Numeral_Onat__of,X36)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X25),X36), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_plus__code__numeral__def)). 6.97/7.19 fof(fact_times__code__numeral__def, axiom, ![X36, X25]:hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X25)),hAPP(c_Code__Numeral_Onat__of,X36)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),X25),X36), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_times__code__numeral__def)). 6.97/7.19 fof(fact_div__code__numeral__def, axiom, ![X36, X25]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X25),X36)=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X25)),hAPP(c_Code__Numeral_Onat__of,X36))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__code__numeral__def)). 6.97/7.19 fof(fact_Id__O__R, axiom, ![X67, X12, X5]:hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X12),c_Relation_OId(X5)),X67)=X67, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Id__O__R)). 6.97/7.19 fof(fact_R__O__Id, axiom, ![X67, X12, X5]:X67=hAPP(hAPP(c_Relation_Orel__comp(X5,X12,X12),X67),c_Relation_OId(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_R__O__Id)). 6.97/7.19 fof(fact_Plus__eq__empty__conv, axiom, ![X11, X4, X12, X5]:((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=X4&X11=c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool)))<=>c_Sum__Type_OPlus(X5,X12,X4,X11)=c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X5,X12),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Plus__eq__empty__conv)). 6.97/7.19 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J, axiom, ![X32]: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),X32)))=hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SetInterval_Otransfer__nat__int__set__functions_I1_J)). 6.97/7.19 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)). 6.97/7.19 fof(fact_atLeastLessThan__upto, axiom, ![X46, X47]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X47),X46)=hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X47,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X46),c_Groups_Oone__class_Oone(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThan__upto)). 6.97/7.19 fof(fact_min__Suc__Suc, axiom, ![X25, X36]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X36)),hAPP(c_Nat_OSuc,X25))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X36),X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__Suc__Suc)). 6.97/7.19 fof(fact_max__Suc__Suc, axiom, ![X25, X36]:hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X36),X25))=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X36)),hAPP(c_Nat_OSuc,X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__Suc__Suc)). 6.97/7.19 fof(fact_zless__iff__Suc__zadd, axiom, ![X14, X9]:(?[X48]:X14=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X9),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X48)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9),X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zless__iff__Suc__zadd)). 6.97/7.19 fof(fact_plus__code__numeral__code, axiom, ![X36, X25]:hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X36))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X25)),hAPP(c_Code__Numeral_Oof__nat,X36)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_plus__code__numeral__code)). 6.97/7.19 fof(fact_times__code__numeral__code, axiom, ![X36, X25]:hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X36))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X25)),hAPP(c_Code__Numeral_Oof__nat,X36)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_times__code__numeral__code)). 6.97/7.19 fof(fact_singleton__rev__conv, axiom, ![X23, X35, X5]:(hAPP(hAPP(c_List_Olist_OCons(X5),X35),c_List_Olist_ONil(X5))=hAPP(c_List_Orev(X5),X23)<=>X23=hAPP(hAPP(c_List_Olist_OCons(X5),X35),c_List_Olist_ONil(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_singleton__rev__conv)). 6.97/7.19 fof(fact_take__replicate, axiom, ![X6, X19, X28, X8]:c_List_Oreplicate(X8,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X28),X19),X6)=hAPP(hAPP(c_List_Otake(X8),X28),c_List_Oreplicate(X8,X19,X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__replicate)). 6.97/7.19 fof(fact_length__upt, axiom, ![X27, X28]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X27),X28)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(X28,X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__upt)). 6.97/7.19 fof(fact_div__nat__def, axiom, ![X25, X36]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X36),X25)=hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X36,X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__nat__def)). 6.97/7.19 fof(fact_atMost__Suc, axiom, ![X33]:hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X33))=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X33)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atMost__Suc)). 6.97/7.19 fof(fact_zle__iff__zadd, axiom, ![X14, X9]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9),X14))<=>?[X48]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X9),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X48))=X14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zle__iff__zadd)). 6.97/7.19 fof(fact_subtract__code__numeral__code, axiom, ![X36, X25]:hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X36))=hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,X25)),hAPP(c_Code__Numeral_Oof__nat,X36)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subtract__code__numeral__code)). 6.97/7.19 fof(fact_trancl__rtrancl__absorb, axiom, ![X67, X5]:c_Transitive__Closure_Ortrancl(X5,X67)=c_Transitive__Closure_Ortrancl(X5,c_Transitive__Closure_Otrancl(X5,X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__rtrancl__absorb)). 6.97/7.19 fof(fact_dvd_OatLeastAtMost__singleton, axiom, ![X2]:c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2,X2)=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dvd_OatLeastAtMost__singleton)). 6.97/7.19 fof(fact_Image__Id, axiom, ![X4, X5]:hAPP(c_Relation_OImage(X5,X5,c_Relation_OId(X5)),X4)=X4, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__Id)). 6.97/7.19 fof(fact_less__iff__Suc__add, axiom, ![X32, X34]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34),X32))<=>?[X145]:hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34),X145))=X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__iff__Suc__add)). 6.97/7.19 fof(fact_mod__nat__def, axiom, ![X25, X36]:hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X36,X25))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X36,X25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__nat__def)). 6.97/7.19 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int, axiom, ![X51, X52]:c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X52,X51)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X52),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X51),c_Groups_Oone__class_Oone(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThanPlusOne__atLeastAtMost__int)). 6.97/7.19 fof(fact_wfP__empty, axiom, ![X5]:c_Wellfounded_OwfP(X5,hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_COMBK(tc_HOL_Obool,X5),c_fFalse))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wfP__empty)). 6.97/7.19 fof(fact_card__atLeastLessThan__int, axiom, ![X51, X52]:hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X52),X51))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X51),X52)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__atLeastLessThan__int)). 6.97/7.19 fof(fact_divmod__nat__zero, axiom, ![X36]:c_Divides_Odivmod__nat(X36,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)),X36), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__zero)). 6.97/7.19 fof(fact_lessThan__Suc, axiom, ![X33]:hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X33),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X33))=hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lessThan__Suc)). 6.97/7.19 fof(fact_zabs__less__one__iff, axiom, ![X14]:(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X14<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X14)),c_Groups_Oone__class_Oone(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zabs__less__one__iff)). 6.97/7.19 fof(fact_mod__code__numeral__def, axiom, ![X36, X25]:hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,X25),hAPP(c_Code__Numeral_Onat__of,X36)))=c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X25,X36), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__code__numeral__def)). 6.97/7.19 fof(fact_quotient__is__empty2, axiom, ![X3, X4, X5]:(X4=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))<=>hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X4),X3)=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_quotient__is__empty2)). 6.97/7.19 fof(fact_nat_Osize_I2_J, axiom, ![X226]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X226)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X226)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat_Osize_I2_J)). 6.97/7.19 fof(fact_trans__trancl, axiom, ![X3, X5]:c_Relation_Otrans(X5,c_Transitive__Closure_Otrancl(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trans__trancl)). 6.97/7.19 fof(fact_divmod__nat__rel__divmod__nat, axiom, ![X25, X36]:hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X36,X25),c_Divides_Odivmod__nat(X36,X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__rel__divmod__nat)). 6.97/7.19 fof(fact_card__atLeastAtMost, axiom, ![X51, X52]:hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X52,X51))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X51)),X52), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__atLeastAtMost)). 6.97/7.19 fof(fact_le__iff__add, axiom, ![X32, X34]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),X32))<=>?[X145]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34),X145)=X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__iff__add)). 6.97/7.19 fof(fact_pdivmod__posDivAlg, axiom, ![X19, X93]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X93=>c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X19),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X93))=c_Divides_Opdivmod(X19,X93))&(c_Divides_Opdivmod(X19,X93)=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),X19))<=X93=c_Groups_Ozero__class_Ozero(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pdivmod__posDivAlg)). 6.97/7.19 fof(fact_iterate_Osimps, axiom, ![X35, X18, X5, X12, X33]:((c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X33=>hAPP(c_Random_Oiterate(X12,X5,X33,X18),X35)=hAPP(c_Product__Type_OPair(X12,X5),X35))&(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X33=>hAPP(c_Random_Oiterate(X12,X5,X33,X18),X35)=hAPP(hAPP(c_Product__Type_Oscomp(X5,X12,X5,tc_prod(X12,X5)),hAPP(X18,X35)),c_Random_Oiterate(X12,X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X33),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_iterate_Osimps)). 6.97/7.19 fof(fact_succ__pred, axiom, ![X6]:c_Int_Osucc(c_Int_Opred(X6))=X6, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_succ__pred)). 6.97/7.19 fof(fact_image__is__empty, axiom, ![X4, X18, X5, X12]:(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(c_Set_Oimage(X12,X5,X18),X4)<=>c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool))=X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__is__empty)). 6.97/7.19 fof(fact_zdiv__minus1__right, axiom, ![X30]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X30), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__minus1__right)). 6.97/7.19 fof(fact_Domain__empty__iff, axiom, ![X3, X12, X5]:(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(c_Relation_ODomain(X5,X12),X3)<=>c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X12),tc_HOL_Obool))=X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__empty__iff)). 6.97/7.19 fof(fact_Range__empty__iff, axiom, ![X3, X5, X12]:(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(c_Relation_ORange(X12,X5),X3)<=>X3=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X12,X5),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__empty__iff)). 6.97/7.19 fof(fact_single__valued__Id, axiom, ![X5]:c_Relation_Osingle__valued(X5,X5,c_Relation_OId(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_single__valued__Id)). 6.97/7.19 fof(fact_distinct__upt, axiom, ![X27, X28]:hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X28,X27))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__upt)). 6.97/7.19 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int, axiom, ![X51, X52]:c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X52,X51)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X52),c_Groups_Oone__class_Oone(tc_Int_Oint))),X51), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastPlusOneLessThan__greaterThanLessThan__int)). 6.97/7.19 fof(fact_butlast_Osimps_I2_J, axiom, ![X6, X8, X41]:((hAPP(hAPP(c_List_Olist_OCons(X8),X6),c_List_Obutlast(X8,X41))=c_List_Obutlast(X8,hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41))<=c_List_Olist_ONil(X8)!=X41)&(c_List_Olist_ONil(X8)=X41=>c_List_Obutlast(X8,hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41))=c_List_Olist_ONil(X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_butlast_Osimps_I2_J)). 6.97/7.19 fof(fact_remove1_Osimps_I2_J, axiom, ![X41, X8, X7, X6]:((c_List_Oremove1(X8,X6,hAPP(hAPP(c_List_Olist_OCons(X8),X7),X41))=hAPP(hAPP(c_List_Olist_OCons(X8),X7),c_List_Oremove1(X8,X6,X41))<=X7!=X6)&(X41=c_List_Oremove1(X8,X6,hAPP(hAPP(c_List_Olist_OCons(X8),X7),X41))<=X6=X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remove1_Osimps_I2_J)). 6.97/7.19 fof(fact_sublist__upt__eq__take, axiom, ![X32, X52, X5]:c_List_Osublist(X5,X52,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X32))=hAPP(hAPP(c_List_Otake(X5),X32),X52), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublist__upt__eq__take)). 6.97/7.19 fof(fact_zmod__eq__0__iff, axiom, ![X97, X34]:(?[X150]:X34=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X97),X150)<=>c_Divides_Odiv__class_Omod(tc_Int_Oint,X34,X97)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__eq__0__iff)). 6.97/7.19 fof(fact_mod__eq__0__iff, axiom, ![X97, X34]:(?[X150]:X34=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),X150)<=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X34,X97)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__eq__0__iff)). 6.97/7.19 fof(fact_last__ConsL, axiom, ![X6, X8, X41]:(c_List_Olist_ONil(X8)=X41=>X6=c_List_Olast(X8,hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__ConsL)). 6.97/7.19 fof(fact_antisym__Id, axiom, ![X5]:c_Relation_Oantisym(X5,c_Relation_OId(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_antisym__Id)). 6.97/7.19 fof(fact_sym__Id, axiom, ![X5]:c_Relation_Osym(X5,c_Relation_OId(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sym__Id)). 6.97/7.19 fof(fact_insert__code, axiom, ![X35, X4, X38, X5]:(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X5),X38),X4),X35))<=>(X35=X38|hBOOL(hAPP(X4,X35)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__code)). 6.97/7.19 fof(fact_eq__mem, axiom, ![X38, X35, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_fequal,X38)))<=>X38=X35), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__mem)). 6.97/7.19 fof(fact_dvd__1__left, axiom, ![X19]:hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dvd__1__left)). 6.97/7.19 fof(fact_nat__of__cases, axiom, ![X38]:(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X38),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))=>~(![X22]:X38!=hAPP(c_Code__Numeral_Onat__of,X22))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__of__cases)). 6.97/7.19 fof(fact_nat__zminus__int, axiom, ![X25]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__zminus__int)). 6.97/7.19 fof(fact_New__DSequence_Opos__decr__bind__def, axiom, ![X18, X35, X5, X12, X47]:((c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X47=>hAPP(c_New__DSequence_Opos__decr__bind(X12,X5,X35,X18),X47)=c_Lazy__Sequence_Oempty(X5))&(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X47=>hAPP(c_Lazy__Sequence_Obind(X12,X5,hAPP(X35,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X47),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(X12,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X5)),X18),X47))=hAPP(c_New__DSequence_Opos__decr__bind(X12,X5,X35,X18),X47))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Opos__decr__bind__def)). 6.97/7.19 fof(fact_New__DSequence_Oneg__decr__bind__def, axiom, ![X18, X35, X5, X12, X47]:((c_Lazy__Sequence_Ohit__bound(X5)=hAPP(c_New__DSequence_Oneg__decr__bind(X12,X5,X35,X18),X47)<=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X47)&(X47!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=>hAPP(c_New__DSequence_Oneg__decr__bind(X12,X5,X35,X18),X47)=c_Lazy__Sequence_Ohb__bind(X12,X5,hAPP(X35,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X47),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X12,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X5))),X18),X47)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Oneg__decr__bind__def)). 6.97/7.19 fof(fact_div__1, axiom, ![X36]:X36=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X36),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__1)). 6.97/7.19 fof(fact_sorted__upt, axiom, ![X27, X28]:c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X28,X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__upt)). 6.97/7.19 fof(fact_wf__measure, axiom, ![X18, X5]:c_Wellfounded_Owf(X5,hAPP(c_Wellfounded_Omeasure(X5),X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__measure)). 6.97/7.19 fof(fact_fun__upd__idem__iff, axiom, ![X38, X35, X18, X12, X5]:(X18=c_Fun_Ofun__upd(X5,X12,X18,X35,X38)<=>X38=hAPP(X18,X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upd__idem__iff)). 6.97/7.19 fof(fact_nat__int, axiom, ![X25]:X25=hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__int)). 6.97/7.19 fof(fact_list__all2__Nil2, axiom, ![X23, X17, X12, X5]:(c_List_Olist_ONil(X5)=X23<=>c_List_Olist__all2(X5,X12,X17,X23,c_List_Olist_ONil(X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__Nil2)). 6.97/7.19 fof(fact_power__eq__if, axiom, ![X81, X36]:((c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X81),X36)<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X36)&(X36!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X81),X36)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X81),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X81),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),c_Groups_Oone__class_Oone(tc_Nat_Onat)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__eq__if)). 6.97/7.19 fof(fact_zmod__minus1__right, axiom, ![X30]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__minus1__right)). 6.97/7.19 fof(fact_mod__1, axiom, ![X36]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X36,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__1)). 6.97/7.19 fof(fact_min__0L, axiom, ![X25]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__0L)). 6.97/7.19 fof(fact_min__0R, axiom, ![X25]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X25),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__0R)). 6.97/7.19 fof(fact_max__0L, axiom, ![X25]:hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25)=X25, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__0L)). 6.97/7.19 fof(fact_max__0R, axiom, ![X25]:X25=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X25),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__0R)). 6.97/7.19 fof(fact_list__all2__eq, axiom, ![X5, X84, X23]:(c_List_Olist__all2(X5,X5,c_fequal,X23,X84)<=>X23=X84), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__eq)). 6.97/7.19 fof(help_c__fequal__2, axiom, ![X38, X35]:(X35!=X38|hBOOL(hAPP(hAPP(c_fequal,X35),X38))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fequal__2)). 6.97/7.19 fof(fact_diff__bin__simps_I1_J, axiom, ![X19]:X19=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19),c_Int_OPls), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I1_J)). 6.97/7.19 fof(fact_mult__Pls, axiom, ![X39]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X39)=c_Int_OPls, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__Pls)). 6.97/7.19 fof(fact_of__nat__nat__of, axiom, ![X19]:hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X19))=X19, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__nat__of)). 6.97/7.19 fof(fact_nat__of__of__nat, axiom, ![X25]:X25=hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__of__of__nat)). 6.97/7.19 fof(fact_nat__gcd_Osimps, axiom, ![X6, X7]:((X6=c_Nitpick_Onat__gcd(X6,X7)<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X7)&(c_Nitpick_Onat__gcd(X6,X7)=c_Nitpick_Onat__gcd(X7,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X6,X7))<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__gcd_Osimps)). 6.97/7.19 fof(fact_inc__shift__def, axiom, ![X19, X40]:((c_Random_Oinc__shift(X40,X19)=c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)<=X19=X40)&(c_Random_Oinc__shift(X40,X19)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X19),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))<=X40!=X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inc__shift__def)). 6.97/7.19 fof(fact_of__nat__cases, axiom, ![X35]:~(![X72]:(X35=hAPP(c_Code__Numeral_Oof__nat,X72)=>~(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X72),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__cases)). 6.97/7.19 fof(fact_coinduct3__lemma, axiom, ![X18, X56, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X56),hAPP(X18,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),X18)),X56))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X5,tc_HOL_Obool),X18))))))=>(c_Orderings_Oorder__class_Omono(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X18)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),X18)),X56))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X5,tc_HOL_Obool),X18)))),hAPP(X18,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),X18)),X56))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X5,tc_HOL_Obool),X18)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_coinduct3__lemma)). 6.97/7.19 fof(fact_inf__Int__eq2, axiom, ![X38, X35, X44, X67, X12, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X35),X38)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),X67),X44)))<=>hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X12,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_COMBC(X12,tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_prod(X5,X12)),tc_fun(X12,tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X12),tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool),X12),c_member(tc_prod(X5,X12)))),c_Product__Type_OPair(X5,X12)))),X67)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_COMBC(X12,tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_prod(X5,X12)),tc_fun(X12,tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X12),tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool),X12),c_member(tc_prod(X5,X12)))),c_Product__Type_OPair(X5,X12)))),X44)),X35),X38))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__Int__eq2)). 6.97/7.19 fof(fact_sup__Un__eq2, axiom, ![X38, X35, X44, X67, X12, X5]:(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X12,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_COMBC(X12,tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_prod(X5,X12)),tc_fun(X12,tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X12),tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool),X12),c_member(tc_prod(X5,X12)))),c_Product__Type_OPair(X5,X12)))),X67)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_COMBC(X12,tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_prod(X5,X12)),tc_fun(X12,tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X12),tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool),X12),c_member(tc_prod(X5,X12)))),c_Product__Type_OPair(X5,X12)))),X44)),X35),X38))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X35),X38)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),X67),X44)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__Un__eq2)). 6.97/7.19 fof(fact_pred__comp__rel__comp__eq, axiom, ![X38, X35, X66, X3, X62, X12, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X62)),hAPP(hAPP(c_Product__Type_OPair(X5,X62),X35),X38)),hAPP(hAPP(c_Relation_Orel__comp(X5,X12,X62),X3),X66)))<=>hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X5,X12,X62,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_COMBC(X12,tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_prod(X5,X12)),tc_fun(X12,tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X12),tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool),X12),c_member(tc_prod(X5,X12)))),c_Product__Type_OPair(X5,X12)))),X3),hAPP(hAPP(c_COMBC(X12,tc_fun(tc_prod(X12,X62),tc_HOL_Obool),tc_fun(X62,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X62,tc_fun(tc_fun(tc_prod(X12,X62),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X12,X62),tc_HOL_Obool),tc_fun(X62,tc_HOL_Obool)),X12),c_COMBC(X62,tc_fun(tc_prod(X12,X62),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X62,tc_prod(X12,X62)),tc_fun(X62,tc_fun(tc_fun(tc_prod(X12,X62),tc_HOL_Obool),tc_HOL_Obool)),X12),hAPP(c_COMBB(tc_prod(X12,X62),tc_fun(tc_fun(tc_prod(X12,X62),tc_HOL_Obool),tc_HOL_Obool),X62),c_member(tc_prod(X12,X62)))),c_Product__Type_OPair(X12,X62)))),X66)),X35),X38))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pred__comp__rel__comp__eq)). 6.97/7.19 fof(fact_pred__subset__eq2, axiom, ![X44, X67, X12, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X12,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_COMBC(X12,tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_prod(X5,X12)),tc_fun(X12,tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X12),tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool),X12),c_member(tc_prod(X5,X12)))),c_Product__Type_OPair(X5,X12)))),X67)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_COMBC(X12,tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_prod(X5,X12)),tc_fun(X12,tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X12),tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool),X12),c_member(tc_prod(X5,X12)))),c_Product__Type_OPair(X5,X12)))),X44)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),X67),X44))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pred__subset__eq2)). 6.97/7.19 fof(fact_Random_Osimps, axiom, ![X58, X50, X5, X59]:((hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X5))=c_Random__Sequence_ORandom(X5,X50,X59,X58)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X59),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X59),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))=>c_Random__Sequence_ORandom(X5,X50,X59,X58)=hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(X50,X58)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(X5,X50,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X59),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X58))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5))))),tc_prod(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(X5)),hAPP(hAPP(c_COMBB(X5,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(X5)),c_Product__Type_Ofst(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Random_Osimps)). 6.97/7.19 fof(fact_INF__INT__eq2, axiom, ![X38, X35, X3, X62, X12, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X12,X62)),hAPP(hAPP(c_Product__Type_OPair(X12,X62),X35),X38)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(tc_prod(X12,X62),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X3)))<=>hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_fun(X62,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X12,X62),tc_HOL_Obool),tc_fun(X12,tc_fun(X62,tc_HOL_Obool)),X5),hAPP(c_COMBC(X12,tc_fun(tc_prod(X12,X62),tc_HOL_Obool),tc_fun(X62,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X62,tc_fun(tc_fun(tc_prod(X12,X62),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X12,X62),tc_HOL_Obool),tc_fun(X62,tc_HOL_Obool)),X12),c_COMBC(X62,tc_fun(tc_prod(X12,X62),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X62,tc_prod(X12,X62)),tc_fun(X62,tc_fun(tc_fun(tc_prod(X12,X62),tc_HOL_Obool),tc_HOL_Obool)),X12),hAPP(c_COMBB(tc_prod(X12,X62),tc_fun(tc_fun(tc_prod(X12,X62),tc_HOL_Obool),tc_HOL_Obool),X62),c_member(tc_prod(X12,X62)))),c_Product__Type_OPair(X12,X62))))),X3)),X35),X38))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF__INT__eq2)). 6.97/7.19 fof(fact_SUP__UN__eq2, axiom, ![X38, X35, X3, X62, X12, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X12,X62)),hAPP(hAPP(c_Product__Type_OPair(X12,X62),X35),X38)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_prod(X12,X62),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X3)))<=>hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_fun(X62,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X12,X62),tc_HOL_Obool),tc_fun(X12,tc_fun(X62,tc_HOL_Obool)),X5),hAPP(c_COMBC(X12,tc_fun(tc_prod(X12,X62),tc_HOL_Obool),tc_fun(X62,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X62,tc_fun(tc_fun(tc_prod(X12,X62),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X12,X62),tc_HOL_Obool),tc_fun(X62,tc_HOL_Obool)),X12),c_COMBC(X62,tc_fun(tc_prod(X12,X62),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X62,tc_prod(X12,X62)),tc_fun(X62,tc_fun(tc_fun(tc_prod(X12,X62),tc_HOL_Obool),tc_HOL_Obool)),X12),hAPP(c_COMBB(tc_prod(X12,X62),tc_fun(tc_fun(tc_prod(X12,X62),tc_HOL_Obool),tc_HOL_Obool),X62),c_member(tc_prod(X12,X62)))),c_Product__Type_OPair(X12,X62))))),X3)),X35),X38))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP__UN__eq2)). 6.97/7.19 fof(fact_listrel__iff__zip, axiom, ![X3, X84, X23, X5]:(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)),X23),X84)),c_List_Olistrel(X5,X3)))<=>(![X22]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X22),hAPP(c_List_Oset(tc_prod(X5,X5)),hAPP(hAPP(c_List_Ozip(X5,X5),X23),X84))))=>hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X5,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5)))),c_Product__Type_OPair(X5,X5)))),X3)),X22)))&hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X84))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__iff__zip)). 6.97/7.19 fof(fact_part__equivp__typedef, axiom, ![X67, X5]:(c_Equiv__Relations_Opart__equivp(X5,X67)=>?[X254]:hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X254),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool)),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBS(X5,X5,tc_HOL_Obool),X67),c_COMBI(X5))))),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5)),c_fequal)),X67)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_part__equivp__typedef)). 6.97/7.19 fof(fact_conversep__converse__eq, axiom, ![X38, X35, X3, X12, X5]:(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X5,X12,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_COMBC(X12,tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_prod(X5,X12)),tc_fun(X12,tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X12),tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool),X12),c_member(tc_prod(X5,X12)))),c_Product__Type_OPair(X5,X12)))),X3)),X35),X38))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X12,X5)),hAPP(hAPP(c_Product__Type_OPair(X12,X5),X35),X38)),hAPP(c_Relation_Oconverse(X5,X12),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_conversep__converse__eq)). 6.97/7.19 fof(fact_max__extp__max__ext__eq, axiom, ![X105, X35, X67, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X35),X105)),c_Wellfounded_Omax__ext(X5,X67)))<=>c_Wellfounded_Omax__extp(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X5,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5)))),c_Product__Type_OPair(X5,X5)))),X67),X35,X105)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__extp__max__ext__eq)). 6.97/7.19 fof(fact_listrelp__listrel__eq, axiom, ![X105, X35, X3, X5]:(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)),X35),X105)),c_List_Olistrel(X5,X3)))<=>c_List_Olistrelp(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X5,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5)))),c_Product__Type_OPair(X5,X5)))),X3),X35,X105)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrelp__listrel__eq)). 6.97/7.19 fof(fact_RangeP__Range__eq, axiom, ![X35, X3, X12, X5]:(hBOOL(hAPP(hAPP(c_member(X12),X35),hAPP(c_Relation_ORange(X5,X12),X3)))<=>hBOOL(hAPP(c_Predicate_ORangeP(X5,X12,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_COMBC(X12,tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_prod(X5,X12)),tc_fun(X12,tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X12),tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool),X12),c_member(tc_prod(X5,X12)))),c_Product__Type_OPair(X5,X12)))),X3)),X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_RangeP__Range__eq)). 6.97/7.19 fof(fact_DomainP__Domain__eq, axiom, ![X35, X3, X12, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_Relation_ODomain(X5,X12),X3)))<=>hBOOL(hAPP(c_Predicate_ODomainP(X5,X12,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_COMBC(X12,tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_prod(X5,X12)),tc_fun(X12,tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X12),tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool),X12),c_member(tc_prod(X5,X12)))),c_Product__Type_OPair(X5,X12)))),X3)),X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_DomainP__Domain__eq)). 6.97/7.19 fof(fact_dvd_OgreaterThanAtMost__empty, axiom, ![X33, X52]:(c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X33,X52)=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))<=hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X52),X33))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dvd_OgreaterThanAtMost__empty)). 6.97/7.19 fof(fact_dvd_OatLeastLessThan__empty__iff, axiom, ![X1, X2]:(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2,X1)<=>~((~(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)))&hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dvd_OatLeastLessThan__empty__iff)). 6.97/7.19 fof(fact_accp__acc__eq, axiom, ![X35, X3, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X35),c_Wellfounded_Oacc(X5,X3)))<=>hBOOL(hAPP(c_Wellfounded_Oaccp(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X5,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5)))),c_Product__Type_OPair(X5,X5)))),X3)),X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_accp__acc__eq)). 6.97/7.19 fof(fact_equivp__equiv, axiom, ![X4, X5]:(c_Equiv__Relations_Oequiv(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X4)<=>c_Equiv__Relations_Oequivp(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X5,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5)))),c_Product__Type_OPair(X5,X5)))),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equivp__equiv)). 6.97/7.19 fof(fact_dvd_OgreaterThanAtMost__empty__iff2, axiom, ![X52, X33]:(~((hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33),X52))&~(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X52),X33)))))<=>c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X33,X52)=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dvd_OgreaterThanAtMost__empty__iff2)). 6.97/7.19 fof(fact_wfP__wf__eq, axiom, ![X3, X5]:(c_Wellfounded_Owf(X5,X3)<=>c_Wellfounded_OwfP(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X5,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5)))),c_Product__Type_OPair(X5,X5)))),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wfP__wf__eq)). 6.97/7.19 fof(fact_pred__equals__eq2, axiom, ![X44, X67, X12, X5]:(X44=X67<=>hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_COMBC(X12,tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_prod(X5,X12)),tc_fun(X12,tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X12),tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool),X12),c_member(tc_prod(X5,X12)))),c_Product__Type_OPair(X5,X12)))),X44)=hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_COMBC(X12,tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_prod(X5,X12)),tc_fun(X12,tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X12),tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_HOL_Obool),X12),c_member(tc_prod(X5,X12)))),c_Product__Type_OPair(X5,X12)))),X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pred__equals__eq2)). 6.97/7.19 fof(fact_rtrancl__induct2, axiom, ![X17, X3, X176, X177, X178, X179, X12, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X12),tc_prod(X5,X12))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X12),tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X179),X178)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X177),X176))),c_Transitive__Closure_Ortrancl(tc_prod(X5,X12),X3)))=>((hBOOL(hAPP(hAPP(X17,X177),X176))<=![X13, X96]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X12),tc_prod(X5,X12))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X12),tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X179),X178)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X13),X96))),c_Transitive__Closure_Ortrancl(tc_prod(X5,X12),X3)))=>![X180, X181]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X12),tc_prod(X5,X12))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X12),tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X13),X96)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X180),X181))),X3))=>(hBOOL(hAPP(hAPP(X17,X180),X181))<=hBOOL(hAPP(hAPP(X17,X13),X96))))))<=hBOOL(hAPP(hAPP(X17,X179),X178)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__induct2)). 6.97/7.19 fof(fact_dvd_OgreaterThanLessThan__empty, axiom, ![X33, X52]:(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X52),X33))=>c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X33,X52)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dvd_OgreaterThanLessThan__empty)). 6.97/7.19 fof(fact_converse__rtrancl__induct2, axiom, ![X17, X3, X176, X177, X178, X179, X12, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X12),tc_prod(X5,X12))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X12),tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X179),X178)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X177),X176))),c_Transitive__Closure_Ortrancl(tc_prod(X5,X12),X3)))=>((hBOOL(hAPP(hAPP(X17,X179),X178))<=![X13, X96, X180, X181]:((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X12),tc_prod(X5,X12))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X12),tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X180),X181)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X177),X176))),c_Transitive__Closure_Ortrancl(tc_prod(X5,X12),X3)))=>(hBOOL(hAPP(hAPP(X17,X180),X181))=>hBOOL(hAPP(hAPP(X17,X13),X96))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X12),tc_prod(X5,X12))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X12),tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X13),X96)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X180),X181))),X3))))<=hBOOL(hAPP(hAPP(X17,X177),X176)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__rtrancl__induct2)). 6.97/7.19 fof(fact_fold__image__Sigma, axiom, ![X50, X11, X12, X4, X5, X62]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X62,tc_prod(X5,X12),c_Groups_Otimes__class_Otimes(X62)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X12,X62),X50)),c_Groups_Oone__class_Oone(X62)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X4),X11))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X62,X5,c_Groups_Otimes__class_Otimes(X62)),hAPP(hAPP(c_COMBS(X5,tc_fun(X12,tc_HOL_Obool),X62),hAPP(hAPP(c_COMBC(X5,X62,tc_fun(tc_fun(X12,tc_HOL_Obool),X62)),hAPP(hAPP(c_COMBB(tc_fun(X12,X62),tc_fun(X62,tc_fun(tc_fun(X12,tc_HOL_Obool),X62)),X5),c_Finite__Set_Ofold__image(X62,X12,c_Groups_Otimes__class_Otimes(X62))),X50)),c_Groups_Oone__class_Oone(X62))),X11)),c_Groups_Oone__class_Oone(X62)),X4)<=![X22]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X12),hAPP(X11,X22)))<=hBOOL(hAPP(hAPP(c_member(X5),X22),X4)))))<=class_Groups_Ocomm__monoid__mult(X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__Sigma)). 6.97/7.19 fof(fact_setsum__product, axiom, ![X11, X50, X62, X4, X18, X12, X5]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5),X18),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X62,X5),X50),X11))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5),hAPP(hAPP(c_COMBC(X12,tc_fun(X62,tc_HOL_Obool),X5),hAPP(hAPP(c_COMBB(tc_fun(X62,X5),tc_fun(tc_fun(X62,tc_HOL_Obool),X5),X12),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X62,X5)),hAPP(hAPP(c_COMBC(X12,tc_fun(X62,X5),tc_fun(X62,X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,X5),tc_fun(tc_fun(X62,X5),tc_fun(X62,X5)),X12),c_COMBB(X5,X5,X62)),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X12),c_Groups_Otimes__class_Otimes(X5)),X18))),X50))),X11)),X4)<=class_Rings_Osemiring__0(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__product)). 6.97/7.19 fof(fact_quotient__diff1, axiom, ![X2, X4, X3, X5]:((hBOOL(hAPP(hAPP(c_member(X5),X2),X4))=>hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X3)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X4),X3)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X3)))<=c_Fun_Oinj__on(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X5),c_Equiv__Relations_Oquotient(X5)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_Oinsert(X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X3),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_quotient__diff1)). 6.97/7.19 fof(fact_smax__insertI, axiom, ![X56, X35, X95, X38]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X38),X95))=>((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)),X35),X56)),X95)),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)),X56),X95)),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)),X35),X38)),c_FunDef_Opair__less)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_smax__insertI)). 6.97/7.19 fof(fact_wmax__insertI, axiom, ![X142, X35, X143, X38]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X38),X143))=>(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)),X35),X38)),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)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X35),X142)),X143)),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)),X142),X143)),c_FunDef_Omax__weak))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wmax__insertI)). 6.97/7.19 fof(fact_smin__insertI, axiom, ![X143, X38, X142, X35]:(((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)),X142),X143)),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)),X142),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X38),X143))),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)),X35),X38)),c_FunDef_Opair__less)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X35),X142))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_smin__insertI)). 6.97/7.19 fof(fact_wmin__insertI, axiom, ![X143, X38, X142, X35]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X35),X142))=>((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)),X142),X143)),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)),X142),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X38),X143))),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)),X35),X38)),c_FunDef_Opair__leq)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wmin__insertI)). 6.97/7.19 fof(fact_converse__rtranclE2, axiom, ![X3, X250, X251, X252, X105, X12, X5]:((hAPP(hAPP(c_Product__Type_OPair(X5,X12),X105),X252)!=hAPP(hAPP(c_Product__Type_OPair(X5,X12),X251),X250)=>~(![X13, X96]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X12),tc_prod(X5,X12))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X12),tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X105),X252)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X13),X96))),X3))=>~(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X12),tc_prod(X5,X12))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X12),tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X13),X96)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X251),X250))),c_Transitive__Closure_Ortrancl(tc_prod(X5,X12),X3)))))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X12),tc_prod(X5,X12))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X12),tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X105),X252)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X251),X250))),c_Transitive__Closure_Ortrancl(tc_prod(X5,X12),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__rtranclE2)). 6.97/7.19 fof(fact_UN__equiv__class2, axiom, ![X125, X103, X18, X62, X151, X152, X12, X153, X154, X5]:(((c_Equiv__Relations_Ocongruent2(X5,X12,tc_fun(X62,tc_HOL_Obool),X153,X151,X18)=>(hBOOL(hAPP(hAPP(c_member(X5),X103),X154))=>(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X62,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X153),hAPP(hAPP(c_Set_Oinsert(X5),X103),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_fun(X62,tc_HOL_Obool)),tc_fun(X62,tc_HOL_Obool),X5),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X62,tc_HOL_Obool)),hAPP(c_Relation_OImage(X12,X12,X151),hAPP(hAPP(c_Set_Oinsert(X12),X125),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool)))))),X18))=hAPP(hAPP(X18,X103),X125)<=hBOOL(hAPP(hAPP(c_member(X12),X125),X152)))))<=c_Equiv__Relations_Oequiv(X12,X152,X151))<=c_Equiv__Relations_Oequiv(X5,X154,X153)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__equiv__class2)). 6.97/7.19 fof(fact_UN__equiv__class__type2, axiom, ![X11, X188, X189, X18, X62, X151, X152, X12, X153, X154, X5]:((((hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X189),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X154),X153)))=>((![X76]:(![X190]:(hBOOL(hAPP(hAPP(c_member(X12),X190),X152))=>hBOOL(hAPP(hAPP(c_member(tc_fun(X62,tc_HOL_Obool)),hAPP(hAPP(X18,X76),X190)),X11)))<=hBOOL(hAPP(hAPP(c_member(X5),X76),X154)))=>hBOOL(hAPP(hAPP(c_member(tc_fun(X62,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X62,tc_HOL_Obool)),X189),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_fun(X62,tc_HOL_Obool)),tc_fun(X62,tc_HOL_Obool),X5),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X62,tc_HOL_Obool)),X188)),X18))),X11)))<=hBOOL(hAPP(hAPP(c_member(tc_fun(X12,tc_HOL_Obool)),X188),hAPP(hAPP(c_Equiv__Relations_Oquotient(X12),X152),X151)))))<=c_Equiv__Relations_Ocongruent2(X5,X12,tc_fun(X62,tc_HOL_Obool),X153,X151,X18))<=c_Equiv__Relations_Oequiv(X12,X152,X151))<=c_Equiv__Relations_Oequiv(X5,X154,X153)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__equiv__class__type2)). 6.97/7.19 fof(fact_coinduct3__mono__lemma, axiom, ![X11, X56, X18, X12, X5]:(class_Orderings_Oorder(X5)=>(c_Orderings_Oorder__class_Omono(X5,tc_fun(X12,tc_HOL_Obool),X18)=>c_Orderings_Oorder__class_Omono(X5,tc_fun(X12,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X5,tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool))),X18)),X56))),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_coinduct3__mono__lemma)). 6.97/7.19 fof(fact_setsum__Sigma, axiom, ![X18, X11, X12, X4, X5, X62]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X12),hAPP(X11,X22))))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X5,X12),X62),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X12,X62),X18)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X4),X11))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X62),hAPP(hAPP(c_COMBS(X5,tc_fun(X12,tc_HOL_Obool),X62),hAPP(hAPP(c_COMBB(tc_fun(X12,X62),tc_fun(tc_fun(X12,tc_HOL_Obool),X62),X5),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X62)),X18)),X11)),X4)))<=class_Groups_Ocomm__monoid__add(X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__Sigma)). 6.97/7.19 fof(fact_fold__image__UN__disjoint, axiom, ![X50, X4, X12, X15, X5, X62]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X15))=>(![X22]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X12),hAPP(X4,X22)))<=hBOOL(hAPP(hAPP(c_member(X5),X22),X15)))=>(![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X15))=>![X115]:(hBOOL(hAPP(hAPP(c_member(X5),X115),X15))=>(c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),hAPP(X4,X22)),hAPP(X4,X115))<=X22!=X115)))=>hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X62,X12,c_Groups_Otimes__class_Otimes(X62)),X50),c_Groups_Oone__class_Oone(X62)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X15),X4))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X62,X5,c_Groups_Otimes__class_Otimes(X62)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),X62,X5),hAPP(hAPP(c_Finite__Set_Ofold__image(X62,X12,c_Groups_Otimes__class_Otimes(X62)),X50),c_Groups_Oone__class_Oone(X62))),X4)),c_Groups_Oone__class_Oone(X62)),X15))))<=class_Groups_Ocomm__monoid__mult(X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__UN__disjoint)). 6.97/7.19 fof(fact_fold__image__Un__Int, axiom, ![X50, X11, X4, X5, X12]:(((hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X12,X5,c_Groups_Otimes__class_Otimes(X12)),X50),c_Groups_Oone__class_Oone(X12)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X12,X5,c_Groups_Otimes__class_Otimes(X12)),X50),c_Groups_Oone__class_Oone(X12)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X12,X5,c_Groups_Otimes__class_Otimes(X12)),X50),c_Groups_Oone__class_Oone(X12)),X4)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X12,X5,c_Groups_Otimes__class_Otimes(X12)),X50),c_Groups_Oone__class_Oone(X12)),X11))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Groups_Ocomm__monoid__mult(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__Un__Int)). 6.97/7.19 fof(fact_fold__image__Un__one, axiom, ![X18, X108, X44, X5, X12]:((((![X22]:(hAPP(X18,X22)=c_Groups_Oone__class_Oone(X12)<=hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X44),X108))))=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X12,X5,c_Groups_Otimes__class_Otimes(X12)),X18),c_Groups_Oone__class_Oone(X12)),X44)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X12,X5,c_Groups_Otimes__class_Otimes(X12)),X18),c_Groups_Oone__class_Oone(X12)),X108))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X12,X5,c_Groups_Otimes__class_Otimes(X12)),X18),c_Groups_Oone__class_Oone(X12)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X44),X108)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X108)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X44)))<=class_Groups_Ocomm__monoid__mult(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__Un__one)). 6.97/7.19 fof(fact_setprod__Un, axiom, ![X18, X11, X4, X5, X12]:(class_Fields_Ofield(X12)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X18),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X18),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X18),X11))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X18),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)))<=![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)))=>hAPP(X18,X22)!=c_Groups_Ozero__class_Ozero(X12)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__Un)). 6.97/7.19 fof(fact_fold__image__distrib, axiom, ![X71, X50, X4, X5, X12]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X12,X5,c_Groups_Otimes__class_Otimes(X12)),hAPP(hAPP(c_COMBS(X5,X12,X12),hAPP(hAPP(c_COMBB(X12,tc_fun(X12,X12),X5),c_Groups_Otimes__class_Otimes(X12)),X50)),X71)),c_Groups_Oone__class_Oone(X12)),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X12,X5,c_Groups_Otimes__class_Otimes(X12)),X50),c_Groups_Oone__class_Oone(X12)),X4)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X12,X5,c_Groups_Otimes__class_Otimes(X12)),X71),c_Groups_Oone__class_Oone(X12)),X4)))<=class_Groups_Ocomm__monoid__mult(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__distrib)). 6.97/7.19 fof(fact_max__ext__additive, axiom, ![X73, X65, X67, X11, X4, X5]:((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X65),X73)),c_Wellfounded_Omax__ext(X5,X67)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X65)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X73))),c_Wellfounded_Omax__ext(X5,X67))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X4),X11)),c_Wellfounded_Omax__ext(X5,X67)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__ext__additive)). 6.97/7.19 fof(fact_setprod__cartesian__product, axiom, ![X4, X11, X18, X62, X12, X5]:(class_Groups_Ocomm__monoid__mult(X5)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12,X5),hAPP(hAPP(c_COMBC(X12,tc_fun(X62,tc_HOL_Obool),X5),hAPP(hAPP(c_COMBB(tc_fun(X62,X5),tc_fun(tc_fun(X62,tc_HOL_Obool),X5),X12),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X62,X5)),X18)),X11)),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X12,X62),X5),hAPP(c_Product__Type_Oprod_Oprod__case(X12,X62,X5),X18)),hAPP(hAPP(c_Product__Type_OSigma(X12,X62),X4),hAPP(c_COMBK(tc_fun(X62,tc_HOL_Obool),X12),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__cartesian__product)). 6.97/7.19 fof(fact_setsum__cartesian__product, axiom, ![X4, X11, X18, X62, X12, X5]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X12,X62),X5),hAPP(c_Product__Type_Oprod_Oprod__case(X12,X62,X5),X18)),hAPP(hAPP(c_Product__Type_OSigma(X12,X62),X4),hAPP(c_COMBK(tc_fun(X62,tc_HOL_Obool),X12),X11)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5),hAPP(hAPP(c_COMBC(X12,tc_fun(X62,tc_HOL_Obool),X5),hAPP(hAPP(c_COMBB(tc_fun(X62,X5),tc_fun(tc_fun(X62,tc_HOL_Obool),X5),X12),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X62,X5)),X18)),X11)),X4)<=class_Groups_Ocomm__monoid__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__cartesian__product)). 6.97/7.19 fof(fact_reduction__pair__def, axiom, ![X17, X5]:(c_FunDef_Oreduction__pair(X5,X17)<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X17)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X17))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X17)))&c_Wellfounded_Owf(X5,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_reduction__pair__def)). 6.97/7.19 fof(fact_setprod__Sigma, axiom, ![X18, X11, X12, X4, X5, X62]:(class_Groups_Ocomm__monoid__mult(X62)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X5,X12),X62),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X12,X62),X18)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X4),X11))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X62),hAPP(hAPP(c_COMBS(X5,tc_fun(X12,tc_HOL_Obool),X62),hAPP(hAPP(c_COMBB(tc_fun(X12,X62),tc_fun(tc_fun(X12,tc_HOL_Obool),X62),X5),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12,X62)),X18)),X11)),X4)<=![X22]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X12),hAPP(X11,X22)))<=hBOOL(hAPP(hAPP(c_member(X5),X22),X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__Sigma)). 6.97/7.19 fof(fact_congruent__def, axiom, ![X18, X3, X12, X5]:(![X22]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X22),X3))=>hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X12),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(tc_fun(X5,X12),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X12,tc_HOL_Obool,X5)),hAPP(hAPP(c_COMBB(X12,tc_fun(X12,tc_HOL_Obool),X5),c_fequal),X18))),X18)),X22)))<=>c_Equiv__Relations_Ocongruent(X5,X12,X3,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_congruent__def)). 6.97/7.19 fof(fact_lexord__append__leftD, axiom, ![X3, X60, X51, X35, X5]:(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),X35),X51)),hAPP(hAPP(c_List_Oappend(X5),X35),X60))),c_List_Olexord(X5,X3)))=>(![X13]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X13),X13)),X3)))=>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)),X51),X60)),c_List_Olexord(X5,X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__append__leftD)). 6.97/7.19 fof(fact_rel__comp__subset__Sigma, axiom, ![X65, X66, X62, X11, X4, X3, X12, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X12,X62),tc_HOL_Obool)),X66),hAPP(hAPP(c_Product__Type_OSigma(X12,X62),X11),hAPP(c_COMBK(tc_fun(X62,tc_HOL_Obool),X12),X65))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X62),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X12,X62),X3),X66)),hAPP(hAPP(c_Product__Type_OSigma(X5,X62),X4),hAPP(c_COMBK(tc_fun(X62,tc_HOL_Obool),X5),X65)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X4),hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X5),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__comp__subset__Sigma)). 6.97/7.19 fof(fact_divmod__nat__rel__mult1__eq, axiom, ![X30, X70, X53, X31, X29]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X31))=>hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X29),X31),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),X30),X53)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X70)),X31))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X70),X31)))))<=hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X29,X31),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X53),X70)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__rel__mult1__eq)). 6.97/7.19 fof(fact_setsum__commute, axiom, ![X4, X11, X18, X62, X12, X5]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X62,X5),hAPP(hAPP(c_COMBC(X62,tc_fun(X12,tc_HOL_Obool),X5),hAPP(hAPP(c_COMBB(tc_fun(X12,X5),tc_fun(tc_fun(X12,tc_HOL_Obool),X5),X62),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5)),hAPP(c_COMBC(X12,X62,X5),X18))),X4)),X11)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5),hAPP(hAPP(c_COMBC(X12,tc_fun(X62,tc_HOL_Obool),X5),hAPP(hAPP(c_COMBB(tc_fun(X62,X5),tc_fun(tc_fun(X62,tc_HOL_Obool),X5),X12),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X62,X5)),X18)),X11)),X4)<=class_Groups_Ocomm__monoid__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__commute)). 6.97/7.19 fof(fact_transpose__column, axiom, ![X47, X23, X5]:((hAPP(hAPP(c_List_Onth(tc_List_Olist(X5)),X23),X47)=hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),X5),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_Nat_Onat,X5),c_List_Onth(X5)),X47)),hAPP(c_List_Ofilter(tc_List_Olist(X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X5)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X47)),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),c_List_Otranspose(X5,X23)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X47),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X23))))<=c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X5))),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__column)). 6.97/7.19 fof(fact_single__valued__confluent, axiom, ![X14, X38, X35, X3, X5]:(c_Relation_Osingle__valued(X5,X5,X3)=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),c_Transitive__Closure_Ortrancl(X5,X3)))=>((hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X38),X14)),c_Transitive__Closure_Ortrancl(X5,X3)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X14),X38)),c_Transitive__Closure_Ortrancl(X5,X3))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X14)),c_Transitive__Closure_Ortrancl(X5,X3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_single__valued__confluent)). 6.97/7.19 fof(fact_nth__nth__transpose__sorted, axiom, ![X46, X47, X23, X5]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),hAPP(c_List_Ofilter(tc_List_Olist(X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X5)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X47)),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),X23))))=>hAPP(hAPP(c_List_Onth(X5),hAPP(hAPP(c_List_Onth(tc_List_Olist(X5)),X23),X46)),X47)=hAPP(hAPP(c_List_Onth(X5),hAPP(hAPP(c_List_Onth(tc_List_Olist(X5)),c_List_Otranspose(X5,X23)),X47)),X46))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X47),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),c_List_Otranspose(X5,X23)))))<=c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X5))),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__nth__transpose__sorted)). 6.97/7.19 fof(fact_zmult1__lemma, axiom, ![X30, X70, X53, X31, X29]:(hBOOL(hAPP(c_Divides_Odivmod__int__rel(X29,X31),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X53),X70)))=>(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X31=>hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X29),X31),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),X30),X53)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X70)),X31))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X70),X31)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult1__lemma)). 6.97/7.19 fof(fact_image__eq__fold__image, axiom, ![X18, X12, X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hAPP(c_Set_Oimage(X5,X12,X18),X4)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(X12,tc_HOL_Obool),X5,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X5,tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X12,tc_fun(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_Set_Oinsert(X12)),X18)),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool))),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__eq__fold__image)). 6.97/7.19 fof(fact_congruent2__implies__congruent__UN, axiom, ![X2, X18, X62, X151, X152, X12, X153, X154, X5]:(c_Equiv__Relations_Oequiv(X5,X154,X153)=>(c_Equiv__Relations_Oequiv(X12,X152,X151)=>((c_Equiv__Relations_Ocongruent(X5,tc_fun(X62,tc_HOL_Obool),X153,hAPP(hAPP(c_COMBB(tc_fun(X12,tc_fun(X62,tc_HOL_Obool)),tc_fun(X62,tc_HOL_Obool),X5),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X62,tc_HOL_Obool)),hAPP(c_Relation_OImage(X12,X12,X151),hAPP(hAPP(c_Set_Oinsert(X12),X2),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool)))))),X18))<=hBOOL(hAPP(hAPP(c_member(X12),X2),X152)))<=c_Equiv__Relations_Ocongruent2(X5,X12,tc_fun(X62,tc_HOL_Obool),X153,X151,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_congruent2__implies__congruent__UN)). 6.97/7.19 fof(fact_listsum__subtractf, axiom, ![X23, X50, X18, X12, X5]:(hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X12,X5),hAPP(hAPP(c_COMBS(X12,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X12),c_Groups_Ominus__class_Ominus(X5)),X18)),X50)),X23))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X12,X5),X18),X23))),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X12,X5),X50),X23)))<=class_Groups_Oab__group__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__subtractf)). 6.97/7.19 fof(fact_listsum__addf, axiom, ![X23, X50, X18, X12, X5]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X12,X5),X18),X23))),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X12,X5),X50),X23)))=hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X12,X5),hAPP(hAPP(c_COMBS(X12,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X12),c_Groups_Oplus__class_Oplus(X5)),X18)),X50)),X23))<=class_Groups_Ocomm__monoid__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__addf)). 6.97/7.19 fof(fact_rtrancl__listrel1__ConsI2, axiom, ![X84, X23, X3, X38, X35, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),c_Transitive__Closure_Ortrancl(X5,X3)))=>(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)),X23),X84)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X3))))=>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),X35),X23)),hAPP(hAPP(c_List_Olist_OCons(X5),X38),X84))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__listrel1__ConsI2)). 6.97/7.19 fof(fact_setsum__Un__zero, axiom, ![X18, X108, X44, X5, X12]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X44))=>((![X22]:(c_Groups_Ozero__class_Ozero(X12)=hAPP(X18,X22)<=hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X44),X108))))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),X44)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),X108))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X44),X108)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X108))))<=class_Groups_Ocomm__monoid__add(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__Un__zero)). 6.97/7.19 fof(fact_INT__simps_I1_J, axiom, ![X11, X4, X12, X5, X65]:((X65=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),X65),hAPP(hAPP(c_COMBC(X5,tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool))),X4)),X11))=c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))&(X65!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),X65),hAPP(hAPP(c_COMBC(X5,tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool))),X4)),X11))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),X65),X4)),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__simps_I1_J)). 6.97/7.19 fof(fact_setprod__Un__one, axiom, ![X18, X108, X44, X5, X12]:((((![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X44),X108)))=>c_Groups_Oone__class_Oone(X12)=hAPP(X18,X22))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X18),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X44),X108))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X18),X44)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X18),X108)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X108)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X44)))<=class_Groups_Ocomm__monoid__mult(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__Un__one)). 6.97/7.19 fof(fact_setprod_Ounion__inter__neutral, axiom, ![X50, X11, X4, X5, X12]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X50),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X50),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X50),X11))<=![X22]:(c_Groups_Oone__class_Oone(X12)=hAPP(X50,X22)<=hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Groups_Ocomm__monoid__mult(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod_Ounion__inter__neutral)). 6.97/7.19 fof(fact_setsum_Ounion__inter__neutral, axiom, ![X50, X11, X4, X5, X12]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X50),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X50),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X50),X11))<=![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)))=>c_Groups_Ozero__class_Ozero(X12)=hAPP(X50,X22))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Groups_Ocomm__monoid__add(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum_Ounion__inter__neutral)). 6.97/7.19 fof(fact_image__INT, axiom, ![X46, X11, X4, X62, X65, X18, X12, X5]:((![X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(X11,X22)),X65))<=hBOOL(hAPP(hAPP(c_member(X62),X22),X4)))=>(hAPP(c_Set_Oimage(X5,X12,X18),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X62,tc_fun(X5,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X62,tc_fun(X12,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool),X62),c_Set_Oimage(X5,X12,X18)),X11))<=hBOOL(hAPP(hAPP(c_member(X62),X46),X4))))<=c_Fun_Oinj__on(X5,X12,X18,X65)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__INT)). 6.97/7.19 fof(fact_INT__extend__simps_I3_J, axiom, ![X11, X4, X12, X5, X65]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),X65),X4)),X11)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),X65),hAPP(hAPP(c_COMBC(X5,tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_Groups_Ominus__class_Ominus(tc_fun(X12,tc_HOL_Obool))),X4)),X11))<=X65!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))),X11)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),X65),X4)),X11)<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=X65)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__extend__simps_I3_J)). 6.97/7.19 fof(fact_rtrancl__Un__separatorE, axiom, ![X104, X17, X1, X2, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X17),X104))))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),c_Transitive__Closure_Ortrancl(X5,X17)))<=![X22]:(![X72]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X22),X72)),X104))=>X22=X72)<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X22)),c_Transitive__Closure_Ortrancl(X5,X17)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__Un__separatorE)). 6.97/7.19 fof(fact_rtrancl__Un__separator__converseE, axiom, ![X104, X17, X1, X2, X5]:((![X22]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X22),X1)),c_Transitive__Closure_Ortrancl(X5,X17)))=>![X72]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X72),X22)),X104))=>X72=X22))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),c_Transitive__Closure_Ortrancl(X5,X17))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X17),X104))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__Un__separator__converseE)). 6.97/7.19 fof(fact_setsum__UNION__zero, axiom, ![X18, X44, X5, X12]:(class_Groups_Ocomm__monoid__add(X12)=>(((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X44))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X5,tc_HOL_Obool),X12),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18)),X44)<=![X262]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X262),X44))=>![X263]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X263),X44))=>(![X22]:((c_Groups_Ozero__class_Ozero(X12)=hAPP(X18,X22)<=hBOOL(hAPP(hAPP(c_member(X5),X22),X263)))<=hBOOL(hAPP(hAPP(c_member(X5),X22),X262)))<=X263!=X262))))<=![X22]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22))<=hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X22),X44))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,tc_HOL_Obool)),X44)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__UNION__zero)). 6.97/7.19 fof(fact_snoc__listrel1__snoc__iff, axiom, ![X3, X38, X84, X35, X23, X5]:(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),X23),hAPP(hAPP(c_List_Olist_OCons(X5),X35),c_List_Olist_ONil(X5)))),hAPP(hAPP(c_List_Oappend(X5),X84),hAPP(hAPP(c_List_Olist_OCons(X5),X38),c_List_Olist_ONil(X5))))),c_List_Olistrel1(X5,X3)))<=>((hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),X3))&X23=X84)|(X38=X35&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)),X23),X84)),c_List_Olistrel1(X5,X3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_snoc__listrel1__snoc__iff)). 6.97/7.19 fof(fact_setsum__Un, axiom, ![X18, X11, X4, X5, X12]:(class_Groups_Oab__group__add(X12)=>((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),X11))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__Un)). 6.97/7.19 fof(fact_setsum__Un__nat, axiom, ![X18, X11, X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X18),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))=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(X5,tc_Nat_Onat),X18),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X18),X11))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X18),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__Un__nat)). 6.97/7.19 fof(fact_setsum__Un__Int, axiom, ![X50, X11, X4, X5, X12]:(class_Groups_Ocomm__monoid__add(X12)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X50),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X50),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X50),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X50),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__Un__Int)). 6.97/7.19 fof(fact_setprod__Un__Int, axiom, ![X50, X11, X4, X5, X12]:(((hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X50),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X50),X11))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X50),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X50),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Groups_Ocomm__monoid__mult(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__Un__Int)). 6.97/7.19 fof(fact_min__max_OSup__fin_Ounion__inter, axiom, ![X11, X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>((hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X4)),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X11))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)))<=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Ounion__inter)). 6.97/7.19 fof(fact_folding__image__simple_Ounion__inter__neutral, axiom, ![X11, X4, X55, X50, X14, X18, X12, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X4))=>((hAPP(X55,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(X18,hAPP(X55,X4)),hAPP(X55,X11))<=![X22]:(hAPP(X50,X22)=X14<=hBOOL(hAPP(hAPP(c_member(X12),X22),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),X4),X11)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X11))))<=c_Finite__Set_Ofolding__image__simple(X5,X12,X18,X14,X50,X55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple_Ounion__inter__neutral)). 6.97/7.19 fof(fact_fold__Un__disjoint, axiom, ![X50, X11, X4, X5, X12]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))=>(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X12,X5,c_Groups_Otimes__class_Otimes(X12)),X50),c_Groups_Oone__class_Oone(X12)),X4)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X12,X5,c_Groups_Otimes__class_Otimes(X12)),X50),c_Groups_Oone__class_Oone(X12)),X11))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X12,X5,c_Groups_Otimes__class_Otimes(X12)),X50),c_Groups_Oone__class_Oone(X12)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))<=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Groups_Ocomm__monoid__mult(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__Un__disjoint)). 6.97/7.19 fof(fact_min__max_OInf__fin_Ounion__inter, axiom, ![X11, X4, X5]:(class_Orderings_Olinorder(X5)=>(((hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X4)),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X11))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Ounion__inter)). 6.97/7.19 fof(fact_max__ext_Ointros, axiom, ![X67, X95, X56, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X56))=>((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X95=>(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X56),X95)),c_Wellfounded_Omax__ext(X5,X67)))<=![X22]:(?[X115]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X22),X115)),X67))&hBOOL(hAPP(hAPP(c_member(X5),X115),X95)))<=hBOOL(hAPP(hAPP(c_member(X5),X22),X56)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X95)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__ext_Ointros)). 6.97/7.19 fof(fact_lexord__append__left__rightI, axiom, ![X38, X35, X51, X3, X1, X2, X5]:(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),X51),hAPP(hAPP(c_List_Olist_OCons(X5),X2),X35))),hAPP(hAPP(c_List_Oappend(X5),X51),hAPP(hAPP(c_List_Olist_OCons(X5),X1),X38)))),c_List_Olexord(X5,X3)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__append__left__rightI)). 6.97/7.19 fof(fact_divmod__nat__rel__mult2__eq, axiom, ![X31, X70, X53, X29, X30]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X31))=>hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X30,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X31)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X53),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X53,X31))),X70)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29)))<=hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X30,X29),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X53),X70)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__rel__mult2__eq)). 6.97/7.19 fof(fact_nth__transpose, axiom, ![X23, X5, X47]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X47),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),c_List_Otranspose(X5,X23))))=>hAPP(hAPP(c_List_Onth(tc_List_Olist(X5)),c_List_Otranspose(X5,X23)),X47)=hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),X5),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_Nat_Onat,X5),c_List_Onth(X5)),X47)),hAPP(c_List_Ofilter(tc_List_Olist(X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X5)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X47)),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__transpose)). 6.97/7.19 fof(fact_setsum__shift__bounds__nat__ivl, axiom, ![X32, X33, X34, X18, X5]:(class_Groups_Ocomm__monoid__add(X5)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Nat_Onat),X18),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X33))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34),X32))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34),X33)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X33)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__shift__bounds__nat__ivl)). 6.97/7.19 fof(fact_same__fstI, axiom, ![X5, X67, X38, X256, X12, X35, X17]:(hBOOL(hAPP(X17,X35))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X12,X12)),hAPP(hAPP(c_Product__Type_OPair(X12,X12),X256),X38)),hAPP(X67,X35)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X12),tc_prod(X5,X12))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X12),tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X35),X256)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X35),X38))),c_Recdef_Osame__fst(X5,X12,X17,X67))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_same__fstI)). 6.97/7.19 fof(fact_rel__pow__Suc__I2, axiom, ![X32, X14, X67, X38, X35, X5]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X38),X14)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X32),X67)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X14)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X32)),X67))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),X67))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__Suc__I2)). 6.97/7.19 fof(fact_lexord__linear, axiom, ![X38, X35, X3, X5]:((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)),X35),X38)),c_List_Olexord(X5,X3)))|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)),X38),X35)),c_List_Olexord(X5,X3)))|X38=X35)<=![X13, X96]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X13),X96)),X3))|X13=X96|hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X96),X13)),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__linear)). 6.97/7.19 fof(fact_rel__pow__Suc__I, axiom, ![X14, X67, X32, X38, X35, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X32),X67)))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X14)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X32)),X67)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X38),X14)),X67)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__Suc__I)). 6.97/7.19 fof(fact_abs__diff__triangle__ineq, axiom, ![X74, X31, X29, X30, X8]:(class_Groups_Oordered__ab__group__add__abs(X8)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X31),X74)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X30),X31))),hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X29),X74)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__diff__triangle__ineq)). 6.97/7.19 fof(fact_lexord__trans, axiom, ![X14, X3, X38, X35, X5]:(((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)),X35),X14)),c_List_Olexord(X5,X3)))<=c_Relation_Otrans(X5,X3))<=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)),X38),X14)),c_List_Olexord(X5,X3))))<=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)),X35),X38)),c_List_Olexord(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__trans)). 6.97/7.19 fof(fact_listrel_OCons, axiom, ![X84, X23, X3, X38, X35, X5]:((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),X35),X23)),hAPP(hAPP(c_List_Olist_OCons(X5),X38),X84))),c_List_Olistrel(X5,X3)))<=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)),X23),X84)),c_List_Olistrel(X5,X3))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel_OCons)). 6.97/7.19 fof(fact_min__max_OInf__fin_Oremove, axiom, ![X35, X4, X5]:(class_Orderings_Olinorder(X5)=>((((hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X35),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))=c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X4)<=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))&(X35=c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X4)<=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))<=hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Oremove)). 6.97/7.19 fof(fact_zmult2__lemma, axiom, ![X31, X70, X53, X29, X30]:(((hBOOL(hAPP(c_Divides_Odivmod__int__rel(X30,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X29),X31)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X53),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X29),c_Divides_Odiv__class_Omod(tc_Int_Oint,X53,X31))),X70))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X31)))<=X29!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))<=hBOOL(hAPP(c_Divides_Odivmod__int__rel(X30,X29),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X53),X70)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult2__lemma)). 6.97/7.19 fof(fact_setsum__mono3, axiom, ![X18, X4, X11, X5, X12]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),X11)))<=![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),c_Groups_Ozero__class_Ozero(X12)),hAPP(X18,X22)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))))<=(class_Groups_Oordered__ab__semigroup__add(X12)&class_Groups_Ocomm__monoid__add(X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__mono3)). 6.97/7.19 fof(fact_min__max_OSup__fin_Oremove, axiom, ![X35, X4, X5]:(class_Orderings_Olinorder(X5)=>((((c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X4)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X35),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))&(c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X4)=X35<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))<=hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Oremove)). 6.97/7.19 fof(fact_setsum__shift__bounds__cl__nat__ivl, axiom, ![X32, X33, X34, X18, X5]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Nat_Onat),X18),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X33))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X34,X32))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34),X33),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X33)))<=class_Groups_Ocomm__monoid__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__shift__bounds__cl__nat__ivl)). 6.97/7.19 fof(fact_transpose__column__length, axiom, ![X47, X23, X5]:((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),hAPP(c_List_Ofilter(tc_List_Olist(X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X5)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X47)),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),c_List_Otranspose(X5,X23)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X5)),X23),X47))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X47),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X23))))<=c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X5))),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__column__length)). 6.97/7.19 fof(fact_foldl__apply, axiom, ![X66, X50, X71, X18, X12, X62, X23, X5]:(![X22]:(hAPP(c_Fun_Ocomp(X12,X62,X12,X71),hAPP(X50,X22))=hAPP(c_Fun_Ocomp(X62,X62,X12,hAPP(X18,X22)),X71)<=hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X23))))=>hAPP(c_List_Ofoldl(X62,X5,hAPP(c_COMBC(X5,X62,X62),X18),hAPP(X71,X66)),X23)=hAPP(X71,hAPP(c_List_Ofoldl(X12,X5,hAPP(c_COMBC(X5,X12,X12),X50),X66),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__apply)). 6.97/7.19 fof(fact_setsum__mono2, axiom, ![X18, X4, X11, X5, X12]:(class_Groups_Oordered__comm__monoid__add(X12)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),X11)))<=![X96]:(hBOOL(hAPP(hAPP(c_member(X5),X96),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),c_Groups_Ozero__class_Ozero(X12)),hAPP(X18,X96)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__mono2)). 6.97/7.19 fof(fact_min__max_OSup__fin_Oinsert__remove, axiom, ![X35, X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>((c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))=X35<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))&(c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X35),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))<=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Oinsert__remove)). 6.97/7.19 fof(fact_setprod__dividef, axiom, ![X50, X18, X4, X5, X12]:(class_Fields_Ofield__inverse__zero(X12)=>(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X18),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X50),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),hAPP(hAPP(c_COMBS(X5,X12,X12),hAPP(hAPP(c_COMBB(X12,tc_fun(X12,X12),X5),c_Rings_Oinverse__class_Odivide(X12)),X18)),X50)),X4)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__dividef)). 6.97/7.19 fof(fact_min__max_OInf__fin_Oinsert__remove, axiom, ![X35, X4, X5]:(class_Orderings_Olinorder(X5)=>(((c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X35),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))<=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))&(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))=>c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))=X35))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Oinsert__remove)). 6.97/7.19 fof(fact_rtrancl__listrel1__ConsI1, axiom, ![X35, X3, X84, X23, X5]:(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)),X23),X84)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X3))))=>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),X35),X23)),hAPP(hAPP(c_List_Olist_OCons(X5),X35),X84))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__listrel1__ConsI1)). 6.97/7.19 fof(fact_folding__one_Oremove, axiom, ![X35, X4, X55, X18, X5]:(((((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))=>hAPP(hAPP(X18,X35),hAPP(X55,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))=hAPP(X55,X4))&(hAPP(X55,X4)=X35<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))<=hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=c_Finite__Set_Ofolding__one(X5,X18,X55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one_Oremove)). 6.97/7.19 fof(fact_equiv__class__subset, axiom, ![X1, X2, X3, X4, X5]:(c_Equiv__Relations_Oequiv(X5,X4,X3)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X3),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X5,X5,X3),hAPP(hAPP(c_Set_Oinsert(X5),X1),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__class__subset)). 6.97/7.19 fof(fact_rel__pow__E2, axiom, ![X67, X32, X14, X35, X5]:((~(![X72, X21]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X72)),X67))=>~(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X72),X14)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X21),X67)))))<=X32=hAPP(c_Nat_OSuc,X21)))<=(X32=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>X14!=X35))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X14)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X32),X67)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__E2)). 6.97/7.19 fof(fact_rel__pow__E, axiom, ![X67, X32, X14, X35, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X14)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X32),X67)))=>((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X32=>X35!=X14)=>~(![X72, X21]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X72)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X21),X67)))=>~(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X72),X14)),X67))))<=hAPP(c_Nat_OSuc,X21)=X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__E)). 6.97/7.19 fof(fact_smax__emptyI, axiom, ![X95]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X95))=>(X95!=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))),X95)),c_FunDef_Omax__strict)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_smax__emptyI)). 6.97/7.19 fof(fact_card__quotient__disjoint, axiom, ![X3, X4, X5]:((hAPP(c_Finite__Set_Ocard(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X4),X3))=hAPP(c_Finite__Set_Ocard(X5),X4)<=c_Fun_Oinj__on(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X5),c_Equiv__Relations_Oquotient(X5)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_Oinsert(X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X3),X4))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__quotient__disjoint)). 6.97/7.19 fof(fact_zdiv__mono2__neg__lemma, axiom, ![X100, X101, X68, X70, X53, X29]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X68),X101)),X100)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X29),X53)),X70)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X70),X29))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X100))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X68))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X68),X29))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X101),X53))))))<=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),X68),X101)),X100)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__mono2__neg__lemma)). 6.97/7.19 fof(fact_zdiv__mono2__lemma, axiom, ![X100, X101, X68, X70, X53, X29]:(((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X68))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X53),X101))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X68),X29))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X70)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X100),X68)))<=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),X68),X101)),X100))))<=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X68),X101)),X100)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X29),X53)),X70)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__mono2__lemma)). 6.97/7.19 fof(fact_folding__one_Oinsert__remove, axiom, ![X35, X4, X55, X18, X5]:(c_Finite__Set_Ofolding__one(X5,X18,X55)=>(((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))=>X35=hAPP(X55,hAPP(hAPP(c_Set_Oinsert(X5),X35),X4)))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>hAPP(hAPP(X18,X35),hAPP(X55,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))=hAPP(X55,hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one_Oinsert__remove)). 6.97/7.19 fof(fact_Times__subset__cancel2, axiom, ![X11, X4, X12, X65, X35, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X12,X5),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X12,X5),X4),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X12),X65))),hAPP(hAPP(c_Product__Type_OSigma(X12,X5),X11),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X12),X65))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),X4),X11)))<=hBOOL(hAPP(hAPP(c_member(X5),X35),X65))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Times__subset__cancel2)). 6.97/7.19 fof(fact_Max_Oremove, axiom, ![X35, X4, X5]:(class_Orderings_Olinorder(X5)=>((((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X35),c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))=c_Big__Operators_Olinorder__class_OMax(X5,X4))&(X35=c_Big__Operators_Olinorder__class_OMax(X5,X4)<=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))<=hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max_Oremove)). 6.97/7.19 fof(fact_fold__graph__permute__diff, axiom, ![X2, X35, X4, X1, X5]:((hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,c_Groups_Otimes__class_Otimes(X5),X1,X4),X35))=>(hBOOL(hAPP(hAPP(c_member(X5),X2),X4))=>(~(hBOOL(hAPP(hAPP(c_member(X5),X1),X4)))=>hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,c_Groups_Otimes__class_Otimes(X5),X2,hAPP(hAPP(c_Set_Oinsert(X5),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),X35)))))<=class_Groups_Oab__semigroup__mult(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__graph__permute__diff)). 6.97/7.19 fof(fact_Min_Ounion__inter, axiom, ![X11, X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))=>(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))),c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olinorder__class_OMin(X5,X4)),c_Big__Operators_Olinorder__class_OMin(X5,X11)))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min_Ounion__inter)). 6.97/7.19 fof(fact_Inf__fin_Ounion__inter, axiom, ![X11, X4, X5]:(class_Lattices_Olattice(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>((hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))),c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Big__Operators_Olattice__class_OInf__fin(X5,X4)),c_Big__Operators_Olattice__class_OInf__fin(X5,X11)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Ounion__inter)). 6.97/7.19 fof(fact_Sup__fin_Ounion__inter, axiom, ![X11, X4, X5]:((((hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),c_Big__Operators_Olattice__class_OSup__fin(X5,X4)),c_Big__Operators_Olattice__class_OSup__fin(X5,X11))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))),c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Lattices_Olattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Ounion__inter)). 6.97/7.19 fof(fact_Max_Ounion__inter, axiom, ![X11, X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)=>hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))),c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olinorder__class_OMax(X5,X4)),c_Big__Operators_Olinorder__class_OMax(X5,X11)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max_Ounion__inter)). 6.97/7.19 fof(fact_fold__graph_H_Oequations_I2_J, axiom, ![X196, X103, X125, X148, X102, X12, X5]:(c_Nitpick_Ofold__graph_H(X5,X12,X102,X148,X125,hAPP(hAPP(X102,X103),X196))<=>(?[X22, X72]:((hBOOL(hAPP(hAPP(c_member(X5),X22),X125))&c_Nitpick_Ofold__graph_H(X5,X12,X102,X148,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X125),hAPP(hAPP(c_Set_Oinsert(X5),X22),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X72))&hAPP(hAPP(X102,X103),X196)=hAPP(hAPP(X102,X22),X72))|(X148=hAPP(hAPP(X102,X103),X196)&X125=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__graph_H_Oequations_I2_J)). 6.97/7.19 fof(fact_nat__diff__add__eq1, axiom, ![X25, X36, X139, X28, X27]:(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),X28),X139)),X36)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),X139)),X25))=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),X28),X27)),X139)),X36)),X25)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X27),X28))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__diff__add__eq1)). 6.97/7.19 fof(fact_nat__diff__add__eq2, axiom, ![X25, X36, X139, X27, X28]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),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),X27),X28)),X139)),X25))=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),X28),X139)),X36)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),X139)),X25))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28),X27))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__diff__add__eq2)). 6.97/7.19 fof(fact_card__Diff__insert, axiom, ![X11, X2, X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>((~(hBOOL(hAPP(hAPP(c_member(X5),X2),X11)))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11))),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X2),X11))))<=hBOOL(hAPP(hAPP(c_member(X5),X2),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Diff__insert)). 6.97/7.19 fof(fact_folding__one_Ounion__inter, axiom, ![X11, X4, X55, X18, X5]:(c_Finite__Set_Ofolding__one(X5,X18,X55)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))=>(hAPP(hAPP(X18,hAPP(X55,X4)),hAPP(X55,X11))=hAPP(hAPP(X18,hAPP(X55,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))),hAPP(X55,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)))<=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one_Ounion__inter)). 6.97/7.19 fof(fact_setsum__addf, axiom, ![X4, X50, X18, X12, X5]:(class_Groups_Ocomm__monoid__add(X5)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5),hAPP(hAPP(c_COMBS(X12,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X12),c_Groups_Oplus__class_Oplus(X5)),X18)),X50)),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5),X18),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5),X50),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__addf)). 6.97/7.19 fof(fact_Inf__fin_Oremove, axiom, ![X35, X4, X5]:(class_Lattices_Olattice(X5)=>((((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X35),c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))=c_Big__Operators_Olattice__class_OInf__fin(X5,X4))&(X35=c_Big__Operators_Olattice__class_OInf__fin(X5,X4)<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))<=hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Oremove)). 6.97/7.19 fof(fact_UN__mono, axiom, ![X50, X18, X12, X11, X4, X5]:((![X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),hAPP(X18,X22)),hAPP(X50,X22)))<=hBOOL(hAPP(hAPP(c_member(X5),X22),X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X4),X18)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X11),X50))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__mono)). 6.97/7.19 fof(fact_INT__anti__mono, axiom, ![X50, X18, X12, X4, X11, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X4))=>(![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),hAPP(X18,X22)),hAPP(X50,X22))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),X4),X18)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),X4),X50))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__anti__mono)). 6.97/7.19 fof(fact_INF__INT__eq, axiom, ![X35, X3, X12, X5]:(hBOOL(hAPP(hAPP(c_member(X12),X35),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X3)))<=>hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool),X5),hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12))),X3)),X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF__INT__eq)). 6.97/7.19 fof(fact_setsum__subtractf, axiom, ![X4, X50, X18, X12, X5]:(class_Groups_Oab__group__add(X5)=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5),X18),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5),X50),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5),hAPP(hAPP(c_COMBS(X12,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X12),c_Groups_Ominus__class_Ominus(X5)),X18)),X50)),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__subtractf)). 6.97/7.19 fof(fact_Cons__listrel1__Cons, axiom, ![X3, X84, X38, X23, X35, X5]:(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),X35),X23)),hAPP(hAPP(c_List_Olist_OCons(X5),X38),X84))),c_List_Olistrel1(X5,X3)))<=>((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)),X23),X84)),c_List_Olistrel1(X5,X3)))&X35=X38)|(X84=X23&hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Cons__listrel1__Cons)). 6.97/7.19 fof(fact_setprod__timesf, axiom, ![X4, X50, X18, X12, X5]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12,X5),X18),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12,X5),X50),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12,X5),hAPP(hAPP(c_COMBS(X12,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X12),c_Groups_Otimes__class_Otimes(X5)),X18)),X50)),X4)<=class_Groups_Ocomm__monoid__mult(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__timesf)). 6.97/7.19 fof(fact_Sup__fin_Oremove, axiom, ![X35, X4, X5]:(class_Lattices_Olattice(X5)=>((((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>c_Big__Operators_Olattice__class_OSup__fin(X5,X4)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X35),c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))))&(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))=>X35=c_Big__Operators_Olattice__class_OSup__fin(X5,X4)))<=hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Oremove)). 6.97/7.19 fof(fact_SUP__UN__eq, axiom, ![X35, X3, X12, X5]:(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool),X5),hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12))),X3)),X35))<=>hBOOL(hAPP(hAPP(c_member(X12),X35),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP__UN__eq)). 6.97/7.19 fof(fact_enum__all__prod__def, axiom, ![X17, X5, X12]:((class_Enum_Oenum(X5)&class_Enum_Oenum(X12))=>(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X5),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool,X5),c_Enum_Oenum__class_Oenum__all(X12)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_prod(X5,X12)),tc_fun(X12,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_prod(X5,X12),tc_HOL_Obool,X12),X17)),c_Product__Type_OPair(X5,X12)))))<=>hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X5,X12)),X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__all__prod__def)). 6.97/7.19 fof(fact_enum__ex__prod__def, axiom, ![X17, X5, X12]:((class_Enum_Oenum(X5)&class_Enum_Oenum(X12))=>(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X5),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool,X5),c_Enum_Oenum__class_Oenum__ex(X12)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_prod(X5,X12)),tc_fun(X12,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_prod(X5,X12),tc_HOL_Obool,X12),X17)),c_Product__Type_OPair(X5,X12)))))<=>hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X5,X12)),X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__ex__prod__def)). 6.97/7.19 fof(fact_total__on__def, axiom, ![X3, X4, X5]:(![X22]:(![X115]:((X115!=X22=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X22),X115)),X3))|hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X115),X22)),X3))))<=hBOOL(hAPP(hAPP(c_member(X5),X115),X4)))<=hBOOL(hAPP(hAPP(c_member(X5),X22),X4)))<=>c_Relation_Ototal__on(X5,X4,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_total__on__def)). 6.97/7.19 fof(fact_Min_Oremove, axiom, ![X35, X4, X5]:(class_Orderings_Olinorder(X5)=>((((c_Big__Operators_Olinorder__class_OMin(X5,X4)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X35),c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))&(c_Big__Operators_Olinorder__class_OMin(X5,X4)=X35<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))<=hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min_Oremove)). 6.97/7.19 fof(fact_listsum__mono, axiom, ![X50, X18, X23, X5, X12]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),hAPP(c_List_Omonoid__add__class_Olistsum(X12),hAPP(hAPP(c_List_Omap(X5,X12),X18),X23))),hAPP(c_List_Omonoid__add__class_Olistsum(X12),hAPP(hAPP(c_List_Omap(X5,X12),X50),X23))))<=![X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),hAPP(X18,X22)),hAPP(X50,X22)))<=hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X23)))))<=(class_Groups_Oordered__ab__semigroup__add(X12)&class_Groups_Omonoid__add(X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__mono)). 6.97/7.19 fof(fact_fold__image__insert, axiom, ![X14, X50, X2, X4, X5, X12]:(class_Groups_Oab__semigroup__mult(X12)=>((~(hBOOL(hAPP(hAPP(c_member(X5),X2),X4)))=>hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X12,X5,c_Groups_Otimes__class_Otimes(X12)),X50),X14),hAPP(hAPP(c_Set_Oinsert(X5),X2),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12),hAPP(X50,X2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X12,X5,c_Groups_Otimes__class_Otimes(X12)),X50),X14),X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__insert)). 6.97/7.19 fof(fact_pair__lessI2, axiom, ![X82, X66, X1, 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),X66),X82))=>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),X2),X66)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X82))),c_FunDef_Opair__less)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__lessI2)). 6.97/7.19 fof(fact_pair__leqI2, axiom, ![X82, X66, 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)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X66)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X82))),c_FunDef_Opair__leq))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X66),X82)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__leqI2)). 6.97/7.19 fof(fact_listrel__iff__nth, axiom, ![X3, X84, X23, X5]:((![X48]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(hAPP(c_List_Onth(X5),X23),X48)),hAPP(hAPP(c_List_Onth(X5),X84),X48))),X3))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X48),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23))))&hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X84)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23))<=>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)),X23),X84)),c_List_Olistrel(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__iff__nth)). 6.97/7.19 fof(fact_prod__fun__imageE, axiom, ![X67, X50, X18, X92, X62, X10, X12, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X12)),X10),hAPP(c_Set_Oimage(tc_prod(X62,X92),tc_prod(X5,X12),c_Product__Type_Omap__pair(X62,X5,X92,X12,X18,X50)),X67)))=>~(![X22, X72]:(~(hBOOL(hAPP(hAPP(c_member(tc_prod(X62,X92)),hAPP(hAPP(c_Product__Type_OPair(X62,X92),X22),X72)),X67)))<=hAPP(hAPP(c_Product__Type_OPair(X5,X12),hAPP(X18,X22)),hAPP(X50,X72))=X10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_prod__fun__imageE)). 6.97/7.19 fof(fact_folding_Ocommute__left__comp_H_H, axiom, ![X50, X62, X11, X4, X55, X18, X12, X5]:(c_Finite__Set_Ofolding(X5,X12,X18,X55)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hAPP(c_Fun_Ocomp(X12,X12,X62,hAPP(X55,X11)),hAPP(c_Fun_Ocomp(X12,X12,X62,hAPP(X55,X4)),X50))=hAPP(c_Fun_Ocomp(X12,X12,X62,hAPP(X55,X4)),hAPP(c_Fun_Ocomp(X12,X12,X62,hAPP(X55,X11)),X50))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Ocommute__left__comp_H_H)). 6.97/7.19 fof(fact_UN__equiv__class__inject, axiom, ![X95, X56, X18, X12, X3, X4, X5]:(c_Equiv__Relations_Oequiv(X5,X4,X3)=>(((hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X56),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X4),X3)))=>(hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X95),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X4),X3)))=>(![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))=>![X72]:(hBOOL(hAPP(hAPP(c_member(X5),X72),X4))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X22),X72)),X3))<=hAPP(X18,X72)=hAPP(X18,X22))))=>X95=X56)))<=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X56),X18)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X95),X18))<=c_Equiv__Relations_Ocongruent(X5,tc_fun(X12,tc_HOL_Obool),X3,X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__equiv__class__inject)). 6.97/7.19 fof(fact_Min_Oinsert__remove, axiom, ![X35, X4, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))=>X35=c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X35),X4)))&(c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X35),c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))<=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min_Oinsert__remove)). 6.97/7.19 fof(fact_UN__equiv__class__type, axiom, ![X11, X56, X18, X12, X3, X4, X5]:(c_Equiv__Relations_Oequiv(X5,X4,X3)=>(((hBOOL(hAPP(hAPP(c_member(tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X56),X18)),X11))<=![X22]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X12,tc_HOL_Obool)),hAPP(X18,X22)),X11))<=hBOOL(hAPP(hAPP(c_member(X5),X22),X4))))<=hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X56),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X4),X3))))<=c_Equiv__Relations_Ocongruent(X5,tc_fun(X12,tc_HOL_Obool),X3,X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__equiv__class__type)). 6.97/7.19 fof(fact_setsum__reindex__nonzero, axiom, ![X12, X71, X18, X44, X5, X62]:(class_Groups_Ocomm__monoid__add(X62)=>((![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X44))=>![X72]:(hBOOL(hAPP(hAPP(c_member(X5),X72),X44))=>(X22!=X72=>(c_Groups_Ozero__class_Ozero(X62)=hAPP(X71,hAPP(X18,X22))<=hAPP(X18,X22)=hAPP(X18,X72)))))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X62),hAPP(c_Fun_Ocomp(X12,X62,X5,X71),X18)),X44)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X62),X71),hAPP(c_Set_Oimage(X5,X12,X18),X44)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X44)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__reindex__nonzero)). 6.97/7.19 fof(fact_Inf__fin_Oinsert__remove, axiom, ![X35, X4, X5]:(class_Lattices_Olattice(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>((c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))=X35<=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))&(c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X35),c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))<=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Oinsert__remove)). 6.97/7.19 fof(fact_lexord__append__leftI, axiom, ![X35, X3, X60, X51, X5]:(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),X35),X51)),hAPP(hAPP(c_List_Oappend(X5),X35),X60))),c_List_Olexord(X5,X3)))<=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)),X51),X60)),c_List_Olexord(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__append__leftI)). 6.97/7.19 fof(fact_listrel1I2, axiom, ![X35, X3, X84, X23, X5]:(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),X35),X23)),hAPP(hAPP(c_List_Olist_OCons(X5),X35),X84))),c_List_Olistrel1(X5,X3)))<=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)),X23),X84)),c_List_Olistrel1(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1I2)). 6.97/7.19 fof(fact_intrel__iff, axiom, ![X60, X51, X38, X35]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X35),X60)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X51),X38)<=>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),X35),X38)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X51),X60))),c_Int_Ointrel))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_intrel__iff)). 6.97/7.19 fof(fact_Sigma__mono, axiom, ![X73, X11, X12, X65, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X65))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X4),X11)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X65),X73)))<=![X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),hAPP(X11,X22)),hAPP(X73,X22)))<=hBOOL(hAPP(hAPP(c_member(X5),X22),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__mono)). 6.97/7.19 fof(fact_fun__upd__image, axiom, ![X38, X18, X12, X4, X35, X5]:((~(hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))=>hAPP(c_Set_Oimage(X5,X12,c_Fun_Ofun__upd(X5,X12,X18,X35,X38)),X4)=hAPP(c_Set_Oimage(X5,X12,X18),X4))&(hAPP(c_Set_Oimage(X5,X12,c_Fun_Ofun__upd(X5,X12,X18,X35,X38)),X4)=hAPP(hAPP(c_Set_Oinsert(X12),X38),hAPP(c_Set_Oimage(X5,X12,X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))<=hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upd__image)). 6.97/7.19 fof(fact_smin__emptyI, axiom, ![X56]:(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)),X56),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))<=X56!=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_smin__emptyI)). 6.97/7.19 fof(fact_reduction__pair__lemma, axiom, ![X44, X67, X17, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X67),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X17)))=>((c_Wellfounded_Owf(X5,X44)=>c_Wellfounded_Owf(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X67),X44)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X44),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X17)))))<=c_FunDef_Oreduction__pair(X5,X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_reduction__pair__lemma)). 6.97/7.19 fof(fact_list__all2__map2, axiom, ![X159, X18, X62, X160, X17, X12, X5]:(c_List_Olist__all2(X5,X62,hAPP(hAPP(c_COMBC(X5,tc_fun(X62,X12),tc_fun(X62,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(tc_fun(X62,X12),tc_fun(X62,tc_HOL_Obool)),X5),c_COMBB(X12,tc_HOL_Obool,X62)),X17)),X18),X160,X159)<=>c_List_Olist__all2(X5,X12,X17,X160,hAPP(hAPP(c_List_Omap(X62,X12),X18),X159))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__map2)). 6.97/7.19 fof(fact_Max_Oinsert__remove, axiom, ![X35, X4, X5]:((((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))=>c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X35),c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))))&(c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))=X35<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max_Oinsert__remove)). 6.97/7.19 fof(fact_inj__on__Un, axiom, ![X11, X4, X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))<=>((c_Fun_Oinj__on(X5,X12,X18,X11)&c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X12,X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11))),hAPP(c_Set_Oimage(X5,X12,X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X4))))&c_Fun_Oinj__on(X5,X12,X18,X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__Un)). 6.97/7.19 fof(fact_nat__less__add__iff1, axiom, ![X32, X34, X51, X47, X46]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X46),X47))=>(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),X47),X46)),X51)),X34)),X32))<=>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),X47),X51)),X34)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X46),X51)),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__less__add__iff1)). 6.97/7.19 fof(fact_nat__le__add__iff1, axiom, ![X32, X34, X51, X47, X46]:((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),X47),X51)),X34)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X46),X51)),X32)))<=>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),X47),X46)),X51)),X34)),X32)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X46),X47))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__le__add__iff1)). 6.97/7.19 fof(fact_nat__less__add__iff2, axiom, ![X32, X34, X51, X46, X47]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X47),X46))=>(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),X47),X51)),X34)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X46),X51)),X32)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34),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),X46),X47)),X51)),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__less__add__iff2)). 6.97/7.19 fof(fact_Image__INT__eq, axiom, ![X11, X62, X4, X3, X12, X5]:((hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X62,tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X62),c_Relation_OImage(X12,X5,X3)),X11))=hAPP(c_Relation_OImage(X12,X5,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X62,tc_fun(X12,tc_HOL_Obool)),X4),X11))<=X4!=c_Orderings_Obot__class_Obot(tc_fun(X62,tc_HOL_Obool)))<=c_Relation_Osingle__valued(X5,X12,hAPP(c_Relation_Oconverse(X12,X5),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__INT__eq)). 6.97/7.19 fof(fact_Sup__fin_Oinsert__remove, axiom, ![X35, X4, X5]:(class_Lattices_Olattice(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>((X35=c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))&(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))=>c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X35),c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Oinsert__remove)). 6.97/7.19 fof(fact_nat__le__add__iff2, axiom, ![X32, X34, X51, X46, X47]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X47),X46))=>(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),X47),X51)),X34)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X46),X51)),X32)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),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),X46),X47)),X51)),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__le__add__iff2)). 6.97/7.19 fof(fact_setprod_Oremove, axiom, ![X50, X35, X4, X5, X12]:(((hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12),hAPP(X50,X35)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X50),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X50),X4)<=hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Groups_Ocomm__monoid__mult(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod_Oremove)). 6.97/7.19 fof(fact_equiv__class__eq, axiom, ![X1, X2, X3, X4, X5]:(c_Equiv__Relations_Oequiv(X5,X4,X3)=>(hAPP(c_Relation_OImage(X5,X5,X3),hAPP(hAPP(c_Set_Oinsert(X5),X1),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))=hAPP(c_Relation_OImage(X5,X5,X3),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__class__eq)). 6.97/7.19 fof(fact_map__pair__imageI, axiom, ![X50, X18, X92, X62, X67, X1, X2, X12, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X62,X92)),hAPP(hAPP(c_Product__Type_OPair(X62,X92),hAPP(X18,X2)),hAPP(X50,X1))),hAPP(c_Set_Oimage(tc_prod(X5,X12),tc_prod(X62,X92),c_Product__Type_Omap__pair(X5,X62,X12,X92,X18,X50)),X67)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X2),X1)),X67))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair__imageI)). 6.97/7.19 fof(fact_folding__image_Odistrib, axiom, ![X71, X50, X4, X55, X14, X18, X12, X5]:(c_Finite__Set_Ofolding__image(X5,X12,X18,X14,X55)=>(hAPP(hAPP(X18,hAPP(hAPP(X55,X50),X4)),hAPP(hAPP(X55,X71),X4))=hAPP(hAPP(X55,hAPP(hAPP(c_COMBS(X12,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X12),X18),X50)),X71)),X4)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image_Odistrib)). 6.97/7.19 fof(fact_fun__left__comm_Ofold__insert__remove, axiom, ![X35, X14, X4, X18, X12, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hAPP(hAPP(c_Finite__Set_Ofold(X5,X12,X18),X14),hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))=hAPP(hAPP(X18,X35),hAPP(hAPP(c_Finite__Set_Ofold(X5,X12,X18),X14),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))))<=c_Finite__Set_Ofun__left__comm(X5,X12,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__insert__remove)). 6.97/7.19 fof(fact_distinct__list__update, axiom, ![X47, X2, X23, X5]:((hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Olist__update(X5,X23),X47),X2)))<=~(hBOOL(hAPP(hAPP(c_member(X5),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X23)),hAPP(hAPP(c_Set_Oinsert(X5),hAPP(hAPP(c_List_Onth(X5),X23),X47)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))))<=hBOOL(hAPP(c_List_Odistinct(X5),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__list__update)). 6.97/7.19 fof(fact_select__weight__member, axiom, ![X66, X23, X5]:(hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Product__Type_Ofst(X5,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(X5,X23),X66))),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X5),X5),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X5)),X23))))<=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,X5),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X5)),X23))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_select__weight__member)). 6.97/7.19 fof(fact_fun__left__comm_Ofold__rec, axiom, ![X14, X35, X4, X18, X12, X5]:(c_Finite__Set_Ofun__left__comm(X5,X12,X18)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hAPP(hAPP(X18,X35),hAPP(hAPP(c_Finite__Set_Ofold(X5,X12,X18),X14),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))=hAPP(hAPP(c_Finite__Set_Ofold(X5,X12,X18),X14),X4)<=hBOOL(hAPP(hAPP(c_member(X5),X35),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__rec)). 6.97/7.19 fof(fact_bij__image__INT, axiom, ![X11, X4, X62, X18, X12, X5]:(hAPP(c_Set_Oimage(X5,X12,X18),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X62,tc_fun(X5,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X62,tc_fun(X12,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool),X62),c_Set_Oimage(X5,X12,X18)),X11))<=c_Fun_Obij__betw(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bij__image__INT)). 6.97/7.19 fof(fact_setsum__diff1_H, axiom, ![X18, X2, X4, X5, X12]:(class_Groups_Ocomm__monoid__add(X12)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hBOOL(hAPP(hAPP(c_member(X5),X2),X4))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),hAPP(X18,X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__diff1_H)). 6.97/7.19 fof(fact_wmax__emptyI, axiom, ![X56]:(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))),X56)),c_FunDef_Omax__weak))<=hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X56))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wmax__emptyI)). 6.97/7.19 fof(fact_folding_Ocommute__left__comp_H, axiom, ![X50, X35, X62, X4, X55, X18, X12, X5]:(c_Finite__Set_Ofolding(X5,X12,X18,X55)=>(hAPP(c_Fun_Ocomp(X12,X12,X62,hAPP(X55,X4)),hAPP(c_Fun_Ocomp(X12,X12,X62,hAPP(X18,X35)),X50))=hAPP(c_Fun_Ocomp(X12,X12,X62,hAPP(X18,X35)),hAPP(c_Fun_Ocomp(X12,X12,X62,hAPP(X55,X4)),X50))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Ocommute__left__comp_H)). 6.97/7.19 fof(fact_fun__left__comm_Ofold__graph__insertE__aux, axiom, ![X2, X38, X4, X14, X18, X12, X5]:(c_Finite__Set_Ofun__left__comm(X5,X12,X18)=>((hBOOL(hAPP(hAPP(c_member(X5),X2),X4))=>?[X261]:(X38=hAPP(hAPP(X18,X2),X261)&hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X12,X18,X14,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X261))))<=hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X12,X18,X14,X4),X38)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__graph__insertE__aux)). 6.97/7.20 fof(fact_INT__extend__simps_I2_J, axiom, ![X11, X4, X12, X5, X65]:((X65!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),X65),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool),X5),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),X4)),X11))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),X65),X11)))&(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),X65),X11))=X4<=X65=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__extend__simps_I2_J)). 6.97/7.20 fof(fact_rel__compI, axiom, ![X66, X10, X62, X3, X1, X2, X12, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X2),X1)),X3))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X12,X62)),hAPP(hAPP(c_Product__Type_OPair(X12,X62),X1),X10)),X66))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X62)),hAPP(hAPP(c_Product__Type_OPair(X5,X62),X2),X10)),hAPP(hAPP(c_Relation_Orel__comp(X5,X12,X62),X3),X66))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__compI)). 6.97/7.20 fof(fact_setsum__strict__mono, axiom, ![X50, X18, X4, X5, X12]:((((![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),hAPP(X18,X22)),hAPP(X50,X22))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X50),X4))))<=X4!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=(class_Groups_Ocomm__monoid__add(X12)&class_Groups_Oordered__cancel__ab__semigroup__add(X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__strict__mono)). 6.97/7.20 fof(fact_card__Un__Int, axiom, ![X11, X4, X5]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X4)),hAPP(c_Finite__Set_Ocard(X5),X11))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Un__Int)). 6.97/7.20 fof(fact_convex__bound__lt, axiom, ![X40, X139, X7, X30, X6, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X6),X30))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X7),X30))=>(((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X139),X40)=c_Groups_Oone__class_Oone(X8)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X139),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X40),X7))),X30)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X40)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X139)))))<=class_Rings_Olinordered__semiring__1__strict(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_convex__bound__lt)). 6.97/7.20 fof(fact_convex__bound__le, axiom, ![X40, X139, X7, X30, X6, X8]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X139))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X40))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X139),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X40),X7))),X30))<=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X139),X40)=c_Groups_Oone__class_Oone(X8))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X7),X30)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),X30)))<=class_Rings_Olinordered__semiring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_convex__bound__le)). 6.97/7.20 fof(fact_folding_Ounion__inter, axiom, ![X11, X4, X55, X18, X12, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hAPP(c_Fun_Ocomp(X12,X12,X12,hAPP(X55,X4)),hAPP(X55,X11))=hAPP(c_Fun_Ocomp(X12,X12,X12,hAPP(X55,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))),hAPP(X55,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))))<=c_Finite__Set_Ofolding(X5,X12,X18,X55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Ounion__inter)). 6.97/7.20 fof(fact_inj__on__image__set__diff, axiom, ![X11, X4, X65, X18, X12, X5]:(((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X12,X18),X4)),hAPP(c_Set_Oimage(X5,X12,X18),X11))=hAPP(c_Set_Oimage(X5,X12,X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X65)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X65)))<=c_Fun_Oinj__on(X5,X12,X18,X65)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__image__set__diff)). 6.97/7.20 fof(fact_diff__frac__eq, axiom, ![X39, X6, X26, X7, X8]:(class_Fields_Ofield(X8)=>(c_Groups_Ozero__class_Ozero(X8)!=X7=>(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X6),X7)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X39),X26))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X6),X26)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X39),X7))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X26))<=c_Groups_Ozero__class_Ozero(X8)!=X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__frac__eq)). 6.97/7.20 fof(fact_card__SigmaI, axiom, ![X11, X12, X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X12),hAPP(X11,X22))))=>hAPP(c_Finite__Set_Ocard(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X4),X11))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_Nat_Onat,X5),c_Finite__Set_Ocard(X12)),X11)),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__SigmaI)). 6.97/7.20 fof(fact_fold__image__cong, axiom, ![X14, X71, X50, X4, X5, X12]:(((hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X12,X5,c_Groups_Otimes__class_Otimes(X12)),X50),X14),X4)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X12,X5,c_Groups_Otimes__class_Otimes(X12)),X71),X14),X4)<=![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))=>hAPP(X71,X22)=hAPP(X50,X22)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Groups_Oab__semigroup__mult(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__cong)). 6.97/7.20 fof(fact_pair__lessI1, axiom, ![X82, X66, X1, X2]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))=>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),X2),X66)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X82))),c_FunDef_Opair__less))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__lessI1)). 6.97/7.20 fof(fact_inj__on__image__Int, axiom, ![X11, X4, X65, X18, X12, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X65))=>(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X12,X18),X4)),hAPP(c_Set_Oimage(X5,X12,X18),X11))=hAPP(c_Set_Oimage(X5,X12,X18),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X65))))<=c_Fun_Oinj__on(X5,X12,X18,X65)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__image__Int)). 6.97/7.20 fof(fact_rel__pow__Suc__D2, axiom, ![X67, X32, X14, X35, X5]:(?[X72]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X72)),X67))&hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X72),X14)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X32),X67))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X14)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X32)),X67)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__Suc__D2)). 6.97/7.20 fof(fact_rel__pow__Suc__E2, axiom, ![X67, X32, X14, X35, X5]:(~(![X72]:(~(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X72),X14)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X32),X67))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X72)),X67))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X14)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X32)),X67)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__Suc__E2)). 6.97/7.20 fof(fact_add__frac__eq, axiom, ![X39, X6, X26, X7, X8]:(class_Fields_Ofield(X8)=>(c_Groups_Ozero__class_Ozero(X8)!=X7=>(X26!=c_Groups_Ozero__class_Ozero(X8)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X6),X7)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X39),X26))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X6),X26)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X39),X7))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X26))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__frac__eq)). 6.97/7.20 fof(fact_pair__leqI1, axiom, ![X82, X66, 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)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X66)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X82))),c_FunDef_Opair__leq))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__leqI1)). 6.97/7.20 fof(fact_rel__pow__Suc__E, axiom, ![X67, X32, X14, X35, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X14)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X32)),X67)))=>~(![X72]:(~(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X72),X14)),X67)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X72)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X32),X67)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__Suc__E)). 6.97/7.20 fof(fact_less__add__iff1, axiom, ![X97, X1, X10, X136, X2, X5]:(class_Rings_Oordered__ring(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X2),X1)),X136)),X10)),X97))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X136)),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X136)),X97))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__add__iff1)). 6.97/7.20 fof(fact_le__add__iff1, axiom, ![X97, X1, X10, X136, X2, X5]:(class_Rings_Oordered__ring(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X136)),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X136)),X97)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X2),X1)),X136)),X10)),X97)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__add__iff1)). 6.97/7.20 fof(fact_setprod_Oinsert__remove, axiom, ![X35, X50, X4, X5, X12]:(class_Groups_Ocomm__monoid__mult(X12)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12),hAPP(X50,X35)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X50),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X50),hAPP(hAPP(c_Set_Oinsert(X5),X35),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod_Oinsert__remove)). 6.97/7.20 fof(fact_inj__on__insert, axiom, ![X4, X2, X18, X12, X5]:((c_Fun_Oinj__on(X5,X12,X18,X4)&~(hBOOL(hAPP(hAPP(c_member(X12),hAPP(X18,X2)),hAPP(c_Set_Oimage(X5,X12,X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))))))<=>c_Fun_Oinj__on(X5,X12,X18,hAPP(hAPP(c_Set_Oinsert(X5),X2),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__insert)). 6.97/7.20 fof(fact_less__add__iff2, axiom, ![X97, X1, X10, X136, X2, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X136)),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X136)),X97)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X1),X2)),X136)),X97))))<=class_Rings_Oordered__ring(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__add__iff2)). 6.97/7.20 fof(fact_le__add__iff2, axiom, ![X97, X1, X10, X136, X2, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X136)),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X136)),X97)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X1),X2)),X136)),X97))))<=class_Rings_Oordered__ring(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__add__iff2)). 6.97/7.20 fof(fact_o__inv__distrib, axiom, ![X50, X62, X18, X12, X5]:(c_Fun_Obij__betw(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))=>(hAPP(c_Fun_Ocomp(X5,X62,X12,c_Hilbert__Choice_Oinv__into(X62,X5,c_Orderings_Otop__class_Otop(tc_fun(X62,tc_HOL_Obool)),X50)),c_Hilbert__Choice_Oinv__into(X5,X12,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X18))=c_Hilbert__Choice_Oinv__into(X62,X12,c_Orderings_Otop__class_Otop(tc_fun(X62,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(X5,X12,X62,X18),X50))<=c_Fun_Obij__betw(X62,X5,X50,c_Orderings_Otop__class_Otop(tc_fun(X62,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_o__inv__distrib)). 6.97/7.20 fof(fact_setsum_Oinsert__remove, axiom, ![X35, X50, X4, X5, X12]:(class_Groups_Ocomm__monoid__add(X12)=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X50),hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),hAPP(X50,X35)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X50),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum_Oinsert__remove)). 6.97/7.20 fof(fact_listrel1I1, axiom, ![X23, X3, X38, X35, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),X3))=>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),X35),X23)),hAPP(hAPP(c_List_Olist_OCons(X5),X38),X23))),c_List_Olistrel1(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1I1)). 6.97/7.20 fof(fact_fold__image__reindex, axiom, ![X14, X50, X71, X12, X4, X5, X62]:(class_Groups_Oab__semigroup__mult(X62)=>((hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X62,X5,c_Groups_Otimes__class_Otimes(X62)),hAPP(c_Fun_Ocomp(X12,X62,X5,X50),X71)),X14),X4)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X62,X12,c_Groups_Otimes__class_Otimes(X62)),X50),X14),hAPP(c_Set_Oimage(X5,X12,X71),X4))<=c_Fun_Oinj__on(X5,X12,X71,X4))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__reindex)). 6.97/7.20 fof(fact_measures__lesseq, axiom, ![X121, X5, X38, X35, X18]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X18,X35)),hAPP(X18,X38)))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),c_List_Omeasures(X5,X121)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),c_List_Omeasures(X5,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X5,tc_Nat_Onat)),X18),X121)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_measures__lesseq)). 6.97/7.20 fof(fact_listsum__mult__const, axiom, ![X23, X10, X18, X12, X5]:(class_Rings_Osemiring__0(X5)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X12,X5),X18),X23))),X10)=hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X12,X5),hAPP(hAPP(c_COMBC(X12,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X12),c_Groups_Otimes__class_Otimes(X5)),X18)),X10)),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__mult__const)). 6.97/7.20 fof(fact_listrel__Cons2, axiom, ![X3, X84, X38, X23, X5]:(~(![X22, X86]:(X23=hAPP(hAPP(c_List_Olist_OCons(X5),X22),X86)=>(~(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)),X86),X84)),c_List_Olistrel(X5,X3))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X22),X38)),X3)))))<=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)),X23),hAPP(hAPP(c_List_Olist_OCons(X5),X38),X84))),c_List_Olistrel(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__Cons2)). 6.97/7.20 fof(fact_pick__member, axiom, ![X23, X5, X47]:(hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Random_Opick(X5,X23),X47)),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X5),X5),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X5)),X23))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X47),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X5),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X5)),X23))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pick__member)). 6.97/7.20 fof(fact_listrel__Cons1, axiom, ![X3, X23, X84, X38, X5]:(~(![X72, X155]:((~(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)),X84),X155)),c_List_Olistrel(X5,X3))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X38),X72)),X3)))<=X23=hAPP(hAPP(c_List_Olist_OCons(X5),X72),X155)))<=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),X38),X84)),X23)),c_List_Olistrel(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__Cons1)). 6.97/7.20 fof(fact_folding__image__simple_Ounion__inter, axiom, ![X11, X4, X55, X50, X14, X18, X12, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X4))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X11))=>hAPP(hAPP(X18,hAPP(X55,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),X4),X11))),hAPP(X55,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),X4),X11)))=hAPP(hAPP(X18,hAPP(X55,X4)),hAPP(X55,X11))))<=c_Finite__Set_Ofolding__image__simple(X5,X12,X18,X14,X50,X55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple_Ounion__inter)). 6.97/7.20 fof(fact_in__measures_I2_J, axiom, ![X121, X18, X38, X35, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X18,X35)),hAPP(X18,X38)))|(hAPP(X18,X38)=hAPP(X18,X35)&hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),c_List_Omeasures(X5,X121)))))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),c_List_Omeasures(X5,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X5,tc_Nat_Onat)),X18),X121))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__measures_I2_J)). 6.97/7.20 fof(fact_INF__commute, axiom, ![X18, X11, X62, X4, X12, X5]:(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,X5),X4),hAPP(hAPP(c_COMBB(tc_fun(X62,X5),X5,X12),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X62,X5),X11)),X18))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X62,X5),X11),hAPP(hAPP(c_COMBB(tc_fun(X12,X5),X5,X62),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,X5),X4)),hAPP(c_COMBC(X12,X62,X5),X18)))<=class_Complete__Lattice_Ocomplete__lattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF__commute)). 6.97/7.20 fof(fact_SUP__commute, axiom, ![X18, X11, X62, X4, X12, X5]:(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X5),X4),hAPP(hAPP(c_COMBB(tc_fun(X62,X5),X5,X12),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X62,X5),X11)),X18))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X62,X5),X11),hAPP(hAPP(c_COMBB(tc_fun(X12,X5),X5,X62),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X5),X4)),hAPP(c_COMBC(X12,X62,X5),X18)))<=class_Complete__Lattice_Ocomplete__lattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP__commute)). 6.97/7.20 fof(fact_eq__equiv__class, axiom, ![X4, X1, X2, X3, X5]:((c_Equiv__Relations_Oequiv(X5,X4,X3)=>(hBOOL(hAPP(hAPP(c_member(X5),X1),X4))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),X3))))<=hAPP(c_Relation_OImage(X5,X5,X3),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))=hAPP(c_Relation_OImage(X5,X5,X3),hAPP(hAPP(c_Set_Oinsert(X5),X1),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__equiv__class)). 6.97/7.20 fof(fact_nth__zip, axiom, ![X45, X5, X41, X8, X28]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X45)))=>hAPP(hAPP(c_Product__Type_OPair(X8,X5),hAPP(hAPP(c_List_Onth(X8),X41),X28)),hAPP(hAPP(c_List_Onth(X5),X45),X28))=hAPP(hAPP(c_List_Onth(tc_prod(X8,X5)),hAPP(hAPP(c_List_Ozip(X8,X5),X41),X45)),X28))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__zip)). 6.97/7.20 fof(fact_UN__insert__distrib, axiom, ![X11, X2, X12, X4, X51, X5]:(hAPP(hAPP(c_Set_Oinsert(X12),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool),X5),hAPP(c_Set_Oinsert(X12),X2)),X11))<=hBOOL(hAPP(hAPP(c_member(X5),X51),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__insert__distrib)). 6.97/7.20 fof(fact_folding_Ocommute__left__comp, axiom, ![X50, X35, X38, X62, X55, X18, X12, X5]:(c_Finite__Set_Ofolding(X5,X12,X18,X55)=>hAPP(c_Fun_Ocomp(X12,X12,X62,hAPP(X18,X38)),hAPP(c_Fun_Ocomp(X12,X12,X62,hAPP(X18,X35)),X50))=hAPP(c_Fun_Ocomp(X12,X12,X62,hAPP(X18,X35)),hAPP(c_Fun_Ocomp(X12,X12,X62,hAPP(X18,X38)),X50))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Ocommute__left__comp)). 6.97/7.20 fof(fact_listsum__map__filter, axiom, ![X18, X17, X23, X5, X12]:(class_Groups_Omonoid__add(X12)=>(![X22]:((hAPP(X18,X22)=c_Groups_Ozero__class_Ozero(X12)<=~(hBOOL(hAPP(X17,X22))))<=hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X23))))=>hAPP(c_List_Omonoid__add__class_Olistsum(X12),hAPP(hAPP(c_List_Omap(X5,X12),X18),hAPP(c_List_Ofilter(X5,X17),X23)))=hAPP(c_List_Omonoid__add__class_Olistsum(X12),hAPP(hAPP(c_List_Omap(X5,X12),X18),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__map__filter)). 6.97/7.20 fof(fact_rtrancl__trans, axiom, ![X10, X3, X1, X2, X5]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X1),X10)),c_Transitive__Closure_Ortrancl(X5,X3)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X10)),c_Transitive__Closure_Ortrancl(X5,X3))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),c_Transitive__Closure_Ortrancl(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__trans)). 6.97/7.20 fof(fact_setprod__diff1, axiom, ![X2, X18, X4, X5, X12]:(class_Fields_Ofield(X12)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hAPP(X18,X2)!=c_Groups_Ozero__class_Ozero(X12)=>((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X18),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))<=~(hBOOL(hAPP(hAPP(c_member(X5),X2),X4))))&(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X18),X4)),hAPP(X18,X2))<=hBOOL(hAPP(hAPP(c_member(X5),X2),X4))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__diff1)). 6.97/7.20 fof(fact_list__update__append, axiom, ![X6, X45, X41, X8, X25]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)))=>hAPP(hAPP(c_List_Olist__update(X8,hAPP(hAPP(c_List_Oappend(X8),X41),X45)),X25),X6)=hAPP(hAPP(c_List_Oappend(X8),hAPP(hAPP(c_List_Olist__update(X8,X41),X25),X6)),X45))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41))))=>hAPP(hAPP(c_List_Olist__update(X8,hAPP(hAPP(c_List_Oappend(X8),X41),X45)),X25),X6)=hAPP(hAPP(c_List_Oappend(X8),X41),hAPP(hAPP(c_List_Olist__update(X8,X45),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41))),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__append)). 6.97/7.20 fof(fact_folding__image__simple_Oinsert__remove, axiom, ![X35, X4, X55, X50, X14, X18, X12, X5]:((hAPP(X55,hAPP(hAPP(c_Set_Oinsert(X12),X35),X4))=hAPP(hAPP(X18,hAPP(X50,X35)),hAPP(X55,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X12),X35),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X4)))<=c_Finite__Set_Ofolding__image__simple(X5,X12,X18,X14,X50,X55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple_Oinsert__remove)). 6.97/7.20 fof(fact_folding__image__simple_Oremove, axiom, ![X35, X4, X55, X50, X14, X18, X12, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X4))=>(hBOOL(hAPP(hAPP(c_member(X12),X35),X4))=>hAPP(X55,X4)=hAPP(hAPP(X18,hAPP(X50,X35)),hAPP(X55,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X12),X35),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool))))))))<=c_Finite__Set_Ofolding__image__simple(X5,X12,X18,X14,X50,X55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple_Oremove)). 6.97/7.20 fof(fact_sequence__trans, axiom, ![X33, X47, X3, X18, X5]:(![X42]:hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(X18,hAPP(c_Nat_OSuc,X42))),hAPP(X18,X42))),c_Transitive__Closure_Ortrancl(X5,X3)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(X18,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X47),X33))),hAPP(X18,X47))),c_Transitive__Closure_Ortrancl(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sequence__trans)). 6.97/7.20 fof(fact_setsum__diff1, axiom, ![X18, X2, X4, X5, X12]:(class_Groups_Oab__group__add(X12)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>((hBOOL(hAPP(hAPP(c_member(X5),X2),X4))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X12),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),X4)),hAPP(X18,X2)))&(~(hBOOL(hAPP(hAPP(c_member(X5),X2),X4)))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__diff1)). 6.97/7.20 fof(fact_subset__equiv__class, axiom, ![X2, X1, X3, X4, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X3),hAPP(hAPP(c_Set_Oinsert(X5),X1),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X5,X5,X3),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),X3))<=hBOOL(hAPP(hAPP(c_member(X5),X1),X4))))<=c_Equiv__Relations_Oequiv(X5,X4,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__equiv__class)). 6.97/7.20 fof(fact_setsum__diff1__ring, axiom, ![X18, X2, X4, X5, X12]:(class_Rings_Oring(X12)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hBOOL(hAPP(hAPP(c_member(X5),X2),X4))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X12),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),X4)),hAPP(X18,X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__diff1__ring)). 6.97/7.20 fof(fact_geometric__sum, axiom, ![X32, X35, X5]:((X35!=c_Groups_Oone__class_Oone(X5)=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X35),X32)),c_Groups_Oone__class_Oone(X5))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X35),c_Groups_Oone__class_Oone(X5)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(c_Power_Opower__class_Opower(X5),X35)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32)))<=class_Fields_Ofield(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_geometric__sum)). 6.97/7.20 fof(fact_folding_Oinsert__remove, axiom, ![X35, X4, X55, X18, X12, X5]:(c_Finite__Set_Ofolding(X5,X12,X18,X55)=>(hAPP(X55,hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))=hAPP(c_Fun_Ocomp(X12,X12,X12,hAPP(X55,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),hAPP(X18,X35))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Oinsert__remove)). 6.97/7.20 fof(fact_setsum__diff__nat__ivl, axiom, ![X18, X24, X32, X34, X5]:(class_Groups_Oab__group__add(X5)=>((hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34),X24))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34),X32)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X32),X24))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32),X24)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__diff__nat__ivl)). 6.97/7.20 fof(fact_folding_Oremove, axiom, ![X35, X4, X55, X18, X12, X5]:(c_Finite__Set_Ofolding(X5,X12,X18,X55)=>((hBOOL(hAPP(hAPP(c_member(X5),X35),X4))=>hAPP(c_Fun_Ocomp(X12,X12,X12,hAPP(X55,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),hAPP(X18,X35))=hAPP(X55,X4))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Oremove)). 6.97/7.20 fof(fact_setsum__add__nat__ivl, axiom, ![X18, X24, X32, X34, X5]:(class_Groups_Ocomm__monoid__add(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),X32))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32),X24))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34),X32))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X32),X24)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34),X24))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__add__nat__ivl)). 6.97/7.20 fof(fact_setprod__mono__one__left, axiom, ![X18, X44, X108, X5, X12]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X44),X108))=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X18),X44)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X18),X108)<=![X22]:(c_Groups_Oone__class_Oone(X12)=hAPP(X18,X22)<=hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X108),X44))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X108)))<=class_Groups_Ocomm__monoid__mult(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__mono__one__left)). 6.97/7.20 fof(fact_setprod__mono__one__right, axiom, ![X18, X44, X108, X5, X12]:(class_Groups_Ocomm__monoid__mult(X12)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X108))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X44),X108))=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X18),X108)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X18),X44)<=![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X108),X44)))=>hAPP(X18,X22)=c_Groups_Oone__class_Oone(X12)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__mono__one__right)). 6.97/7.20 fof(fact_setsum__mono__zero__right, axiom, ![X18, X44, X108, X5, X12]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X108))=>((![X22]:(hAPP(X18,X22)=c_Groups_Ozero__class_Ozero(X12)<=hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X108),X44))))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),X108)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),X44))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X44),X108))))<=class_Groups_Ocomm__monoid__add(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__mono__zero__right)). 6.97/7.20 fof(fact_setsum__Un__disjoint, axiom, ![X50, X11, X4, X5, X12]:((((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X50),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X50),X11))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X50),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))<=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Groups_Ocomm__monoid__add(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__Un__disjoint)). 6.97/7.20 fof(fact_setprod_Ounion__disjoint, axiom, ![X50, X11, X4, X5, X12]:(class_Groups_Ocomm__monoid__mult(X12)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>((hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X50),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X50),X11))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X50),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod_Ounion__disjoint)). 6.97/7.20 fof(fact_converse__rtrancl__into__rtrancl, axiom, ![X10, X3, X1, X2, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),X3))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X10)),c_Transitive__Closure_Ortrancl(X5,X3)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X1),X10)),c_Transitive__Closure_Ortrancl(X5,X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__rtrancl__into__rtrancl)). 6.97/7.20 fof(fact_setsum__diff1__nat, axiom, ![X18, X4, X2, X5]:((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X18),X4)),hAPP(X18,X2))<=hBOOL(hAPP(hAPP(c_member(X5),X2),X4)))&(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X18),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))<=~(hBOOL(hAPP(hAPP(c_member(X5),X2),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__diff1__nat)). 6.97/7.20 fof(fact_setsum__mono__zero__left, axiom, ![X18, X44, X108, X5, X12]:((((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),X108)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),X44)<=![X22]:(hAPP(X18,X22)=c_Groups_Ozero__class_Ozero(X12)<=hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X108),X44)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X44),X108)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X108)))<=class_Groups_Ocomm__monoid__add(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__mono__zero__left)). 6.97/7.20 fof(fact_take__add, axiom, ![X41, X8, X27, X28]:(hAPP(hAPP(c_List_Oappend(X8),hAPP(hAPP(c_List_Otake(X8),X28),X41)),hAPP(hAPP(c_List_Otake(X8),X27),hAPP(hAPP(c_List_Odrop(X8),X28),X41)))=hAPP(hAPP(c_List_Otake(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),X27)),X41)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),X27)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__add)). 6.97/7.20 fof(fact_zmult2__lemma__aux4, axiom, ![X53, X29, X70, 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__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X70))=>(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),X29),c_Divides_Odiv__class_Omod(tc_Int_Oint,X53,X31))),X70)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X29),X31)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X70),X29))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult2__lemma__aux4)). 6.97/7.20 fof(fact_zmult2__lemma__aux1, axiom, ![X53, X70, X29, X31]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X29),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X29),c_Divides_Odiv__class_Omod(tc_Int_Oint,X53,X31))),X70)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X70),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X29),X70)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult2__lemma__aux1)). 6.97/7.20 fof(fact_rtrancl_Ortrancl__into__rtrancl, axiom, ![X10, X3, X1, X2, X5]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X10)),c_Transitive__Closure_Ortrancl(X5,X3)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X1),X10)),X3)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),c_Transitive__Closure_Ortrancl(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl_Ortrancl__into__rtrancl)). 6.97/7.20 fof(fact_zip__append, axiom, ![X144, X45, X110, X5, X41, X8]:((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X144)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X45)=>hAPP(hAPP(c_List_Ozip(X8,X5),hAPP(hAPP(c_List_Oappend(X8),X41),X45)),hAPP(hAPP(c_List_Oappend(X5),X110),X144))=hAPP(hAPP(c_List_Oappend(tc_prod(X8,X5)),hAPP(hAPP(c_List_Ozip(X8,X5),X41),X110)),hAPP(hAPP(c_List_Ozip(X8,X5),X45),X144)))<=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X110)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__append)). 6.97/7.20 fof(fact_take__hd__drop, axiom, ![X41, X8, X25]:(hAPP(hAPP(c_List_Otake(X8),hAPP(c_Nat_OSuc,X25)),X41)=hAPP(hAPP(c_List_Oappend(X8),hAPP(hAPP(c_List_Otake(X8),X25),X41)),hAPP(hAPP(c_List_Olist_OCons(X8),hAPP(c_List_Ohd(X8),hAPP(hAPP(c_List_Odrop(X8),X25),X41))),c_List_Olist_ONil(X8)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__hd__drop)). 6.97/7.20 fof(fact_hom__fold1__commute, axiom, ![X20, X71, X5]:(class_Lattices_Oab__semigroup__idem__mult(X5)=>(((X20!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(c_Set_Oimage(X5,X5,X71),X20))=hAPP(X71,hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X20)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X20)))<=![X22, X72]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(X71,X22)),hAPP(X71,X72))=hAPP(X71,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X22),X72)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hom__fold1__commute)). 6.97/7.20 fof(fact_ball__Un, axiom, ![X17, X11, X4, X5]:(![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11)))=>hBOOL(hAPP(X17,X22)))<=>(![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X11))=>hBOOL(hAPP(X17,X22)))&![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))=>hBOOL(hAPP(X17,X22))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ball__Un)). 6.97/7.20 fof(fact_setsum__bounded, axiom, ![X281, X18, X4, X5, X12]:((![X42]:(hBOOL(hAPP(hAPP(c_member(X5),X42),X4))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),hAPP(X18,X42)),X281)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X12),hAPP(c_Finite__Set_Ocard(X5),X4))),X281))))<=(class_Groups_Oordered__ab__semigroup__add(X12)&class_Rings_Osemiring__1(X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__bounded)). 6.97/7.20 fof(fact_equiv__class__nondisjoint, axiom, ![X1, X2, X35, X3, X4, X5]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),X3))<=hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X3),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X5,X5,X3),hAPP(hAPP(c_Set_Oinsert(X5),X1),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))))<=c_Equiv__Relations_Oequiv(X5,X4,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__class__nondisjoint)). 6.97/7.20 fof(fact_insort__left__comm, axiom, ![X23, X38, X35, X5]:(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X35),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X38),X23))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X38),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X35),X23))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__left__comm)). 6.97/7.20 fof(fact_insort__key__left__comm, axiom, ![X23, X12, X38, X35, X18, X5]:((hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X12,X5,X18),X38),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X12,X5,X18),X35),X23))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X12,X5,X18),X35),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X12,X5,X18),X38),X23))<=hAPP(X18,X35)!=hAPP(X18,X38))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__key__left__comm)). 6.97/7.20 fof(fact_rel__comp__mono, axiom, ![X66, X197, X62, X3, X37, X12, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),X37),X3))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X62),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X12,X62),X37),X197)),hAPP(hAPP(c_Relation_Orel__comp(X5,X12,X62),X3),X66)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X12,X62),tc_HOL_Obool)),X197),X66)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__comp__mono)). 6.97/7.20 fof(fact_folding__one_Oclosed, axiom, ![X4, X55, X18, X5]:(c_Finite__Set_Ofolding__one(X5,X18,X55)=>((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4=>(hBOOL(hAPP(hAPP(c_member(X5),hAPP(X55,X4)),X4))<=![X22, X72]:hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(X18,X22),X72)),hAPP(hAPP(c_Set_Oinsert(X5),X22),hAPP(hAPP(c_Set_Oinsert(X5),X72),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one_Oclosed)). 6.97/7.20 fof(fact_folding_Ounion, axiom, ![X11, X4, X55, X18, X12, X5]:(c_Finite__Set_Ofolding(X5,X12,X18,X55)=>(((hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>hAPP(X55,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))=hAPP(c_Fun_Ocomp(X12,X12,X12,hAPP(X55,X4)),hAPP(X55,X11)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Ounion)). 6.97/7.20 fof(fact_insort__key_Osimps_I2_J, axiom, ![X84, X12, X38, X35, X18, X5]:(class_Orderings_Olinorder(X5)=>((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X18,X35)),hAPP(X18,X38))))=>hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X12,X5,X18),X35),hAPP(hAPP(c_List_Olist_OCons(X12),X38),X84))=hAPP(hAPP(c_List_Olist_OCons(X12),X38),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X12,X5,X18),X35),X84)))&(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X12,X5,X18),X35),hAPP(hAPP(c_List_Olist_OCons(X12),X38),X84))=hAPP(hAPP(c_List_Olist_OCons(X12),X35),hAPP(hAPP(c_List_Olist_OCons(X12),X38),X84))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X18,X35)),hAPP(X18,X38)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__key_Osimps_I2_J)). 6.97/7.20 fof(fact_insert__partition, axiom, ![X55, X35, X5]:(~(hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X35),X55)))=>(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X35),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X55))=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))<=![X22]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X22),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X35),X55)))=>![X115]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X115),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X35),X55)))=>(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X22),X115)=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))<=X22!=X115))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__partition)). 6.97/7.20 fof(fact_UN__equiv__class, axiom, ![X2, X18, X12, X3, X4, X5]:(((hAPP(X18,X2)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X3),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X18)<=hBOOL(hAPP(hAPP(c_member(X5),X2),X4)))<=c_Equiv__Relations_Ocongruent(X5,tc_fun(X12,tc_HOL_Obool),X3,X18))<=c_Equiv__Relations_Oequiv(X5,X4,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__equiv__class)). 6.97/7.20 fof(fact_map__pair__surj, axiom, ![X50, X62, X92, X18, X5, X12]:(hAPP(c_Set_Oimage(X12,X5,X18),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))=>(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X5,X62),tc_HOL_Obool))=hAPP(c_Set_Oimage(tc_prod(X12,X92),tc_prod(X5,X62),c_Product__Type_Omap__pair(X12,X5,X92,X62,X18,X50)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X12,X92),tc_HOL_Obool)))<=c_Orderings_Otop__class_Otop(tc_fun(X62,tc_HOL_Obool))=hAPP(c_Set_Oimage(X92,X62,X50),c_Orderings_Otop__class_Otop(tc_fun(X92,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair__surj)). 6.97/7.20 fof(fact_sorted__list__of__set__insert, axiom, ![X35, X4, X5]:(class_Orderings_Olinorder(X5)=>(c_List_Olinorder__class_Osorted__list__of__set(X5,hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X35),c_List_Olinorder__class_Osorted__list__of__set(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__list__of__set__insert)). 6.97/7.20 fof(fact_card_Ounion__inter__neutral, axiom, ![X11, X4, X5]:(((hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X4)),hAPP(c_Finite__Set_Ocard(X5),X11))<=(c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<=?[X22]:hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card_Ounion__inter__neutral)). 6.97/7.20 fof(fact_mono__Int, axiom, ![X11, X4, X18, X12, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),hAPP(X18,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),hAPP(X18,X4)),hAPP(X18,X11))))<=c_Orderings_Oorder__class_Omono(tc_fun(X5,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool),X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mono__Int)). 6.97/7.20 fof(fact_ball__UN, axiom, ![X17, X11, X4, X12, X5]:(![X22]:(hBOOL(hAPP(X17,X22))<=hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X4),X11))))<=>![X22]:(hBOOL(hAPP(hAPP(c_member(X12),X22),X4))=>![X115]:(hBOOL(hAPP(X17,X115))<=hBOOL(hAPP(hAPP(c_member(X5),X115),hAPP(X11,X22)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ball__UN)). 6.97/7.20 fof(fact_mono__Un, axiom, ![X11, X4, X18, X12, X5]:(c_Orderings_Oorder__class_Omono(tc_fun(X5,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool),X18)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),hAPP(X18,X4)),hAPP(X18,X11))),hAPP(X18,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mono__Un)). 6.97/7.20 fof(fact_Image__subset__eq, axiom, ![X11, X4, X3, X12, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X12,X5,X3),X4)),X11))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),X4),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X12,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X12,hAPP(c_Relation_Oconverse(X12,X5),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X11)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__subset__eq)). 6.97/7.20 fof(fact_folding__image__simple_Ounion__disjoint, axiom, ![X11, X4, X55, X50, X14, X18, X12, X5]:(c_Finite__Set_Ofolding__image__simple(X5,X12,X18,X14,X50,X55)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X4))=>((hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),X4),X11)=c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool))=>hAPP(hAPP(X18,hAPP(X55,X4)),hAPP(X55,X11))=hAPP(X55,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),X4),X11)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple_Ounion__disjoint)). 6.97/7.20 fof(fact_fold__sup__le__sup, axiom, ![X10, X1, X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X10),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X1),X10)))<=![X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X22),X1))<=hBOOL(hAPP(hAPP(c_member(X5),X22),X4)))))<=class_Lattices_Osemilattice__sup(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__sup__le__sup)). 6.97/7.20 fof(fact_min__max_Ofold__sup__le__sup, axiom, ![X10, X1, X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X10),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X1),X10)))<=![X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X22),X1))<=hBOOL(hAPP(hAPP(c_member(X5),X22),X4)))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ofold__sup__le__sup)). 6.97/7.20 fof(fact_inf__le__fold__inf, axiom, ![X10, X1, X4, X5]:(class_Lattices_Osemilattice__inf(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X1),X22)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X1),X10)),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X10),X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__le__fold__inf)). 6.97/7.20 fof(fact_min__max_Oinf__le__fold__inf, axiom, ![X10, X1, X4, X5]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X1),X10)),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X10),X4)))<=![X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X1),X22))<=hBOOL(hAPP(hAPP(c_member(X5),X22),X4))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__le__fold__inf)). 6.97/7.20 fof(fact_transD, axiom, ![X10, X1, X2, X3, X5]:(((hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X10)),X3))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X1),X10)),X3)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),X3)))<=c_Relation_Otrans(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transD)). 6.97/7.20 fof(fact_fold1__in, axiom, ![X4, X5]:(class_Groups_Oab__semigroup__mult(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>((![X22, X72]:hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X22),X72)),hAPP(hAPP(c_Set_Oinsert(X5),X22),hAPP(hAPP(c_Set_Oinsert(X5),X72),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))=>hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X4)),X4)))<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__in)). 6.97/7.20 fof(fact_surj__Compl__image__subset, axiom, ![X4, X18, X5, X12]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X12,X5,X18),X4))),hAPP(c_Set_Oimage(X12,X5,X18),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X12,tc_HOL_Obool)),X4))))<=c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))=hAPP(c_Set_Oimage(X12,X5,X18),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_surj__Compl__image__subset)). 6.97/7.20 fof(fact_setsum__diff, axiom, ![X18, X11, X4, X5, X12]:(((hAPP(hAPP(c_Groups_Ominus__class_Ominus(X12),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),X11))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Groups_Oab__group__add(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__diff)). 6.97/7.20 fof(fact_fold1__Un, axiom, ![X11, X4, X5]:(class_Groups_Oab__semigroup__mult(X5)=>(((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))=>((hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X4)),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X11))=hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11))<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X11))<=X4!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__Un)). 6.97/7.20 fof(fact_setsum__cl__ivl__Suc, axiom, ![X18, X34, X32, X5]:(((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X34,X32))),hAPP(X18,hAPP(c_Nat_OSuc,X32)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X34,hAPP(c_Nat_OSuc,X32)))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X32)),X34))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X32)),X34))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X34,hAPP(c_Nat_OSuc,X32)))=c_Groups_Ozero__class_Ozero(X5)))<=class_Groups_Ocomm__monoid__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__cl__ivl__Suc)). 6.97/7.20 fof(fact_fun__left__comm_Ofold__insert, axiom, ![X14, X35, X4, X18, X12, X5]:(c_Finite__Set_Ofun__left__comm(X5,X12,X18)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hAPP(hAPP(X18,X35),hAPP(hAPP(c_Finite__Set_Ofold(X5,X12,X18),X14),X4))=hAPP(hAPP(c_Finite__Set_Ofold(X5,X12,X18),X14),hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))<=~(hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__insert)). 6.97/7.20 fof(fact_setsum__diff__nat, axiom, ![X18, X4, X11, X5]:((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X18),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X18),X11))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__diff__nat)). 6.97/7.20 fof(fact_id__take__nth__drop, axiom, ![X41, X8, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)))=>hAPP(hAPP(c_List_Oappend(X8),hAPP(hAPP(c_List_Otake(X8),X28),X41)),hAPP(hAPP(c_List_Olist_OCons(X8),hAPP(hAPP(c_List_Onth(X8),X41),X28)),hAPP(hAPP(c_List_Odrop(X8),hAPP(c_Nat_OSuc,X28)),X41)))=X41), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_id__take__nth__drop)). 6.97/7.20 fof(fact_list__all2I, axiom, ![X17, X1, X2, X12, X5]:(![X22]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X12)),X22),hAPP(c_List_Oset(tc_prod(X5,X12)),hAPP(hAPP(c_List_Ozip(X5,X12),X2),X1))))=>hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X12,tc_HOL_Obool),X17),X22)))=>(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X2)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12)),X1)=>c_List_Olist__all2(X5,X12,X17,X2,X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2I)). 6.97/7.20 fof(fact_gauss__sum, axiom, ![X32, X5]:(class_Rings_Ocomm__semiring__1(X5)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oone__class_Oone(X5)),c_Groups_Oone__class_Oone(X5))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),c_Nat_Osemiring__1__class_Oof__nat(X5)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X32)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X32)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X32)),c_Groups_Oone__class_Oone(X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_gauss__sum)). 6.97/7.20 fof(fact_list__all2__def, axiom, ![X84, X23, X17, X12, X5]:((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12)),X84)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)&![X22]:(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X12,tc_HOL_Obool),X17),X22))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X12)),X22),hAPP(c_List_Oset(tc_prod(X5,X12)),hAPP(hAPP(c_List_Ozip(X5,X12),X23),X84))))))<=>c_List_Olist__all2(X5,X12,X17,X23,X84)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__def)). 6.97/7.20 fof(fact_card__Diff1__less, axiom, ![X35, X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X5),X4)))<=hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Diff1__less)). 6.97/7.20 fof(fact_subset__insert__iff, axiom, ![X11, X35, X4, X5]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))<=~(hBOOL(hAPP(hAPP(c_member(X5),X35),X4))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X11))<=hBOOL(hAPP(hAPP(c_member(X5),X35),X4))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__insert__iff)). 6.97/7.20 fof(fact_rtrancl__listrel1__if__listrel, axiom, ![X3, X84, X23, X5]:(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)),X23),X84)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X3))))<=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)),X23),X84)),c_List_Olistrel(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__listrel1__if__listrel)). 6.97/7.20 fof(fact_min__max_OSup__fin_Ohom__commute, axiom, ![X20, X71, X5]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X20))=>(X20!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(c_Set_Oimage(X5,X5,X71),X20))=hAPP(X71,c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X20))))<=![X22, X72]:hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),hAPP(X71,X22)),hAPP(X71,X72))=hAPP(X71,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X22),X72)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Ohom__commute)). 6.97/7.20 fof(fact_min__max_OInf__fin_Ohom__commute, axiom, ![X20, X71, X5]:((![X22, X72]:hAPP(X71,hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X22),X72))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),hAPP(X71,X22)),hAPP(X71,X72))=>((c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(c_Set_Oimage(X5,X5,X71),X20))=hAPP(X71,c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X20))<=X20!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X20))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Ohom__commute)). 6.97/7.20 fof(fact_setsum__left__distrib, axiom, ![X3, X4, X18, X12, X5]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5),hAPP(hAPP(c_COMBC(X12,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X12),c_Groups_Otimes__class_Otimes(X5)),X18)),X3)),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5),X18),X4)),X3)<=class_Rings_Osemiring__0(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__left__distrib)). 6.97/7.20 fof(fact_norm__frac_Opinduct, axiom, ![X17, X103, X109]:(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),X109),X103)))=>(![X13, X96]:(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),X13),X96)))=>(hBOOL(hAPP(hAPP(X17,X13),X96))<=(hBOOL(hAPP(hAPP(X17,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X13)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X96)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X96),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))=>hBOOL(hAPP(hAPP(X17,X109),X103)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_norm__frac_Opinduct)). 6.97/7.20 fof(fact_combine__common__factor, axiom, ![X31, X29, X282, X30, X8]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X282)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X282)),X31))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29)),X282)),X31)<=class_Rings_Osemiring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_combine__common__factor)). 6.97/7.20 fof(fact_min__max_Odistrib__inf__le, axiom, ![X26, X7, X6, X8]:(class_Orderings_Olinorder(X8)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X6),X7)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X6),X26))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X6),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X7),X26))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Odistrib__inf__le)). 6.97/7.20 fof(fact_distrib__inf__le, axiom, ![X26, X7, X6, X8]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),X7)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),X26))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X7),X26))))<=class_Lattices_Olattice(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distrib__inf__le)). 6.97/7.20 fof(fact_min__max_Odistrib__sup__le, axiom, ![X26, X7, X6, X8]:(class_Orderings_Olinorder(X8)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X6),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X7),X26))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X6),X7)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X6),X26))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Odistrib__sup__le)). 6.97/7.20 fof(fact_distrib__sup__le, axiom, ![X26, X7, X6, X8]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X7),X26))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),X7)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),X26))))<=class_Lattices_Olattice(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distrib__sup__le)). 6.97/7.20 fof(fact_aset_I5_J, axiom, ![X4, X82, X73]:((![X22]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22),X73)),X82))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22),X82)))<=![X115]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X115),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X73)))=>![X158]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X158),X4))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X158),X115)!=X22)))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X82),X4)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_aset_I5_J)). 6.97/7.20 fof(fact_bset_I7_J, axiom, ![X11, X82, X73]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73))=>(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X82),X11))=>![X22]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X82),X22))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X82),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X22),X73))))<=![X115]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X115),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X73)))=>![X158]:(X22!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X158),X115)<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X158),X11))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bset_I7_J)). 6.97/7.20 fof(fact_abs__mult__less, axiom, ![X74, X29, X31, X30, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),X30)),X31))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),X29)),X74))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),X30)),hAPP(c_Groups_Oabs__class_Oabs(X8),X29))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X74)))))<=class_Rings_Olinordered__idom(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__mult__less)). 6.97/7.20 fof(fact_Int_OMin__def, axiom, c_Int_OMin=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int_OMin__def)). 6.97/7.20 fof(fact_bex__Un, axiom, ![X17, X11, X4, X5]:(?[X22]:(hBOOL(hAPP(X17,X22))&hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))))<=>(?[X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))&hBOOL(hAPP(X17,X22)))|?[X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X11))&hBOOL(hAPP(X17,X22))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bex__Un)). 6.97/7.20 fof(fact_rel__compE, axiom, ![X66, X3, X62, X198, X12, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X12)),X198),hAPP(hAPP(c_Relation_Orel__comp(X5,X62,X12),X3),X66)))=>~(![X22, X72, X116]:((~(hBOOL(hAPP(hAPP(c_member(tc_prod(X62,X12)),hAPP(hAPP(c_Product__Type_OPair(X62,X12),X72),X116)),X66)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X62)),hAPP(hAPP(c_Product__Type_OPair(X5,X62),X22),X72)),X3)))<=X198=hAPP(hAPP(c_Product__Type_OPair(X5,X12),X22),X116)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__compE)). 6.97/7.20 fof(fact_min__max_OInf__fin_Oclosed, axiom, ![X4, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>((hBOOL(hAPP(hAPP(c_member(X5),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X4)),X4))<=![X22, X72]:hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X22),X72)),hAPP(hAPP(c_Set_Oinsert(X5),X22),hAPP(hAPP(c_Set_Oinsert(X5),X72),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))))<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Oclosed)). 6.97/7.20 fof(fact_inf__period_I3_J, axiom, ![X82, X73, X97, X5]:((class_Rings_Ocomm__ring(X5)&class_Rings_Odvd(X5))=>(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X97),X73))=>![X22, X145]:(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X97),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X22),X82)))<=>hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X97),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X145),X73))),X82)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__period_I3_J)). 6.97/7.20 fof(fact_min__max_OSup__fin_Oclosed, axiom, ![X4, X5]:(((X4!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>(hBOOL(hAPP(hAPP(c_member(X5),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X4)),X4))<=![X22, X72]:hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X22),X72)),hAPP(hAPP(c_Set_Oinsert(X5),X22),hAPP(hAPP(c_Set_Oinsert(X5),X72),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Oclosed)). 6.97/7.20 fof(fact_coinduct__lemma, axiom, ![X18, X56, X5]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X56),c_Inductive_Ocomplete__lattice__class_Ogfp(X5,X18))),hAPP(X18,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X56),c_Inductive_Ocomplete__lattice__class_Ogfp(X5,X18)))))<=c_Orderings_Oorder__class_Omono(X5,X5,X18))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X56),hAPP(X18,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X56),c_Inductive_Ocomplete__lattice__class_Ogfp(X5,X18))))))<=class_Complete__Lattice_Ocomplete__lattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_coinduct__lemma)). 6.97/7.20 fof(fact_right__diff__distrib__number__of, axiom, ![X31, X29, X40, X5]:((class_Rings_Oring(X5)&class_Int_Onumber(X5))=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X40)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X29),X31))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X40)),X29)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X40)),X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_right__diff__distrib__number__of)). 6.97/7.20 fof(fact_inj__image__Compl__subset, axiom, ![X4, X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X12,X18),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X4))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X12,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X12,X18),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__image__Compl__subset)). 6.97/7.20 fof(fact_upd__conv__take__nth__drop, axiom, ![X30, X41, X8, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)))=>hAPP(hAPP(c_List_Oappend(X8),hAPP(hAPP(c_List_Otake(X8),X28),X41)),hAPP(hAPP(c_List_Olist_OCons(X8),X30),hAPP(hAPP(c_List_Odrop(X8),hAPP(c_Nat_OSuc,X28)),X41)))=hAPP(hAPP(c_List_Olist__update(X8,X41),X28),X30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upd__conv__take__nth__drop)). 6.97/7.20 fof(fact_setsum__divide__distrib, axiom, ![X3, X4, X18, X12, X5]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5),hAPP(hAPP(c_COMBC(X12,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X12),c_Rings_Oinverse__class_Odivide(X5)),X18)),X3)),X4)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5),X18),X4)),X3)<=class_Fields_Ofield(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__divide__distrib)). 6.97/7.20 fof(fact_right__distrib__number__of, axiom, ![X31, X29, X40, X5]:((class_Int_Onumber(X5)&class_Rings_Osemiring(X5))=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X40)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X29),X31))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X40)),X29)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X40)),X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_right__distrib__number__of)). 6.97/7.20 fof(fact_in__inv__image, axiom, ![X18, X3, X12, X38, X35, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X12,X12)),hAPP(hAPP(c_Product__Type_OPair(X12,X12),hAPP(X18,X35)),hAPP(X18,X38))),X3))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),hAPP(hAPP(c_Relation_Oinv__image(X12,X5),X3),X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__inv__image)). 6.97/7.20 fof(fact_div__mult__div__if__dvd, axiom, ![X39, X26, X6, X7, X8]:((hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X8),X7),X6))=>(hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X6),X39)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X26))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),X6),X7)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),X39),X26))<=hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X8),X26),X39))))<=class_Divides_Osemiring__div(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__div__if__dvd)). 6.97/7.20 fof(fact_refl__on__INTER, axiom, ![X3, X4, X12, X44, X5]:(![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X44))=>c_Relation_Orefl__on(X12,hAPP(X4,X22),hAPP(X3,X22)))=>c_Relation_Orefl__on(X12,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),X44),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(tc_prod(X12,X12),tc_HOL_Obool)),X44),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__on__INTER)). 6.97/7.20 fof(fact_refl__on__UNION, axiom, ![X3, X4, X12, X44, X5]:(![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X44))=>c_Relation_Orefl__on(X12,hAPP(X4,X22),hAPP(X3,X22)))=>c_Relation_Orefl__on(X12,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X44),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_prod(X12,X12),tc_HOL_Obool)),X44),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__on__UNION)). 6.97/7.20 fof(fact_fun__left__comm_Ofold__insert2, axiom, ![X14, X35, X4, X18, X12, X5]:(((hAPP(hAPP(c_Finite__Set_Ofold(X5,X12,X18),hAPP(hAPP(X18,X35),X14)),X4)=hAPP(hAPP(c_Finite__Set_Ofold(X5,X12,X18),X14),hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))<=~(hBOOL(hAPP(hAPP(c_member(X5),X35),X4))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=c_Finite__Set_Ofun__left__comm(X5,X12,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__insert2)). 6.97/7.20 fof(fact_listrel1E, axiom, ![X3, X84, X23, X5]:(~(![X22, X72]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X22),X72)),X3))=>![X140, X141]:(hAPP(hAPP(c_List_Oappend(X5),X140),hAPP(hAPP(c_List_Olist_OCons(X5),X22),X141))=X23=>X84!=hAPP(hAPP(c_List_Oappend(X5),X140),hAPP(hAPP(c_List_Olist_OCons(X5),X72),X141)))))<=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)),X23),X84)),c_List_Olistrel1(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1E)). 6.97/7.20 fof(fact_take__Suc__conv__app__nth, axiom, ![X41, X8, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)))=>hAPP(hAPP(c_List_Oappend(X8),hAPP(hAPP(c_List_Otake(X8),X28),X41)),hAPP(hAPP(c_List_Olist_OCons(X8),hAPP(hAPP(c_List_Onth(X8),X41),X28)),c_List_Olist_ONil(X8)))=hAPP(hAPP(c_List_Otake(X8),hAPP(c_Nat_OSuc,X28)),X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__Suc__conv__app__nth)). 6.97/7.20 fof(fact_insort__key__remove1, axiom, ![X18, X23, X2, X5, X12]:(class_Orderings_Olinorder(X12)=>(hBOOL(hAPP(hAPP(c_member(X5),X2),hAPP(c_List_Oset(X5),X23)))=>(c_List_Olinorder__class_Osorted(X12,hAPP(hAPP(c_List_Omap(X5,X12),X18),X23))=>(X2=hAPP(c_List_Ohd(X5),hAPP(c_List_Ofilter(X5,hAPP(hAPP(c_COMBB(X12,tc_HOL_Obool,X5),hAPP(c_fequal,hAPP(X18,X2))),X18)),X23))=>hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X12,X18),X2),c_List_Oremove1(X5,X2,X23))=X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__key__remove1)). 6.97/7.20 fof(fact_folding__one_Ounion__disjoint, axiom, ![X11, X4, X55, X18, X5]:(c_Finite__Set_Ofolding__one(X5,X18,X55)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(X4!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))=>(X11!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)=>hAPP(X55,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(X18,hAPP(X55,X4)),hAPP(X55,X11)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one_Ounion__disjoint)). 6.97/7.20 fof(fact_sorted__map__same, axiom, ![X23, X50, X18, X12, X5]:(c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X12,X5),X18),hAPP(c_List_Ofilter(X12,hAPP(hAPP(c_COMBC(X12,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,tc_HOL_Obool),X12),c_fequal),X18)),hAPP(X50,X23))),X23)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__map__same)). 6.97/7.20 fof(fact_min__max_OInf__fin_Ounion__idem, axiom, ![X11, X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))=>(X11!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X4)),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X11))=c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Ounion__idem)). 6.97/7.20 fof(fact_nat__gcd_Opinduct, axiom, ![X17, X103, X109]:((hBOOL(hAPP(hAPP(X17,X109),X103))<=![X22, X72]:(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),X22),X72)))=>(hBOOL(hAPP(hAPP(X17,X22),X72))<=(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X72=>hBOOL(hAPP(hAPP(X17,X72),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22,X72)))))))<=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),X109),X103)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__gcd_Opinduct)). 6.97/7.20 fof(fact_mod__lemma, axiom, ![X53, X29, X70, X31]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X70),X29))=>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),X29),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X53,X31))),X70)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X31))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__lemma)). 6.97/7.20 fof(fact_filter__insort, axiom, ![X35, X17, X23, X18, X12, X5]:(class_Orderings_Olinorder(X5)=>((hBOOL(hAPP(X17,X35))=>hAPP(c_List_Ofilter(X12,X17),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X12,X5,X18),X35),X23))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X12,X5,X18),X35),hAPP(c_List_Ofilter(X12,X17),X23)))<=c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X12,X5),X18),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__insort)). 6.97/7.20 fof(fact_min__max_OSup__fin_Ounion__idem, axiom, ![X11, X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))=>(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X11=>c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X4)),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X11))))<=X4!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Ounion__idem)). 6.97/7.20 fof(fact_transfer__int__nat__sum__prod2_I2_J, axiom, ![X18, X4, X5]:(![X22]:(c_Nat__Transfer_Ois__nat(hAPP(X18,X22))<=hBOOL(hAPP(hAPP(c_member(X5),X22),X4)))=>hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X5),c_Int_Onat),X18)),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,tc_Int_Oint),X18),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__sum__prod2_I2_J)). 6.97/7.20 fof(fact_transfer__int__nat__sum__prod2_I1_J, axiom, ![X18, X4, X5]:(![X22]:(c_Nat__Transfer_Ois__nat(hAPP(X18,X22))<=hBOOL(hAPP(hAPP(c_member(X5),X22),X4)))=>hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X5),c_Int_Onat),X18)),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Int_Oint),X18),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__sum__prod2_I1_J)). 6.97/7.20 fof(fact_card__Diff__subset__Int, axiom, ![X11, X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)))=>hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X4)),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Diff__subset__Int)). 6.97/7.20 fof(fact_exE__realizer, axiom, ![X62, X18, X104, X24, X5, X12, X17]:((hBOOL(hAPP(X104,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X12,X5,X62),X18),X24)))<=![X22, X72]:(hBOOL(hAPP(hAPP(X17,X72),X22))=>hBOOL(hAPP(X104,hAPP(hAPP(X18,X22),X72)))))<=hBOOL(hAPP(hAPP(X17,hAPP(c_Product__Type_Osnd(X12,X5),X24)),hAPP(c_Product__Type_Ofst(X12,X5),X24)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_exE__realizer)). 6.97/7.20 fof(fact_left__distrib__number__of, axiom, ![X40, X29, X30, X5]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X30),hAPP(c_Int_Onumber__class_Onumber__of(X5),X40))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X29),hAPP(c_Int_Onumber__class_Onumber__of(X5),X40)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X29)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X40))<=(class_Int_Onumber(X5)&class_Rings_Osemiring(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_left__distrib__number__of)). 6.97/7.20 fof(fact_measures__less, axiom, ![X121, X5, X38, X35, X18]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),c_List_Omeasures(X5,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X5,tc_Nat_Onat)),X18),X121))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X18,X35)),hAPP(X18,X38)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_measures__less)). 6.97/7.20 fof(fact_setsum__head__upt__Suc, axiom, ![X18, X32, X34, X5]:(class_Groups_Ocomm__monoid__add(X5)=>(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(X18,X34)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X34)),X32)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34),X32))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__head__upt__Suc)). 6.97/7.20 fof(fact_zmult2__lemma__aux2, axiom, ![X53, X70, X29, X31]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X29),X70))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X70),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),X29),c_Divides_Odiv__class_Omod(tc_Int_Oint,X53,X31))),X70)),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)),X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult2__lemma__aux2)). 6.97/7.20 fof(fact_zmult2__lemma__aux3, axiom, ![X53, X29, X70, X31]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X70),X29))=>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),X29),c_Divides_Odiv__class_Omod(tc_Int_Oint,X53,X31))),X70))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X70)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult2__lemma__aux3)). 6.97/7.20 fof(fact_listsum__map__remove1, axiom, ![X18, X23, X35, X5, X12]:(class_Groups_Ocomm__monoid__add(X12)=>(hAPP(c_List_Omonoid__add__class_Olistsum(X12),hAPP(hAPP(c_List_Omap(X5,X12),X18),X23))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),hAPP(X18,X35)),hAPP(c_List_Omonoid__add__class_Olistsum(X12),hAPP(hAPP(c_List_Omap(X5,X12),X18),c_List_Oremove1(X5,X35,X23))))<=hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__map__remove1)). 6.97/7.20 fof(fact_congruent2I_H, axiom, ![X62, X18, X151, X12, X153, X5]:(![X245, X246]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X245),X246)),X153))=>![X247, X248]:(hAPP(hAPP(X18,X246),X248)=hAPP(hAPP(X18,X245),X247)<=hBOOL(hAPP(hAPP(c_member(tc_prod(X12,X12)),hAPP(hAPP(c_Product__Type_OPair(X12,X12),X247),X248)),X151))))=>c_Equiv__Relations_Ocongruent2(X5,X12,X62,X153,X151,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_congruent2I_H)). 6.97/7.20 fof(fact_left__diff__distrib__number__of, axiom, ![X40, X29, X30, X5]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X30),X29)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X40))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X30),hAPP(c_Int_Onumber__class_Onumber__of(X5),X40))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X29),hAPP(c_Int_Onumber__class_Onumber__of(X5),X40)))<=(class_Rings_Oring(X5)&class_Int_Onumber(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_left__diff__distrib__number__of)). 6.97/7.20 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J, axiom, ![X11, X4]:((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),X4)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X11)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X4),X11)<=c_Nat__Transfer_Onat__set(X11))<=c_Nat__Transfer_Onat__set(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J)). 6.97/7.20 fof(fact_Sup__fin_Oclosed, axiom, ![X4, X5]:(class_Lattices_Olattice(X5)=>((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4=>(hBOOL(hAPP(hAPP(c_member(X5),c_Big__Operators_Olattice__class_OSup__fin(X5,X4)),X4))<=![X22, X72]:hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X22),X72)),hAPP(hAPP(c_Set_Oinsert(X5),X22),hAPP(hAPP(c_Set_Oinsert(X5),X72),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Oclosed)). 6.97/7.20 fof(fact_Inf__fin_Oclosed, axiom, ![X4, X5]:((((![X22, X72]:hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X22),X72)),hAPP(hAPP(c_Set_Oinsert(X5),X22),hAPP(hAPP(c_Set_Oinsert(X5),X72),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))=>hBOOL(hAPP(hAPP(c_member(X5),c_Big__Operators_Olattice__class_OInf__fin(X5,X4)),X4)))<=X4!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Lattices_Olattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Oclosed)). 6.97/7.20 fof(fact_Diff__mono, axiom, ![X11, X73, X65, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X65))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X73),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X65),X73))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__mono)). 6.97/7.20 fof(fact_Int__mono, axiom, ![X73, X11, X65, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X65))=>(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),X11)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X65),X73)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X73)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__mono)). 6.97/7.20 fof(fact_Un__mono, axiom, ![X73, X11, X65, X4, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X73))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X65),X73))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X65))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__mono)). 6.97/7.20 fof(fact_trancl__subset__Sigma__aux, axiom, ![X4, X3, X1, X2, X5]:(((hBOOL(hAPP(hAPP(c_member(X5),X2),X4))|X1=X2)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X4),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X4)))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),c_Transitive__Closure_Ortrancl(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__subset__Sigma__aux)). 6.97/7.20 fof(fact_card__Diff__singleton, axiom, ![X35, X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X4)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))<=hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Diff__singleton)). 6.97/7.20 fof(fact_setsum__abs, axiom, ![X4, X18, X12, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Oabs__class_Oabs(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5),X18),X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5),hAPP(hAPP(c_COMBB(X5,X5,X12),c_Groups_Oabs__class_Oabs(X5)),X18)),X4)))<=class_Groups_Oordered__ab__group__add__abs(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__abs)). 6.97/7.20 fof(fact_Image__Int__eq, axiom, ![X11, X4, X67, X12, X5]:(hAPP(c_Relation_OImage(X12,X5,X67),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X12,X5,X67),X4)),hAPP(c_Relation_OImage(X12,X5,X67),X11))<=c_Relation_Osingle__valued(X5,X12,hAPP(c_Relation_Oconverse(X12,X5),X67))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__Int__eq)). 6.97/7.20 fof(fact_mult__strict__mono, axiom, ![X74, X31, X29, X30, X8]:(class_Rings_Olinordered__semiring__strict(X8)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X31),X74))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X74)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X31)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X29))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__strict__mono)). 6.97/7.20 fof(fact_mult__strict__mono_H, axiom, ![X74, X31, X29, X30, X8]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X30))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X31))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X74)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X31),X74)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),X29)))<=class_Rings_Olinordered__semiring__strict(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__strict__mono_H)). 6.97/7.20 fof(fact_mult__le__less__imp__less, axiom, ![X74, X31, X29, X30, X8]:(class_Rings_Olinordered__semiring__strict(X8)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X31),X74))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X30))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X31))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X74))))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__le__less__imp__less)). 6.97/7.20 fof(fact_mult__less__le__imp__less, axiom, ![X74, X31, X29, X30, X8]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X30))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X74)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X31))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X31),X74)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),X29)))<=class_Rings_Olinordered__semiring__strict(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__less__le__imp__less)). 6.97/7.20 fof(fact_frac__less2, axiom, ![X26, X39, X7, X6, X8]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X39))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X6),X26)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X7),X39)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X39),X26))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),X7)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X6)))<=class_Fields_Olinordered__field(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_frac__less2)). 6.97/7.20 fof(fact_listsum__update__nat, axiom, ![X25, X163, X19]:(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,X163),X19),X25))=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),X163)),X25)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X163),X19))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X163)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__update__nat)). 6.97/7.20 fof(fact_Least__Suc2, axiom, ![X34, X104, X32, X17]:(hBOOL(hAPP(X17,X32))=>(hBOOL(hAPP(X104,X34))=>((hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,X104))=c_Orderings_Oord__class_OLeast(tc_Nat_Onat,X17)<=![X145]:(hBOOL(hAPP(X17,hAPP(c_Nat_OSuc,X145)))<=>hBOOL(hAPP(X104,X145))))<=~(hBOOL(hAPP(X17,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Least__Suc2)). 6.97/7.20 fof(fact_frac__less, axiom, ![X26, X39, X7, X6, X8]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X6),X7))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X39))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X6),X26)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X7),X39)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X39),X26)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X6)))<=class_Fields_Olinordered__field(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_frac__less)). 6.97/7.20 fof(fact_mult__mono_H, axiom, ![X74, X31, X29, X30, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),X29))=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X31))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X74))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X30)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X31),X74))))<=class_Rings_Oordered__semiring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__mono_H)). 6.97/7.20 fof(fact_mult__mono, axiom, ![X74, X31, X29, X30, X8]:(class_Rings_Oordered__semiring(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),X29))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X29))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X74)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X31))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X31),X74))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__mono)). 6.97/7.20 fof(fact_frac__le, axiom, ![X26, X39, X7, X6, X8]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),X7))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X39))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X39),X26))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X6),X26)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X7),X39))))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X6)))<=class_Fields_Olinordered__field(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_frac__le)). 6.97/7.20 fof(fact_fold1__Un2, axiom, ![X11, X4, X5]:(class_Lattices_Oab__semigroup__idem__mult(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))=>(X11!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X4)),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X11))))<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__Un2)). 6.97/7.20 fof(fact_map__pair__inj__on, axiom, ![X11, X50, X92, X62, X4, X18, X12, X5]:((c_Fun_Oinj__on(tc_prod(X5,X62),tc_prod(X12,X92),c_Product__Type_Omap__pair(X5,X12,X62,X92,X18,X50),hAPP(hAPP(c_Product__Type_OSigma(X5,X62),X4),hAPP(c_COMBK(tc_fun(X62,tc_HOL_Obool),X5),X11)))<=c_Fun_Oinj__on(X62,X92,X50,X11))<=c_Fun_Oinj__on(X5,X12,X18,X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair__inj__on)). 6.97/7.20 fof(fact_in__finite__psubset, axiom, ![X11, X4, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X4),X11))&hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11)))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X4),X11)),c_Wellfounded_Ofinite__psubset(X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__finite__psubset)). 6.97/7.20 fof(fact_card__Diff1__le, axiom, ![X35, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X5),X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Diff1__le)). 6.97/7.20 fof(fact_diff__card__le__card__Diff, axiom, ![X4, X11, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))=>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(X5),X4)),hAPP(c_Finite__Set_Ocard(X5),X11))),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__card__le__card__Diff)). 6.97/7.20 fof(fact_listsum__const__mult, axiom, ![X23, X18, X10, X12, X5]:(class_Rings_Osemiring__0(X5)=>hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X12,X5),hAPP(hAPP(c_COMBB(X5,X5,X12),hAPP(c_Groups_Otimes__class_Otimes(X5),X10)),X18)),X23))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X12,X5),X18),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__const__mult)). 6.97/7.20 fof(fact_mlex__leq, axiom, ![X67, X5, X38, X35, X18]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),X67))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),c_Wellfounded_Omlex__prod(X5,X18,X67))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X18,X35)),hAPP(X18,X38)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mlex__leq)). 6.97/7.20 fof(fact_filter__equals__takeWhile__sorted__rev, axiom, ![X82, X23, X18, X12, X5]:((c_List_Olinorder__class_Osorted(X5,hAPP(c_List_Orev(X5),hAPP(hAPP(c_List_Omap(X12,X5),X18),X23)))=>c_List_OtakeWhile(X12,hAPP(hAPP(c_COMBB(X5,tc_HOL_Obool,X12),hAPP(c_Orderings_Oord__class_Oless(X5),X82)),X18),X23)=hAPP(c_List_Ofilter(X12,hAPP(hAPP(c_COMBB(X5,tc_HOL_Obool,X12),hAPP(c_Orderings_Oord__class_Oless(X5),X82)),X18)),X23))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__equals__takeWhile__sorted__rev)). 6.97/7.20 fof(fact_decr__mult__lemma, axiom, ![X33, X17, X97]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X97))=>(![X22]:(hBOOL(hAPP(X17,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X22),X97)))<=hBOOL(hAPP(X17,X22)))=>(![X22]:(hBOOL(hAPP(X17,X22))=>hBOOL(hAPP(X17,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X97)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_decr__mult__lemma)). 6.97/7.20 fof(fact_quotientI, axiom, ![X3, X4, X35, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X35),X4))=>hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X3),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_quotientI)). 6.97/7.20 fof(fact_folding_Ocommute__comp_H_H, axiom, ![X11, X4, X55, X18, X12, X5]:(c_Finite__Set_Ofolding(X5,X12,X18,X55)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))=>hAPP(c_Fun_Ocomp(X12,X12,X12,hAPP(X55,X4)),hAPP(X55,X11))=hAPP(c_Fun_Ocomp(X12,X12,X12,hAPP(X55,X11)),hAPP(X55,X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Ocommute__comp_H_H)). 6.97/7.20 fof(fact_mem__splitI2, axiom, ![X10, X14, X62, X12, X5, X24]:(![X13, X96]:(hAPP(hAPP(c_Product__Type_OPair(X5,X12),X13),X96)=X24=>hBOOL(hAPP(hAPP(c_member(X62),X14),hAPP(hAPP(X10,X13),X96))))=>hBOOL(hAPP(hAPP(c_member(X62),X14),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X12,tc_fun(X62,tc_HOL_Obool)),X10),X24)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mem__splitI2)). 6.97/7.20 fof(fact_power__Suc__less, axiom, ![X25, X30, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X30))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25))),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),c_Groups_Oone__class_Oone(X8)))))<=class_Rings_Olinordered__semidom(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__Suc__less)). 6.97/7.20 fof(fact_fold__graph__insert__swap, axiom, ![X14, X38, X4, X1, X5]:((hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,c_Groups_Otimes__class_Otimes(X5),X1,X4),X38))=>(~(hBOOL(hAPP(hAPP(c_member(X5),X1),X4)))=>hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,c_Groups_Otimes__class_Otimes(X5),X14,hAPP(hAPP(c_Set_Oinsert(X5),X1),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X14),X38)))))<=class_Groups_Oab__semigroup__mult(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__graph__insert__swap)). 6.97/7.20 fof(fact_INFI__set__fold, axiom, ![X18, X23, X12, X5]:(class_Complete__Lattice_Ocomplete__lattice(X5)=>hAPP(c_List_Ofoldl(X5,X12,hAPP(c_COMBC(X12,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X12),c_Lattices_Osemilattice__inf__class_Oinf(X5)),X18)),c_Orderings_Otop__class_Otop(X5)),X23)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,X5),hAPP(c_List_Oset(X12),X23)),X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INFI__set__fold)). 6.97/7.20 fof(fact_atLeastLessThan__add__Un, axiom, ![X33, X46, X47]:(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X47),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X33))=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,X47),X46)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X46),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X33)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X47),X46))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThan__add__Un)). 6.97/7.20 fof(fact_length__takeWhile__less__P__nth, axiom, ![X23, X5, X17, X46]:(![X42]:(hBOOL(hAPP(X17,hAPP(hAPP(c_List_Onth(X5),X23),X42)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),X46)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X46),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X46),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X17,X23)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__takeWhile__less__P__nth)). 6.97/7.20 fof(fact_SUPR__set__fold, axiom, ![X18, X23, X12, X5]:(class_Complete__Lattice_Ocomplete__lattice(X5)=>hAPP(c_List_Ofoldl(X5,X12,hAPP(c_COMBC(X12,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X12),c_Lattices_Osemilattice__sup__class_Osup(X5)),X18)),c_Orderings_Obot__class_Obot(X5)),X23)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X5),hAPP(c_List_Oset(X12),X23)),X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUPR__set__fold)). 6.97/7.20 fof(fact_quotient__disj, axiom, ![X95, X56, X3, X4, X5]:(c_Equiv__Relations_Oequiv(X5,X4,X3)=>(hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X56),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X4),X3)))=>((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X56),X95)|X95=X56)<=hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X95),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X4),X3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_quotient__disj)). 6.97/7.20 fof(fact_union__comp__emptyL, axiom, ![X11, X65, X4, X5]:(hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X4),X65)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))=>(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))=hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X4),X11)),X65)<=hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X11),X65)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_union__comp__emptyL)). 6.97/7.20 fof(fact_union__comp__emptyR, axiom, ![X65, X11, X4, X5]:((hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X11),X65))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))<=hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X4),X65)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)))<=hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X4),X11)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_union__comp__emptyR)). 6.97/7.20 fof(fact_bij__image__Compl__eq, axiom, ![X4, X18, X12, X5]:(c_Fun_Obij__betw(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))=>hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X12,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X12,X18),X4))=hAPP(c_Set_Oimage(X5,X12,X18),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bij__image__Compl__eq)). 6.97/7.20 fof(fact_abs__triangle__ineq3, axiom, ![X29, X30, X8]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),X30)),hAPP(c_Groups_Oabs__class_Oabs(X8),X29)))),hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X30),X29))))<=class_Groups_Oordered__ab__group__add__abs(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__triangle__ineq3)). 6.97/7.20 fof(fact_UN__finite__subset, axiom, ![X65, X4, X5]:(![X48]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X48)),X4)),X65))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X4)),X65))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__finite__subset)). 6.97/7.20 fof(fact_fun__left__comm__idem_Ofold__insert__idem, axiom, ![X35, X14, X4, X18, X12, X5]:(c_Finite__Set_Ofun__left__comm__idem(X5,X12,X18)=>(hAPP(hAPP(X18,X35),hAPP(hAPP(c_Finite__Set_Ofold(X5,X12,X18),X14),X4))=hAPP(hAPP(c_Finite__Set_Ofold(X5,X12,X18),X14),hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem_Ofold__insert__idem)). 6.97/7.20 fof(fact_fun__left__comm__idem_Ofold__insert__idem2, axiom, ![X35, X14, X4, X18, X12, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hAPP(hAPP(c_Finite__Set_Ofold(X5,X12,X18),hAPP(hAPP(X18,X35),X14)),X4)=hAPP(hAPP(c_Finite__Set_Ofold(X5,X12,X18),X14),hAPP(hAPP(c_Set_Oinsert(X5),X35),X4)))<=c_Finite__Set_Ofun__left__comm__idem(X5,X12,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem_Ofold__insert__idem2)). 6.97/7.20 fof(fact_length__filter__less, axiom, ![X17, X23, X35, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23)))=>(~(hBOOL(hAPP(X17,X35)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,X17),X23))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__filter__less)). 6.97/7.20 fof(fact_congruent2D, axiom, ![X235, X236, X237, X238, X18, X151, X153, X62, X12, X5]:(c_Equiv__Relations_Ocongruent2(X5,X12,X62,X153,X151,X18)=>((hAPP(hAPP(X18,X237),X235)=hAPP(hAPP(X18,X238),X236)<=hBOOL(hAPP(hAPP(c_member(tc_prod(X12,X12)),hAPP(hAPP(c_Product__Type_OPair(X12,X12),X236),X235)),X151)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X238),X237)),X153)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_congruent2D)). 6.97/7.20 fof(fact_divide__strict__left__mono, axiom, ![X31, X30, X29, X8]:(class_Fields_Olinordered__field(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X29),X30))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X31),X30)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X31),X29))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X31))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__strict__left__mono)). 6.97/7.20 fof(fact_divide__left__mono, axiom, ![X31, X30, X29, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X29),X30))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X31))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X31),X30)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X31),X29)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29))))))<=class_Fields_Olinordered__field(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__left__mono)). 6.97/7.20 fof(fact_bset_I5_J, axiom, ![X82, X11, X73]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73))=>![X22]:(![X115]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X115),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X73)))=>![X158]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X158),X11))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X158),X115)!=X22))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22),X82))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X22),X73)),X82))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bset_I5_J)). 6.97/7.20 fof(fact_bset_I6_J, axiom, ![X82, X11, X73]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73))=>![X22]:(![X115]:(![X158]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X158),X11))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X158),X115)!=X22)<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X115),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X73))))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X22),X73)),X82))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22),X82))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bset_I6_J)). 6.97/7.20 fof(fact_aset_I7_J, axiom, ![X82, X4, X73]:(![X22]:(![X115]:(![X158]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X158),X115)!=X22<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X158),X4)))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X115),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X73))))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X82),X22))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X82),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22),X73)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_aset_I7_J)). 6.97/7.20 fof(fact_aset_I8_J, axiom, ![X82, X4, X73]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73))=>![X22]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X82),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22),X73)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X82),X22)))<=![X115]:(![X158]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X158),X4))=>X22!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X158),X115))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X115),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X73)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_aset_I8_J)). 6.97/7.20 fof(fact_divide__strict__left__mono__neg, axiom, ![X31, X29, X30, X8]:(class_Fields_Olinordered__field(X8)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X31),c_Groups_Ozero__class_Ozero(X8)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X31),X30)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X31),X29)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__strict__left__mono__neg)). 6.97/7.20 fof(fact_zmult__zless__mono2__lemma, axiom, ![X19, X27, X28]:((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_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19)),X28)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19)),X27))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X28),X27))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult__zless__mono2__lemma)). 6.97/7.20 fof(fact_unique__quotient__lemma, axiom, ![X70, X53, X100, X101, X29]:(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),X29),X101)),X100)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X29),X53)),X70)))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X100),X29))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X70),X29))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X101),X53))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X100)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_unique__quotient__lemma)). 6.97/7.20 fof(fact_unique__quotient__lemma__neg, axiom, ![X70, X53, X100, X101, X29]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X53),X101))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X29),X100)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X29),X70)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X70),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),X29),X101)),X100)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X29),X53)),X70)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_unique__quotient__lemma__neg)). 6.97/7.20 fof(fact_lexord__irreflexive, axiom, ![X38, X3, X5]:(~(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)),X38),X38)),c_List_Olexord(X5,X3))))<=![X22]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X22),X22)),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__irreflexive)). 6.97/7.20 fof(fact_inj__on__INTER, axiom, ![X4, X18, X62, X12, X5, X15]:((c_Fun_Oinj__on(X12,X62,X18,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),X15),X4))<=![X42]:(hBOOL(hAPP(hAPP(c_member(X5),X42),X15))=>c_Fun_Oinj__on(X12,X62,X18,hAPP(X4,X42))))<=X15!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__INTER)). 6.97/7.20 fof(fact_divide__left__mono__neg, axiom, ![X31, X29, X30, X8]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X31),c_Groups_Ozero__class_Ozero(X8)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X31),X30)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X31),X29)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),X29)))<=class_Fields_Olinordered__field__inverse__zero(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__left__mono__neg)). 6.97/7.20 fof(fact_card__insert, axiom, ![X35, X4, X5]:(hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))=hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__insert)). 6.97/7.20 fof(fact_Int__insert__right, axiom, ![X11, X4, X2, X5]:((hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X2),X11))<=~(hBOOL(hAPP(hAPP(c_member(X5),X2),X4))))&(hBOOL(hAPP(hAPP(c_member(X5),X2),X4))=>hAPP(hAPP(c_Set_Oinsert(X5),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X2),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__insert__right)). 6.97/7.20 fof(fact_pair__imageI, axiom, ![X18, X62, X4, X1, X2, X12, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X2),X1)),X4))=>hBOOL(hAPP(hAPP(c_member(X62),hAPP(hAPP(X18,X2),X1)),hAPP(c_Set_Oimage(tc_prod(X5,X12),X62,hAPP(c_Product__Type_Oprod_Oprod__case(X5,X12,X62),X18)),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__imageI)). 6.97/7.20 fof(fact_card__Suc__Diff1, axiom, ![X35, X4, X5]:((hBOOL(hAPP(hAPP(c_member(X5),X35),X4))=>hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))=hAPP(c_Finite__Set_Ocard(X5),X4))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Suc__Diff1)). 6.97/7.20 fof(fact_image__set__diff, axiom, ![X11, X4, X18, X12, X5]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X12,X18),X4)),hAPP(c_Set_Oimage(X5,X12,X18),X11))=hAPP(c_Set_Oimage(X5,X12,X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11))<=c_Fun_Oinj__on(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__set__diff)). 6.97/7.20 fof(fact_image__Int, axiom, ![X11, X4, X18, X12, X5]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X12,X18),X4)),hAPP(c_Set_Oimage(X5,X12,X18),X11))=hAPP(c_Set_Oimage(X5,X12,X18),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11))<=c_Fun_Oinj__on(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__Int)). 6.97/7.20 fof(fact_UN__least, axiom, ![X65, X11, X12, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X4),X11)),X65))<=![X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),hAPP(X11,X22)),X65))<=hBOOL(hAPP(hAPP(c_member(X5),X22),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__least)). 6.97/7.20 fof(fact_nth__append, axiom, ![X45, X41, X8, X25]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41))))=>hAPP(hAPP(c_List_Onth(X8),hAPP(hAPP(c_List_Oappend(X8),X41),X45)),X25)=hAPP(hAPP(c_List_Onth(X8),X45),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41))))&(hAPP(hAPP(c_List_Onth(X8),X41),X25)=hAPP(hAPP(c_List_Onth(X8),hAPP(hAPP(c_List_Oappend(X8),X41),X45)),X25)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__append)). 6.97/7.20 fof(fact_UN__subset__iff, axiom, ![X11, X4, X15, X12, X5]:(![X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(X4,X22)),X11))<=hBOOL(hAPP(hAPP(c_member(X12),X22),X15)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X15),X4)),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__subset__iff)). 6.97/7.20 fof(fact_INT__subset__iff, axiom, ![X4, X15, X12, X11, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),X15),X4)))<=>![X22]:(hBOOL(hAPP(hAPP(c_member(X12),X22),X15))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(X4,X22))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__subset__iff)). 6.97/7.20 fof(fact_list__update__append1, axiom, ![X6, X45, X41, X8, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)))=>hAPP(hAPP(c_List_Olist__update(X8,hAPP(hAPP(c_List_Oappend(X8),X41),X45)),X28),X6)=hAPP(hAPP(c_List_Oappend(X8),hAPP(hAPP(c_List_Olist__update(X8,X41),X28),X6)),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__append1)). 6.97/7.20 fof(fact_INT__greatest, axiom, ![X11, X65, X12, X4, X5]:(![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),X65),hAPP(X11,X22))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),X65),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),X4),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__greatest)). 6.97/7.20 fof(fact_weak__coinduct__image, axiom, ![X18, X50, X12, X56, X2, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X2),X56))=>(hBOOL(hAPP(hAPP(c_member(X12),hAPP(X50,X2)),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X12,tc_HOL_Obool),X18)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X12,X50),X56)),hAPP(X18,hAPP(c_Set_Oimage(X5,X12,X50),X56)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_weak__coinduct__image)). 6.97/7.20 fof(fact_Un__Int__assoc__eq, axiom, ![X65, X11, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X65),X4))<=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X65))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)),X65)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Int__assoc__eq)). 6.97/7.20 fof(fact_acyclic__insert, axiom, ![X3, X35, X38, X5]:((c_Wellfounded_Oacyclic(X5,X3)&~(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),c_Transitive__Closure_Ortrancl(X5,X3)))))<=>c_Wellfounded_Oacyclic(X5,hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X38),X35)),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acyclic__insert)). 6.97/7.20 fof(fact_wf__insert, axiom, ![X3, X35, X38, X5]:(c_Wellfounded_Owf(X5,hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X38),X35)),X3))<=>(~(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),c_Transitive__Closure_Ortrancl(X5,X3))))&c_Wellfounded_Owf(X5,X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__insert)). 6.97/7.20 fof(fact_sorted__rev__nth__mono, axiom, ![X27, X28, X41, X8]:(class_Orderings_Olinorder(X8)=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X27),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_List_Onth(X8),X41),X27)),hAPP(hAPP(c_List_Onth(X8),X41),X28))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28),X27)))<=c_List_Olinorder__class_Osorted(X8,hAPP(c_List_Orev(X8),X41)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__rev__nth__mono)). 6.97/7.20 fof(fact_reduction__pairI, axiom, ![X44, X67, X5]:(c_Wellfounded_Owf(X5,X67)=>(c_FunDef_Oreduction__pair(X5,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X67),X44))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X67),X44)),X67)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_reduction__pairI)). 6.97/7.20 fof(fact_folding_Oinsert, axiom, ![X35, X4, X55, X18, X12, X5]:(((hAPP(X55,hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))=hAPP(c_Fun_Ocomp(X12,X12,X12,hAPP(X55,X4)),hAPP(X18,X35))<=~(hBOOL(hAPP(hAPP(c_member(X5),X35),X4))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=c_Finite__Set_Ofolding(X5,X12,X18,X55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Oinsert)). 6.97/7.20 fof(fact_Ints__odd__less__0, axiom, ![X2, X5]:(class_Rings_Olinordered__idom(X5)=>(hBOOL(hAPP(hAPP(c_member(X5),X2),c_Int_Oring__1__class_OInts(X5)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),c_Groups_Ozero__class_Ozero(X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oone__class_Oone(X5)),X2)),X2)),c_Groups_Ozero__class_Ozero(X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__odd__less__0)). 6.97/7.20 fof(fact_div__mod__equality, axiom, ![X31, X29, X30, X8]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),X30),X29)),X29)),c_Divides_Odiv__class_Omod(X8,X30,X29))),X31)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X31)<=class_Divides_Osemiring__div(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mod__equality)). 6.97/7.20 fof(fact_div__mod__equality2, axiom, ![X31, X30, X29, X8]:(class_Divides_Osemiring__div(X8)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X31)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),X30),X29))),c_Divides_Odiv__class_Omod(X8,X30,X29))),X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mod__equality2)). 6.97/7.20 fof(fact_bij__betw__combine, axiom, ![X73, X65, X11, X4, X18, X12, X5]:(((hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),X11),X73)=c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool))=>c_Fun_Obij__betw(X5,X12,X18,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X65),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),X11),X73)))<=c_Fun_Obij__betw(X5,X12,X18,X65,X73))<=c_Fun_Obij__betw(X5,X12,X18,X4,X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bij__betw__combine)). 6.97/7.20 fof(fact_nth__take__lemma, axiom, ![X45, X41, X8, X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X45)))=>(hAPP(hAPP(c_List_Otake(X8),X19),X41)=hAPP(hAPP(c_List_Otake(X8),X19),X45)<=![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),X19))=>hAPP(hAPP(c_List_Onth(X8),X41),X42)=hAPP(hAPP(c_List_Onth(X8),X45),X42))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__take__lemma)). 6.97/7.20 fof(fact_comp__surj, axiom, ![X50, X62, X18, X5, X12]:(hAPP(c_Set_Oimage(X12,X5,X18),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))=>(c_Orderings_Otop__class_Otop(tc_fun(X62,tc_HOL_Obool))=hAPP(c_Set_Oimage(X12,X62,hAPP(c_Fun_Ocomp(X5,X62,X12,X50),X18)),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))<=hAPP(c_Set_Oimage(X5,X62,X50),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X62,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comp__surj)). 6.97/7.20 fof(fact_takeWhile__eq__take__P__nth, axiom, ![X17, X23, X5, X32]:(![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),X32))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)))=>hBOOL(hAPP(X17,hAPP(hAPP(c_List_Onth(X5),X23),X42)))))=>(c_List_OtakeWhile(X5,X17,X23)=hAPP(hAPP(c_List_Otake(X5),X32),X23)<=(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)))=>~(hBOOL(hAPP(X17,hAPP(hAPP(c_List_Onth(X5),X23),X32))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__eq__take__P__nth)). 6.97/7.20 fof(fact_pick_Osimps, axiom, ![X41, X6, X8, X28]:((hAPP(c_Random_Opick(X8,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X8)),X6),X41)),X28)=hAPP(c_Random_Opick(X8,X41),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X28),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X8),X6)))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X28),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X8),X6)))))&(hAPP(c_Random_Opick(X8,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X8)),X6),X41)),X28)=hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X8),X6)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X28),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X8),X6))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pick_Osimps)). 6.97/7.20 fof(fact_insort__insert__insort__key, axiom, ![X23, X12, X35, X18, X5]:((~(hBOOL(hAPP(hAPP(c_member(X5),hAPP(X18,X35)),hAPP(c_Set_Oimage(X12,X5,X18),hAPP(c_List_Oset(X12),X23)))))=>c_List_Olinorder__class_Oinsort__insert__key(X12,X5,X18,X35,X23)=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X12,X5,X18),X35),X23))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__insert__insort__key)). 6.97/7.20 fof(fact_fold1Set_Oequations, axiom, ![X102, X125, X103, X18, X5]:(hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X18,hAPP(hAPP(c_Set_Oinsert(X5),X103),X125)),X102))<=>?[X13, X54]:((hAPP(hAPP(c_Set_Oinsert(X5),X103),X125)=hAPP(hAPP(c_Set_Oinsert(X5),X13),X54)&~(hBOOL(hAPP(hAPP(c_member(X5),X13),X54))))&hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,X18,X13,X54),X102)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1Set_Oequations)). 6.97/7.20 fof(fact_strict__below__fold1__iff, axiom, ![X35, X4, X5]:(class_Orderings_Olinorder(X5)=>(((![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X35),X22)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X35),hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X4))))<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_strict__below__fold1__iff)). 6.97/7.20 fof(fact_min__max_Obelow__fold1__iff, axiom, ![X35, X4, X5]:(class_Orderings_Olinorder(X5)=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X4)))<=>![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),X22))))<=X4!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Obelow__fold1__iff)). 6.97/7.20 fof(fact_below__fold1__iff, axiom, ![X35, X4, X5]:(class_Lattices_Osemilattice__inf(X5)=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),hAPP(c_Finite__Set_Ofold1(X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X4)))<=>![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),X22))))<=X4!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_below__fold1__iff)). 6.97/7.20 fof(fact_Diff1__fold__graph, axiom, ![X38, X35, X4, X14, X18, X12, X5]:((hBOOL(hAPP(hAPP(c_member(X5),X35),X4))=>hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X12,X18,X14,X4),hAPP(hAPP(X18,X35),X38))))<=hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X12,X18,X14,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X38))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff1__fold__graph)). 6.97/7.20 fof(fact_finite__range__imageI, axiom, ![X18, X62, X50, X12, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_Oimage(X12,X5,X50),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X62),hAPP(c_Set_Oimage(X12,X62,hAPP(hAPP(c_COMBB(X5,X62,X12),X18),X50)),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__range__imageI)). 6.97/7.20 fof(fact_mem__splitE, axiom, ![X24, X10, X62, X12, X14, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X14),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X12,X62,tc_fun(X5,tc_HOL_Obool)),X10),X24)))=>~(![X22, X72]:(X24=hAPP(hAPP(c_Product__Type_OPair(X12,X62),X22),X72)=>~(hBOOL(hAPP(hAPP(c_member(X5),X14),hAPP(hAPP(X10,X22),X72))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mem__splitE)). 6.97/7.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, axiom, ![X74, X31, X29, X30, X8]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X31),X74))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X29),X74))<=class_Rings_Ocomm__semiring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J)). 6.97/7.20 fof(fact_card__Diff__singleton__if, axiom, ![X35, X4, X5]:(((~(hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))=>hAPP(c_Finite__Set_Ocard(X5),X4)=hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))&(hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X4)),c_Groups_Oone__class_Oone(tc_Nat_Onat))<=hBOOL(hAPP(hAPP(c_member(X5),X35),X4))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Diff__singleton__if)). 6.97/7.20 fof(fact_gfp__fun__UnI2, axiom, ![X56, X2, X18, X5]:(c_Orderings_Oorder__class_Omono(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X18)=>(hBOOL(hAPP(hAPP(c_member(X5),X2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X5,tc_HOL_Obool),X18)))=>hBOOL(hAPP(hAPP(c_member(X5),X2),hAPP(X18,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X56),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X5,tc_HOL_Obool),X18))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_gfp__fun__UnI2)). 6.97/7.20 fof(fact_mono__sup, axiom, ![X11, X4, X18, X5, X12]:((c_Orderings_Oorder__class_Omono(X5,X12,X18)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X12),hAPP(X18,X4)),hAPP(X18,X11))),hAPP(X18,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X4),X11)))))<=(class_Lattices_Osemilattice__sup(X12)&class_Lattices_Osemilattice__sup(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mono__sup)). 6.97/7.20 fof(fact_folding__idem_Ounion__idem, axiom, ![X11, X4, X55, X18, X12, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))=>hAPP(c_Fun_Ocomp(X12,X12,X12,hAPP(X55,X4)),hAPP(X55,X11))=hAPP(X55,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))))<=c_Finite__Set_Ofolding__idem(X5,X12,X18,X55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__idem_Ounion__idem)). 6.97/7.20 fof(fact_append__eq__append__conv2, axiom, ![X174, X83, X84, X23, X5]:(?[X140]:((hAPP(hAPP(c_List_Oappend(X5),X140),X84)=X174&X23=hAPP(hAPP(c_List_Oappend(X5),X83),X140))|(X83=hAPP(hAPP(c_List_Oappend(X5),X23),X140)&X84=hAPP(hAPP(c_List_Oappend(X5),X140),X174)))<=>hAPP(hAPP(c_List_Oappend(X5),X83),X174)=hAPP(hAPP(c_List_Oappend(X5),X23),X84)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__eq__append__conv2)). 6.97/7.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, axiom, ![X211, X207, X208, X209, X8]:(class_Rings_Ocomm__semiring__1(X8)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X209),X208)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X207),X211))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X209),X207)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X208),X211))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J)). 6.97/7.20 fof(fact_folding__image__simple_Oinsert, axiom, ![X35, X4, X55, X50, X14, X18, X12, X5]:(((~(hBOOL(hAPP(hAPP(c_member(X12),X35),X4)))=>hAPP(X55,hAPP(hAPP(c_Set_Oinsert(X12),X35),X4))=hAPP(hAPP(X18,hAPP(X50,X35)),hAPP(X55,X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X4)))<=c_Finite__Set_Ofolding__image__simple(X5,X12,X18,X14,X50,X55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple_Oinsert)). 6.97/7.20 fof(fact_wfP__SUP, axiom, ![X5, X3, X12]:((c_Wellfounded_OwfP(X12,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_fun(X12,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X3))<=![X42, X43]:(hAPP(X3,X43)!=hAPP(X3,X42)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),c_Predicate_ODomainP(X12,X12,hAPP(X3,X42))),c_Predicate_ORangeP(X12,X12,hAPP(X3,X43)))=c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool))))<=![X42]:c_Wellfounded_OwfP(X12,hAPP(X3,X42))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wfP__SUP)). 6.97/7.20 fof(fact_set__drop__subset__set__drop, axiom, ![X23, X5, X34, X32]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32),X34))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Odrop(X5),X34),X23))),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Odrop(X5),X32),X23))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__drop__subset__set__drop)). 6.97/7.20 fof(fact_set__take__subset__set__take, axiom, ![X23, X5, X32, X34]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),X32))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Otake(X5),X34),X23))),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Otake(X5),X32),X23))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__take__subset__set__take)). 6.97/7.20 fof(fact_gt__half__sum, axiom, ![X29, X30, X8]:(class_Fields_Olinordered__field(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),c_Groups_Oone__class_Oone(X8)),c_Groups_Oone__class_Oone(X8)))),X29))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_gt__half__sum)). 6.97/7.20 fof(fact_folding__one__idem_Ohom__commute, axiom, ![X20, X71, X55, X18, X5]:((((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X20=>hAPP(X55,hAPP(c_Set_Oimage(X5,X5,X71),X20))=hAPP(X71,hAPP(X55,X20)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X20)))<=![X22, X72]:hAPP(hAPP(X18,hAPP(X71,X22)),hAPP(X71,X72))=hAPP(X71,hAPP(hAPP(X18,X22),X72)))<=c_Finite__Set_Ofolding__one__idem(X5,X18,X55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one__idem_Ohom__commute)). 6.97/7.20 fof(fact_converseE, axiom, ![X3, X212, X12, X5]:(~(![X22, X72]:(~(hBOOL(hAPP(hAPP(c_member(tc_prod(X12,X5)),hAPP(hAPP(c_Product__Type_OPair(X12,X5),X22),X72)),X3)))<=hAPP(hAPP(c_Product__Type_OPair(X5,X12),X72),X22)=X212))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X12)),X212),hAPP(c_Relation_Oconverse(X12,X5),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converseE)). 6.97/7.20 fof(fact_less__half__sum, axiom, ![X29, X30, X8]:(class_Fields_Olinordered__field(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),c_Groups_Oone__class_Oone(X8)),c_Groups_Oone__class_Oone(X8)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__half__sum)). 6.97/7.20 fof(fact_min__max_Omono__sup, axiom, ![X11, X4, X18, X5, X12]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X12),hAPP(X18,X4)),hAPP(X18,X11))),hAPP(X18,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X4),X11))))<=c_Orderings_Oorder__class_Omono(X5,X12,X18))<=(class_Orderings_Olinorder(X5)&class_Lattices_Osemilattice__sup(X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Omono__sup)). 6.97/7.20 fof(fact_order__fun_I1_J, axiom, ![X50, X18, X5, X12]:((class_Orderings_Oorder(X12)&class_Enum_Oenum(X5))=>(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X5),hAPP(hAPP(c_COMBS(X5,X12,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X12,tc_fun(X12,tc_HOL_Obool),X5),c_Orderings_Oord__class_Oless__eq(X12)),X18)),X50)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X12)),X18),X50)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__fun_I1_J)). 6.97/7.20 fof(fact_setsum__reindex, axiom, ![X71, X11, X18, X12, X5, X62]:((c_Fun_Oinj__on(X5,X12,X18,X11)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X62),hAPP(c_Fun_Ocomp(X12,X62,X5,X71),X18)),X11)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X62),X71),hAPP(c_Set_Oimage(X5,X12,X18),X11)))<=class_Groups_Ocomm__monoid__add(X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__reindex)). 6.97/7.20 fof(fact_abs__setsum__abs, axiom, ![X4, X18, X12, X5]:(class_Groups_Oordered__ab__group__add__abs(X5)=>hAPP(c_Groups_Oabs__class_Oabs(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5),hAPP(hAPP(c_COMBB(X5,X5,X12),c_Groups_Oabs__class_Oabs(X5)),X18)),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5),hAPP(hAPP(c_COMBB(X5,X5,X12),c_Groups_Oabs__class_Oabs(X5)),X18)),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__setsum__abs)). 6.97/7.20 fof(fact_rev__nth, axiom, ![X41, X8, X25]:(hAPP(hAPP(c_List_Onth(X8),X41),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)),hAPP(c_Nat_OSuc,X25)))=hAPP(hAPP(c_List_Onth(X8),hAPP(c_List_Orev(X8),X41)),X25)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__nth)). 6.97/7.20 fof(fact_mem__Sigma__iff, axiom, ![X11, X4, X1, X2, X12, X5]:((hBOOL(hAPP(hAPP(c_member(X12),X1),hAPP(X11,X2)))&hBOOL(hAPP(hAPP(c_member(X5),X2),X4)))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X2),X1)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X4),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mem__Sigma__iff)). 6.97/7.20 fof(fact_folding__one__idem_Ounion__idem, axiom, ![X11, X4, X55, X18, X5]:(c_Finite__Set_Ofolding__one__idem(X5,X18,X55)=>((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))=>(X11!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>hAPP(X55,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(X18,hAPP(X55,X4)),hAPP(X55,X11)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one__idem_Ounion__idem)). 6.97/7.20 fof(fact_card__bij__eq, axiom, ![X50, X11, X4, X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,X4)=>((c_Fun_Oinj__on(X12,X5,X50,X11)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X12,X5,X50),X11)),X4))=>((hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X11))=>hAPP(c_Finite__Set_Ocard(X12),X11)=hAPP(c_Finite__Set_Ocard(X5),X4))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X12,X18),X4)),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__bij__eq)). 6.97/7.20 fof(fact_power__strict__mono, axiom, ![X25, X29, X30, X8]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X30))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X29),X25)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),X29)))<=class_Rings_Olinordered__semidom(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__strict__mono)). 6.97/7.20 fof(fact_add__number__of__left, axiom, ![X26, X39, X40, X8]:(class_Int_Onumber__ring(X8)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),X40)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),X39)),X26))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X40),X39))),X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__number__of__left)). 6.97/7.20 fof(fact_min__max_OInf__fin_Osubset__idem, axiom, ![X11, X4, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>((hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X11)),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X4))=c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X4)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X4)))<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Osubset__idem)). 6.97/7.20 fof(fact_min__max_OSup__fin_Osubset__idem, axiom, ![X11, X4, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X4))=>hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X11)),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X4))=c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X4))<=X11!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Osubset__idem)). 6.97/7.20 fof(fact_dvd__div__mult, axiom, ![X31, X29, X30, X8]:((hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X31)),X30)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),X29),X30)),X31)<=hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X8),X30),X29)))<=class_Divides_Osemiring__div(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dvd__div__mult)). 6.97/7.20 fof(fact_Image__subset, axiom, ![X65, X11, X4, X3, X12, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X4),hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X5),X11))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X12,X3),X65)),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__subset)). 6.97/7.20 fof(fact_Cons__acc__listrel1I, axiom, ![X23, X3, X35, X5]:((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23)),c_Wellfounded_Oacc(tc_List_Olist(X5),c_List_Olistrel1(X5,X3))))<=hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X23),c_Wellfounded_Oacc(tc_List_Olist(X5),c_List_Olistrel1(X5,X3)))))<=hBOOL(hAPP(hAPP(c_member(X5),X35),c_Wellfounded_Oacc(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Cons__acc__listrel1I)). 6.97/7.20 fof(fact_power__strict__decreasing, axiom, ![X30, X168, X25, X8]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X30))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X168)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),c_Groups_Oone__class_Oone(X8)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),X168)))<=class_Rings_Olinordered__semidom(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__strict__decreasing)). 6.97/7.20 fof(fact_power__decreasing, axiom, ![X30, X168, X25, X8]:(class_Rings_Olinordered__semidom(X8)=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),c_Groups_Oone__class_Oone(X8)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X168)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X30)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X168)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__decreasing)). 6.97/7.20 fof(fact_min__max_Omono__inf, axiom, ![X11, X4, X18, X5, X12]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),hAPP(X18,hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X4),X11))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X12),hAPP(X18,X4)),hAPP(X18,X11))))<=c_Orderings_Oorder__class_Omono(X5,X12,X18))<=(class_Orderings_Olinorder(X5)&class_Lattices_Osemilattice__inf(X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Omono__inf)). 6.97/7.20 fof(fact_mono__inf, axiom, ![X11, X4, X18, X5, X12]:((c_Orderings_Oorder__class_Omono(X5,X12,X18)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),hAPP(X18,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X4),X11))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X12),hAPP(X18,X4)),hAPP(X18,X11)))))<=(class_Lattices_Osemilattice__inf(X5)&class_Lattices_Osemilattice__inf(X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mono__inf)). 6.97/7.20 fof(fact_card__Un__disjoint, axiom, ![X11, X4, X5]:(((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X4)),hAPP(c_Finite__Set_Ocard(X5),X11))=hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Un__disjoint)). 6.97/7.20 fof(fact_folding__image__simple__idem_Ounion__idem, axiom, ![X11, X4, X55, X50, X14, X18, X12, X5]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X11))=>hAPP(X55,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(X18,hAPP(X55,X4)),hAPP(X55,X11)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X4)))<=c_Finite__Set_Ofolding__image__simple__idem(X5,X12,X18,X14,X50,X55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple__idem_Ounion__idem)). 6.97/7.20 fof(fact_Image__mono, axiom, ![X4, X107, X3, X37, X12, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),X37),X3))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X12,X37),X107)),hAPP(c_Relation_OImage(X5,X12,X3),X4)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X107),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__mono)). 6.97/7.20 fof(fact_mod__diff__cong, axiom, ![X68, X29, X69, X31, X30, X8]:(((c_Divides_Odiv__class_Omod(X8,X29,X31)=c_Divides_Odiv__class_Omod(X8,X68,X31)=>c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X69),X68),X31)=c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X30),X29),X31))<=c_Divides_Odiv__class_Omod(X8,X69,X31)=c_Divides_Odiv__class_Omod(X8,X30,X31))<=class_Divides_Oring__div(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__diff__cong)). 6.97/7.20 fof(fact_fold1__antimono, axiom, ![X11, X4, X5]:((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4=>((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X11)),hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X4))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__antimono)). 6.97/7.20 fof(fact_fold__image__1, axiom, ![X18, X44, X5, X12]:(class_Groups_Ocomm__monoid__mult(X12)=>((![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X44))=>c_Groups_Oone__class_Oone(X12)=hAPP(X18,X22))=>c_Groups_Oone__class_Oone(X12)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X12,X5,c_Groups_Otimes__class_Otimes(X12)),X18),c_Groups_Oone__class_Oone(X12)),X44))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X44)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__1)). 6.97/7.20 fof(fact_folding_Ocommute__comp_H, axiom, ![X35, X4, X55, X18, X12, X5]:(c_Finite__Set_Ofolding(X5,X12,X18,X55)=>(hAPP(c_Fun_Ocomp(X12,X12,X12,hAPP(X18,X35)),hAPP(X55,X4))=hAPP(c_Fun_Ocomp(X12,X12,X12,hAPP(X55,X4)),hAPP(X18,X35))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Ocommute__comp_H)). 6.97/7.20 fof(fact_times__divide__times__eq, axiom, ![X39, X26, X7, X6, X8]:(class_Fields_Ofield__inverse__zero(X8)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X6),X7)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X26),X39))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X6),X26)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X39))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_times__divide__times__eq)). 6.97/7.20 fof(fact_equiv__class__self, axiom, ![X2, X3, X4, X5]:(c_Equiv__Relations_Oequiv(X5,X4,X3)=>(hBOOL(hAPP(hAPP(c_member(X5),X2),hAPP(c_Relation_OImage(X5,X5,X3),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))<=hBOOL(hAPP(hAPP(c_member(X5),X2),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__class__self)). 6.97/7.20 fof(fact_inj__on__iff__card__le, axiom, ![X11, X12, X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X4)),hAPP(c_Finite__Set_Ocard(X12),X11)))<=>?[X185]:(c_Fun_Oinj__on(X5,X12,X185,X4)&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X12,X185),X4)),X11)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__iff__card__le)). 6.97/7.20 fof(fact_transfer__int__nat__sum__prod_I2_J, axiom, ![X18, X4, X5]:((class_Groups_Ocomm__monoid__mult(X5)&class_Groups_Ocomm__monoid__add(X5))=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),X18),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBB(tc_Int_Oint,X5,tc_Nat_Onat),X18),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X4))<=c_Nat__Transfer_Onat__set(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__sum__prod_I2_J)). 6.97/7.20 fof(fact_transfer__int__nat__sum__prod_I1_J, axiom, ![X18, X4, X5]:((c_Nat__Transfer_Onat__set(X4)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X18),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBB(tc_Int_Oint,X5,tc_Nat_Onat),X18),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X4)))<=(class_Groups_Ocomm__monoid__add(X5)&class_Groups_Ocomm__monoid__mult(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__sum__prod_I1_J)). 6.97/7.20 fof(fact_zdiv__mono2, axiom, ![X29, X68, X30]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),X29)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),X68)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X68),X29)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X68)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__mono2)). 6.97/7.20 fof(fact_zdiv__mono2__neg, axiom, ![X29, X68, X30]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X68),X29))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),X68)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),X29))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X68)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__mono2__neg)). 6.97/7.20 fof(fact_divide__less__eq, axiom, ![X2, X10, X1, X5]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X10)))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X10)))=>((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),c_Groups_Ozero__class_Ozero(X5))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X2)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),c_Groups_Ozero__class_Ozero(X5)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X10)),X1))))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X1),X10)),X2)))<=class_Fields_Olinordered__field__inverse__zero(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__less__eq)). 6.97/7.20 fof(fact_divide__le__eq, axiom, ![X2, X10, X1, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X1),X10)),X2))<=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X10)))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X10)))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),c_Groups_Ozero__class_Ozero(X5)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X10)),X1)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X2))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),c_Groups_Ozero__class_Ozero(X5)))))))))<=class_Fields_Olinordered__field__inverse__zero(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__le__eq)). 6.97/7.20 fof(fact_less__divide__eq, axiom, ![X10, X1, X2, X5]:(class_Fields_Olinordered__field__inverse__zero(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X1),X10)))<=>((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X10)))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),c_Groups_Ozero__class_Ozero(X5)))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),c_Groups_Ozero__class_Ozero(X5)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),c_Groups_Ozero__class_Ozero(X5))))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X10))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X10)),X1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__divide__eq)). 6.97/7.20 fof(fact_le__divide__eq, axiom, ![X10, X1, X2, X5]:(class_Fields_Olinordered__field__inverse__zero(X5)=>(((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X10)))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),c_Groups_Ozero__class_Ozero(X5)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X10))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X2),c_Groups_Ozero__class_Ozero(X5)))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),c_Groups_Ozero__class_Ozero(X5)))))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X10)),X1))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X10))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X1),X10))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__divide__eq)). 6.97/7.20 fof(fact_setsum__shift__bounds__cl__Suc__ivl, axiom, ![X32, X34, X18, X5]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Nat_Onat),X18),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X34,X32))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X34),hAPP(c_Nat_OSuc,X32)))<=class_Groups_Ocomm__monoid__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__shift__bounds__cl__Suc__ivl)). 6.97/7.20 fof(fact_sorted__list__of__set__remove, axiom, ![X35, X4, X5]:((c_List_Olinorder__class_Osorted__list__of__set(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))=c_List_Oremove1(X5,X35,c_List_Olinorder__class_Osorted__list__of__set(X5,X4))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__list__of__set__remove)). 6.97/7.20 fof(fact_INT__absorb, axiom, ![X4, X12, X15, X33, X5]:(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),X15),X4)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),hAPP(X4,X33)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),X15),X4))<=hBOOL(hAPP(hAPP(c_member(X5),X33),X15))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__absorb)). 6.97/7.20 fof(fact_UN__absorb, axiom, ![X4, X12, X15, X33, X5]:(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X15),X4)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),hAPP(X4,X33)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X15),X4))<=hBOOL(hAPP(hAPP(c_member(X5),X33),X15))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__absorb)). 6.97/7.20 fof(fact_fold1__strict__below__iff, axiom, ![X35, X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X4)),X35))<=>?[X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X22),X35))&hBOOL(hAPP(hAPP(c_member(X5),X22),X4))))<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__strict__below__iff)). 6.97/7.20 fof(fact_fold1__below__iff, axiom, ![X35, X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X4)),X35))<=>?[X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X22),X35))))<=X4!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__below__iff)). 6.97/7.20 fof(fact_folding__one__idem_Osubset__idem, axiom, ![X11, X4, X55, X18, X5]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X4))=>hAPP(X55,X4)=hAPP(hAPP(X18,hAPP(X55,X11)),hAPP(X55,X4)))<=X11!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=c_Finite__Set_Ofolding__one__idem(X5,X18,X55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one__idem_Osubset__idem)). 6.97/7.20 fof(fact_mult__number__of__left, axiom, ![X26, X39, X40, X8]:(class_Int_Onumber__ring(X8)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),X40)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),X39)),X26))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X40),X39))),X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__number__of__left)). 6.97/7.20 fof(fact_add__number__of__diff1, axiom, ![X31, X39, X40, X8]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X40),X39))),X31)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),X40)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),X39)),X31))<=class_Int_Onumber__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__number__of__diff1)). 6.97/7.20 fof(fact_sorted__equals__nth__mono, axiom, ![X23, X5]:(class_Orderings_Olinorder(X5)=>(c_List_Olinorder__class_Osorted(X5,X23)<=>![X43]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)))=>![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_List_Onth(X5),X23),X42)),hAPP(hAPP(c_List_Onth(X5),X23),X43)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X43)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__equals__nth__mono)). 6.97/7.20 fof(fact_INT__I, axiom, ![X11, X1, X12, X4, X5]:(hBOOL(hAPP(hAPP(c_member(X12),X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),X4),X11)))<=![X22]:(hBOOL(hAPP(hAPP(c_member(X12),X1),hAPP(X11,X22)))<=hBOOL(hAPP(hAPP(c_member(X5),X22),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__I)). 6.97/7.20 fof(fact_mod__add__cong, axiom, ![X68, X29, X69, X31, X30, X8]:(((c_Divides_Odiv__class_Omod(X8,X29,X31)=c_Divides_Odiv__class_Omod(X8,X68,X31)=>c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29),X31)=c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X69),X68),X31))<=c_Divides_Odiv__class_Omod(X8,X30,X31)=c_Divides_Odiv__class_Omod(X8,X69,X31))<=class_Divides_Osemiring__div(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__add__cong)). 6.97/7.20 fof(fact_all__set__conv__all__nth, axiom, ![X17, X23, X5]:(![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)))=>hBOOL(hAPP(X17,hAPP(hAPP(c_List_Onth(X5),X23),X42))))<=>![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X23)))=>hBOOL(hAPP(X17,X22)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_all__set__conv__all__nth)). 6.97/7.20 fof(fact_abs__triangle__ineq2, axiom, ![X29, X30, X8]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),X30)),hAPP(c_Groups_Oabs__class_Oabs(X8),X29))),hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X30),X29))))<=class_Groups_Oordered__ab__group__add__abs(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__triangle__ineq2)). 6.97/7.20 fof(fact_abs__triangle__ineq2__sym, axiom, ![X29, X30, X8]:(class_Groups_Oordered__ab__group__add__abs(X8)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),X30)),hAPP(c_Groups_Oabs__class_Oabs(X8),X29))),hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X29),X30))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__triangle__ineq2__sym)). 6.97/7.20 fof(fact_INT__iff, axiom, ![X11, X4, X12, X1, X5]:(![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X1),hAPP(X11,X22)))<=hBOOL(hAPP(hAPP(c_member(X12),X22),X4)))<=>hBOOL(hAPP(hAPP(c_member(X5),X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),X4),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__iff)). 6.97/7.20 fof(fact_list__size__pointwise, axiom, ![X50, X18, X23, X5]:(![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X23)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X18,X22)),hAPP(X50,X22))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X5,X18,X23)),c_List_Olist_Olist__size(X5,X50,X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__size__pointwise)). 6.97/7.20 fof(fact_mod__mult__cong, axiom, ![X68, X29, X69, X31, X30, X8]:((c_Divides_Odiv__class_Omod(X8,X69,X31)=c_Divides_Odiv__class_Omod(X8,X30,X31)=>(c_Divides_Odiv__class_Omod(X8,X29,X31)=c_Divides_Odiv__class_Omod(X8,X68,X31)=>c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29),X31)=c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X69),X68),X31)))<=class_Divides_Osemiring__div(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__cong)). 6.97/7.20 fof(fact_abs__triangle__ineq4, axiom, ![X29, X30, X8]:(class_Groups_Oordered__ab__group__add__abs(X8)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X30),X29))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),X30)),hAPP(c_Groups_Oabs__class_Oabs(X8),X29))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__triangle__ineq4)). 6.97/7.20 fof(fact_abs__triangle__ineq, axiom, ![X29, X30, X8]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),X30)),hAPP(c_Groups_Oabs__class_Oabs(X8),X29))))<=class_Groups_Oordered__ab__group__add__abs(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__triangle__ineq)). 6.97/7.20 fof(fact_nth__drop_H, axiom, ![X41, X8, X28]:(hAPP(hAPP(c_List_Olist_OCons(X8),hAPP(hAPP(c_List_Onth(X8),X41),X28)),hAPP(hAPP(c_List_Odrop(X8),hAPP(c_Nat_OSuc,X28)),X41))=hAPP(hAPP(c_List_Odrop(X8),X28),X41)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__drop_H)). 6.97/7.20 fof(fact_power__diff, axiom, ![X36, X25, X30, X8]:(((hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),X25))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X36)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X36)))<=X30!=c_Groups_Ozero__class_Ozero(X8))<=class_Fields_Ofield(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__diff)). 6.97/7.20 fof(fact_Image__singleton__iff, axiom, ![X2, X3, X12, X1, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X12,X5)),hAPP(hAPP(c_Product__Type_OPair(X12,X5),X2),X1)),X3))<=>hBOOL(hAPP(hAPP(c_member(X5),X1),hAPP(c_Relation_OImage(X12,X5,X3),hAPP(hAPP(c_Set_Oinsert(X12),X2),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__singleton__iff)). 6.97/7.20 fof(fact_wf__iff__no__infinite__down__chain, axiom, ![X3, X5]:(~(?[X185]:![X42]:hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(X185,hAPP(c_Nat_OSuc,X42))),hAPP(X185,X42))),X3)))<=>c_Wellfounded_Owf(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__iff__no__infinite__down__chain)). 6.97/7.20 fof(fact_power__minus, axiom, ![X25, X30, X8]:(class_Rings_Oring__1(X8)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),c_Groups_Oone__class_Oone(X8))),X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25))=hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X30)),X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__minus)). 6.97/7.20 fof(fact_diff__divide__eq__iff, axiom, ![X7, X6, X26, X8]:((c_Groups_Ozero__class_Ozero(X8)!=X26=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X7),X26))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X6)),X7)),X26))<=class_Fields_Ofield(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__divide__eq__iff)). 6.97/7.20 fof(fact_add__divide__eq__iff, axiom, ![X7, X6, X26, X8]:(class_Fields_Ofield(X8)=>(c_Groups_Ozero__class_Ozero(X8)!=X26=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X7),X26))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X6)),X7)),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__divide__eq__iff)). 6.97/7.20 fof(fact_setprod__insert, axiom, ![X18, X2, X4, X5, X12]:(class_Groups_Ocomm__monoid__mult(X12)=>((hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12),hAPP(X18,X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X18),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X18),hAPP(hAPP(c_Set_Oinsert(X5),X2),X4))<=~(hBOOL(hAPP(hAPP(c_member(X5),X2),X4))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__insert)). 6.97/7.20 fof(fact_add__frac__num, axiom, ![X26, X6, X7, X8]:(class_Fields_Ofield__inverse__zero(X8)=>(c_Groups_Ozero__class_Ozero(X8)!=X7=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X6),X7)),X26)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X7))),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__frac__num)). 6.97/7.20 fof(fact_divide__diff__eq__iff, axiom, ![X7, X6, X26, X8]:(class_Fields_Ofield(X8)=>(X26!=c_Groups_Ozero__class_Ozero(X8)=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X7))),X26)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X6),X26)),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__diff__eq__iff)). 6.97/7.20 fof(fact_divide__add__eq__iff, axiom, ![X7, X6, X26, X8]:((hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X7))),X26)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X6),X26)),X7)<=X26!=c_Groups_Ozero__class_Ozero(X8))<=class_Fields_Ofield(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__add__eq__iff)). 6.97/7.20 fof(fact_div__mult__self1, axiom, ![X31, X30, X29, X8]:(class_Divides_Osemiring__div(X8)=>(hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X29))),X29)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X31),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),X30),X29))<=c_Groups_Ozero__class_Ozero(X8)!=X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__self1)). 6.97/7.20 fof(fact_fold__graph_OinsertI, axiom, ![X38, X14, X18, X12, X4, X35, X5]:((hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X12,X18,X14,X4),X38))=>hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X12,X18,X14,hAPP(hAPP(c_Set_Oinsert(X5),X35),X4)),hAPP(hAPP(X18,X35),X38))))<=~(hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__graph_OinsertI)). 6.97/7.20 fof(fact_list__update__swap, axiom, ![X224, X6, X41, X8, X225, X28]:(hAPP(hAPP(c_List_Olist__update(X8,hAPP(hAPP(c_List_Olist__update(X8,X41),X28),X6)),X225),X224)=hAPP(hAPP(c_List_Olist__update(X8,hAPP(hAPP(c_List_Olist__update(X8,X41),X225),X224)),X28),X6)<=X225!=X28), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__swap)). 6.97/7.20 fof(fact_setsum__insert, axiom, ![X18, X2, X55, X5, X12]:(((~(hBOOL(hAPP(hAPP(c_member(X5),X2),X55)))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),hAPP(hAPP(c_Set_Oinsert(X5),X2),X55))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12),hAPP(X18,X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),X55)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X55)))<=class_Groups_Ocomm__monoid__add(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__insert)). 6.97/7.20 fof(fact_add__num__frac, axiom, ![X6, X26, X7, X8]:((c_Groups_Ozero__class_Ozero(X8)!=X7=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X7))),X7)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X26),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X6),X7)))<=class_Fields_Ofield__inverse__zero(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__num__frac)). 6.97/7.20 fof(fact_div__mult__self2, axiom, ![X31, X30, X29, X8]:(class_Divides_Osemiring__div(X8)=>(X29!=c_Groups_Ozero__class_Ozero(X8)=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X31))),X29)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X31),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),X30),X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__self2)). 6.97/7.20 fof(fact_set__update__subsetI, axiom, ![X47, X35, X4, X23, X5]:((hBOOL(hAPP(hAPP(c_member(X5),X35),X4))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist__update(X5,X23),X47),X35))),X4)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X23)),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__update__subsetI)). 6.97/7.20 fof(fact_power__less__power__Suc, axiom, ![X25, X30, X8]:(class_Rings_Olinordered__semidom(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Oone__class_Oone(X8)),X30)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__less__power__Suc)). 6.97/7.20 fof(fact_transfer__nat__int__sum__prod_I2_J, axiom, ![X4, X18, X5]:((class_Groups_Ocomm__monoid__mult(X5)&class_Groups_Ocomm__monoid__add(X5))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Int_Oint),X18),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X5),X18),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__sum__prod_I2_J)). 6.97/7.20 fof(fact_transfer__nat__int__sum__prod_I1_J, axiom, ![X4, X18, X5]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Int_Oint),X18),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),X4)<=(class_Groups_Ocomm__monoid__mult(X5)&class_Groups_Ocomm__monoid__add(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__sum__prod_I1_J)). 6.97/7.20 fof(fact_fun__left__comm_Ofold__graph__insertE, axiom, ![X60, X4, X35, X14, X18, X12, X5]:((hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X12,X18,X14,hAPP(hAPP(c_Set_Oinsert(X5),X35),X4)),X60))=>(~(hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))=>~(![X72]:(hAPP(hAPP(X18,X35),X72)=X60=>~(hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X12,X18,X14,X4),X72)))))))<=c_Finite__Set_Ofun__left__comm(X5,X12,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__graph__insertE)). 6.97/7.20 fof(fact_list__all2__update__cong2, axiom, ![X47, X38, X35, X84, X23, X17, X12, X5]:(c_List_Olist__all2(X5,X12,X17,X23,X84)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X47),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12)),X84)))=>c_List_Olist__all2(X5,X12,X17,hAPP(hAPP(c_List_Olist__update(X5,X23),X47),X35),hAPP(hAPP(c_List_Olist__update(X12,X84),X47),X38)))<=hBOOL(hAPP(hAPP(X17,X35),X38)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__update__cong2)). 6.97/7.20 fof(fact_Sup__fin_Ounion__idem, axiom, ![X11, X4, X5]:(class_Lattices_Olattice(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(X4!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X11=>c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),c_Big__Operators_Olattice__class_OSup__fin(X5,X4)),c_Big__Operators_Olattice__class_OSup__fin(X5,X11)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Ounion__idem)). 6.97/7.20 fof(fact_list__all2__update__cong, axiom, ![X38, X35, X84, X17, X12, X23, X5, X47]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X47),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)))=>((hBOOL(hAPP(hAPP(X17,X35),X38))=>c_List_Olist__all2(X5,X12,X17,hAPP(hAPP(c_List_Olist__update(X5,X23),X47),X35),hAPP(hAPP(c_List_Olist__update(X12,X84),X47),X38)))<=c_List_Olist__all2(X5,X12,X17,X23,X84))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__update__cong)). 6.97/7.20 fof(fact_finite__UN, axiom, ![X11, X12, X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X12),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X4),X11)))<=>![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X12),hAPP(X11,X22)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__UN)). 6.97/7.20 fof(fact_finite__UN__I, axiom, ![X11, X12, X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X12),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X4),X11)))<=![X13]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X12),hAPP(X11,X13)))<=hBOOL(hAPP(hAPP(c_member(X5),X13),X4))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__UN__I)). 6.97/7.20 fof(fact_finite__SigmaI, axiom, ![X11, X12, X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(![X13]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X12),hAPP(X11,X13)))<=hBOOL(hAPP(hAPP(c_member(X5),X13),X4)))=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X4),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__SigmaI)). 6.97/7.20 fof(fact_ivl__disj__un_I17_J, axiom, ![X51, X34, X52, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X52),X34))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X34),X51))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X52),X34)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X34),X51))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X52),X51)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I17_J)). 6.97/7.20 fof(fact_min__max_Ofold__inf__le__inf, axiom, ![X1, X2, X4, X5]:(class_Orderings_Olinorder(X5)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X1),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X2),X1)))<=hBOOL(hAPP(hAPP(c_member(X5),X2),X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ofold__inf__le__inf)). 6.97/7.20 fof(fact_fold__inf__le__inf, axiom, ![X1, X2, X4, X5]:(class_Lattices_Osemilattice__inf(X5)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X1),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X2),X1)))<=hBOOL(hAPP(hAPP(c_member(X5),X2),X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__inf__le__inf)). 6.97/7.20 fof(fact_congruentI, axiom, ![X12, X18, X3, X5]:(c_Equiv__Relations_Ocongruent(X5,X12,X3,X18)<=![X72, X116]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X72),X116)),X3))=>hAPP(X18,X116)=hAPP(X18,X72))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_congruentI)). 6.97/7.20 fof(fact_Inf__fin_Ohom__commute, axiom, ![X20, X71, X5]:((((hAPP(X71,c_Big__Operators_Olattice__class_OInf__fin(X5,X20))=c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(c_Set_Oimage(X5,X5,X71),X20))<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X20)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X20)))<=![X22, X72]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),hAPP(X71,X22)),hAPP(X71,X72))=hAPP(X71,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X22),X72)))<=class_Lattices_Olattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Ohom__commute)). 6.97/7.20 fof(fact_Min_Ohom__commute, axiom, ![X20, X71, X5]:(class_Orderings_Olinorder(X5)=>(![X22, X72]:hAPP(X71,hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X22),X72))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),hAPP(X71,X22)),hAPP(X71,X72))=>((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X20=>hAPP(X71,c_Big__Operators_Olinorder__class_OMin(X5,X20))=c_Big__Operators_Olinorder__class_OMin(X5,hAPP(c_Set_Oimage(X5,X5,X71),X20)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X20))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min_Ohom__commute)). 6.97/7.20 fof(fact_Sup__fin_Ohom__commute, axiom, ![X20, X71, X5]:(class_Lattices_Olattice(X5)=>(![X22, X72]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),hAPP(X71,X22)),hAPP(X71,X72))=hAPP(X71,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X22),X72))=>((X20!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(c_Set_Oimage(X5,X5,X71),X20))=hAPP(X71,c_Big__Operators_Olattice__class_OSup__fin(X5,X20)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X20))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Ohom__commute)). 6.97/7.20 fof(fact_Max_Ohom__commute, axiom, ![X20, X71, X5]:((![X22, X72]:hAPP(X71,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X22),X72))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),hAPP(X71,X22)),hAPP(X71,X72))=>((c_Big__Operators_Olinorder__class_OMax(X5,hAPP(c_Set_Oimage(X5,X5,X71),X20))=hAPP(X71,c_Big__Operators_Olinorder__class_OMax(X5,X20))<=X20!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X20))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max_Ohom__commute)). 6.97/7.20 fof(fact_min__max_Osup__le__fold__sup, axiom, ![X1, X2, X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hBOOL(hAPP(hAPP(c_member(X5),X2),X4))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X2),X1)),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X1),X4)))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__le__fold__sup)). 6.97/7.20 fof(fact_sup__le__fold__sup, axiom, ![X1, X2, X4, X5]:(class_Lattices_Osemilattice__sup(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X2),X1)),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X1),X4)))<=hBOOL(hAPP(hAPP(c_member(X5),X2),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__le__fold__sup)). 6.97/7.20 fof(fact_inj__transfer, axiom, ![X35, X17, X18, X12, X5]:((![X72]:(hBOOL(hAPP(hAPP(c_member(X12),X72),hAPP(c_Set_Oimage(X5,X12,X18),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))=>hBOOL(hAPP(X17,hAPP(c_Hilbert__Choice_Oinv__into(X5,X12,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X18),X72))))=>hBOOL(hAPP(X17,X35)))<=c_Fun_Oinj__on(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__transfer)). 6.97/7.20 fof(fact_nonzero__power__divide, axiom, ![X25, X30, X29, X8]:(class_Fields_Ofield(X8)=>(hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X30),X29)),X25)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X29),X25))<=c_Groups_Ozero__class_Ozero(X8)!=X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nonzero__power__divide)). 6.97/7.20 fof(fact_Int__atLeastLessThan, axiom, ![X97, X10, X1, X2, X5]:(class_Orderings_Olinorder(X5)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X2),X1)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X10),X97))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X2),X10)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X1),X97))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__atLeastLessThan)). 6.97/7.20 fof(fact_finite__equiv__class, axiom, ![X56, X3, X4, X5]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X56))<=hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X56),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X4),X3))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X4),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X4)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__equiv__class)). 6.97/7.20 fof(fact_div__pos__neg, axiom, ![X29, X30]:((hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),X29)=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),X30),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X29))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X29),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)),X30))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__pos__neg)). 6.97/7.20 fof(fact_div__neg__neg, axiom, ![X29, X30]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),X29)=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),X30),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X29)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__neg__neg)). 6.97/7.20 fof(fact_image__subsetI, axiom, ![X11, X18, X12, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X12,X18),X4)),X11))<=![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))=>hBOOL(hAPP(hAPP(c_member(X12),hAPP(X18,X22)),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__subsetI)). 6.97/7.20 fof(fact_Min__Un, axiom, ![X11, X4, X5]:(((X4!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))=>(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X11=>c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olinorder__class_OMin(X5,X4)),c_Big__Operators_Olinorder__class_OMin(X5,X11)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min__Un)). 6.97/7.20 fof(fact_SUP__le__iff, axiom, ![X51, X94, X4, X12, X5]:(class_Complete__Lattice_Ocomplete__lattice(X5)=>(![X22]:(hBOOL(hAPP(hAPP(c_member(X12),X22),X4))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X94,X22)),X51)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X5),X4),X94)),X51)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP__le__iff)). 6.97/7.20 fof(fact_SUP__leI, axiom, ![X51, X94, X4, X5, X12]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X12),X4),X94)),X51))<=![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),hAPP(X94,X42)),X51))<=hBOOL(hAPP(hAPP(c_member(X5),X42),X4))))<=class_Complete__Lattice_Ocomplete__lattice(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP__leI)). 6.97/7.20 fof(fact_le__INF__iff, axiom, ![X94, X4, X12, X51, X5]:(class_Complete__Lattice_Ocomplete__lattice(X5)=>(![X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X51),hAPP(X94,X22)))<=hBOOL(hAPP(hAPP(c_member(X12),X22),X4)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X51),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,X5),X4),X94))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__INF__iff)). 6.97/7.20 fof(fact_le__INFI, axiom, ![X94, X51, X4, X5, X12]:((![X42]:(hBOOL(hAPP(hAPP(c_member(X5),X42),X4))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),X51),hAPP(X94,X42))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),X51),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X12),X4),X94))))<=class_Complete__Lattice_Ocomplete__lattice(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__INFI)). 6.97/7.20 fof(fact_card__inj__on__le, axiom, ![X11, X4, X18, X12, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X12,X18),X4)),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X4)),hAPP(c_Finite__Set_Ocard(X12),X11)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X11))))<=c_Fun_Oinj__on(X5,X12,X18,X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__inj__on__le)). 6.97/7.20 fof(fact_setsum__right__distrib, axiom, ![X4, X18, X12, X3, X5]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5),X18),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5),hAPP(hAPP(c_COMBB(X5,X5,X12),hAPP(c_Groups_Otimes__class_Otimes(X5),X3)),X18)),X4)<=class_Rings_Osemiring__0(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__right__distrib)). 6.97/7.20 fof(fact_folding__image_Ocong, axiom, ![X71, X50, X4, X55, X14, X18, X12, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X4))=>(![X22]:(hAPP(X71,X22)=hAPP(X50,X22)<=hBOOL(hAPP(hAPP(c_member(X12),X22),X4)))=>hAPP(hAPP(X55,X71),X4)=hAPP(hAPP(X55,X50),X4)))<=c_Finite__Set_Ofolding__image(X5,X12,X18,X14,X55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image_Ocong)). 6.97/7.20 fof(fact_setprod__pos__nat__iff, axiom, ![X18, X44, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X44))=>(![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X44))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X18,X22))))<=>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(X5,tc_Nat_Onat),X18),X44))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__pos__nat__iff)). 6.97/7.20 fof(fact_Inf__fin_Ounion__idem, axiom, ![X11, X4, X5]:(((X4!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))=>(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X11=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Big__Operators_Olattice__class_OInf__fin(X5,X4)),c_Big__Operators_Olattice__class_OInf__fin(X5,X11))=c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Lattices_Olattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Ounion__idem)). 6.97/7.20 fof(fact_setprod__pos, axiom, ![X18, X4, X5, X12]:(class_Rings_Olinordered__semidom(X12)=>(![X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),c_Groups_Ozero__class_Ozero(X12)),hAPP(X18,X22)))<=hBOOL(hAPP(hAPP(c_member(X5),X22),X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),c_Groups_Ozero__class_Ozero(X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X18),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__pos)). 6.97/7.20 fof(fact_setprod__nonneg, axiom, ![X18, X4, X5, X12]:((![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),c_Groups_Ozero__class_Ozero(X12)),hAPP(X18,X22))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),c_Groups_Ozero__class_Ozero(X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X18),X4))))<=class_Rings_Olinordered__semidom(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__nonneg)). 6.97/7.20 fof(fact_sym__def, axiom, ![X3, X5]:(![X22, X72]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X22),X72)),X3))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X72),X22)),X3)))<=>c_Relation_Osym(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sym__def)). 6.97/7.20 fof(fact_abs__eq__mult, axiom, ![X29, X30, X8]:(class_Rings_Oordered__ring__abs(X8)=>(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),X30)),hAPP(c_Groups_Oabs__class_Oabs(X8),X29))=hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29))<=((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X30))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),c_Groups_Ozero__class_Ozero(X8))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X29),c_Groups_Ozero__class_Ozero(X8)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X29)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__eq__mult)). 6.97/7.20 fof(fact_Max__Un, axiom, ![X11, X4, X5]:(class_Orderings_Olinorder(X5)=>((((X11!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olinorder__class_OMax(X5,X4)),c_Big__Operators_Olinorder__class_OMax(X5,X11))=c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11)))<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max__Un)). 6.97/7.20 fof(fact_insert__Diff__if, axiom, ![X4, X11, X35, X5]:((~(hBOOL(hAPP(hAPP(c_member(X5),X35),X11)))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X35),X4)),X11)=hAPP(hAPP(c_Set_Oinsert(X5),X35),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11)))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X35),X4)),X11)<=hBOOL(hAPP(hAPP(c_member(X5),X35),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__Diff__if)). 6.97/7.20 fof(fact_single__Diff__lessThan, axiom, ![X33, X5]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X33),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X33))=hAPP(hAPP(c_Set_Oinsert(X5),X33),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))<=class_Orderings_Oorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_single__Diff__lessThan)). 6.97/7.20 fof(fact_Diff__insert__absorb, axiom, ![X4, X35, X5]:(~(hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))=>X4=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X35),X4)),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__insert__absorb)). 6.97/7.20 fof(fact_converse__iff, axiom, ![X3, X1, X2, X12, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X12,X5)),hAPP(hAPP(c_Product__Type_OPair(X12,X5),X1),X2)),X3))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X2),X1)),hAPP(c_Relation_Oconverse(X12,X5),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__iff)). 6.97/7.20 fof(fact_fun__left__comm__idem_Ofold__set, axiom, ![X23, X38, X18, X12, X5]:(hAPP(hAPP(c_Finite__Set_Ofold(X5,X12,X18),X38),hAPP(c_List_Oset(X5),X23))=hAPP(c_List_Ofoldl(X12,X5,hAPP(c_COMBC(X5,X12,X12),X18),X38),X23)<=c_Finite__Set_Ofun__left__comm__idem(X5,X12,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem_Ofold__set)). 6.97/7.20 fof(fact_folding__one_Oeq__fold_H, axiom, ![X35, X4, X55, X18, X5]:(c_Finite__Set_Ofolding__one(X5,X18,X55)=>((hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,X18),X35),X4)=hAPP(X55,hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))<=~(hBOOL(hAPP(hAPP(c_member(X5),X35),X4))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one_Oeq__fold_H)). 6.97/7.20 fof(fact_card__Diff__subset, axiom, ![X4, X11, X5]:((hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X4)),hAPP(c_Finite__Set_Ocard(X5),X11))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Diff__subset)). 6.97/7.20 fof(fact_dvd__div__div__eq__mult, axiom, ![X97, X1, X10, X2, X5]:(class_Divides_Osemiring__div(X5)=>(((hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X2),X1))=>(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X10),X97))=>(hAPP(hAPP(c_Divides_Odiv__class_Odiv(X5),X97),X10)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X5),X1),X2)<=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X10)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X97))))<=X10!=c_Groups_Ozero__class_Ozero(X5))<=X2!=c_Groups_Ozero__class_Ozero(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dvd__div__div__eq__mult)). 6.97/7.20 fof(fact_SUP2__iff, axiom, ![X10, X1, X11, X4, X62, X12, X5]:(?[X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))&hBOOL(hAPP(hAPP(hAPP(X11,X22),X1),X10)))<=>hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_fun(X62,tc_HOL_Obool))),X4),X11),X1),X10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP2__iff)). 6.97/7.20 fof(fact_min__max_Ofold__inf__insert, axiom, ![X2, X1, X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X1),hAPP(hAPP(c_Set_Oinsert(X5),X2),X4))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X2),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X1),X4)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ofold__inf__insert)). 6.97/7.20 fof(fact_div__geq, axiom, ![X36, X25]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))=>(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X36),X25)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),X25)),X25))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X36),X25))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__geq)). 6.97/7.20 fof(fact_fold__inf__insert, axiom, ![X2, X1, X4, X5]:(class_Lattices_Osemilattice__inf(X5)=>(hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X1),hAPP(hAPP(c_Set_Oinsert(X5),X2),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X2),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X1),X4))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__inf__insert)). 6.97/7.20 fof(fact_fold__sup__insert, axiom, ![X2, X1, X4, X5]:(class_Lattices_Osemilattice__sup(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X1),hAPP(hAPP(c_Set_Oinsert(X5),X2),X4))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X2),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X1),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__sup__insert)). 6.97/7.20 fof(fact_min__max_Ofold__sup__insert, axiom, ![X2, X1, X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X2),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X1),X4))=hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X1),hAPP(hAPP(c_Set_Oinsert(X5),X2),X4)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ofold__sup__insert)). 6.97/7.20 fof(fact_take__Cons_H, axiom, ![X41, X6, X8, X25]:((hAPP(hAPP(c_List_Otake(X8),X25),hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41))=c_List_Olist_ONil(X8)<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X25)&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X25=>hAPP(hAPP(c_List_Otake(X8),X25),hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41))=hAPP(hAPP(c_List_Olist_OCons(X8),X6),hAPP(hAPP(c_List_Otake(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X41)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__Cons_H)). 6.97/7.20 fof(fact_set__remove1__eq, axiom, ![X35, X23, X5]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X23)),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))=hAPP(c_List_Oset(X5),c_List_Oremove1(X5,X35,X23))<=hBOOL(hAPP(c_List_Odistinct(X5),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__remove1__eq)). 6.97/7.20 fof(fact_inj__on__strict__subset, axiom, ![X4, X11, X18, X12, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X12,X18),X4)),hAPP(c_Set_Oimage(X5,X12,X18),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X4),X11)))<=c_Fun_Oinj__on(X5,X12,X18,X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__strict__subset)). 6.97/7.20 fof(fact_mlex__less, axiom, ![X67, X5, X38, X35, X18]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),c_Wellfounded_Omlex__prod(X5,X18,X67)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X18,X35)),hAPP(X18,X38)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mlex__less)). 6.97/7.20 fof(fact_split__div_H, axiom, ![X32, X34, X17]:(hBOOL(hAPP(X17,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X34),X32)))<=>((hBOOL(hAPP(X17,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&X32=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|?[X150]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),hAPP(c_Nat_OSuc,X150))))&hBOOL(hAPP(X17,X150)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X150)),X34))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__div_H)). 6.97/7.20 fof(fact_UN__I, axiom, ![X11, X1, X12, X4, X2, X5]:((hBOOL(hAPP(hAPP(c_member(X12),X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X4),X11)))<=hBOOL(hAPP(hAPP(c_member(X12),X1),hAPP(X11,X2))))<=hBOOL(hAPP(hAPP(c_member(X5),X2),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__I)). 6.97/7.20 fof(fact_mult__less__cancel__right__disj, axiom, ![X1, X10, X2, X5]:(class_Rings_Olinordered__ring__strict(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X10)))<=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),X1))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X10)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),c_Groups_Ozero__class_Ozero(X5)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X1),X2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__less__cancel__right__disj)). 6.97/7.20 fof(fact_mult__strict__right__mono, axiom, ![X31, X29, X30, X8]:(class_Rings_Olinordered__semiring__strict(X8)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X31))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X31))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__strict__right__mono)). 6.97/7.20 fof(fact_comm__mult__strict__left__mono, axiom, ![X31, X29, X30, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),X29))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X30)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X29)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X31))))<=class_Rings_Olinordered__comm__semiring__strict(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__mult__strict__left__mono)). 6.97/7.20 fof(fact_mult__less__cancel__left__pos, axiom, ![X1, X2, X10, X5]:(class_Rings_Olinordered__ring__strict(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X10))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),X1))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__less__cancel__left__pos)). 6.97/7.20 fof(fact_mult__strict__left__mono, axiom, ![X31, X29, X30, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),X29))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X31))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X30)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X29)))))<=class_Rings_Olinordered__semiring__strict(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__strict__left__mono)). 6.97/7.20 fof(fact_divide__strict__right__mono, axiom, ![X31, X29, X30, X8]:(class_Fields_Olinordered__field(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),X29))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X31))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X30),X31)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X29),X31)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__strict__right__mono)). 6.97/7.20 fof(fact_mult__right__mono, axiom, ![X31, X29, X30, X8]:(class_Rings_Oordered__semiring(X8)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X31)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X31)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__right__mono)). 6.97/7.20 fof(fact_comm__mult__left__mono, axiom, ![X31, X29, X30, X8]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X30)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X29)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X31)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),X29)))<=class_Rings_Oordered__comm__semiring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__mult__left__mono)). 6.97/7.20 fof(fact_mult__le__cancel__left__pos, axiom, ![X1, X2, X10, X5]:(class_Rings_Olinordered__ring__strict(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X10))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X2),X1))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__le__cancel__left__pos)). 6.97/7.20 fof(fact_mult__left__mono, axiom, ![X31, X29, X30, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),X29))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X31))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X30)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X29)))))<=class_Rings_Oordered__semiring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__left__mono)). 6.97/7.20 fof(fact_mult__strict__left__mono__neg, axiom, ![X31, X30, X29, X8]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X31),c_Groups_Ozero__class_Ozero(X8)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X30)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X29))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X29),X30)))<=class_Rings_Olinordered__ring__strict(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__strict__left__mono__neg)). 6.97/7.20 fof(fact_divide__strict__right__mono__neg, axiom, ![X31, X30, X29, X8]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X31),c_Groups_Ozero__class_Ozero(X8)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X30),X31)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X29),X31))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X29),X30)))<=class_Fields_Olinordered__field(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__strict__right__mono__neg)). 6.97/7.20 fof(fact_posDivAlg__div__mod, axiom, ![X93, X19]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X93))=>c_Divides_OposDivAlg(X19,X93)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19),X93)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19,X93)))<=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_posDivAlg__div__mod)). 6.97/7.20 fof(fact_negDivAlg__div__mod, axiom, ![X93, X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>(hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19),X93)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19,X93))=c_Divides_OnegDivAlg(X19,X93)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X93)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negDivAlg__div__mod)). 6.97/7.20 fof(fact_mult__right__mono__neg, axiom, ![X31, X30, X29, X8]:(class_Rings_Oordered__ring(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X29),X30))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X31),c_Groups_Ozero__class_Ozero(X8)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X31)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__right__mono__neg)). 6.97/7.20 fof(fact_mult__le__cancel__left__neg, axiom, ![X1, X2, X10, X5]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X1)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X1),X2)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),c_Groups_Ozero__class_Ozero(X5))))<=class_Rings_Olinordered__ring__strict(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__le__cancel__left__neg)). 6.97/7.20 fof(fact_mult__left__mono__neg, axiom, ![X31, X30, X29, X8]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X30)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X29)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X31),c_Groups_Ozero__class_Ozero(X8))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X29),X30)))<=class_Rings_Oordered__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__left__mono__neg)). 6.97/7.20 fof(fact_add__diff__assoc2, axiom, ![X28, X27, X19]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27),X28)),X19)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X27),X19)),X28)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19),X27))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__diff__assoc2)). 6.97/7.20 fof(fact_listrel1__subset__listrel, axiom, ![X37, X3, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),X37))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool)),c_List_Olistrel1(X5,X3)),c_List_Olistrel(X5,X37)))<=c_Relation_Orefl__on(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X37))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1__subset__listrel)). 6.97/7.20 fof(fact_transfer__nat__int__set__relations_I4_J, axiom, ![X11, X4]:(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)),X4)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X11)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X4),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__set__relations_I4_J)). 6.97/7.20 fof(fact_Inter__subset, axiom, ![X11, X4, X5]:(![X241]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X241),X4))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X241),X11)))=>(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))!=X4=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X4)),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__subset)). 6.97/7.20 fof(fact_list__ball__nth, axiom, ![X17, X23, X5, X32]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)))=>(hBOOL(hAPP(X17,hAPP(hAPP(c_List_Onth(X5),X23),X32)))<=![X22]:(hBOOL(hAPP(X17,X22))<=hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X23)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ball__nth)). 6.97/7.20 fof(fact_in__rtrancl__UnI, axiom, ![X44, X67, X35, X5]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X35),c_Transitive__Closure_Ortrancl(X5,X67)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X35),c_Transitive__Closure_Ortrancl(X5,X44))))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X35),c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X67),X44))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__rtrancl__UnI)). 6.97/7.20 fof(fact_rtrancl__power, axiom, ![X67, X24, X5]:(?[X48]:hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X24),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X48),X67)))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X24),c_Transitive__Closure_Ortrancl(X5,X67)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__power)). 6.97/7.20 fof(fact_ImageE, axiom, ![X4, X3, X12, X1, X5]:(~(![X22]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X12,X5)),hAPP(hAPP(c_Product__Type_OPair(X12,X5),X22),X1)),X3))=>~(hBOOL(hAPP(hAPP(c_member(X12),X22),X4)))))<=hBOOL(hAPP(hAPP(c_member(X5),X1),hAPP(c_Relation_OImage(X12,X5,X3),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ImageE)). 6.97/7.20 fof(fact_Image__iff, axiom, ![X4, X3, X12, X1, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X1),hAPP(c_Relation_OImage(X12,X5,X3),X4)))<=>?[X22]:(hBOOL(hAPP(hAPP(c_member(X12),X22),X4))&hBOOL(hAPP(hAPP(c_member(tc_prod(X12,X5)),hAPP(hAPP(c_Product__Type_OPair(X12,X5),X22),X1)),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__iff)). 6.97/7.20 fof(fact_fold__graph_H_Ointros_I2_J, axiom, ![X38, X14, X18, X12, X4, X35, X5]:((c_Nitpick_Ofold__graph_H(X5,X12,X18,X14,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X38)=>c_Nitpick_Ofold__graph_H(X5,X12,X18,X14,X4,hAPP(hAPP(X18,X35),X38)))<=hBOOL(hAPP(hAPP(c_member(X5),X35),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__graph_H_Ointros_I2_J)). 6.97/7.20 fof(fact_transfer__int__nat__set__relations_I4_J, axiom, ![X11, X4]:(c_Nat__Transfer_Onat__set(X4)=>((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),X4)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X11)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X4),X11)))<=c_Nat__Transfer_Onat__set(X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__set__relations_I4_J)). 6.97/7.20 fof(fact_quotientE, axiom, ![X3, X4, X56, X5]:(~(![X22]:(~(hBOOL(hAPP(hAPP(c_member(X5),X22),X4)))<=hAPP(c_Relation_OImage(X5,X5,X3),hAPP(hAPP(c_Set_Oinsert(X5),X22),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))=X56))<=hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X56),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_quotientE)). 6.97/7.20 fof(fact_folding_Ocommute__comp, axiom, ![X35, X38, X55, X18, X12, X5]:(c_Finite__Set_Ofolding(X5,X12,X18,X55)=>hAPP(c_Fun_Ocomp(X12,X12,X12,hAPP(X18,X35)),hAPP(X18,X38))=hAPP(c_Fun_Ocomp(X12,X12,X12,hAPP(X18,X38)),hAPP(X18,X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Ocommute__comp)). 6.97/7.20 fof(fact_refl__on__def, axiom, ![X3, X4, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X4),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X4))))&![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X22),X22)),X3))))<=>c_Relation_Orefl__on(X5,X4,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__on__def)). 6.97/7.20 fof(fact_equiv__type, axiom, ![X3, X4, X5]:(c_Equiv__Relations_Oequiv(X5,X4,X3)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X4),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__type)). 6.97/7.20 fof(fact_the__inv__into__into, axiom, ![X11, X35, X4, X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,X4)=>(hBOOL(hAPP(hAPP(c_member(X12),X35),hAPP(c_Set_Oimage(X5,X12,X18),X4)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))=>hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Fun_Othe__inv__into(X5,X12,X4,X18),X35)),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__inv__into__into)). 6.97/7.20 fof(fact_wf__union__compatible, axiom, ![X44, X67, X5]:((c_Wellfounded_Owf(X5,X44)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X67),X44)),X67))=>c_Wellfounded_Owf(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X67),X44))))<=c_Wellfounded_Owf(X5,X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__union__compatible)). 6.97/7.20 fof(fact_sort__foldl__insort, axiom, ![X23, X5]:(class_Orderings_Olinorder(X5)=>hAPP(c_List_Ofoldl(tc_List_Olist(X5),X5,hAPP(c_COMBC(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5))),c_List_Olist_ONil(X5)),X23)=c_List_Olinorder__class_Osort__key(X5,X5,c_COMBI(X5),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sort__foldl__insort)). 6.97/7.20 fof(fact_mod__pos__neg, axiom, ![X29, X30]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X29),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>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),X30),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X29))))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X29))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__pos__neg)). 6.97/7.20 fof(fact_mod__neg__neg, axiom, ![X29, X30]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>(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),X30),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X29))))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X29)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__neg__neg)). 6.97/7.20 fof(fact_nth__drop, axiom, ![X41, X8, X28, X25]:(hAPP(hAPP(c_List_Onth(X8),hAPP(hAPP(c_List_Odrop(X8),X25),X41)),X28)=hAPP(hAPP(c_List_Onth(X8),X41),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X28))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X28)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__drop)). 6.97/7.20 fof(fact_zip__rev, axiom, ![X45, X5, X41, X8]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X45)=>hAPP(hAPP(c_List_Ozip(X8,X5),hAPP(c_List_Orev(X8),X41)),hAPP(c_List_Orev(X5),X45))=hAPP(c_List_Orev(tc_prod(X8,X5)),hAPP(hAPP(c_List_Ozip(X8,X5),X41),X45))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__rev)). 6.97/7.20 fof(fact_diff__Suc__diff__eq2, axiom, ![X36, X27, X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19),X27))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X27)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X36))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X27),X19))),X36)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__Suc__diff__eq2)). 6.97/7.20 fof(fact_diff__Suc__diff__eq1, axiom, ![X36, X27, X19]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X27),X19)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X19)),hAPP(c_Nat_OSuc,X27))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19),X27))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__Suc__diff__eq1)). 6.97/7.20 fof(fact_sym__trans__comp__subset, axiom, ![X3, X5]:((c_Relation_Otrans(X5,X3)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(c_Relation_Oconverse(X5,X5),X3)),X3)),X3)))<=c_Relation_Osym(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sym__trans__comp__subset)). 6.97/7.20 fof(fact_refl__on__comp__subset, axiom, ![X3, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(c_Relation_Oconverse(X5,X5),X3)),X3)))<=c_Relation_Orefl__on(X5,X4,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__on__comp__subset)). 6.97/7.20 fof(fact_minus__number__of__mult, axiom, ![X26, X39, X8]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X39))),X26)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),X39))),X26)<=class_Int_Onumber__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__number__of__mult)). 6.97/7.20 fof(fact_add__strict__mono, axiom, ![X74, X31, X29, X30, X8]:(class_Groups_Oordered__cancel__ab__semigroup__add(X8)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X29),X74)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X31),X74)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__strict__mono)). 6.97/7.20 fof(fact_add__le__less__mono, axiom, ![X74, X31, X29, X30, X8]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X31),X74))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X29),X74))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),X29)))<=class_Groups_Oordered__cancel__ab__semigroup__add(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__le__less__mono)). 6.97/7.20 fof(fact_add__less__le__mono, axiom, ![X74, X31, X29, X30, X8]:(class_Groups_Oordered__cancel__ab__semigroup__add(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),X29))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X31),X74))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X29),X74)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__less__le__mono)). 6.97/7.20 fof(fact_add__mono, axiom, ![X74, X31, X29, X30, X8]:(class_Groups_Oordered__ab__semigroup__add(X8)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X31),X74))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X29),X74))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__mono)). 6.97/7.20 fof(fact_inf__mono, axiom, ![X74, X29, X31, X30, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),X31))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X30),X29)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X31),X74)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X29),X74))))<=class_Lattices_Osemilattice__inf(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__mono)). 6.97/7.20 fof(fact_power__mono, axiom, ![X25, X29, X30, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),X29))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X29),X25)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X30))))<=class_Rings_Olinordered__semidom(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__mono)). 6.97/7.20 fof(fact_divide__right__mono, axiom, ![X31, X29, X30, X8]:(class_Fields_Olinordered__field__inverse__zero(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),X29))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X31))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X30),X31)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X29),X31)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__right__mono)). 6.97/7.20 fof(fact_sup__mono, axiom, ![X74, X29, X31, X30, X8]:(class_Lattices_Osemilattice__sup(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),X31))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X29),X74))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X30),X29)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X31),X74)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__mono)). 6.97/7.20 fof(fact_Int__insert__left, axiom, ![X11, X65, X2, X5]:((hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X2),X11)),X65)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X65)<=~(hBOOL(hAPP(hAPP(c_member(X5),X2),X65))))&(hBOOL(hAPP(hAPP(c_member(X5),X2),X65))=>hAPP(hAPP(c_Set_Oinsert(X5),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X65))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X2),X11)),X65))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__insert__left)). 6.97/7.20 fof(fact_fold1__eq__fold, axiom, ![X2, X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(~(hBOOL(hAPP(hAPP(c_member(X5),X2),X4)))=>hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Groups_Otimes__class_Otimes(X5)),X2),X4)=hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(hAPP(c_Set_Oinsert(X5),X2),X4))))<=class_Groups_Oab__semigroup__mult(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__eq__fold)). 6.97/7.20 fof(fact_power__strict__increasing__iff, axiom, ![X38, X35, X1, X5]:(class_Rings_Olinordered__semidom(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Oone__class_Oone(X5)),X1))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X1),X35)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X1),X38)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X35),X38))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__strict__increasing__iff)). 6.97/7.20 fof(fact_power__increasing, axiom, ![X30, X168, X25, X8]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Oone__class_Oone(X8)),X30))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X168))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X168)))<=class_Rings_Olinordered__semidom(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__increasing)). 6.97/7.20 fof(fact_power__increasing__iff, axiom, ![X38, X35, X1, X5]:(class_Rings_Olinordered__semidom(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Oone__class_Oone(X5)),X1))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X35),X38))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X1),X35)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X1),X38)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__increasing__iff)). 6.97/7.20 fof(fact_bex__reg__right, axiom, ![X17, X104, X67, X5]:((![X22]:(hBOOL(hAPP(X104,X22))=>hBOOL(hAPP(X17,X22)))=>(?[X22]:(hBOOL(hAPP(X17,X22))&hBOOL(hAPP(hAPP(c_member(X5),X22),c_Quotient_ORespects(X5,X67))))<=?[X76]:hBOOL(hAPP(X104,X76))))<=c_Equiv__Relations_Oequivp(X5,X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bex__reg__right)). 6.97/7.20 fof(fact_max__number__of, axiom, ![X40, X139, X5]:((class_Int_Onumber(X5)&class_Orderings_Oord(X5))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X139)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X40)))=>hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X139)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X40))=hAPP(c_Int_Onumber__class_Onumber__of(X5),X40))&(hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X139)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X40))=hAPP(c_Int_Onumber__class_Onumber__of(X5),X139)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X139)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X40))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__number__of)). 6.97/7.20 fof(fact_divide__right__mono__neg, axiom, ![X31, X29, X30, X8]:(class_Fields_Olinordered__field__inverse__zero(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),X29))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X31),c_Groups_Ozero__class_Ozero(X8)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X29),X31)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X30),X31)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__right__mono__neg)). 6.97/7.20 fof(fact_max__add__distrib__left, axiom, ![X26, X7, X6, X8]:(class_Groups_Oordered__ab__semigroup__add__imp__le(X8)=>hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X6),X26)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X7),X26))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X6),X7)),X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__add__distrib__left)). 6.97/7.20 fof(fact_add__divide__distrib, axiom, ![X31, X29, X30, X8]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X30),X31)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X29),X31))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29)),X31)<=class_Rings_Odivision__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__divide__distrib)). 6.97/7.20 fof(fact_min__number__of, axiom, ![X40, X139, X5]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X139)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X40)))=>hAPP(c_Int_Onumber__class_Onumber__of(X5),X139)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X139)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X40)))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X139)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X40))))=>hAPP(c_Int_Onumber__class_Onumber__of(X5),X40)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X139)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X40))))<=(class_Orderings_Oord(X5)&class_Int_Onumber(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__number__of)). 6.97/7.20 fof(fact_sup__inf__distrib2, axiom, ![X6, X26, X7, X8]:(class_Lattices_Odistrib__lattice(X8)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X7),X6)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X26),X6))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X7),X26)),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__inf__distrib2)). 6.97/7.20 fof(fact_max__diff__distrib__left, axiom, ![X26, X7, X6, X8]:(class_Groups_Oordered__ab__group__add(X8)=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X6),X7)),X26)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X6),X26)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X7),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__diff__distrib__left)). 6.97/7.20 fof(fact_min__diff__distrib__left, axiom, ![X26, X7, X6, X8]:(class_Groups_Oordered__ab__group__add(X8)=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X6),X7)),X26)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X6),X26)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X7),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__diff__distrib__left)). 6.97/7.20 fof(fact_min__add__distrib__left, axiom, ![X26, X7, X6, X8]:(class_Groups_Oordered__ab__semigroup__add__imp__le(X8)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X6),X7)),X26)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X6),X26)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X7),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__add__distrib__left)). 6.97/7.20 fof(fact_div__add__self1, axiom, ![X30, X29, X8]:(class_Divides_Osemiring__div(X8)=>(hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X29),X30)),X29)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),X30),X29)),c_Groups_Oone__class_Oone(X8))<=c_Groups_Ozero__class_Ozero(X8)!=X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__add__self1)). 6.97/7.20 fof(fact_inf__sup__distrib2, axiom, ![X6, X26, X7, X8]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X7),X26)),X6)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X7),X6)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X26),X6))<=class_Lattices_Odistrib__lattice(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__distrib2)). 6.97/7.20 fof(fact_comm__semiring__class_Odistrib, axiom, ![X31, X29, X30, X8]:(class_Rings_Ocomm__semiring(X8)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29)),X31)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__class_Odistrib)). 6.97/7.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, axiom, ![X29, X36, X30, X8]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29)),X36)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X36)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X36))<=class_Rings_Ocomm__semiring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J)). 6.97/7.20 fof(fact_diff__divide__distrib, axiom, ![X31, X29, X30, X8]:(class_Rings_Odivision__ring(X8)=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X30),X29)),X31)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X30),X31)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X29),X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__divide__distrib)). 6.97/7.20 fof(fact_INF2__iff, axiom, ![X10, X1, X11, X4, X62, X12, X5]:(![X22]:(hBOOL(hAPP(hAPP(hAPP(X11,X22),X1),X10))<=hBOOL(hAPP(hAPP(c_member(X5),X22),X4)))<=>hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_fun(X62,tc_HOL_Obool))),X4),X11),X1),X10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF2__iff)). 6.97/7.20 fof(fact_rev__ImageI, axiom, ![X3, X1, X12, X4, X2, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X2),X4))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X2),X1)),X3))=>hBOOL(hAPP(hAPP(c_member(X12),X1),hAPP(c_Relation_OImage(X5,X12,X3),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__ImageI)). 6.97/7.20 fof(fact_fun__left__comm_Ofun__comp__comm, axiom, ![X38, X35, X18, X12, X5]:(c_Finite__Set_Ofun__left__comm(X5,X12,X18)=>hAPP(c_Fun_Ocomp(X12,X12,X12,hAPP(X18,X35)),hAPP(X18,X38))=hAPP(c_Fun_Ocomp(X12,X12,X12,hAPP(X18,X38)),hAPP(X18,X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofun__comp__comm)). 6.97/7.20 fof(fact_INF2__I, axiom, ![X62, X12, X10, X1, X11, X4, X5]:(![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))=>hBOOL(hAPP(hAPP(hAPP(X11,X22),X1),X10)))=>hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_fun(X62,tc_HOL_Obool))),X4),X11),X1),X10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF2__I)). 6.97/7.20 fof(fact_div__add__self2, axiom, ![X30, X29, X8]:(class_Divides_Osemiring__div(X8)=>(hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29)),X29)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),X30),X29)),c_Groups_Oone__class_Oone(X8))<=X29!=c_Groups_Ozero__class_Ozero(X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__add__self2)). 6.97/7.20 fof(fact_inj__fun, axiom, ![X62, X18, X12, X5]:(c_Fun_Oinj__on(X5,tc_fun(X62,X12),hAPP(hAPP(c_COMBB(X12,tc_fun(X62,X12),X5),c_COMBK(X12,X62)),X18),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))<=c_Fun_Oinj__on(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__fun)). 6.97/7.20 fof(fact_list__all2__all__nthI, axiom, ![X17, X1, X12, X2, X5]:((c_List_Olist__all2(X5,X12,X17,X2,X1)<=![X48]:(hBOOL(hAPP(hAPP(X17,hAPP(hAPP(c_List_Onth(X5),X2),X48)),hAPP(hAPP(c_List_Onth(X12),X1),X48)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X48),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X2)))))<=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12)),X1)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__all__nthI)). 6.97/7.20 fof(fact_mult__right__le__one__le, axiom, ![X7, X6, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X6))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X6),X7)),X6))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X7),c_Groups_Oone__class_Oone(X8))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X7))))<=class_Rings_Olinordered__idom(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__right__le__one__le)). 6.97/7.20 fof(fact_mult__left__le__one__le, axiom, ![X7, X6, X8]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X6)),X6))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X7),c_Groups_Oone__class_Oone(X8))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X7)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X6)))<=class_Rings_Olinordered__idom(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__left__le__one__le)). 6.97/7.20 fof(fact_SigmaE, axiom, ![X11, X4, X10, X12, X5]:(~(![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))=>![X72]:(hBOOL(hAPP(hAPP(c_member(X12),X72),hAPP(X11,X22)))=>X10!=hAPP(hAPP(c_Product__Type_OPair(X5,X12),X22),X72))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X12)),X10),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X4),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SigmaE)). 6.97/7.20 fof(fact_list__all2__conv__all__nth, axiom, ![X84, X23, X17, X12, X5]:((![X42]:(hBOOL(hAPP(hAPP(X17,hAPP(hAPP(c_List_Onth(X5),X23),X42)),hAPP(hAPP(c_List_Onth(X12),X84),X42)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23))))&hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12)),X84)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23))<=>c_List_Olist__all2(X5,X12,X17,X23,X84)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__conv__all__nth)). 6.97/7.20 fof(fact_INF__less__iff, axiom, ![X2, X18, X4, X12, X5]:((class_Orderings_Olinorder(X5)&class_Complete__Lattice_Ocomplete__lattice(X5))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,X5),X4),X18)),X2))<=>?[X22]:(hBOOL(hAPP(hAPP(c_member(X12),X22),X4))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(X18,X22)),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF__less__iff)). 6.97/7.20 fof(fact_less__SUP__iff, axiom, ![X18, X4, X12, X2, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X5),X4),X18)))<=>?[X22]:(hBOOL(hAPP(hAPP(c_member(X12),X22),X4))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),hAPP(X18,X22)))))<=(class_Complete__Lattice_Ocomplete__lattice(X5)&class_Orderings_Olinorder(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__SUP__iff)). 6.97/7.20 fof(fact_ivl__disj__un_I15_J, axiom, ![X51, X34, X52, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X52),X34))=>(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X52,X34)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X34),X51))=c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X52,X51)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X34),X51))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I15_J)). 6.97/7.20 fof(fact_sum__squares__ge__zero, axiom, ![X7, X6, X8]:(class_Rings_Olinordered__ring(X8)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X6),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__squares__ge__zero)). 6.97/7.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, axiom, ![X36, X30, X8]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),c_Groups_Oone__class_Oone(X8))),X36)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X36)),X36)<=class_Rings_Ocomm__semiring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J)). 6.97/7.20 fof(fact_mult__dvd__mono, axiom, ![X74, X31, X29, X30, X8]:((hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X8),X30),X29))=>(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X74)))<=hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X8),X31),X74))))<=class_Rings_Ocomm__semiring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__dvd__mono)). 6.97/7.20 fof(fact_ivl__disj__un_I21_J, axiom, ![X51, X34, X52, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X52),X34))=>(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X52),X34)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X34,X51))=c_SetInterval_Oord__class_OatLeastAtMost(X5,X52,X51)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X34),X51))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I21_J)). 6.97/7.20 fof(fact_folding__idem_Oidem__left__comp, axiom, ![X50, X35, X62, X55, X18, X12, X5]:(c_Finite__Set_Ofolding__idem(X5,X12,X18,X55)=>hAPP(c_Fun_Ocomp(X12,X12,X62,hAPP(X18,X35)),hAPP(c_Fun_Ocomp(X12,X12,X62,hAPP(X18,X35)),X50))=hAPP(c_Fun_Ocomp(X12,X12,X62,hAPP(X18,X35)),X50)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__idem_Oidem__left__comp)). 6.97/7.20 fof(fact_min__max_Osup__mono, axiom, ![X74, X29, X31, X30, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),X31))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X30),X29)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X31),X74)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X29),X74))))<=class_Orderings_Olinorder(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__mono)). 6.97/7.20 fof(fact_min__max_Oinf__mono, axiom, ![X74, X29, X31, X30, X8]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X29),X74))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X30),X29)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X31),X74))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),X31)))<=class_Orderings_Olinorder(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__mono)). 6.97/7.20 fof(fact_min__max_Osup__inf__distrib2, axiom, ![X6, X26, X7, X8]:(hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X7),X6)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X26),X6))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X7),X26)),X6)<=class_Orderings_Olinorder(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__inf__distrib2)). 6.97/7.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, axiom, ![X53, X7, X6, X8]:(class_Rings_Ocomm__semiring__1(X8)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X6),X53)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X53))=hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X6),X7)),X53)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J)). 6.97/7.20 fof(fact_min__max_Oinf__sup__distrib2, axiom, ![X6, X26, X7, X8]:(class_Orderings_Olinorder(X8)=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X7),X26)),X6)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X7),X6)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X26),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__sup__distrib2)). 6.97/7.20 fof(fact_Cantor__Bernstein, axiom, ![X50, X11, X4, X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,X4)=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X12,X5,X50),X11)),X4))=>?[X205]:c_Fun_Obij__betw(X5,X12,X205,X4,X11))<=c_Fun_Oinj__on(X12,X5,X50,X11))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X12,X18),X4)),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Cantor__Bernstein)). 6.97/7.20 fof(fact_power__mult__distrib, axiom, ![X25, X29, X30, X8]:(hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29)),X25)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X29),X25))<=class_Groups_Ocomm__monoid__mult(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__mult__distrib)). 6.97/7.20 fof(fact_power__divide, axiom, ![X25, X29, X30, X8]:(class_Fields_Ofield__inverse__zero(X8)=>hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X30),X29)),X25)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X29),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__divide)). 6.97/7.20 fof(fact_Suc__mult__less__cancel1, axiom, ![X32, X34, X33]:(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,X33)),X34)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X33)),X32)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__mult__less__cancel1)). 6.97/7.20 fof(fact_map__eq__conv, axiom, ![X50, X23, X18, X5, X12]:(![X22]:(hBOOL(hAPP(hAPP(c_member(X12),X22),hAPP(c_List_Oset(X12),X23)))=>hAPP(X18,X22)=hAPP(X50,X22))<=>hAPP(hAPP(c_List_Omap(X12,X5),X50),X23)=hAPP(hAPP(c_List_Omap(X12,X5),X18),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__eq__conv)). 6.97/7.20 fof(fact_folding__idem_Oinsert__idem, axiom, ![X35, X4, X55, X18, X12, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hAPP(X55,hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))=hAPP(c_Fun_Ocomp(X12,X12,X12,hAPP(X55,X4)),hAPP(X18,X35)))<=c_Finite__Set_Ofolding__idem(X5,X12,X18,X55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__idem_Oinsert__idem)). 6.97/7.20 fof(fact_min__max_Osup__inf__distrib1, axiom, ![X26, X7, X6, X8]:(class_Orderings_Olinorder(X8)=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X6),X7)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X6),X26))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X6),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X7),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__inf__distrib1)). 6.97/7.20 fof(fact_wf__eq__minimal, axiom, ![X3, X5]:(c_Wellfounded_Owf(X5,X3)<=>![X264]:(?[X22]:(![X72]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X72),X22)),X3))=>~(hBOOL(hAPP(hAPP(c_member(X5),X72),X264))))&hBOOL(hAPP(hAPP(c_member(X5),X22),X264)))<=?[X22]:hBOOL(hAPP(hAPP(c_member(X5),X22),X264)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__eq__minimal)). 6.97/7.20 fof(fact_Un__least, axiom, ![X11, X65, X4, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X65))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11)),X65)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X65))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__least)). 6.97/7.20 fof(fact_Int__greatest, axiom, ![X11, X4, X65, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X65),X4))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X65),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X65),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__greatest)). 6.97/7.20 fof(fact_o__inv__o__cancel, axiom, ![X50, X62, X18, X12, X5]:(X50=hAPP(c_Fun_Ocomp(X12,X62,X5,hAPP(c_Fun_Ocomp(X5,X62,X12,X50),c_Hilbert__Choice_Oinv__into(X5,X12,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X18))),X18)<=c_Fun_Oinj__on(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_o__inv__o__cancel)). 6.97/7.20 fof(fact_setsum__eq__1__iff, axiom, ![X18, X4, X5]:((c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X18),X4)<=>?[X22]:((hAPP(X18,X22)=c_Groups_Oone__class_Oone(tc_Nat_Onat)&![X115]:((hAPP(X18,X115)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<=X115!=X22)<=hBOOL(hAPP(hAPP(c_member(X5),X115),X4))))&hBOOL(hAPP(hAPP(c_member(X5),X22),X4))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__eq__1__iff)). 6.97/7.20 fof(fact_setsum__nonneg__0, axiom, ![X47, X18, X66, X5, X12]:(class_Groups_Oordered__ab__group__add(X12)=>((((hBOOL(hAPP(hAPP(c_member(X5),X47),X66))=>c_Groups_Ozero__class_Ozero(X12)=hAPP(X18,X47))<=c_Groups_Ozero__class_Ozero(X12)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),X66))<=![X42]:(hBOOL(hAPP(hAPP(c_member(X5),X42),X66))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),c_Groups_Ozero__class_Ozero(X12)),hAPP(X18,X42)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X66)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__nonneg__0)). 6.97/7.20 fof(fact_inf__sup__distrib1, axiom, ![X26, X7, X6, X8]:(class_Lattices_Odistrib__lattice(X8)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),X7)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),X26))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X7),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__distrib1)). 6.97/7.20 fof(fact_INF__subset, axiom, ![X18, X11, X4, X5, X12]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X12),X11),X18)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X12),X4),X18)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11)))<=class_Complete__Lattice_Ocomplete__lattice(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF__subset)). 6.97/7.20 fof(fact_min__max_Oinf__sup__distrib1, axiom, ![X26, X7, X6, X8]:(hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X6),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X7),X26))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X6),X7)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X6),X26))<=class_Orderings_Olinorder(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__sup__distrib1)). 6.97/7.20 fof(fact_SUP__subset, axiom, ![X18, X11, X4, X5, X12]:(class_Complete__Lattice_Ocomplete__lattice(X12)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X12),X4),X18)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X12),X11),X18)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP__subset)). 6.97/7.20 fof(fact_insort__is__Cons, axiom, ![X2, X18, X23, X5, X12]:((![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X23)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),hAPP(X18,X2)),hAPP(X18,X22))))=>hAPP(hAPP(c_List_Olist_OCons(X5),X2),X23)=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X12,X18),X2),X23))<=class_Orderings_Olinorder(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__is__Cons)). 6.97/7.20 fof(fact_acc_Osimps, axiom, ![X3, X2, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X2),c_Wellfounded_Oacc(X5,X3)))<=>![X22]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X22),X2)),X3))=>hBOOL(hAPP(hAPP(c_member(X5),X22),c_Wellfounded_Oacc(X5,X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acc_Osimps)). 6.97/7.20 fof(fact_RangeE, axiom, ![X3, X12, X1, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X1),hAPP(c_Relation_ORange(X12,X5),X3)))=>~(![X22]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(X12,X5)),hAPP(hAPP(c_Product__Type_OPair(X12,X5),X22),X1)),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_RangeE)). 6.97/7.20 fof(fact_not__acc__down, axiom, ![X67, X35, X5]:(~(hBOOL(hAPP(hAPP(c_member(X5),X35),c_Wellfounded_Oacc(X5,X67))))=>~(![X116]:(hBOOL(hAPP(hAPP(c_member(X5),X116),c_Wellfounded_Oacc(X5,X67)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X116),X35)),X67))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__acc__down)). 6.97/7.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, axiom, ![X26, X7, X6, X8]:(class_Rings_Ocomm__semiring__1(X8)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X6),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X7),X26))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X6),X7)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X6),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J)). 6.97/7.20 fof(fact_Range__iff, axiom, ![X3, X12, X2, X5]:(?[X72]:hBOOL(hAPP(hAPP(c_member(tc_prod(X12,X5)),hAPP(hAPP(c_Product__Type_OPair(X12,X5),X72),X2)),X3))<=>hBOOL(hAPP(hAPP(c_member(X5),X2),hAPP(c_Relation_ORange(X12,X5),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__iff)). 6.97/7.20 fof(fact_DomainE, axiom, ![X3, X12, X2, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X2),hAPP(c_Relation_ODomain(X5,X12),X3)))=>~(![X72]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X2),X72)),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_DomainE)). 6.97/7.20 fof(fact_listsum__abs, axiom, ![X23, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Oabs__class_Oabs(X5),hAPP(c_List_Omonoid__add__class_Olistsum(X5),X23))),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X5,X5),c_Groups_Oabs__class_Oabs(X5)),X23))))<=class_Groups_Oordered__ab__group__add__abs(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__abs)). 6.97/7.20 fof(fact_acc_OaccI, axiom, ![X3, X35, X5]:(![X72]:(hBOOL(hAPP(hAPP(c_member(X5),X72),c_Wellfounded_Oacc(X5,X3)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X72),X35)),X3)))=>hBOOL(hAPP(hAPP(c_member(X5),X35),c_Wellfounded_Oacc(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acc_OaccI)). 6.97/7.20 fof(fact_Domain__iff, axiom, ![X3, X12, X2, X5]:(?[X72]:hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X2),X72)),X3))<=>hBOOL(hAPP(hAPP(c_member(X5),X2),hAPP(c_Relation_ODomain(X5,X12),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__iff)). 6.97/7.20 fof(fact_append__in__lists__conv, axiom, ![X4, X84, X23, X5]:((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X23),c_List_Olists(X5,X4)))&hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X84),c_List_Olists(X5,X4))))<=>hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),hAPP(hAPP(c_List_Oappend(X5),X23),X84)),c_List_Olists(X5,X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__in__lists__conv)). 6.97/7.20 fof(fact_sup__inf__distrib1, axiom, ![X26, X7, X6, X8]:(class_Lattices_Odistrib__lattice(X8)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X7),X26))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),X7)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__inf__distrib1)). 6.97/7.20 fof(fact_image__surj__f__inv__f, axiom, ![X4, X18, X5, X12]:(c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))=hAPP(c_Set_Oimage(X12,X5,X18),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))=>hAPP(c_Set_Oimage(X12,X5,X18),hAPP(c_Set_Oimage(X5,X12,c_Hilbert__Choice_Oinv__into(X12,X5,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)),X18)),X4))=X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__surj__f__inv__f)). 6.97/7.20 fof(fact_abs__add__abs, axiom, ![X29, X30, X8]:(hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),X30)),hAPP(c_Groups_Oabs__class_Oabs(X8),X29)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),X30)),hAPP(c_Groups_Oabs__class_Oabs(X8),X29))<=class_Groups_Oordered__ab__group__add__abs(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__add__abs)). 6.97/7.20 fof(fact_q__neg__lemma, axiom, ![X100, X101, X68]:(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),X68),X101)),X100)),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)),X68))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X101),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)),X100)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_q__neg__lemma)). 6.97/7.20 fof(fact_fold1__insert, axiom, ![X35, X4, X5]:((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X35),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X4))<=~(hBOOL(hAPP(hAPP(c_member(X5),X35),X4))))))<=class_Groups_Oab__semigroup__mult(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__insert)). 6.97/7.20 fof(fact_zmult__zless__mono2, axiom, ![X19, X27, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X28),X27))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19),X28)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19),X27)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult__zless__mono2)). 6.97/7.20 fof(fact_takeWhile__append2, axiom, ![X84, X17, X23, X5]:(![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X23)))=>hBOOL(hAPP(X17,X22)))=>c_List_OtakeWhile(X5,X17,hAPP(hAPP(c_List_Oappend(X5),X23),X84))=hAPP(hAPP(c_List_Oappend(X5),X23),c_List_OtakeWhile(X5,X17,X84))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__append2)). 6.97/7.20 fof(fact_ivl__disj__un_I18_J, axiom, ![X51, X34, X52, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X52),X34))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X34),X51))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X52,X34)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X34,X51))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X52),X51)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I18_J)). 6.97/7.20 fof(fact_mult__less__cancel2, axiom, ![X32, X33, X34]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X33)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X33)))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34),X32))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__less__cancel2)). 6.97/7.20 fof(fact_nat__mult__less__cancel1, axiom, ![X32, X34, X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34),X32))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X34)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__less__cancel1)). 6.97/7.20 fof(fact_insert__fold1SetE, axiom, ![X35, X56, X2, X18, X5]:(hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X18,hAPP(hAPP(c_Set_Oinsert(X5),X2),X56)),X35))=>~(![X13, X54]:((hBOOL(hAPP(hAPP(c_member(X5),X13),X54))<=hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,X18,X13,X54),X35)))<=hAPP(hAPP(c_Set_Oinsert(X5),X2),X56)=hAPP(hAPP(c_Set_Oinsert(X5),X13),X54)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__fold1SetE)). 6.97/7.20 fof(fact_acc__downwards, axiom, ![X1, X3, X2, X5]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X1),X2)),c_Transitive__Closure_Ortrancl(X5,X3)))=>hBOOL(hAPP(hAPP(c_member(X5),X1),c_Wellfounded_Oacc(X5,X3))))<=hBOOL(hAPP(hAPP(c_member(X5),X2),c_Wellfounded_Oacc(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acc__downwards)). 6.97/7.20 fof(fact_zdiv__mono1, axiom, ![X29, X69, X30]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),X29)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X69),X29)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X29)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X30),X69))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__mono1)). 6.97/7.20 fof(fact_div__le__mono2, axiom, ![X19, X25, X36]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X36))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X36),X25))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19),X25)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19),X36))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__le__mono2)). 6.97/7.20 fof(fact_zdiv__mono1__neg, axiom, ![X29, X69, X30]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X30),X69))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X29),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),X69),X29)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),X29))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__mono1__neg)). 6.97/7.20 fof(fact_nth__eq__iff__index__eq, axiom, ![X46, X47, X23, X5]:((((hAPP(hAPP(c_List_Onth(X5),X23),X46)=hAPP(hAPP(c_List_Onth(X5),X23),X47)<=>X47=X46)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X47),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23))))<=hBOOL(hAPP(c_List_Odistinct(X5),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__eq__iff__index__eq)). 6.97/7.20 fof(fact_single__valued__def, axiom, ![X3, X12, X5]:(![X22, X72]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X22),X72)),X3))=>![X116]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X22),X116)),X3))=>X72=X116))<=>c_Relation_Osingle__valued(X5,X12,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_single__valued__def)). 6.97/7.20 fof(fact_power__add, axiom, ![X25, X36, X30, X8]:(class_Groups_Omonoid__mult(X8)=>hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X25))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X36)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__add)). 6.97/7.20 fof(fact_double__diff, axiom, ![X65, X11, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))=>(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X65),X4))=X4<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X65)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_double__diff)). 6.97/7.20 fof(fact_le__div__geq, axiom, ![X36, X25]:((hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X36),X25)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),X25)),X25))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X36)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__div__geq)). 6.97/7.20 fof(fact_unity__coeff__ex, axiom, ![X52, X17, X5]:((class_Rings_Osemiring__0(X5)&class_Rings_Odvd(X5))=>(?[X22]:hBOOL(hAPP(X17,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X52),X22)))<=>?[X22]:(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X52),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X22),c_Groups_Ozero__class_Ozero(X5))))&hBOOL(hAPP(X17,X22))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_unity__coeff__ex)). 6.97/7.20 fof(fact_finite__quotient, axiom, ![X3, X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X4),X3)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X4),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__quotient)). 6.97/7.20 fof(fact_inj__on__Inter, axiom, ![X18, X12, X5, X44]:((c_Fun_Oinj__on(X5,X12,X18,c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X44))<=![X54]:(c_Fun_Oinj__on(X5,X12,X18,X54)<=hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X54),X44))))<=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))!=X44), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__Inter)). 6.97/7.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, axiom, ![X53, X81, X6, X8]:(hAPP(hAPP(c_Power_Opower__class_Opower(X8),X6),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X81),X53))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X6),X81)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X6),X53))<=class_Rings_Ocomm__semiring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J)). 6.97/7.20 fof(fact_refl__on__Int, axiom, ![X66, X11, X3, X4, X5]:(c_Relation_Orefl__on(X5,X4,X3)=>(c_Relation_Orefl__on(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),X66))<=c_Relation_Orefl__on(X5,X11,X66))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__on__Int)). 6.97/7.20 fof(fact_refl__on__Un, axiom, ![X66, X11, X3, X4, X5]:((c_Relation_Orefl__on(X5,X11,X66)=>c_Relation_Orefl__on(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),X66)))<=c_Relation_Orefl__on(X5,X4,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__on__Un)). 6.97/7.20 fof(fact_nat__mult__div__cancel1, axiom, ![X25, X36, 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_Nat_Onat),X36),X25)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X36)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__div__cancel1)). 6.97/7.20 fof(fact_zdiff__int__split, axiom, ![X38, X35, X17]:(hBOOL(hAPP(X17,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X35),X38))))<=>((hBOOL(hAPP(X17,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X35)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X38))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X38),X35)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X35),X38))=>hBOOL(hAPP(X17,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiff__int__split)). 6.97/7.20 fof(fact_sorted__append, axiom, ![X84, X23, X5]:((((c_List_Olinorder__class_Osorted(X5,X84)&![X22]:(![X115]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X22),X115))<=hBOOL(hAPP(hAPP(c_member(X5),X115),hAPP(c_List_Oset(X5),X84))))<=hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X23)))))&c_List_Olinorder__class_Osorted(X5,X23))<=>c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Oappend(X5),X23),X84)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__append)). 6.97/7.20 fof(fact_Int__greaterThanAtMost, axiom, ![X97, X10, X1, X2, X5]:(class_Orderings_Olinorder(X5)=>c_SetInterval_Oord__class_OgreaterThanAtMost(X5,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X2),X10),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X1),X97))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X2,X1)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X10,X97))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__greaterThanAtMost)). 6.97/7.20 fof(fact_Int__greaterThanLessThan, axiom, ![X97, X10, X1, X2, X5]:(class_Orderings_Olinorder(X5)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X2,X1)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X10,X97))=c_SetInterval_Oord__class_OgreaterThanLessThan(X5,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X2),X10),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X1),X97))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__greaterThanLessThan)). 6.97/7.20 fof(fact_Int__atLeastAtMost, axiom, ![X97, X10, X1, X2, X5]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X10,X97))=c_SetInterval_Oord__class_OatLeastAtMost(X5,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X2),X10),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X1),X97))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__atLeastAtMost)). 6.97/7.20 fof(fact_finite__cartesian__product, axiom, ![X11, X12, X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X11))=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X4),hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X5),X11)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__cartesian__product)). 6.97/7.20 fof(fact_of__int__setprod, axiom, ![X4, X18, X12, X5]:((class_Groups_Ocomm__monoid__mult(X5)&class_Rings_Oring__1(X5))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12,X5),hAPP(hAPP(c_COMBB(tc_Int_Oint,X5,X12),c_Int_Oring__1__class_Oof__int(X5)),X18)),X4)=hAPP(c_Int_Oring__1__class_Oof__int(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12,tc_Int_Oint),X18),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__setprod)). 6.97/7.20 fof(fact_of__nat__setprod, axiom, ![X4, X18, X12, X5]:(hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12,tc_Nat_Onat),X18),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,X12),c_Nat_Osemiring__1__class_Oof__nat(X5)),X18)),X4)<=(class_Rings_Osemiring__1(X5)&class_Groups_Ocomm__monoid__mult(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__setprod)). 6.97/7.20 fof(fact_folding__image__simple__idem_Oinsert__idem, axiom, ![X35, X4, X55, X50, X14, X18, X12, X5]:(c_Finite__Set_Ofolding__image__simple__idem(X5,X12,X18,X14,X50,X55)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X4))=>hAPP(hAPP(X18,hAPP(X50,X35)),hAPP(X55,X4))=hAPP(X55,hAPP(hAPP(c_Set_Oinsert(X12),X35),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple__idem_Oinsert__idem)). 6.97/7.20 fof(fact_list__all2__nthD2, axiom, ![X24, X84, X23, X17, X12, X5]:(c_List_Olist__all2(X5,X12,X17,X23,X84)=>(hBOOL(hAPP(hAPP(X17,hAPP(hAPP(c_List_Onth(X5),X23),X24)),hAPP(hAPP(c_List_Onth(X12),X84),X24)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12)),X84))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__nthD2)). 6.97/7.20 fof(fact_ivl__diff, axiom, ![X34, X32, X47, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X47),X32))=>hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X32),X34)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X47),X34)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X47),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__diff)). 6.97/7.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, axiom, ![X31, X29, X30, X8]:(class_Rings_Ocomm__semiring__1(X8)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29)),X31)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X31)),X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J)). 6.97/7.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, axiom, ![X207, X208, X209, X8]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X209),X208)),X207)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X209),X207)),X208)<=class_Rings_Ocomm__semiring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J)). 6.97/7.20 fof(fact_listsum__triv, axiom, ![X23, X3, X12, X5]:(class_Rings_Osemiring__1(X5)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12)),X23))),X3)=hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X12,X5),hAPP(c_COMBK(X5,X12),X3)),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__triv)). 6.97/7.20 fof(fact_folding__one_Oinsert, axiom, ![X35, X4, X55, X18, X5]:(((~(hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))=>(hAPP(X55,hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))=hAPP(hAPP(X18,X35),hAPP(X55,X4))<=X4!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=c_Finite__Set_Ofolding__one(X5,X18,X55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one_Oinsert)). 6.97/7.20 fof(fact_zadd__zless__mono, axiom, ![X26, X112, X39, X170]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X170),X39))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X170),X112)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X39),X26)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X112),X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__zless__mono)). 6.97/7.20 fof(fact_diff__less__mono, axiom, ![X31, X29, X30]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X30),X31)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X29),X31))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__less__mono)). 6.97/7.20 fof(fact_diff__less__mono2, axiom, ![X93, X25, X36]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X36),X25))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X36),X93))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X93),X25)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X93),X36))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__less__mono2)). 6.97/7.20 fof(fact_add__less__mono, axiom, ![X93, X19, X27, X28]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),X93))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),X19)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27),X93))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28),X27))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__less__mono)). 6.97/7.20 fof(fact_folding__idem_Osubset__comp__idem, axiom, ![X11, X4, X55, X18, X12, X5]:(c_Finite__Set_Ofolding__idem(X5,X12,X18,X55)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hAPP(c_Fun_Ocomp(X12,X12,X12,hAPP(X55,X4)),hAPP(X55,X11))=hAPP(X55,X4)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__idem_Osubset__comp__idem)). 6.97/7.20 fof(fact_log_Osimps, axiom, ![X28, X29]:((c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)=c_Random_Olog(X29,X28)<=(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X29),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X28),X29))))&(~((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X29),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X28),X29))))=>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(X29,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X28),X29)))=c_Random_Olog(X29,X28))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_log_Osimps)). 6.97/7.20 fof(fact_add__le__mono, axiom, ![X93, X19, X27, X28]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19),X93))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),X19)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27),X93))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28),X27))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__le__mono)). 6.97/7.20 fof(fact_mult__le__mono, axiom, ![X93, X19, X27, X28]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X19)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),X93)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19),X93)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28),X27))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__le__mono)). 6.97/7.20 fof(fact_Diff__subset__conv, axiom, ![X65, X11, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X65)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11)),X65))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__subset__conv)). 6.97/7.20 fof(fact_div__mult__swap, axiom, ![X30, X29, X31, X8]:(class_Divides_Osemiring__div(X8)=>(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X8),X31),X29))=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),X29),X31))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29)),X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__swap)). 6.97/7.20 fof(fact_q__pos__lemma, axiom, ![X100, X101, X68]:(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),X68),X101)),X100)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X100),X68))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X68))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X101))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_q__pos__lemma)). 6.97/7.20 fof(fact_divmod__int__def, axiom, ![X29, X30]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X29))=>c_Divides_OnegDivAlg(X30,X29)=c_Divides_Odivmod__int(X30,X29))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X29)))=>c_Divides_Odivmod__int(X30,X29)=hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X30),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X29)))))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30))=>((c_Divides_OposDivAlg(X30,X29)=c_Divides_Odivmod__int(X30,X29)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X29)))&(((c_Divides_Odivmod__int(X30,X29)=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_Groups_Ozero__class_Ozero(tc_Int_Oint)=X30)&(hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X30),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X29)))=c_Divides_Odivmod__int(X30,X29)<=X30!=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)),X29))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__def)). 6.97/7.20 fof(fact_subset__card__intvl__is__intvl, axiom, ![X33, X4]:(X4=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X33),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X4)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X4),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X33),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__card__intvl__is__intvl)). 6.97/7.20 fof(fact_power__Suc__less__one, axiom, ![X25, X30, X8]:(class_Rings_Olinordered__semidom(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X30))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),c_Groups_Oone__class_Oone(X8)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),hAPP(c_Nat_OSuc,X25))),c_Groups_Oone__class_Oone(X8)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__Suc__less__one)). 6.97/7.20 fof(fact_image__mono, axiom, ![X18, X12, X11, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X12,X18),X4)),hAPP(c_Set_Oimage(X5,X12,X18),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__mono)). 6.97/7.20 fof(fact_length__transpose__sorted, axiom, ![X23, X5]:(((X23!=c_List_Olist_ONil(tc_List_Olist(X5))=>hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),c_List_Otranspose(X5,X23))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X5)),X23),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))&(X23=c_List_Olist_ONil(tc_List_Olist(X5))=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),c_List_Otranspose(X5,X23))))<=c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X5))),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__transpose__sorted)). 6.97/7.20 fof(fact_ivl__disj__un_I19_J, axiom, ![X51, X34, X52, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X52),X34))=>(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X52,X34)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X34,X51))=c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X52,X51)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X34),X51))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I19_J)). 6.97/7.20 fof(fact_ivl__disj__un_I16_J, axiom, ![X51, X34, X52, X5]:(((hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X52,X34)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X34,X51))=c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X52,X51)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X34),X51)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X52),X34)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I16_J)). 6.97/7.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, axiom, ![X30, X36, X8]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X36))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),c_Groups_Oone__class_Oone(X8))),X36)<=class_Rings_Ocomm__semiring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J)). 6.97/7.20 fof(fact_Compl__subset__Compl__iff, axiom, ![X11, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X4)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X11)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__subset__Compl__iff)). 6.97/7.20 fof(fact_insert__mono, axiom, ![X2, X73, X65, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X65),X73))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X2),X65)),hAPP(hAPP(c_Set_Oinsert(X5),X2),X73)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__mono)). 6.97/7.20 fof(fact_ivl__disj__un_I22_J, axiom, ![X51, X34, X52, X5]:(class_Orderings_Olinorder(X5)=>((hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X52,X34)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X34,X51))=c_SetInterval_Oord__class_OatLeastAtMost(X5,X52,X51)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X34),X51)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X52),X34)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I22_J)). 6.97/7.20 fof(fact_ivl__disj__un_I20_J, axiom, ![X51, X34, X52, X5]:(class_Orderings_Olinorder(X5)=>((c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X52,X51)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X52,X34)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X34,X51))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X34),X51)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X52),X34)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I20_J)). 6.97/7.20 fof(fact_of__nat__setsum, axiom, ![X4, X18, X12, X5]:(class_Rings_Osemiring__1(X5)=>hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,tc_Nat_Onat),X18),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,X12),c_Nat_Osemiring__1__class_Oof__nat(X5)),X18)),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__setsum)). 6.97/7.20 fof(fact_folding__image_Oreindex, axiom, ![X50, X71, X4, X55, X14, X18, X12, X5]:(((c_Fun_Oinj__on(X12,X12,X71,X4)=>hAPP(hAPP(X55,hAPP(c_Fun_Ocomp(X12,X5,X12,X50),X71)),X4)=hAPP(hAPP(X55,X50),hAPP(c_Set_Oimage(X12,X12,X71),X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X4)))<=c_Finite__Set_Ofolding__image(X5,X12,X18,X14,X55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image_Oreindex)). 6.97/7.20 fof(fact_self__quotient__aux2, axiom, ![X53, X70, X30]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X53),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)),X70)))<=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X70),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X53))=X30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_self__quotient__aux2)). 6.97/7.20 fof(fact_setsum__abs__ge__zero, axiom, ![X4, X18, X12, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5),hAPP(hAPP(c_COMBB(X5,X5,X12),c_Groups_Oabs__class_Oabs(X5)),X18)),X4)))<=class_Groups_Oordered__ab__group__add__abs(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__abs__ge__zero)). 6.97/7.20 fof(fact_map__fun__upd, axiom, ![X60, X18, X12, X23, X38, X5]:(~(hBOOL(hAPP(hAPP(c_member(X5),X38),hAPP(c_List_Oset(X5),X23))))=>hAPP(hAPP(c_List_Omap(X5,X12),c_Fun_Ofun__upd(X5,X12,X18,X38,X60)),X23)=hAPP(hAPP(c_List_Omap(X5,X12),X18),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__fun__upd)). 6.97/7.20 fof(fact_fun__left__comm_Ofold__fun__comm, axiom, ![X14, X35, X4, X18, X12, X5]:((hAPP(hAPP(c_Finite__Set_Ofold(X5,X12,X18),hAPP(hAPP(X18,X35),X14)),X4)=hAPP(hAPP(X18,X35),hAPP(hAPP(c_Finite__Set_Ofold(X5,X12,X18),X14),X4))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=c_Finite__Set_Ofun__left__comm(X5,X12,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__fun__comm)). 6.97/7.20 fof(fact_min__max_OSup__fin_Oinsert__idem, axiom, ![X35, X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X35),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X4))<=X4!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Oinsert__idem)). 6.97/7.20 fof(fact_fold1__set, axiom, ![X23, X5]:(class_Lattices_Oab__semigroup__idem__mult(X5)=>(hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(c_List_Oset(X5),X23))=hAPP(c_List_Ofoldl(X5,X5,c_Groups_Otimes__class_Otimes(X5),hAPP(c_List_Ohd(X5),X23)),hAPP(c_List_Otl(X5),X23))<=c_List_Olist_ONil(X5)!=X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__set)). 6.97/7.20 fof(fact_all__nat__less__eq, axiom, ![X17, X32]:(![X21]:(hBOOL(hAPP(X17,X21))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X32)))<=>![X22]:(hBOOL(hAPP(X17,X22))<=hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X22),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_all__nat__less__eq)). 6.97/7.20 fof(fact_acc__downward, axiom, ![X2, X3, X1, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X1),c_Wellfounded_Oacc(X5,X3)))=>(hBOOL(hAPP(hAPP(c_member(X5),X2),c_Wellfounded_Oacc(X5,X3)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acc__downward)). 6.97/7.20 fof(fact_setsum__negf, axiom, ![X4, X18, X12, X5]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5),hAPP(hAPP(c_COMBB(X5,X5,X12),c_Groups_Ouminus__class_Ouminus(X5)),X18)),X4)=hAPP(c_Groups_Ouminus__class_Ouminus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5),X18),X4))<=class_Groups_Oab__group__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__negf)). 6.97/7.20 fof(fact_min__max_OInf__fin_Oinsert__idem, axiom, ![X35, X4, X5]:(class_Orderings_Olinorder(X5)=>((c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X35),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X4))<=X4!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Oinsert__idem)). 6.97/7.20 fof(fact_fun__upd__twist, axiom, ![X97, X1, X34, X12, X5, X10, X2]:(c_Fun_Ofun__upd(X5,X12,c_Fun_Ofun__upd(X5,X12,X34,X10,X97),X2,X1)=c_Fun_Ofun__upd(X5,X12,c_Fun_Ofun__upd(X5,X12,X34,X2,X1),X10,X97)<=X2!=X10), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upd__twist)). 6.97/7.20 fof(fact_Not__Domain__rtrancl, axiom, ![X38, X67, X35, X5]:((X35=X38<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),c_Transitive__Closure_Ortrancl(X5,X67))))<=~(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_Relation_ODomain(X5,X5),X67))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Not__Domain__rtrancl)). 6.97/7.20 fof(fact_Cons__in__lists__iff, axiom, ![X4, X23, X35, X5]:((hBOOL(hAPP(hAPP(c_member(X5),X35),X4))&hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X23),c_List_Olists(X5,X4))))<=>hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23)),c_List_Olists(X5,X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Cons__in__lists__iff)). 6.97/7.20 fof(fact_subset__image__iff, axiom, ![X4, X18, X12, X11, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(c_Set_Oimage(X12,X5,X18),X4)))<=>?[X275]:(X11=hAPP(c_Set_Oimage(X12,X5,X18),X275)&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),X275),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__image__iff)). 6.97/7.20 fof(fact_folding__image__simple__idem_Osubset__idem, axiom, ![X11, X4, X55, X50, X14, X18, X12, X5]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),X11),X4))=>hAPP(X55,X4)=hAPP(hAPP(X18,hAPP(X55,X11)),hAPP(X55,X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X4)))<=c_Finite__Set_Ofolding__image__simple__idem(X5,X12,X18,X14,X50,X55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple__idem_Osubset__idem)). 6.97/7.20 fof(fact_list__ex1__iff, axiom, ![X23, X17, X5]:(?[X22]:((hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X23)))&![X72]:((hBOOL(hAPP(hAPP(c_member(X5),X72),hAPP(c_List_Oset(X5),X23)))&hBOOL(hAPP(X17,X72)))=>X22=X72))&hBOOL(hAPP(X17,X22)))<=>c_List_Olist__ex1(X5,X17,X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex1__iff)). 6.97/7.20 fof(fact_list__ex1__iff__raw, axiom, ![X23, X17, X5]:(c_List_Olist__ex1(X5,X17,X23)<=>?[X22]:((![X72]:((hBOOL(hAPP(X17,X72))&hBOOL(hAPP(hAPP(c_member(X5),X72),hAPP(c_List_Oset(X5),X23))))=>X22=X72)&hBOOL(hAPP(X17,X22)))&hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X23))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex1__iff__raw)). 6.97/7.20 fof(fact_power__gt1__lemma, axiom, ![X25, X30, X8]:(class_Rings_Olinordered__semidom(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Oone__class_Oone(X8)),X30))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Oone__class_Oone(X8)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__gt1__lemma)). 6.97/7.20 fof(fact_self__quotient__aux1, axiom, ![X53, X70, X30]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X70),X30))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X53)))<=X30=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X70),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X53)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_self__quotient__aux1)). 6.97/7.20 fof(fact_Sup__fin_Osubset__idem, axiom, ![X11, X4, X5]:(class_Lattices_Olattice(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X4))=>c_Big__Operators_Olattice__class_OSup__fin(X5,X4)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),c_Big__Operators_Olattice__class_OSup__fin(X5,X11)),c_Big__Operators_Olattice__class_OSup__fin(X5,X4)))<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Osubset__idem)). 6.97/7.20 fof(fact_Min_Osubset__idem, axiom, ![X11, X4, X5]:(class_Orderings_Olinorder(X5)=>(((c_Big__Operators_Olinorder__class_OMin(X5,X4)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olinorder__class_OMin(X5,X11)),c_Big__Operators_Olinorder__class_OMin(X5,X4))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X4)))<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X11)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min_Osubset__idem)). 6.97/7.20 fof(fact_finite__empty__induct, axiom, ![X17, X4, X5]:(((![X13, X54]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X54))=>((hBOOL(hAPP(X17,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X54),hAPP(hAPP(c_Set_Oinsert(X5),X13),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))<=hBOOL(hAPP(X17,X54)))<=hBOOL(hAPP(hAPP(c_member(X5),X13),X54))))=>hBOOL(hAPP(X17,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))<=hBOOL(hAPP(X17,X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__empty__induct)). 6.97/7.20 fof(fact_refl__onI, axiom, ![X4, X3, X5]:((c_Relation_Orefl__on(X5,X4,X3)<=![X22]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X22),X22)),X3))<=hBOOL(hAPP(hAPP(c_member(X5),X22),X4))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X4),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__onI)). 6.97/7.20 fof(fact_Inf__fin_Osubset__idem, axiom, ![X11, X4, X5]:(class_Lattices_Olattice(X5)=>((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X11=>(c_Big__Operators_Olattice__class_OInf__fin(X5,X4)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Big__Operators_Olattice__class_OInf__fin(X5,X11)),c_Big__Operators_Olattice__class_OInf__fin(X5,X4))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X4))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Osubset__idem)). 6.97/7.20 fof(fact_Max_Osubset__idem, axiom, ![X11, X4, X5]:(class_Orderings_Olinorder(X5)=>(((c_Big__Operators_Olinorder__class_OMax(X5,X4)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olinorder__class_OMax(X5,X11)),c_Big__Operators_Olinorder__class_OMax(X5,X4))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X4)))<=X11!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max_Osubset__idem)). 6.97/7.20 fof(fact_of__nat__diff, axiom, ![X36, X25, X8]:(class_Rings_Oring__1(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X36))=>hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),X25))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),X36)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__diff)). 6.97/7.20 fof(fact_mult__less__cancel__left__disj, axiom, ![X1, X2, X10, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X1)))<=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),c_Groups_Ozero__class_Ozero(X5)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X1),X2)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),X1))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X10)))))<=class_Rings_Olinordered__ring__strict(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__less__cancel__left__disj)). 6.97/7.20 fof(fact_mult__divide__mult__cancel__left, axiom, ![X29, X30, X31, X8]:((c_Groups_Ozero__class_Ozero(X8)!=X31=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X30)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X29))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X30),X29))<=class_Fields_Ofield__inverse__zero(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__divide__mult__cancel__left)). 6.97/7.20 fof(fact_weak__coinduct, axiom, ![X18, X56, X2, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X2),X56))=>(hBOOL(hAPP(hAPP(c_member(X5),X2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X5,tc_HOL_Obool),X18)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X56),hAPP(X18,X56))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_weak__coinduct)). 6.97/7.20 fof(fact_finite__subset__induct, axiom, ![X17, X4, X55, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X55))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X55),X4))=>((![X13, X234]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X234))=>(hBOOL(hAPP(hAPP(c_member(X5),X13),X4))=>((hBOOL(hAPP(X17,X234))=>hBOOL(hAPP(X17,hAPP(hAPP(c_Set_Oinsert(X5),X13),X234))))<=~(hBOOL(hAPP(hAPP(c_member(X5),X13),X234))))))=>hBOOL(hAPP(X17,X55)))<=hBOOL(hAPP(X17,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__subset__induct)). 6.97/7.20 fof(fact_div__mult__mult1, axiom, ![X29, X30, X31, X8]:(class_Divides_Osemiring__div(X8)=>(X31!=c_Groups_Ozero__class_Ozero(X8)=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X30)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X29))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),X30),X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__mult1)). 6.97/7.20 fof(fact_finite__Diff__insert, axiom, ![X11, X2, X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X2),X11))))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Diff__insert)). 6.97/7.20 fof(fact_in__set__butlast__appendI, axiom, ![X84, X23, X35, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),c_List_Obutlast(X5,hAPP(hAPP(c_List_Oappend(X5),X23),X84)))))<=(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),c_List_Obutlast(X5,X23))))|hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),c_List_Obutlast(X5,X84)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__butlast__appendI)). 6.97/7.20 fof(fact_mult__divide__mult__cancel__right, axiom, ![X29, X30, X31, X8]:(class_Fields_Ofield__inverse__zero(X8)=>(X31!=c_Groups_Ozero__class_Ozero(X8)=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X31))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X30),X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__divide__mult__cancel__right)). 6.97/7.20 fof(fact_max__extp_Osimps, axiom, ![X125, X103, X67, X5]:(c_Wellfounded_Omax__extp(X5,X67,X103,X125)<=>(((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X125))&c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X125)&![X22]:(?[X115]:(hBOOL(hAPP(hAPP(X67,X22),X115))&hBOOL(hAPP(hAPP(c_member(X5),X115),X125)))<=hBOOL(hAPP(hAPP(c_member(X5),X22),X103))))&hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X103)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__extp_Osimps)). 6.97/7.20 fof(fact_foldl__assoc, axiom, ![X83, X38, X35, X5]:(hAPP(c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X35),X38)),X83)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X35),hAPP(c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),X38),X83))<=class_Groups_Osemigroup__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__assoc)). 6.97/7.20 fof(fact_folding__idem_Oin__comp__idem, axiom, ![X35, X4, X55, X18, X12, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hBOOL(hAPP(hAPP(c_member(X5),X35),X4))=>hAPP(c_Fun_Ocomp(X12,X12,X12,hAPP(X55,X4)),hAPP(X18,X35))=hAPP(X55,X4)))<=c_Finite__Set_Ofolding__idem(X5,X12,X18,X55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__idem_Oin__comp__idem)). 6.97/7.20 fof(fact_finite__INT, axiom, ![X4, X12, X15, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X12),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),X15),X4)))<=?[X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X15))&hBOOL(hAPP(c_Finite__Set_Ofinite(X12),hAPP(X4,X22))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__INT)). 6.97/7.20 fof(fact_max__extp_Ointros, axiom, ![X67, X95, X56, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X56))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X95))=>(X95!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>(c_Wellfounded_Omax__extp(X5,X67,X56,X95)<=![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X56))=>?[X115]:(hBOOL(hAPP(hAPP(X67,X22),X115))&hBOOL(hAPP(hAPP(c_member(X5),X115),X95)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__extp_Ointros)). 6.97/7.20 fof(fact_atLeastatMost__subset__iff, axiom, ![X97, X10, X1, X2, X5]:(class_Orderings_Oorder(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X10,X97)))<=>(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X2),X1)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X10),X2))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X1),X97)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastatMost__subset__iff)). 6.97/7.20 fof(fact_all__nth__imp__all__set, axiom, ![X35, X17, X23, X5]:((hBOOL(hAPP(X17,X35))<=hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23))))<=![X42]:(hBOOL(hAPP(X17,hAPP(hAPP(c_List_Onth(X5),X23),X42)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_all__nth__imp__all__set)). 6.97/7.20 fof(fact_inv__image__comp, axiom, ![X56, X18, X12, X5]:(X56=hAPP(c_Set_Oimage(X12,X5,c_Hilbert__Choice_Oinv__into(X5,X12,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X18)),hAPP(c_Set_Oimage(X5,X12,X18),X56))<=c_Fun_Oinj__on(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inv__image__comp)). 6.97/7.20 fof(fact_inj__imp__surj__inv, axiom, ![X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))=>hAPP(c_Set_Oimage(X12,X5,c_Hilbert__Choice_Oinv__into(X5,X12,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X18)),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__imp__surj__inv)). 6.97/7.20 fof(fact_refl__onD, axiom, ![X2, X3, X4, X5]:((hBOOL(hAPP(hAPP(c_member(X5),X2),X4))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X2)),X3)))<=c_Relation_Orefl__on(X5,X4,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__onD)). 6.97/7.20 fof(fact_abs__setprod, axiom, ![X4, X18, X12, X5]:(hAPP(c_Groups_Oabs__class_Oabs(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12,X5),X18),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12,X5),hAPP(hAPP(c_COMBB(X5,X5,X12),c_Groups_Oabs__class_Oabs(X5)),X18)),X4)<=class_Fields_Olinordered__field(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__setprod)). 6.97/7.20 fof(fact_SUPR__apply, axiom, ![X35, X18, X4, X62, X12, X5]:(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,X5),X4),hAPP(hAPP(c_COMBC(X12,X62,X5),X18),X35))=hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X62,X5)),X4),X18),X35)<=class_Complete__Lattice_Ocomplete__lattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUPR__apply)). 6.97/7.20 fof(fact_nth__map, axiom, ![X18, X12, X23, X5, X32]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)))=>hAPP(hAPP(c_List_Onth(X12),hAPP(hAPP(c_List_Omap(X5,X12),X18),X23)),X32)=hAPP(X18,hAPP(hAPP(c_List_Onth(X5),X23),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__map)). 6.97/7.20 fof(fact_of__int__setsum, axiom, ![X4, X18, X12, X5]:(hAPP(c_Int_Oring__1__class_Oof__int(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,tc_Int_Oint),X18),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5),hAPP(hAPP(c_COMBB(tc_Int_Oint,X5,X12),c_Int_Oring__1__class_Oof__int(X5)),X18)),X4)<=class_Rings_Oring__1(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__setsum)). 6.97/7.20 fof(fact_div__mult__mult2, axiom, ![X29, X30, X31, X8]:((X31!=c_Groups_Ozero__class_Ozero(X8)=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),X30),X29)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X31)))<=class_Divides_Osemiring__div(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__mult2)). 6.97/7.20 fof(fact_INT__lower, axiom, ![X11, X12, X4, X2, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X2),X4))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),X4),X11)),hAPP(X11,X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__lower)). 6.97/7.20 fof(fact_UN__upper, axiom, ![X11, X12, X4, X2, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),hAPP(X11,X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X4),X11)))<=hBOOL(hAPP(hAPP(c_member(X5),X2),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__upper)). 6.97/7.20 fof(fact_in__set__conv__decomp__last, axiom, ![X23, X35, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23)))<=>?[X155, X194]:(hAPP(hAPP(c_List_Oappend(X5),X155),hAPP(hAPP(c_List_Olist_OCons(X5),X35),X194))=X23&~(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X194)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__conv__decomp__last)). 6.97/7.20 fof(fact_in__set__conv__decomp__first, axiom, ![X23, X35, X5]:(?[X155]:(~(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X155))))&?[X194]:X23=hAPP(hAPP(c_List_Oappend(X5),X155),hAPP(hAPP(c_List_Olist_OCons(X5),X35),X194)))<=>hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__conv__decomp__first)). 6.97/7.20 fof(fact_fold1__insert__idem, axiom, ![X35, X4, X5]:(class_Lattices_Oab__semigroup__idem__mult(X5)=>((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X35),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X4))=hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(hAPP(c_Set_Oinsert(X5),X35),X4)))<=X4!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__insert__idem)). 6.97/7.20 fof(fact_take__Suc, axiom, ![X25, X8, X41]:(c_List_Olist_ONil(X8)!=X41=>hAPP(hAPP(c_List_Otake(X8),hAPP(c_Nat_OSuc,X25)),X41)=hAPP(hAPP(c_List_Olist_OCons(X8),hAPP(c_List_Ohd(X8),X41)),hAPP(hAPP(c_List_Otake(X8),X25),hAPP(c_List_Otl(X8),X41)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__Suc)). 6.97/7.20 fof(fact_wf__map__pair__image, axiom, ![X18, X12, X3, X5]:((c_Wellfounded_Owf(X12,hAPP(c_Set_Oimage(tc_prod(X5,X5),tc_prod(X12,X12),c_Product__Type_Omap__pair(X5,X12,X5,X12,X18,X18)),X3))<=c_Fun_Oinj__on(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))<=c_Wellfounded_Owf(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__map__pair__image)). 6.97/7.20 fof(fact_bij__betw__comp__iff2, axiom, ![X4, X18, X62, X137, X107, X138, X12, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X62,X5,X18),X4)),X107))=>(c_Fun_Obij__betw(X62,X12,hAPP(c_Fun_Ocomp(X5,X12,X62,X138),X18),X4,X137)<=>c_Fun_Obij__betw(X62,X5,X18,X4,X107)))<=c_Fun_Obij__betw(X5,X12,X138,X107,X137)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bij__betw__comp__iff2)). 6.97/7.20 fof(fact_nth__Cons_H, axiom, ![X41, X6, X8, X25]:((hAPP(hAPP(c_List_Onth(X8),X41),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_List_Onth(X8),hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41)),X25)<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X25)&(X6=hAPP(hAPP(c_List_Onth(X8),hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41)),X25)<=X25=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__Cons_H)). 6.97/7.20 fof(fact_fun__left__comm_Ofold__set__remdups, axiom, ![X23, X38, X18, X12, X5]:(hAPP(c_List_Ofoldl(X12,X5,hAPP(c_COMBC(X5,X12,X12),X18),X38),c_List_Oremdups(X5,X23))=hAPP(hAPP(c_Finite__Set_Ofold(X5,X12,X18),X38),hAPP(c_List_Oset(X5),X23))<=c_Finite__Set_Ofun__left__comm(X5,X12,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__set__remdups)). 6.97/7.20 fof(fact_mod__diff__eq, axiom, ![X31, X29, X30, X8]:(c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),c_Divides_Odiv__class_Omod(X8,X30,X31)),c_Divides_Odiv__class_Omod(X8,X29,X31)),X31)=c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X30),X29),X31)<=class_Divides_Oring__div(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__diff__eq)). 6.97/7.20 fof(fact_listsum__distinct__conv__setsum__set, axiom, ![X18, X23, X5, X12]:(class_Groups_Ocomm__monoid__add(X12)=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),hAPP(c_List_Oset(X5),X23))=hAPP(c_List_Omonoid__add__class_Olistsum(X12),hAPP(hAPP(c_List_Omap(X5,X12),X18),X23))<=hBOOL(hAPP(c_List_Odistinct(X5),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__distinct__conv__setsum__set)). 6.97/7.20 fof(fact_listrel1__mono, axiom, ![X66, X3, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),X66))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool)),c_List_Olistrel1(X5,X3)),c_List_Olistrel1(X5,X66)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1__mono)). 6.97/7.20 fof(fact_listrel__mono, axiom, ![X66, X3, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),X66))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool)),c_List_Olistrel(X5,X3)),c_List_Olistrel(X5,X66)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__mono)). 6.97/7.20 fof(fact_Domain__mono, axiom, ![X66, X3, X12, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),X3),X66))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5,X12),X3)),hAPP(c_Relation_ODomain(X5,X12),X66)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__mono)). 6.97/7.20 fof(fact_Union__mono, axiom, ![X11, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X4),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X4)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__mono)). 6.97/7.20 fof(fact_list__size__estimation, axiom, ![X18, X38, X23, X35, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X38),c_List_Olist_Olist__size(X5,X18,X23)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X38),hAPP(X18,X35))))<=hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__size__estimation)). 6.97/7.20 fof(fact_list__size__estimation_H, axiom, ![X18, X38, X23, X35, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X38),hAPP(X18,X35)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X38),c_List_Olist_Olist__size(X5,X18,X23))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__size__estimation_H)). 6.97/7.20 fof(fact_takeWhile__append1, axiom, ![X84, X17, X23, X35, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23)))=>(~(hBOOL(hAPP(X17,X35)))=>c_List_OtakeWhile(X5,X17,hAPP(hAPP(c_List_Oappend(X5),X23),X84))=c_List_OtakeWhile(X5,X17,X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__append1)). 6.97/7.20 fof(fact_Inter__anti__mono, axiom, ![X4, X11, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X4)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X11),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__anti__mono)). 6.97/7.20 fof(fact_distinct__insort, axiom, ![X23, X35, X18, X5, X12]:(((~(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23))))&hBOOL(hAPP(c_List_Odistinct(X5),X23)))<=>hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X12,X18),X35),X23))))<=class_Orderings_Olinorder(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__insort)). 6.97/7.20 fof(fact_mult__eq__if, axiom, ![X25, X36]:((X36!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X25)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X25)))&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X25)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<=X36=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__eq__if)). 6.97/7.20 fof(fact_neg__divide__less__eq, axiom, ![X2, X1, X10, X5]:(class_Fields_Olinordered__field(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),c_Groups_Ozero__class_Ozero(X5)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X10)),X1))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X1),X10)),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__divide__less__eq)). 6.97/7.20 fof(fact_neg__divide__le__eq, axiom, ![X2, X1, X10, X5]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X10)),X1))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X1),X10)),X2)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),c_Groups_Ozero__class_Ozero(X5))))<=class_Fields_Olinordered__field(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__divide__le__eq)). 6.97/7.20 fof(fact_Diff__iff, axiom, ![X11, X4, X10, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11)))<=>(hBOOL(hAPP(hAPP(c_member(X5),X10),X4))&~(hBOOL(hAPP(hAPP(c_member(X5),X10),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__iff)). 6.97/7.20 fof(fact_mult__imp__less__div__pos, axiom, ![X6, X26, X7, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X7))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X7)),X6))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X26),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X6),X7)))))<=class_Fields_Olinordered__field(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__imp__less__div__pos)). 6.97/7.20 fof(fact_mult__imp__le__div__pos, axiom, ![X6, X26, X7, X8]:(class_Fields_Olinordered__field(X8)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X7)),X6))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X26),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X6),X7))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__imp__le__div__pos)). 6.97/7.20 fof(fact_zdiv__zmult2__eq, axiom, ![X29, X30, X31]:(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),X29)),X31)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X29),X31))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__zmult2__eq)). 6.97/7.20 fof(fact_mult__imp__div__pos__less, axiom, ![X26, X6, X7, X8]:(class_Fields_Olinordered__field(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X7))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X6),X7)),X26))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X7)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__imp__div__pos__less)). 6.97/7.20 fof(fact_mult__imp__div__pos__le, axiom, ![X26, X6, X7, X8]:(class_Fields_Olinordered__field(X8)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X7)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X6),X7)),X26)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__imp__div__pos__le)). 6.97/7.20 fof(fact_neg__less__divide__eq, axiom, ![X1, X2, X10, X5]:(class_Fields_Olinordered__field(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),c_Groups_Ozero__class_Ozero(X5)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X1),X10)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X10)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__less__divide__eq)). 6.97/7.20 fof(fact_all__nat__less, axiom, ![X17, X32]:(![X21]:(hBOOL(hAPP(X17,X21))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X32)))<=>![X22]:(hBOOL(hAPP(X17,X22))<=hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X22),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_all__nat__less)). 6.97/7.20 fof(fact_neg__le__divide__eq, axiom, ![X1, X2, X10, X5]:(class_Fields_Olinordered__field(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),c_Groups_Ozero__class_Ozero(X5)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X10)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X1),X10)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__le__divide__eq)). 6.97/7.20 fof(fact_inj__comp, axiom, ![X50, X62, X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))=>(c_Fun_Oinj__on(X62,X5,X50,c_Orderings_Otop__class_Otop(tc_fun(X62,tc_HOL_Obool)))=>c_Fun_Oinj__on(X62,X12,hAPP(c_Fun_Ocomp(X5,X12,X62,X18),X50),c_Orderings_Otop__class_Otop(tc_fun(X62,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__comp)). 6.97/7.20 fof(fact_mult__le__cancel1, axiom, ![X32, X34, X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X34)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X32)))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),X32))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__le__cancel1)). 6.97/7.20 fof(fact_ivl__disj__un_I14_J, axiom, ![X51, X52, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X52),X51))=>hAPP(c_SetInterval_Oord__class_OatLeast(X5),X52)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X52),X51)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X51)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I14_J)). 6.97/7.20 fof(fact_ivl__disj__un_I8_J, axiom, ![X51, X52, X5]:(class_Orderings_Olinorder(X5)=>(hAPP(c_SetInterval_Oord__class_OlessThan(X5),X51)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X52)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X52),X51))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X52),X51)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I8_J)). 6.97/7.20 fof(fact_mult__le__cancel2, axiom, ![X32, X33, X34]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),X32))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X33)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X33)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__le__cancel2)). 6.97/7.20 fof(fact_INFI__apply, axiom, ![X35, X18, X4, X62, X12, X5]:(class_Complete__Lattice_Ocomplete__lattice(X5)=>hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X62,X5)),X4),X18),X35)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,X5),X4),hAPP(hAPP(c_COMBC(X12,X62,X5),X18),X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INFI__apply)). 6.97/7.20 fof(fact_drop__Cons_H, axiom, ![X41, X6, X8, X25]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X25=>hAPP(hAPP(c_List_Odrop(X8),X25),hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41))=hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41))&(hAPP(hAPP(c_List_Odrop(X8),X25),hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41))=hAPP(hAPP(c_List_Odrop(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X41)<=X25!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__Cons_H)). 6.97/7.20 fof(fact_setprod__pos__nat, axiom, ![X18, X44, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X44))=>(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(X5,tc_Nat_Onat),X18),X44)))<=![X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X18,X22)))<=hBOOL(hAPP(hAPP(c_member(X5),X22),X44))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__pos__nat)). 6.97/7.20 fof(fact_append__eq__Cons__conv, axiom, ![X23, X35, X83, X84, X5]:((?[X203]:(X23=hAPP(hAPP(c_List_Oappend(X5),X203),X83)&X84=hAPP(hAPP(c_List_Olist_OCons(X5),X35),X203))|(X83=hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23)&X84=c_List_Olist_ONil(X5)))<=>hAPP(hAPP(c_List_Oappend(X5),X84),X83)=hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__eq__Cons__conv)). 6.97/7.20 fof(fact_power__eq__imp__eq__base, axiom, ![X29, X25, X30, X8]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X29))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))=>X30=X29))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X30)))<=hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25)=hAPP(hAPP(c_Power_Opower__class_Opower(X8),X29),X25))<=class_Rings_Olinordered__semidom(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__eq__imp__eq__base)). 6.97/7.20 fof(fact_listsum__setsum__nth, axiom, ![X23, X5]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(c_List_Onth(X5),X23)),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(X5)),X23)))=hAPP(c_List_Omonoid__add__class_Olistsum(X5),X23)<=class_Groups_Ocomm__monoid__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__setsum__nth)). 6.97/7.20 fof(fact_mult__pos__neg, axiom, ![X29, X30, X8]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X29),c_Groups_Ozero__class_Ozero(X8)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29)),c_Groups_Ozero__class_Ozero(X8))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X30)))<=class_Rings_Olinordered__semiring__strict(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__pos__neg)). 6.97/7.20 fof(fact_mult__pos__neg2, axiom, ![X29, X30, X8]:(class_Rings_Olinordered__semiring__strict(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X30))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X30)),c_Groups_Ozero__class_Ozero(X8)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X29),c_Groups_Ozero__class_Ozero(X8)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__pos__neg2)). 6.97/7.20 fof(fact_divide__neg__pos, axiom, ![X7, X6, X8]:(class_Fields_Olinordered__field(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X6),c_Groups_Ozero__class_Ozero(X8)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X7))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X6),X7)),c_Groups_Ozero__class_Ozero(X8)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__neg__pos)). 6.97/7.20 fof(fact_divide__pos__neg, axiom, ![X7, X6, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X6))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X7),c_Groups_Ozero__class_Ozero(X8)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X6),X7)),c_Groups_Ozero__class_Ozero(X8)))))<=class_Fields_Olinordered__field(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__pos__neg)). 6.97/7.20 fof(fact_split__mult__neg__le, axiom, ![X29, X30, X8]:(class_Rings_Oordered__cancel__semiring(X8)=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X30))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X29),c_Groups_Ozero__class_Ozero(X8))))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X29))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),c_Groups_Ozero__class_Ozero(X8)))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29)),c_Groups_Ozero__class_Ozero(X8))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__mult__neg__le)). 6.97/7.20 fof(fact_mult__le__0__iff, axiom, ![X1, X2, X5]:(class_Rings_Olinordered__ring__strict(X5)=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X1),c_Groups_Ozero__class_Ozero(X5)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X2)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X2),c_Groups_Ozero__class_Ozero(X5)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X1))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X1)),c_Groups_Ozero__class_Ozero(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__le__0__iff)). 6.97/7.20 fof(fact_divide__nonneg__neg, axiom, ![X7, X6, X8]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X6),X7)),c_Groups_Ozero__class_Ozero(X8)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X7),c_Groups_Ozero__class_Ozero(X8))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X6)))<=class_Fields_Olinordered__field(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__nonneg__neg)). 6.97/7.20 fof(fact_divide__nonpos__pos, axiom, ![X7, X6, X8]:(class_Fields_Olinordered__field(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),c_Groups_Ozero__class_Ozero(X8)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X7))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X6),X7)),c_Groups_Ozero__class_Ozero(X8)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__nonpos__pos)). 6.97/7.20 fof(fact_add__neg__neg, axiom, ![X29, X30, X8]:(class_Groups_Oordered__comm__monoid__add(X8)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X29),c_Groups_Ozero__class_Ozero(X8)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29)),c_Groups_Ozero__class_Ozero(X8))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),c_Groups_Ozero__class_Ozero(X8))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__neg__neg)). 6.97/7.20 fof(fact_add__nonpos__neg, axiom, ![X29, X30, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),c_Groups_Ozero__class_Ozero(X8)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X29),c_Groups_Ozero__class_Ozero(X8)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29)),c_Groups_Ozero__class_Ozero(X8)))))<=class_Groups_Oordered__comm__monoid__add(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__nonpos__neg)). 6.97/7.20 fof(fact_rotate1__hd__tl, axiom, ![X8, X41]:(hAPP(c_List_Orotate1(X8),X41)=hAPP(hAPP(c_List_Oappend(X8),hAPP(c_List_Otl(X8),X41)),hAPP(hAPP(c_List_Olist_OCons(X8),hAPP(c_List_Ohd(X8),X41)),c_List_Olist_ONil(X8)))<=c_List_Olist_ONil(X8)!=X41), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate1__hd__tl)). 6.97/7.20 fof(fact_add__neg__nonpos, axiom, ![X29, X30, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),c_Groups_Ozero__class_Ozero(X8)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29)),c_Groups_Ozero__class_Ozero(X8)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X29),c_Groups_Ozero__class_Ozero(X8)))))<=class_Groups_Oordered__comm__monoid__add(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__neg__nonpos)). 6.97/7.20 fof(fact_add__nonpos__nonpos, axiom, ![X29, X30, X8]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29)),c_Groups_Ozero__class_Ozero(X8)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X29),c_Groups_Ozero__class_Ozero(X8))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),c_Groups_Ozero__class_Ozero(X8))))<=class_Groups_Oordered__comm__monoid__add(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__nonpos__nonpos)). 6.97/7.20 fof(fact_less__1__mult, axiom, ![X25, X36, X8]:(class_Rings_Olinordered__semidom(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Oone__class_Oone(X8)),X36))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Oone__class_Oone(X8)),X25))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Oone__class_Oone(X8)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X36),X25)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__1__mult)). 6.97/7.20 fof(fact_add__pos__pos, axiom, ![X29, X30, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X30))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X29))))<=class_Groups_Oordered__comm__monoid__add(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__pos__pos)). 6.97/7.20 fof(fact_mult__pos__pos, axiom, ![X29, X30, X8]:(class_Rings_Olinordered__semiring__strict(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X30))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X29))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__pos__pos)). 6.97/7.20 fof(fact_divide__pos__pos, axiom, ![X7, X6, X8]:(class_Fields_Olinordered__field(X8)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X6),X7)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X7)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__pos__pos)). 6.97/7.20 fof(fact_mult__nonneg__nonneg, axiom, ![X29, X30, X8]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X29))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X30)))<=class_Rings_Oordered__cancel__semiring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__nonneg__nonneg)). 6.97/7.20 fof(fact_one__less__power, axiom, ![X25, X30, X8]:(class_Rings_Olinordered__semidom(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Oone__class_Oone(X8)),X30))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Oone__class_Oone(X8)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__less__power)). 6.97/7.20 fof(fact_Min__antimono, axiom, ![X20, X94, X5]:(((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X94=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X20))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Big__Operators_Olinorder__class_OMin(X5,X20)),c_Big__Operators_Olinorder__class_OMin(X5,X94)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X94),X20)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min__antimono)). 6.97/7.20 fof(fact_zero__le__mult__iff, axiom, ![X1, X2, X5]:(class_Rings_Olinordered__ring__strict(X5)=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X2),c_Groups_Ozero__class_Ozero(X5)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X1),c_Groups_Ozero__class_Ozero(X5))))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X2))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X1))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__mult__iff)). 6.97/7.20 fof(fact_split__mult__pos__le, axiom, ![X29, X30, X8]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X29),c_Groups_Ozero__class_Ozero(X8)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),c_Groups_Ozero__class_Ozero(X8))))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X30))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X29))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29))))<=class_Rings_Oordered__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__mult__pos__le)). 6.97/7.20 fof(fact_divide__nonneg__pos, axiom, ![X7, X6, X8]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X7))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X6),X7))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X6)))<=class_Fields_Olinordered__field(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__nonneg__pos)). 6.97/7.20 fof(fact_mult__neg__neg, axiom, ![X29, X30, X8]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X29),c_Groups_Ozero__class_Ozero(X8)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),c_Groups_Ozero__class_Ozero(X8))))<=class_Rings_Olinordered__ring__strict(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__neg__neg)). 6.97/7.20 fof(fact_Max__mono, axiom, ![X20, X94, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X94),X20))=>((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X20))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Big__Operators_Olinorder__class_OMax(X5,X94)),c_Big__Operators_Olinorder__class_OMax(X5,X20))))<=X94!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max__mono)). 6.97/7.20 fof(fact_add__less__cancel__right, axiom, ![X1, X10, X2, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),X1))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X2),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X1),X10))))<=class_Groups_Oordered__ab__semigroup__add__imp__le(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__less__cancel__right)). 6.97/7.20 fof(fact_divmod__int__rel__div__mod, axiom, ![X30, X29]:(hBOOL(hAPP(c_Divides_Odivmod__int__rel(X30,X29),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),X29)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X29))))<=c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X29), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__rel__div__mod)). 6.97/7.20 fof(fact_divide__neg__neg, axiom, ![X7, X6, X8]:(class_Fields_Olinordered__field(X8)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X7),c_Groups_Ozero__class_Ozero(X8)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X6),X7))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X6),c_Groups_Ozero__class_Ozero(X8))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__neg__neg)). 6.97/7.20 fof(fact_select, axiom, ![X66, X5, X23]:(X23!=c_List_Olist_ONil(X5)=>hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Product__Type_Ofst(X5,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(X5,X23),X66))),hAPP(c_List_Oset(X5),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_select)). 6.97/7.20 fof(fact_add__strict__right__mono, axiom, ![X31, X29, X30, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X29),X31)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),X29)))<=class_Groups_Oordered__cancel__ab__semigroup__add(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__strict__right__mono)). 6.97/7.20 fof(fact_add__less__cancel__left, axiom, ![X1, X2, X10, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),X1))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X10),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X10),X1))))<=class_Groups_Oordered__ab__semigroup__add__imp__le(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__less__cancel__left)). 6.97/7.20 fof(fact_add__strict__left__mono, axiom, ![X31, X29, X30, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X31),X30)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X31),X29)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),X29)))<=class_Groups_Oordered__cancel__ab__semigroup__add(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__strict__left__mono)). 6.97/7.20 fof(fact_add__le__cancel__right, axiom, ![X1, X10, X2, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X2),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X1),X10)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X2),X1)))<=class_Groups_Oordered__ab__semigroup__add__imp__le(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__le__cancel__right)). 6.97/7.20 fof(fact_divide__nonpos__neg, axiom, ![X7, X6, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),c_Groups_Ozero__class_Ozero(X8)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X6),X7)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X7),c_Groups_Ozero__class_Ozero(X8)))))<=class_Fields_Olinordered__field(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__nonpos__neg)). 6.97/7.20 fof(fact_inv__into__injective, axiom, ![X38, X35, X18, X4, X12, X5]:(hAPP(c_Hilbert__Choice_Oinv__into(X5,X12,X4,X18),X38)=hAPP(c_Hilbert__Choice_Oinv__into(X5,X12,X4,X18),X35)=>((X38=X35<=hBOOL(hAPP(hAPP(c_member(X12),X38),hAPP(c_Set_Oimage(X5,X12,X18),X4))))<=hBOOL(hAPP(hAPP(c_member(X12),X35),hAPP(c_Set_Oimage(X5,X12,X18),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inv__into__injective)). 6.97/7.20 fof(fact_abs__number__of, axiom, ![X6, X8]:((class_Int_Onumber__ring(X8)&class_Rings_Olinordered__idom(X8))=>((hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),X6))=hAPP(c_Groups_Ouminus__class_Ouminus(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),X6))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),X6)),c_Groups_Ozero__class_Ozero(X8))))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),X6)),c_Groups_Ozero__class_Ozero(X8))))=>hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),X6))=hAPP(c_Int_Onumber__class_Onumber__of(X8),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__number__of)). 6.97/7.20 fof(fact_add__right__mono, axiom, ![X31, X29, X30, X8]:(class_Groups_Oordered__ab__semigroup__add(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X29),X31)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__right__mono)). 6.97/7.20 fof(fact_add__le__cancel__left, axiom, ![X1, X2, X10, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X2),X1))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X10),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X10),X1))))<=class_Groups_Oordered__ab__semigroup__add__imp__le(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__le__cancel__left)). 6.97/7.20 fof(fact_add__left__mono, axiom, ![X31, X29, X30, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),X29))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X31),X30)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X31),X29))))<=class_Groups_Oordered__ab__semigroup__add(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__left__mono)). 6.97/7.20 fof(fact_min__max_OInf__le__Sup, axiom, ![X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(X4!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X4)),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X4)))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__le__Sup)). 6.97/7.20 fof(fact_set__zip__leftD, axiom, ![X84, X23, X38, X35, X12, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X35),X38)),hAPP(c_List_Oset(tc_prod(X5,X12)),hAPP(hAPP(c_List_Ozip(X5,X12),X23),X84))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__zip__leftD)). 6.97/7.20 fof(fact_set__zip__rightD, axiom, ![X84, X23, X38, X35, X12, X5]:(hBOOL(hAPP(hAPP(c_member(X12),X38),hAPP(c_List_Oset(X12),X84)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X35),X38)),hAPP(c_List_Oset(tc_prod(X5,X12)),hAPP(hAPP(c_List_Ozip(X5,X12),X23),X84))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__zip__rightD)). 6.97/7.20 fof(fact_Ball__set__replicate, axiom, ![X17, X2, X32, X5]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X32|hBOOL(hAPP(X17,X2)))<=>![X22]:(hBOOL(hAPP(X17,X22))<=hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),c_List_Oreplicate(X5,X32,X2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ball__set__replicate)). 6.97/7.20 fof(fact_folding__one__idem_Oinsert__idem, axiom, ![X35, X4, X55, X18, X5]:(c_Finite__Set_Ofolding__one__idem(X5,X18,X55)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hAPP(X55,hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))=hAPP(hAPP(X18,X35),hAPP(X55,X4))<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one__idem_Oinsert__idem)). 6.97/7.20 fof(fact_mod__add__eq, axiom, ![X31, X29, X30, X8]:(c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29),X31)=c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),c_Divides_Odiv__class_Omod(X8,X30,X31)),c_Divides_Odiv__class_Omod(X8,X29,X31)),X31)<=class_Divides_Osemiring__div(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__add__eq)). 6.97/7.20 fof(fact_mod__mult__eq, axiom, ![X31, X29, X30, X8]:(c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29),X31)=c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Divides_Odiv__class_Omod(X8,X30,X31)),c_Divides_Odiv__class_Omod(X8,X29,X31)),X31)<=class_Divides_Osemiring__div(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__eq)). 6.97/7.20 fof(fact_ex__nat__less__eq, axiom, ![X17, X32]:(?[X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X32))&hBOOL(hAPP(X17,X21)))<=>?[X22]:(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X22),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32)))&hBOOL(hAPP(X17,X22)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ex__nat__less__eq)). 6.97/7.20 fof(fact_card__Plus__conv__if, axiom, ![X11, X12, X4, X5]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))&hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X11)))=>hAPP(c_Finite__Set_Ocard(tc_sum(X5,X12)),c_Sum__Type_OPlus(X5,X12,X4,X11))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X4)),hAPP(c_Finite__Set_Ocard(X12),X11)))&(hAPP(c_Finite__Set_Ocard(tc_sum(X5,X12)),c_Sum__Type_OPlus(X5,X12,X4,X11))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<=~((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))&hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X11)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Plus__conv__if)). 6.97/7.20 fof(fact_image__uminus__atLeastLessThan, axiom, ![X38, X35, X5]:(c_SetInterval_Oord__class_OgreaterThanAtMost(X5,hAPP(c_Groups_Ouminus__class_Ouminus(X5),X38),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X35))=hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X35),X38))<=class_Groups_Oordered__ab__group__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__uminus__atLeastLessThan)). 6.97/7.20 fof(fact_diff__diff__right, axiom, ![X28, X27, X19]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X28),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X27),X19))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),X19)),X27)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19),X27))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__diff__right)). 6.97/7.20 fof(fact_add__diff__assoc, axiom, ![X28, X27, X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19),X27))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X27),X19))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),X27)),X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__diff__assoc)). 6.97/7.20 fof(fact_folding__image__simple__idem_Oin__idem, axiom, ![X35, X4, X55, X50, X14, X18, X12, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X4))=>(hBOOL(hAPP(hAPP(c_member(X12),X35),X4))=>hAPP(X55,X4)=hAPP(hAPP(X18,hAPP(X50,X35)),hAPP(X55,X4))))<=c_Finite__Set_Ofolding__image__simple__idem(X5,X12,X18,X14,X50,X55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple__idem_Oin__idem)). 6.97/7.20 fof(fact_list__all2__map1, axiom, ![X159, X160, X18, X62, X17, X12, X5]:(c_List_Olist__all2(X62,X12,hAPP(hAPP(c_COMBB(X5,tc_fun(X12,tc_HOL_Obool),X62),X17),X18),X160,X159)<=>c_List_Olist__all2(X5,X12,X17,hAPP(hAPP(c_List_Omap(X62,X5),X18),X160),X159)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__map1)). 6.97/7.20 fof(fact_subset__singletonD, axiom, ![X35, X4, X5]:((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=X4|X4=hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__singletonD)). 6.97/7.20 fof(fact_minus__apply, axiom, ![X35, X11, X4, X12, X5]:(class_Groups_Ominus(X5)=>hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12,X5)),X4),X11),X35)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(X4,X35)),hAPP(X11,X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__apply)). 6.97/7.20 fof(fact_sup__apply, axiom, ![X35, X50, X18, X12, X5]:(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,X5)),X18),X50),X35)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),hAPP(X18,X35)),hAPP(X50,X35))<=class_Lattices_Olattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__apply)). 6.97/7.20 fof(fact_UnionI, axiom, ![X4, X65, X56, X5]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X56),X65))=>(hBOOL(hAPP(hAPP(c_member(X5),X4),X56))=>hBOOL(hAPP(hAPP(c_member(X5),X4),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X65))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UnionI)). 6.97/7.20 fof(fact_mod__mult__mult2, axiom, ![X29, X31, X30, X8]:(c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X31))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Divides_Odiv__class_Omod(X8,X30,X29)),X31)<=class_Divides_Osemiring__div(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__mult2)). 6.97/7.20 fof(fact_inf__fun__def, axiom, ![X35, X50, X18, X12, X5]:(class_Lattices_Olattice(X5)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),hAPP(X18,X35)),hAPP(X50,X35))=hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,X5)),X18),X50),X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__fun__def)). 6.97/7.20 fof(fact_mod__mult__mult1, axiom, ![X29, X30, X31, X8]:(c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X29))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),c_Divides_Odiv__class_Omod(X8,X30,X29))<=class_Divides_Osemiring__div(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__mult1)). 6.97/7.20 fof(fact_remove1__append, axiom, ![X84, X23, X35, X5]:((hAPP(hAPP(c_List_Oappend(X5),c_List_Oremove1(X5,X35,X23)),X84)=c_List_Oremove1(X5,X35,hAPP(hAPP(c_List_Oappend(X5),X23),X84))<=hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23))))&(c_List_Oremove1(X5,X35,hAPP(hAPP(c_List_Oappend(X5),X23),X84))=hAPP(hAPP(c_List_Oappend(X5),X23),c_List_Oremove1(X5,X35,X84))<=~(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remove1__append)). 6.97/7.20 fof(fact_rtrancl__listrel1__eq__len, axiom, ![X3, X38, X35, X5]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X35)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X38)<=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)),X35),X38)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__listrel1__eq__len)). 6.97/7.20 fof(fact_nat__mod__eq__lemma, axiom, ![X7, X25, X6]:(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X6,X25)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X7,X25)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7),X6))=>?[X150]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X150))=X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mod__eq__lemma)). 6.97/7.20 fof(fact_distinct__set__sublists, axiom, ![X23, X5]:(hBOOL(hAPP(c_List_Odistinct(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool)),c_List_Oset(X5)),c_Enum_Osublists(X5,X23))))<=hBOOL(hAPP(c_List_Odistinct(X5),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__set__sublists)). 6.97/7.20 fof(fact_INF2__E, axiom, ![X2, X10, X1, X11, X4, X62, X12, X5]:(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_fun(X62,tc_HOL_Obool))),X4),X11),X1),X10))=>(~(hBOOL(hAPP(hAPP(hAPP(X11,X2),X1),X10)))=>~(hBOOL(hAPP(hAPP(c_member(X5),X2),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF2__E)). 6.97/7.20 fof(fact_max__of__mono, axiom, ![X32, X34, X18, X5, X12]:((class_Orderings_Olinorder(X5)&class_Orderings_Olinorder(X12))=>(c_Orderings_Oorder__class_Omono(X5,X12,X18)=>hAPP(X18,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X34),X32))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X12),hAPP(X18,X34)),hAPP(X18,X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__of__mono)). 6.97/7.20 fof(fact_insert__subset, axiom, ![X11, X4, X35, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X35),X4)),X11))<=>(hBOOL(hAPP(hAPP(c_member(X5),X35),X11))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__subset)). 6.97/7.20 fof(fact_wf__Un, axiom, ![X66, X3, X5]:(c_Wellfounded_Owf(X5,X3)=>((c_Wellfounded_Owf(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),X66))<=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5,X5),X3)),hAPP(c_Relation_ORange(X5,X5),X66))=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))<=c_Wellfounded_Owf(X5,X66))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__Un)). 6.97/7.20 fof(fact_min__of__mono, axiom, ![X32, X34, X18, X5, X12]:((hAPP(X18,hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X34),X32))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X12),hAPP(X18,X34)),hAPP(X18,X32))<=c_Orderings_Oorder__class_Omono(X5,X12,X18))<=(class_Orderings_Olinorder(X5)&class_Orderings_Olinorder(X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__of__mono)). 6.97/7.20 fof(fact_divide__less__0__iff, axiom, ![X1, X2, X5]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X2))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X1),c_Groups_Ozero__class_Ozero(X5))))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),c_Groups_Ozero__class_Ozero(X5)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X1))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X2),X1)),c_Groups_Ozero__class_Ozero(X5))))<=class_Fields_Olinordered__field__inverse__zero(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__less__0__iff)). 6.97/7.20 fof(fact_divide__le__0__iff, axiom, ![X1, X2, X5]:(class_Fields_Olinordered__field__inverse__zero(X5)=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X1),c_Groups_Ozero__class_Ozero(X5)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X2)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X2),c_Groups_Ozero__class_Ozero(X5)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X1))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X2),X1)),c_Groups_Ozero__class_Ozero(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__le__0__iff)). 6.97/7.20 fof(fact_inv__into__image__cancel, axiom, ![X44, X4, X18, X12, X5]:((hAPP(c_Set_Oimage(X12,X5,c_Hilbert__Choice_Oinv__into(X5,X12,X4,X18)),hAPP(c_Set_Oimage(X5,X12,X18),X44))=X44<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X44),X4)))<=c_Fun_Oinj__on(X5,X12,X18,X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inv__into__image__cancel)). 6.97/7.20 fof(fact_power__inject__base, axiom, ![X29, X25, X30, X8]:((hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),hAPP(c_Nat_OSuc,X25))=hAPP(hAPP(c_Power_Opower__class_Opower(X8),X29),hAPP(c_Nat_OSuc,X25))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X29))=>X29=X30)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X30))))<=class_Rings_Olinordered__semidom(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__inject__base)). 6.97/7.20 fof(fact_Ints__diff, axiom, ![X1, X2, X5]:(class_Rings_Oring__1(X5)=>(hBOOL(hAPP(hAPP(c_member(X5),X2),c_Int_Oring__1__class_OInts(X5)))=>(hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X2),X1)),c_Int_Oring__1__class_OInts(X5)))<=hBOOL(hAPP(hAPP(c_member(X5),X1),c_Int_Oring__1__class_OInts(X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__diff)). 6.97/7.20 fof(fact_Nats__add, axiom, ![X1, X2, X5]:(class_Rings_Osemiring__1(X5)=>(hBOOL(hAPP(hAPP(c_member(X5),X2),c_Nat_Osemiring__1__class_ONats(X5)))=>(hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X2),X1)),c_Nat_Osemiring__1__class_ONats(X5)))<=hBOOL(hAPP(hAPP(c_member(X5),X1),c_Nat_Osemiring__1__class_ONats(X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nats__add)). 6.97/7.20 fof(fact_Ints__add, axiom, ![X1, X2, X5]:(((hBOOL(hAPP(hAPP(c_member(X5),X1),c_Int_Oring__1__class_OInts(X5)))=>hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X2),X1)),c_Int_Oring__1__class_OInts(X5))))<=hBOOL(hAPP(hAPP(c_member(X5),X2),c_Int_Oring__1__class_OInts(X5))))<=class_Rings_Oring__1(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__add)). 6.97/7.20 fof(fact_Nats__mult, axiom, ![X1, X2, X5]:((hBOOL(hAPP(hAPP(c_member(X5),X2),c_Nat_Osemiring__1__class_ONats(X5)))=>(hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X1)),c_Nat_Osemiring__1__class_ONats(X5)))<=hBOOL(hAPP(hAPP(c_member(X5),X1),c_Nat_Osemiring__1__class_ONats(X5)))))<=class_Rings_Osemiring__1(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nats__mult)). 6.97/7.20 fof(fact_less__diff__iff, axiom, ![X32, X34, X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X34))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34),X32))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X34),X33)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X32),X33))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__diff__iff)). 6.97/7.20 fof(fact_le__diff__iff, axiom, ![X32, X34, X33]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X32))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),X32))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X34),X33)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X32),X33)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X34))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__diff__iff)). 6.97/7.20 fof(fact_Ints__mult, axiom, ![X1, X2, X5]:(((hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X1)),c_Int_Oring__1__class_OInts(X5)))<=hBOOL(hAPP(hAPP(c_member(X5),X1),c_Int_Oring__1__class_OInts(X5))))<=hBOOL(hAPP(hAPP(c_member(X5),X2),c_Int_Oring__1__class_OInts(X5))))<=class_Rings_Oring__1(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__mult)). 6.97/7.20 fof(fact_zero__less__divide__iff, axiom, ![X1, X2, X5]:(class_Fields_Olinordered__field__inverse__zero(X5)=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X1),c_Groups_Ozero__class_Ozero(X5)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),c_Groups_Ozero__class_Ozero(X5))))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X1))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X2))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X2),X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__divide__iff)). 6.97/7.20 fof(fact_zero__le__divide__iff, axiom, ![X1, X2, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X2),X1)))<=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X1))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X2)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X2),c_Groups_Ozero__class_Ozero(X5)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X1),c_Groups_Ozero__class_Ozero(X5))))))<=class_Fields_Olinordered__field__inverse__zero(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__divide__iff)). 6.97/7.20 fof(fact_SUP2__E, axiom, ![X10, X1, X11, X4, X62, X12, X5]:(~(![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))=>~(hBOOL(hAPP(hAPP(hAPP(X11,X22),X1),X10)))))<=hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_fun(X62,tc_HOL_Obool))),X4),X11),X1),X10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP2__E)). 6.97/7.20 fof(fact_distinct__append, axiom, ![X84, X23, X5]:(hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Oappend(X5),X23),X84)))<=>((hBOOL(hAPP(c_List_Odistinct(X5),X23))&hBOOL(hAPP(c_List_Odistinct(X5),X84)))&c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X23)),hAPP(c_List_Oset(X5),X84)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__append)). 6.97/7.20 fof(fact_zdiff__int, axiom, ![X36, X25]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X36))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X36)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiff__int)). 6.97/7.20 fof(fact_in__rel__def, axiom, ![X38, X35, X67, X12, X5]:(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X5,X12,X67),X35),X38))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X35),X38)),X67))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__rel__def)). 6.97/7.20 fof(fact_irrefl__def, axiom, ![X3, X5]:(c_Relation_Oirrefl(X5,X3)<=>![X22]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X22),X22)),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_irrefl__def)). 6.97/7.20 fof(fact_power__le__imp__le__base, axiom, ![X29, X25, X30, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),hAPP(c_Nat_OSuc,X25))),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X29),hAPP(c_Nat_OSuc,X25))))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X29))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),X29))))<=class_Rings_Olinordered__semidom(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__le__imp__le__base)). 6.97/7.20 fof(fact_antisym__def, axiom, ![X3, X5]:(c_Relation_Oantisym(X5,X3)<=>![X22, X72]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X22),X72)),X3))=>(X72=X22<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X72),X22)),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_antisym__def)). 6.97/7.20 fof(fact_psubset__imp__ex__mem, axiom, ![X11, X4, X5]:(?[X96]:hBOOL(hAPP(hAPP(c_member(X5),X96),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X4)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X4),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_psubset__imp__ex__mem)). 6.97/7.20 fof(fact_Pow__mono, axiom, ![X11, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X5),X4)),hAPP(c_Set_OPow(X5),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__mono)). 6.97/7.20 fof(fact_UN__iff, axiom, ![X11, X4, X12, X1, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X4),X11)))<=>?[X22]:(hBOOL(hAPP(hAPP(c_member(X12),X22),X4))&hBOOL(hAPP(hAPP(c_member(X5),X1),hAPP(X11,X22))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__iff)). 6.97/7.20 fof(fact_UN__E, axiom, ![X11, X4, X12, X1, X5]:(~(![X22]:(hBOOL(hAPP(hAPP(c_member(X12),X22),X4))=>~(hBOOL(hAPP(hAPP(c_member(X5),X1),hAPP(X11,X22))))))<=hBOOL(hAPP(hAPP(c_member(X5),X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X4),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__E)). 6.97/7.20 fof(fact_trans__def, axiom, ![X3, X5]:(c_Relation_Otrans(X5,X3)<=>![X22, X72]:(![X116]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X22),X116)),X3))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X72),X116)),X3)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X22),X72)),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trans__def)). 6.97/7.20 fof(fact_inv__inv__eq, axiom, ![X18, X12, X5]:(c_Hilbert__Choice_Oinv__into(X12,X5,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(X5,X12,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X18))=X18<=c_Fun_Obij__betw(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inv__inv__eq)). 6.97/7.20 fof(fact_set__update__memI, axiom, ![X35, X23, X5, X32]:(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist__update(X5,X23),X32),X35))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__update__memI)). 6.97/7.20 fof(fact_folding__one__idem_Oeq__fold__idem_H, axiom, ![X2, X4, X55, X18, X5]:(c_Finite__Set_Ofolding__one__idem(X5,X18,X55)=>(hAPP(X55,hAPP(hAPP(c_Set_Oinsert(X5),X2),X4))=hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,X18),X2),X4)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one__idem_Oeq__fold__idem_H)). 6.97/7.20 fof(fact_Bex__set__replicate, axiom, ![X17, X2, X32, X5]:((X32!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&hBOOL(hAPP(X17,X2)))<=>?[X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),c_List_Oreplicate(X5,X32,X2))))&hBOOL(hAPP(X17,X22)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Bex__set__replicate)). 6.97/7.20 fof(fact_Inf__binary, axiom, ![X1, X2, X5]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X2),X1)=c_Complete__Lattice_OInf__class_OInf(X5,hAPP(hAPP(c_Set_Oinsert(X5),X2),hAPP(hAPP(c_Set_Oinsert(X5),X1),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))<=class_Complete__Lattice_Ocomplete__lattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__binary)). 6.97/7.20 fof(fact_rtrancl__subset__rtrancl, axiom, ![X66, X3, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X3)),c_Transitive__Closure_Ortrancl(X5,X66)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),c_Transitive__Closure_Ortrancl(X5,X66)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__subset__rtrancl)). 6.97/7.20 fof(fact_fold1Set_Ointros, axiom, ![X35, X4, X2, X18, X5]:(hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,X18,X2,X4),X35))=>(hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X18,hAPP(hAPP(c_Set_Oinsert(X5),X2),X4)),X35))<=~(hBOOL(hAPP(hAPP(c_member(X5),X2),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1Set_Ointros)). 6.97/7.20 fof(fact_sorted_OCons, axiom, ![X35, X23, X5]:(class_Orderings_Olinorder(X5)=>(![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X23)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),X22)))=>(c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23))<=c_List_Olinorder__class_Osorted(X5,X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted_OCons)). 6.97/7.20 fof(fact_Sup__binary, axiom, ![X1, X2, X5]:(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X2),X1)=c_Complete__Lattice_OSup__class_OSup(X5,hAPP(hAPP(c_Set_Oinsert(X5),X2),hAPP(hAPP(c_Set_Oinsert(X5),X1),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))<=class_Complete__Lattice_Ocomplete__lattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__binary)). 6.97/7.20 fof(fact_list__all2__Cons, axiom, ![X84, X38, X23, X35, X17, X12, X5]:(c_List_Olist__all2(X5,X12,X17,hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23),hAPP(hAPP(c_List_Olist_OCons(X12),X38),X84))<=>(c_List_Olist__all2(X5,X12,X17,X23,X84)&hBOOL(hAPP(hAPP(X17,X35),X38)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__Cons)). 6.97/7.20 fof(fact_comm__monoid__big_OF__eq, axiom, ![X50, X4, X55, X14, X18, X12, X5]:(((hAPP(hAPP(X55,X50),X4)=X14<=~(hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X4))))&(hAPP(hAPP(X55,X50),X4)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X12,X18),X50),X14),X4)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X4))))<=c_Big__Operators_Ocomm__monoid__big(X5,X12,X18,X14,X55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__monoid__big_OF__eq)). 6.97/7.20 fof(fact_folding__image_Oeq__fold, axiom, ![X50, X4, X55, X14, X18, X12, X5]:(c_Finite__Set_Ofolding__image(X5,X12,X18,X14,X55)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X4))=>hAPP(hAPP(X55,X50),X4)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X12,X18),X50),X14),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image_Oeq__fold)). 6.97/7.20 fof(fact_Int__atLeastAtMostL2, axiom, ![X10, X1, X2, X5]:(c_SetInterval_Oord__class_OatLeastAtMost(X5,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X2),X10),X1)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X2,X1)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X10))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__atLeastAtMostL2)). 6.97/7.20 fof(fact_sorted_Oequations_I2_J, axiom, ![X103, X125, X5]:(((![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X103)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X125),X22)))&c_List_Olinorder__class_Osorted(X5,X103))<=>c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X125),X103)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted_Oequations_I2_J)). 6.97/7.20 fof(fact_sorted__Cons, axiom, ![X23, X35, X5]:(((![X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),X22))<=hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X23))))&c_List_Olinorder__class_Osorted(X5,X23))<=>c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__Cons)). 6.97/7.20 fof(fact_ivl__disj__un_I12_J, axiom, ![X51, X52, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X52),X51))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X52,X51)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X51))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X52))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I12_J)). 6.97/7.20 fof(fact_ivl__disj__un_I11_J, axiom, ![X51, X52, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X52),X51))=>hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X52)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X52,X51)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X51)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I11_J)). 6.97/7.20 fof(fact_Int__atLeastAtMostL1, axiom, ![X97, X1, X2, X5]:(c_SetInterval_Oord__class_OatLeastAtMost(X5,X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X1),X97))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X2,X1)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X97))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__atLeastAtMostL1)). 6.97/7.20 fof(fact_Int__atLeastAtMostR2, axiom, ![X97, X10, X2, X5]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X2)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X10,X97))=c_SetInterval_Oord__class_OatLeastAtMost(X5,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X2),X10),X97)<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__atLeastAtMostR2)). 6.97/7.20 fof(fact_filter_Osimps_I2_J, axiom, ![X23, X5, X35, X17]:((hAPP(hAPP(c_List_Olist_OCons(X5),X35),hAPP(c_List_Ofilter(X5,X17),X23))=hAPP(c_List_Ofilter(X5,X17),hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23))<=hBOOL(hAPP(X17,X35)))&(hAPP(c_List_Ofilter(X5,X17),X23)=hAPP(c_List_Ofilter(X5,X17),hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23))<=~(hBOOL(hAPP(X17,X35))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter_Osimps_I2_J)). 6.97/7.20 fof(fact_ivl__disj__un_I13_J, axiom, ![X51, X52, X5]:((hAPP(c_SetInterval_Oord__class_OatLeast(X5),X52)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X52,X51)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X51))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X52),X51)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I13_J)). 6.97/7.20 fof(fact_ivl__disj__un_I7_J, axiom, ![X51, X52, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X52),X51))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X52)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X52,X51))=hAPP(c_SetInterval_Oord__class_OlessThan(X5),X51))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I7_J)). 6.97/7.20 fof(fact_ivl__disj__un_I9_J, axiom, ![X51, X52, X5]:(class_Orderings_Olinorder(X5)=>(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X52)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X52,X51))=hAPP(c_SetInterval_Oord__class_OatMost(X5),X51)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X52),X51)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I9_J)). 6.97/7.20 fof(fact_ivl__disj__un_I10_J, axiom, ![X51, X52, X5]:(class_Orderings_Olinorder(X5)=>(hAPP(c_SetInterval_Oord__class_OatMost(X5),X51)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X52)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X52,X51))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X52),X51)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I10_J)). 6.97/7.20 fof(fact_Int__atLeastAtMostR1, axiom, ![X97, X10, X1, X5]:(class_Orderings_Olinorder(X5)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X1)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X10,X97))=c_SetInterval_Oord__class_OatLeastAtMost(X5,X10,hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X1),X97))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__atLeastAtMostR1)). 6.97/7.20 fof(fact_single__valuedD, axiom, ![X14, X38, X35, X3, X12, X5]:(((hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X35),X14)),X3))=>X38=X14)<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X35),X38)),X3)))<=c_Relation_Osingle__valued(X5,X12,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_single__valuedD)). 6.97/7.20 fof(fact_sorted__insort__key, axiom, ![X23, X35, X18, X12, X5]:((c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X12,X5),X18),X23))<=>c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X12,X5),X18),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X12,X5,X18),X35),X23))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__insort__key)). 6.97/7.20 fof(fact_power__one__over, axiom, ![X25, X30, X8]:(class_Fields_Ofield__inverse__zero(X8)=>hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),c_Groups_Oone__class_Oone(X8)),X30)),X25)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),c_Groups_Oone__class_Oone(X8)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__one__over)). 6.97/7.20 fof(fact_foldl__absorb0, axiom, ![X83, X35, X5]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X35),hAPP(c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),c_Groups_Ozero__class_Ozero(X5)),X83))=hAPP(c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),X35),X83)<=class_Groups_Omonoid__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__absorb0)). 6.97/7.20 fof(fact_fun__left__comm_Ofun__left__comm, axiom, ![X14, X38, X35, X18, X12, X5]:(hAPP(hAPP(X18,X35),hAPP(hAPP(X18,X38),X14))=hAPP(hAPP(X18,X38),hAPP(hAPP(X18,X35),X14))<=c_Finite__Set_Ofun__left__comm(X5,X12,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofun__left__comm)). 6.97/7.20 fof(fact_psubset__trans, axiom, ![X65, X11, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X4),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X4),X65))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X11),X65)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_psubset__trans)). 6.97/7.20 fof(fact_subset__psubset__trans, axiom, ![X65, X11, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X11),X65))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X4),X65)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__psubset__trans)). 6.97/7.20 fof(fact_psubset__subset__trans, axiom, ![X65, X11, X4, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X4),X65))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X65)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X4),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_psubset__subset__trans)). 6.97/7.20 fof(fact_subset__trans, axiom, ![X65, X11, X4, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X65))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X65)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__trans)). 6.97/7.20 fof(fact_min__max_Osup__left__commute, axiom, ![X26, X7, X6, X8]:(class_Orderings_Olinorder(X8)=>hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X7),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X6),X26))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X6),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X7),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__left__commute)). 6.97/7.20 fof(fact_part__equivp__def, axiom, ![X67, X5]:((![X22, X72]:(((hBOOL(hAPP(hAPP(X67,X72),X72))&hAPP(X67,X22)=hAPP(X67,X72))&hBOOL(hAPP(hAPP(X67,X22),X22)))<=>hBOOL(hAPP(hAPP(X67,X22),X72)))&?[X22]:hBOOL(hAPP(hAPP(X67,X22),X22)))<=>c_Equiv__Relations_Opart__equivp(X5,X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_part__equivp__def)). 6.97/7.20 fof(fact_butlast__take, axiom, ![X41, X8, X25]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)))=>hAPP(hAPP(c_List_Otake(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X41)=c_List_Obutlast(X8,hAPP(hAPP(c_List_Otake(X8),X25),X41))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_butlast__take)). 6.97/7.20 fof(fact_atMost__Int__atLeast, axiom, ![X32, X5]:(class_Orderings_Oorder(X5)=>hAPP(hAPP(c_Set_Oinsert(X5),X32),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X32)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atMost__Int__atLeast)). 6.97/7.20 fof(fact_surj__iff, axiom, ![X18, X5, X12]:(c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))=hAPP(c_Set_Oimage(X12,X5,X18),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))<=>hAPP(c_Fun_Ocomp(X12,X5,X5,X18),c_Hilbert__Choice_Oinv__into(X12,X5,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)),X18))=c_Fun_Oid(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_surj__iff)). 6.97/7.20 fof(fact_less__fun__def, axiom, ![X50, X18, X5, X12]:(class_Orderings_Oord(X12)=>((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X12)),X50),X18)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X12)),X18),X50)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,X12)),X18),X50)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__fun__def)). 6.97/7.20 fof(fact_ex__nat__less, axiom, ![X17, X32]:(?[X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X32))&hBOOL(hAPP(X17,X21)))<=>?[X22]:(hBOOL(hAPP(X17,X22))&hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X22),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ex__nat__less)). 6.97/7.20 fof(fact_mod__minus__cong, axiom, ![X69, X29, X30, X8]:(class_Divides_Oring__div(X8)=>(c_Divides_Odiv__class_Omod(X8,hAPP(c_Groups_Ouminus__class_Ouminus(X8),X69),X29)=c_Divides_Odiv__class_Omod(X8,hAPP(c_Groups_Ouminus__class_Ouminus(X8),X30),X29)<=c_Divides_Odiv__class_Omod(X8,X30,X29)=c_Divides_Odiv__class_Omod(X8,X69,X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__minus__cong)). 6.97/7.20 fof(fact_list__all2__appendI, axiom, ![X97, X10, X1, X2, X17, X12, X5]:(c_List_Olist__all2(X5,X12,X17,X2,X1)=>(c_List_Olist__all2(X5,X12,X17,hAPP(hAPP(c_List_Oappend(X5),X2),X10),hAPP(hAPP(c_List_Oappend(X12),X1),X97))<=c_List_Olist__all2(X5,X12,X17,X10,X97))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__appendI)). 6.97/7.20 fof(fact_min__max_Oinf_Oleft__commute, axiom, ![X31, X30, X29, X8]:(class_Orderings_Olinorder(X8)=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X30),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X29),X31))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X29),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X30),X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf_Oleft__commute)). 6.97/7.20 fof(fact_inf2I, axiom, ![X12, X5, X11, X38, X35, X4]:((hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X12,tc_HOL_Obool))),X4),X11),X35),X38))<=hBOOL(hAPP(hAPP(X11,X35),X38)))<=hBOOL(hAPP(hAPP(X4,X35),X38))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf2I)). 6.97/7.20 fof(fact_bij__def, axiom, ![X18, X12, X5]:(c_Fun_Obij__betw(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))<=>(c_Fun_Oinj__on(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))&hAPP(c_Set_Oimage(X5,X12,X18),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bij__def)). 6.97/7.20 fof(fact_atLeastLessThan__subset__iff, axiom, ![X97, X10, X1, X2, X5]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X10),X2))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X1),X97)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X1),X2)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X2),X1)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X10),X97))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThan__subset__iff)). 6.97/7.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, axiom, ![X36, X8]:(class_Rings_Ocomm__semiring__1(X8)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X36),X36)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),c_Groups_Oone__class_Oone(X8)),c_Groups_Oone__class_Oone(X8))),X36)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J)). 6.97/7.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, axiom, ![X74, X31, X30, X8]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X31),X74))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X31),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X74))<=class_Rings_Ocomm__semiring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J)). 6.97/7.20 fof(fact_power__Suc2, axiom, ![X25, X30, X8]:(class_Groups_Omonoid__mult(X8)=>hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),hAPP(c_Nat_OSuc,X25))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25)),X30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__Suc2)). 6.97/7.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J, axiom, ![X53, X6, X8]:(class_Rings_Ocomm__semiring__1(X8)=>hAPP(hAPP(c_Power_Opower__class_Opower(X8),X6),hAPP(c_Nat_OSuc,X53))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X6),X53)),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J)). 6.97/7.20 fof(fact_Int__iff, axiom, ![X11, X4, X10, X5]:((hBOOL(hAPP(hAPP(c_member(X5),X10),X4))&hBOOL(hAPP(hAPP(c_member(X5),X10),X11)))<=>hBOOL(hAPP(hAPP(c_member(X5),X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__iff)). 6.97/7.20 fof(fact_transfer__int__nat__set__relations_I5_J, axiom, ![X11, X4]:(c_Nat__Transfer_Onat__set(X4)=>((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),X4)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X11)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X4),X11)))<=c_Nat__Transfer_Onat__set(X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__set__relations_I5_J)). 6.97/7.20 fof(fact_insort__insert__insort, axiom, ![X23, X35, X5]:((c_List_Olinorder__class_Oinsort__insert__key(X5,X5,c_COMBI(X5),X35,X23)=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X35),X23)<=~(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23)))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__insert__insort)). 6.97/7.20 fof(fact_Union__least, axiom, ![X65, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X4)),X65))<=![X241]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X241),X4))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X241),X65)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__least)). 6.97/7.20 fof(fact_mod__div__decomp, axiom, ![X29, X30, X8]:(class_Divides_Osemiring__div(X8)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),X30),X29)),X29)),c_Divides_Odiv__class_Omod(X8,X30,X29))=X30), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__div__decomp)). 6.97/7.20 fof(fact_card__image__le, axiom, ![X18, X12, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X12),hAPP(c_Set_Oimage(X5,X12,X18),X4))),hAPP(c_Finite__Set_Ocard(X5),X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__image__le)). 6.97/7.20 fof(fact_card__insert__le, axiom, ![X35, X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X4)),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__insert__le)). 6.97/7.20 fof(fact_Inter__greatest, axiom, ![X65, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X65),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X4)))<=![X241]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X241),X4))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X65),X241)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__greatest)). 6.97/7.20 fof(fact_SUP1__iff, axiom, ![X1, X11, X4, X12, X5]:(?[X22]:(hBOOL(hAPP(hAPP(X11,X22),X1))&hBOOL(hAPP(hAPP(c_member(X5),X22),X4)))<=>hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X4),X11),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP1__iff)). 6.97/7.20 fof(fact_inf__left__commute, axiom, ![X26, X7, X6, X8]:(class_Lattices_Osemilattice__inf(X8)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X7),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),X26))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X7),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__left__commute)). 6.97/7.20 fof(fact_surj__imp__inj__inv, axiom, ![X18, X5, X12]:(c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))=hAPP(c_Set_Oimage(X12,X5,X18),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))=>c_Fun_Oinj__on(X5,X12,c_Hilbert__Choice_Oinv__into(X12,X5,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)),X18),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_surj__imp__inj__inv)). 6.97/7.20 fof(fact_finite__Union, axiom, ![X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,tc_HOL_Obool)),X4))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X4)))<=![X249]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X249))<=hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X249),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Union)). 6.97/7.20 fof(fact_semiring__div__class_Omod__div__equality_H, axiom, ![X29, X30, X8]:(class_Divides_Osemiring__div(X8)=>X30=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),c_Divides_Odiv__class_Omod(X8,X30,X29)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),X30),X29)),X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_semiring__div__class_Omod__div__equality_H)). 6.97/7.20 fof(fact_mod__div__equality2, axiom, ![X30, X29, X8]:(class_Divides_Osemiring__div(X8)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),X30),X29))),c_Divides_Odiv__class_Omod(X8,X30,X29))=X30), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__div__equality2)). 6.97/7.20 fof(fact_div__neg__pos__less0, axiom, ![X29, X30]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),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)),X29))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),X29)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__neg__pos__less0)). 6.97/7.20 fof(fact_neg__imp__zdiv__neg__iff, axiom, ![X2, 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),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),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)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__imp__zdiv__neg__iff)). 6.97/7.20 fof(fact_div__nonneg__neg__le0, axiom, ![X29, X30]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X29),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),X30),X29)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__nonneg__neg__le0)). 6.97/7.20 fof(fact_div__nonpos__pos__le0, axiom, ![X29, X30]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X30),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)),X29))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),X29)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__nonpos__pos__le0)). 6.97/7.20 fof(fact_inf__sup__aci_I3_J, axiom, ![X26, X7, X6, X8]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X7),X26))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X7),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),X26))<=class_Lattices_Olattice(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__aci_I3_J)). 6.97/7.20 fof(fact_nat__0__less__mult__iff, axiom, ![X32, X34]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X34))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32)))<=>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),X34),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__0__less__mult__iff)). 6.97/7.20 fof(fact_pos__imp__zdiv__nonneg__iff, axiom, ![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_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)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__imp__zdiv__nonneg__iff)). 6.97/7.20 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J, axiom, ![X7, X6]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6))=>(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),X6),X7)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Divides_Otransfer__nat__int__function__closures_I1_J)). 6.97/7.20 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J, axiom, ![X7, 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),X6),X7)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7)))<=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__function__closures_I1_J)). 6.97/7.20 fof(fact_setprod__reindex__id, axiom, ![X11, X18, X5, X12]:(class_Groups_Ocomm__monoid__mult(X12)=>(c_Fun_Oinj__on(X5,X12,X18,X11)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X18),X11)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12,X12),c_Fun_Oid(X12)),hAPP(c_Set_Oimage(X5,X12,X18),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__reindex__id)). 6.97/7.20 fof(fact_setsum__reindex__id, axiom, ![X11, X18, X5, X12]:((c_Fun_Oinj__on(X5,X12,X18,X11)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X18),X11)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X12),c_Fun_Oid(X12)),hAPP(c_Set_Oimage(X5,X12,X18),X11)))<=class_Groups_Ocomm__monoid__add(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__reindex__id)). 6.97/7.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, axiom, ![X211, X207, X209, X8]:(class_Rings_Ocomm__semiring__1(X8)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X209),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X207),X211))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X207),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X209),X211))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J)). 6.97/7.20 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J, axiom, ![X7, X6]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),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_Otimes__class_Otimes(tc_Int_Oint),X6),X7)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J)). 6.97/7.20 fof(fact_neg__imp__zdiv__nonneg__iff, axiom, ![X2, 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__eq(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),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__imp__zdiv__nonneg__iff)). 6.97/7.20 fof(fact_sorted__many__eq, axiom, ![X83, X38, X35, X5]:((c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X35),hAPP(hAPP(c_List_Olist_OCons(X5),X38),X83)))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),X38))&c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X38),X83))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__many__eq)). 6.97/7.20 fof(fact_le__add__diff, axiom, ![X36, X25, X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X36),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X36)),X19)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__add__diff)). 6.97/7.20 fof(fact_sup__left__commute, axiom, ![X26, X7, X6, X8]:(class_Lattices_Osemilattice__sup(X8)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),X26))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X7),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__left__commute)). 6.97/7.20 fof(fact_inv__into__into, axiom, ![X4, X18, X12, X35, X5]:(hBOOL(hAPP(hAPP(c_member(X12),hAPP(c_Hilbert__Choice_Oinv__into(X12,X5,X4,X18),X35)),X4))<=hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_Set_Oimage(X12,X5,X18),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inv__into__into)). 6.97/7.20 fof(fact_inf__sup__aci_I7_J, axiom, ![X26, X7, X6, X8]:(class_Lattices_Olattice(X8)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X7),X26))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__aci_I7_J)). 6.97/7.20 fof(fact_pred__nat__trancl__eq__le, axiom, ![X32, X34]:(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),X34),X32)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pred__nat__trancl__eq__le)). 6.97/7.20 fof(fact_nat__mult__dvd__cancel__disj, axiom, ![X32, X34, X33]:((hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34),X32))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X33)<=>hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X34)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__dvd__cancel__disj)). 6.97/7.20 fof(fact_DomainI, axiom, ![X3, X1, X2, X12, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X2),hAPP(c_Relation_ODomain(X5,X12),X3)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X2),X1)),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_DomainI)). 6.97/7.20 fof(fact_zadd__strict__right__mono, axiom, ![X19, X27, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X28),X19)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X27),X19)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X28),X27))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__strict__right__mono)). 6.97/7.20 fof(fact_add__less__mono1, axiom, ![X19, X27, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),X19)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27),X19)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28),X27))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__less__mono1)). 6.97/7.20 fof(fact_nat__add__left__cancel__less, axiom, ![X32, X34, X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34),X32))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X34)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__add__left__cancel__less)). 6.97/7.20 fof(fact_nat__diff__split__asm, axiom, ![X1, X2, X17]:(hBOOL(hAPP(X17,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)))<=>~(((~(hBOOL(hAPP(X17,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)))|?[X254]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X254)=X2&~(hBOOL(hAPP(X17,X254))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__diff__split__asm)). 6.97/7.20 fof(fact_zadd__left__mono, axiom, ![X19, X27, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X28),X27))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19),X28)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19),X27)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__left__mono)). 6.97/7.20 fof(fact_div__le__mono, axiom, ![X19, X25, X36]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X36),X25))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X36),X19)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X25),X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__le__mono)). 6.97/7.20 fof(fact_diff__le__mono, axiom, ![X93, X25, X36]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X36),X25))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),X93)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X93)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__le__mono)). 6.97/7.20 fof(fact_nat__diff__split, axiom, ![X1, X2, X17]:(hBOOL(hAPP(X17,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)))<=>(![X254]:(hBOOL(hAPP(X17,X254))<=X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X254))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))=>hBOOL(hAPP(X17,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__diff__split)). 6.97/7.20 fof(fact_inj__image__subset__iff, axiom, ![X11, X4, X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X12,X18),X4)),hAPP(c_Set_Oimage(X5,X12,X18),X11)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__image__subset__iff)). 6.97/7.20 fof(fact_diff__le__mono2, axiom, ![X93, X25, X36]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X93),X25)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X93),X36)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X36),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__le__mono2)). 6.97/7.20 fof(fact_add__le__mono1, axiom, ![X19, X27, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),X19)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27),X19)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28),X27))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__le__mono1)). 6.97/7.20 fof(fact_nat__add__left__cancel__le, axiom, ![X32, X34, X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X34)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__add__left__cancel__le)). 6.97/7.20 fof(fact_drop__Cons__number__of, axiom, ![X41, X6, X8, X40]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)=>hAPP(hAPP(c_List_Odrop(X8),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)),hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41))=hAPP(hAPP(c_List_Odrop(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X41))&(hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41)=hAPP(hAPP(c_List_Odrop(X8),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)),hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41))<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__Cons__number__of)). 6.97/7.20 fof(fact_Sup__fin_Oeq__fold__idem_H, axiom, ![X2, X4, X5]:((c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X2),X4))=hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X2),X4)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Lattices_Olattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Oeq__fold__idem_H)). 6.97/7.20 fof(fact_nonzero__abs__divide, axiom, ![X30, X29, X8]:(class_Fields_Olinordered__field(X8)=>(hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X30),X29))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),X30)),hAPP(c_Groups_Oabs__class_Oabs(X8),X29))<=X29!=c_Groups_Ozero__class_Ozero(X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nonzero__abs__divide)). 6.97/7.20 fof(fact_Inf__fin_Oeq__fold__idem_H, axiom, ![X2, X4, X5]:((c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X2),X4))=hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X2),X4)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Lattices_Olattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Oeq__fold__idem_H)). 6.97/7.20 fof(fact_inf__Inf__fold__inf, axiom, ![X11, X4, X5]:(class_Complete__Lattice_Ocomplete__lattice(X5)=>(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X11),c_Complete__Lattice_OInf__class_OInf(X5,X4))=hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X11),X4)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__Inf__fold__inf)). 6.97/7.20 fof(fact_trans__O__subset, axiom, ![X3, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X3),X3)),X3))<=c_Relation_Otrans(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trans__O__subset)). 6.97/7.20 fof(fact_transfer__nat__int__set__relations_I5_J, axiom, ![X11, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X4),X11))<=>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)),X4)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__set__relations_I5_J)). 6.97/7.20 fof(fact_Least__Suc, axiom, ![X32, X17]:(hBOOL(hAPP(X17,X32))=>(~(hBOOL(hAPP(X17,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=>hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),X17),c_Nat_OSuc)))=c_Orderings_Oord__class_OLeast(tc_Nat_Onat,X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Least__Suc)). 6.97/7.20 fof(fact_subset__insert, axiom, ![X11, X4, X35, X5]:(~(hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X35),X11)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__insert)). 6.97/7.20 fof(fact_pos__add__strict, axiom, ![X31, X29, X30, X8]:(class_Rings_Olinordered__semidom(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X30))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X29),X31))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X31)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__add__strict)). 6.97/7.20 fof(fact_add__strict__increasing2, axiom, ![X31, X29, X30, X8]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X31)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X29),X31)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X30)))<=class_Groups_Oordered__comm__monoid__add(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__strict__increasing2)). 6.97/7.20 fof(fact_add__strict__increasing, axiom, ![X31, X29, X30, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X30))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X31)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X29),X31))))<=class_Groups_Oordered__comm__monoid__add(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__strict__increasing)). 6.97/7.20 fof(fact_add__increasing, axiom, ![X31, X29, X30, X8]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X29),X31))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X31))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X30)))<=class_Groups_Oordered__comm__monoid__add(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__increasing)). 6.97/7.20 fof(fact_rtrancl__mono, axiom, ![X66, X3, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X3)),c_Transitive__Closure_Ortrancl(X5,X66)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),X66))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__mono)). 6.97/7.20 fof(fact_mono__Field, axiom, ![X66, X3, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),X66))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OField(X5),X3)),hAPP(c_Relation_OField(X5),X66)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mono__Field)). 6.97/7.20 fof(fact_nth__mem, axiom, ![X23, X5, X32]:(hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_List_Onth(X5),X23),X32)),hAPP(c_List_Oset(X5),X23)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__mem)). 6.97/7.20 fof(fact_elem__le__listsum__nat, axiom, ![X163, X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X163)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X163),X19)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X163)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_elem__le__listsum__nat)). 6.97/7.20 fof(fact_INF1__iff, axiom, ![X1, X11, X4, X12, X5]:(![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))=>hBOOL(hAPP(hAPP(X11,X22),X1)))<=>hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),X4),X11),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF1__iff)). 6.97/7.20 fof(fact_add__increasing2, axiom, ![X30, X29, X31, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X31))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X31)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X29),X30))))<=class_Groups_Oordered__comm__monoid__add(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__increasing2)). 6.97/7.20 fof(fact_insert__image, axiom, ![X18, X12, X4, X35, X5]:(hAPP(c_Set_Oimage(X5,X12,X18),X4)=hAPP(hAPP(c_Set_Oinsert(X12),hAPP(X18,X35)),hAPP(c_Set_Oimage(X5,X12,X18),X4))<=hBOOL(hAPP(hAPP(c_member(X5),X35),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__image)). 6.97/7.20 fof(fact_image__constant, axiom, ![X10, X12, X4, X35, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X35),X4))=>hAPP(c_Set_Oimage(X5,X12,hAPP(c_COMBK(X12,X5),X10)),X4)=hAPP(hAPP(c_Set_Oinsert(X12),X10),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__constant)). 6.97/7.20 fof(fact_setsum__constant, axiom, ![X4, X38, X12, X5]:(class_Rings_Osemiring__1(X5)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),hAPP(c_Finite__Set_Ocard(X12),X4))),X38)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5),hAPP(c_COMBK(X5,X12),X38)),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__constant)). 6.97/7.20 fof(fact_INF1__I, axiom, ![X12, X1, X11, X4, X5]:(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),X4),X11),X1))<=![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))=>hBOOL(hAPP(hAPP(X11,X22),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF1__I)). 6.97/7.20 fof(fact_card__insert__disjoint, axiom, ![X35, X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(~(hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))=>hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))=hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__insert__disjoint)). 6.97/7.20 fof(fact_hd__drop__conv__nth, axiom, ![X25, X8, X41]:(c_List_Olist_ONil(X8)!=X41=>(hAPP(hAPP(c_List_Onth(X8),X41),X25)=hAPP(c_List_Ohd(X8),hAPP(hAPP(c_List_Odrop(X8),X25),X41))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__drop__conv__nth)). 6.97/7.20 fof(fact_wfI__pf, axiom, ![X67, X5]:(![X54]:(X54=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X54),hAPP(c_Relation_OImage(X5,X5,X67),X54))))=>c_Wellfounded_Owf(X5,X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wfI__pf)). 6.97/7.20 fof(fact_fold1__eq__fold__idem, axiom, ![X2, X4, X5]:(class_Lattices_Oab__semigroup__idem__mult(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Groups_Otimes__class_Otimes(X5)),X2),X4)=hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(hAPP(c_Set_Oinsert(X5),X2),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__eq__fold__idem)). 6.97/7.20 fof(fact_Times__eq__cancel2, axiom, ![X11, X4, X12, X65, X35, X5]:((hAPP(hAPP(c_Product__Type_OSigma(X12,X5),X4),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X12),X65))=hAPP(hAPP(c_Product__Type_OSigma(X12,X5),X11),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X12),X65))<=>X11=X4)<=hBOOL(hAPP(hAPP(c_member(X5),X35),X65))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Times__eq__cancel2)). 6.97/7.20 fof(fact_list__eq__iff__nth__eq, axiom, ![X5, X84, X23]:(X84=X23<=>(![X42]:(hAPP(hAPP(c_List_Onth(X5),X23),X42)=hAPP(hAPP(c_List_Onth(X5),X84),X42)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23))))&hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X84)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__eq__iff__nth__eq)). 6.97/7.20 fof(fact_pos__imp__zdiv__pos__iff, axiom, ![X47, X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33))=>(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),X47),X33)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X33),X47)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__imp__zdiv__pos__iff)). 6.97/7.20 fof(fact_setprod_Oeq__fold, axiom, ![X50, X4, X5, X12]:(class_Groups_Ocomm__monoid__mult(X12)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X50),X4)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X12,X5,c_Groups_Otimes__class_Otimes(X12)),X50),c_Groups_Oone__class_Oone(X12)),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod_Oeq__fold)). 6.97/7.20 fof(fact_setsum_Oeq__fold, axiom, ![X50, X4, X5, X12]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X12),X50),X4)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X12,X5,c_Groups_Oplus__class_Oplus(X12)),X50),c_Groups_Ozero__class_Ozero(X12)),X4))<=class_Groups_Ocomm__monoid__add(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum_Oeq__fold)). 6.97/7.20 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J, axiom, ![X31, X29, X30, X8]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29)),X31)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X29),X31))<=class_Groups_Oab__semigroup__add(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ab__semigroup__add__class_Oadd__ac_I1_J)). 6.97/7.20 fof(fact_Max__insert, axiom, ![X35, X4, X5]:(class_Orderings_Olinorder(X5)=>((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4=>hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X35),c_Big__Operators_Olinorder__class_OMax(X5,X4))=c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X35),X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max__insert)). 6.97/7.20 fof(fact_inf__assoc, axiom, ![X26, X7, X6, X8]:(class_Lattices_Osemilattice__inf(X8)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),X7)),X26)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X7),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__assoc)). 6.97/7.20 fof(fact_inf__sup__aci_I2_J, axiom, ![X26, X7, X6, X8]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),X7)),X26)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X7),X26))<=class_Lattices_Olattice(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__aci_I2_J)). 6.97/7.20 fof(fact_setprod__constant, axiom, ![X38, X4, X5, X12]:(class_Groups_Ocomm__monoid__mult(X12)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hAPP(hAPP(c_Power_Opower__class_Opower(X12),X38),hAPP(c_Finite__Set_Ocard(X5),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),hAPP(c_COMBK(X12,X5),X38)),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__constant)). 6.97/7.20 fof(fact_Min__insert, axiom, ![X35, X4, X5]:(((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X35),c_Big__Operators_Olinorder__class_OMin(X5,X4))=c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X35),X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min__insert)). 6.97/7.20 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J, axiom, ![X31, X29, X30, X8]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29)),X31)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X31))<=class_Groups_Oab__semigroup__mult(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ab__semigroup__mult__class_Omult__ac_I1_J)). 6.97/7.20 fof(fact_times__divide__eq__right, axiom, ![X31, X29, X30, X8]:(class_Rings_Odivision__ring(X8)=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29)),X31)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X29),X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_times__divide__eq__right)). 6.97/7.20 fof(fact_sup__assoc, axiom, ![X26, X7, X6, X8]:(class_Lattices_Osemilattice__sup(X8)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),X7)),X26)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X7),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__assoc)). 6.97/7.20 fof(fact_listrel1__eq__len, axiom, ![X3, X84, X23, X5]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X84)<=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)),X23),X84)),c_List_Olistrel1(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1__eq__len)). 6.97/7.20 fof(fact_Sup__fin_Oinsert__idem, axiom, ![X35, X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X35),c_Big__Operators_Olattice__class_OSup__fin(X5,X4))<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4))<=class_Lattices_Olattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Oinsert__idem)). 6.97/7.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, axiom, ![X31, X29, X30, X8]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X29),X31))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29)),X31)<=class_Rings_Ocomm__semiring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J)). 6.97/7.20 fof(fact_power__commutes, axiom, ![X25, X30, X8]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25)),X30)<=class_Groups_Omonoid__mult(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__commutes)). 6.97/7.20 fof(fact_card__psubset, axiom, ![X4, X11, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X4),X11))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X4)),hAPP(c_Finite__Set_Ocard(X5),X11)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__psubset)). 6.97/7.20 fof(fact_inj__on__fun__updI, axiom, ![X35, X38, X4, X18, X12, X5]:((~(hBOOL(hAPP(hAPP(c_member(X12),X38),hAPP(c_Set_Oimage(X5,X12,X18),X4))))=>c_Fun_Oinj__on(X5,X12,c_Fun_Ofun__upd(X5,X12,X18,X35,X38),X4))<=c_Fun_Oinj__on(X5,X12,X18,X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__fun__updI)). 6.97/7.20 fof(fact_Inf__fin_Oinsert__idem, axiom, ![X35, X4, X5]:(class_Lattices_Olattice(X5)=>((X4!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X35),c_Big__Operators_Olattice__class_OInf__fin(X5,X4))=c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X35),X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Oinsert__idem)). 6.97/7.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, axiom, ![X207, X208, X209, X8]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X209),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X208),X207))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X209),X208)),X207)<=class_Rings_Ocomm__semiring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J)). 6.97/7.20 fof(fact_inf__sup__aci_I6_J, axiom, ![X26, X7, X6, X8]:(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X7),X26))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),X7)),X26)<=class_Lattices_Olattice(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__aci_I6_J)). 6.97/7.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, axiom, ![X53, X81, X6, X8]:(class_Rings_Ocomm__semiring__1(X8)=>hAPP(hAPP(c_Power_Opower__class_Opower(X8),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X81),X53))=hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X6),X81)),X53)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J)). 6.97/7.20 fof(fact_power__mult, axiom, ![X25, X36, X30, X8]:(hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X36)),X25)=hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X25))<=class_Groups_Omonoid__mult(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__mult)). 6.97/7.20 fof(fact_pos__divide__less__eq, axiom, ![X2, X1, X10, X5]:(class_Fields_Olinordered__field(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X10))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X10)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X1),X10)),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__divide__less__eq)). 6.97/7.20 fof(fact_pos__divide__le__eq, axiom, ![X2, X1, X10, X5]:(class_Fields_Olinordered__field(X5)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X1),X10)),X2))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X10))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X10)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__divide__le__eq)). 6.97/7.20 fof(fact_pos__less__divide__eq, axiom, ![X1, X2, X10, X5]:(class_Fields_Olinordered__field(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X10))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X10)),X1))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X1),X10)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__less__divide__eq)). 6.97/7.20 fof(fact_pos__le__divide__eq, axiom, ![X1, X2, X10, X5]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X1),X10)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X10)),X1)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X10)))<=class_Fields_Olinordered__field(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__le__divide__eq)). 6.97/7.20 fof(fact_Diff__partition, axiom, ![X11, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))=>X11=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__partition)). 6.97/7.20 fof(fact_range, axiom, ![X134, X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X19))=>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(X19),X134))),X19))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_range)). 6.97/7.20 fof(fact_in__lists__conv__set, axiom, ![X4, X23, X5]:(![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X23)))=>hBOOL(hAPP(hAPP(c_member(X5),X22),X4)))<=>hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X23),c_List_Olists(X5,X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__lists__conv__set)). 6.97/7.20 fof(fact_listrelp_Oequations_I2_J, axiom, ![X148, X125, X102, X103, X3, X5]:(c_List_Olistrelp(X5,X3,hAPP(hAPP(c_List_Olist_OCons(X5),X103),X102),hAPP(hAPP(c_List_Olist_OCons(X5),X125),X148))<=>(hBOOL(hAPP(hAPP(X3,X103),X125))&c_List_Olistrelp(X5,X3,X102,X148))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrelp_Oequations_I2_J)). 6.97/7.20 fof(fact_remdups_Osimps_I2_J, axiom, ![X23, X35, X5]:((c_List_Oremdups(X5,X23)=c_List_Oremdups(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23))<=hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23))))&(~(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23))))=>hAPP(hAPP(c_List_Olist_OCons(X5),X35),c_List_Oremdups(X5,X23))=c_List_Oremdups(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remdups_Osimps_I2_J)). 6.97/7.20 fof(fact_INF__leI, axiom, ![X94, X4, X47, X5, X12]:(class_Complete__Lattice_Ocomplete__lattice(X12)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X12),X4),X94)),hAPP(X94,X47)))<=hBOOL(hAPP(hAPP(c_member(X5),X47),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF__leI)). 6.97/7.20 fof(fact_le__SUPI, axiom, ![X94, X4, X47, X5, X12]:(class_Complete__Lattice_Ocomplete__lattice(X12)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),hAPP(X94,X47)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X12),X4),X94)))<=hBOOL(hAPP(hAPP(c_member(X5),X47),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__SUPI)). 6.97/7.20 fof(fact_length__remove1, axiom, ![X23, X35, X5]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oremove1(X5,X35,X23))<=hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23))))&(~(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23))))=>hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oremove1(X5,X35,X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__remove1)). 6.97/7.20 fof(fact_ivl__disj__int_I11_J, axiom, ![X51, X34, X52, X5]:(class_Orderings_Oorder(X5)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X52),X34)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X34),X51))=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I11_J)). 6.97/7.20 fof(fact_le__sup__iff, axiom, ![X14, X38, X35, X5]:(class_Lattices_Osemilattice__sup(X5)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X38),X14))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),X14)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X35),X38)),X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__sup__iff)). 6.97/7.20 fof(fact_le__infI, axiom, ![X29, X30, X6, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),X30))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),X29))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X30),X29)))))<=class_Lattices_Osemilattice__inf(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__infI)). 6.97/7.20 fof(fact_abs__mult__pos, axiom, ![X7, X6, X8]:((hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X6))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),X7)),X6)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X6)))<=class_Rings_Olinordered__idom(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__mult__pos)). 6.97/7.20 fof(fact_fun__left__comm_Ofold__graph__fold, axiom, ![X14, X4, X18, X12, X5]:(c_Finite__Set_Ofun__left__comm(X5,X12,X18)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X12,X18,X14,X4),hAPP(hAPP(c_Finite__Set_Ofold(X5,X12,X18),X14),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__graph__fold)). 6.97/7.20 fof(fact_select__weigth__select, axiom, ![X5, X23]:(X23!=c_List_Olist_ONil(X5)=>c_Random_Oselect__weight(X5,hAPP(hAPP(c_List_Omap(X5,tc_prod(tc_Code__Numeral_Ocode__numeral,X5)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X5),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X23))=c_Random_Oselect(X5,X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_select__weigth__select)). 6.97/7.20 fof(fact_less__add__eq__less, axiom, ![X25, X36, X93, X19]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X25)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X93)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X36),X25)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),X93))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__add__eq__less)). 6.97/7.20 fof(fact_power__gt1, axiom, ![X25, X30, X8]:(class_Rings_Olinordered__semidom(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Oone__class_Oone(X8)),X30))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Oone__class_Oone(X8)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),hAPP(c_Nat_OSuc,X25)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__gt1)). 6.97/7.20 fof(fact_elem__le__sum, axiom, ![X186, X32]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32),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)),X186)))<=hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X32),hAPP(c_List_Oset(tc_Nat_Onat),X186)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_elem__le__sum)). 6.97/7.20 fof(fact_lists_Osimps, axiom, ![X4, X2, X5]:(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X2),c_List_Olists(X5,X4)))<=>(?[X13, X193]:((X2=hAPP(hAPP(c_List_Olist_OCons(X5),X13),X193)&hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X193),c_List_Olists(X5,X4))))&hBOOL(hAPP(hAPP(c_member(X5),X13),X4)))|X2=c_List_Olist_ONil(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists_Osimps)). 6.97/7.20 fof(fact_antisymD, axiom, ![X1, X2, X3, X5]:(c_Relation_Oantisym(X5,X3)=>((X2=X1<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X1),X2)),X3)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X1)),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_antisymD)). 6.97/7.20 fof(fact_minus__Max__eq__Min, axiom, ![X44, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X44))=>(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X44=>c_Big__Operators_Olinorder__class_OMin(X5,hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),X44))=hAPP(c_Groups_Ouminus__class_Ouminus(X5),c_Big__Operators_Olinorder__class_OMax(X5,X44))))<=class_Groups_Olinordered__ab__group__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__Max__eq__Min)). 6.97/7.20 fof(fact_minus__Min__eq__Max, axiom, ![X44, X5]:(((X44!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>c_Big__Operators_Olinorder__class_OMax(X5,hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),X44))=hAPP(c_Groups_Ouminus__class_Ouminus(X5),c_Big__Operators_Olinorder__class_OMin(X5,X44)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X44)))<=class_Groups_Olinordered__ab__group__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__Min__eq__Max)). 6.97/7.20 fof(fact_add__gr__0, axiom, ![X32, X34]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X34)))<=>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),X34),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__gr__0)). 6.97/7.20 fof(fact_doubleton__eq__iff, axiom, ![X97, X10, X1, X2, X5]:(((X10=X1&X2=X97)|(X10=X2&X1=X97))<=>hAPP(hAPP(c_Set_Oinsert(X5),X10),hAPP(hAPP(c_Set_Oinsert(X5),X97),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))=hAPP(hAPP(c_Set_Oinsert(X5),X2),hAPP(hAPP(c_Set_Oinsert(X5),X1),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_doubleton__eq__iff)). 6.97/7.20 fof(fact_minus__min__eq__max, axiom, ![X7, X6, X8]:(class_Groups_Olinordered__ab__group__add(X8)=>hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X6)),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X7))=hAPP(c_Groups_Ouminus__class_Ouminus(X8),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X6),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__min__eq__max)). 6.97/7.20 fof(fact_compl__sup, axiom, ![X7, X6, X8]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X6)),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X7))=hAPP(c_Groups_Ouminus__class_Ouminus(X8),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),X7))<=class_Lattices_Oboolean__algebra(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__sup)). 6.97/7.20 fof(fact_compl__inf, axiom, ![X7, X6, X8]:(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X6)),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X7))=hAPP(c_Groups_Ouminus__class_Ouminus(X8),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),X7))<=class_Lattices_Oboolean__algebra(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__inf)). 6.97/7.20 fof(fact_add__eq__if, axiom, ![X25, X36]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X25)=X25<=X36=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X25)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X25))<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X36)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__eq__if)). 6.97/7.20 fof(fact_minus__max__eq__min, axiom, ![X7, X6, X8]:(class_Groups_Olinordered__ab__group__add(X8)=>hAPP(c_Groups_Ouminus__class_Ouminus(X8),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X6),X7))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X6)),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__max__eq__min)). 6.97/7.20 fof(fact_minus__add__distrib, axiom, ![X29, X30, X8]:(hAPP(c_Groups_Ouminus__class_Ouminus(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X30)),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X29))<=class_Groups_Oab__group__add(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__add__distrib)). 6.97/7.20 fof(fact_minus__add, axiom, ![X29, X30, X8]:(hAPP(c_Groups_Ouminus__class_Ouminus(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X29)),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X30))<=class_Groups_Ogroup__add(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__add)). 6.97/7.20 fof(fact_last__conv__nth, axiom, ![X8, X41]:(hAPP(hAPP(c_List_Onth(X8),X41),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_List_Olast(X8,X41)<=X41!=c_List_Olist_ONil(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__conv__nth)). 6.97/7.20 fof(fact_psubset__card__mono, axiom, ![X4, X11, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X4),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X4)),hAPP(c_Finite__Set_Ocard(X5),X11))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_psubset__card__mono)). 6.97/7.20 fof(fact_card__mono, axiom, ![X4, X11, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X4)),hAPP(c_Finite__Set_Ocard(X5),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__mono)). 6.97/7.20 fof(fact_strict__monoD, axiom, ![X38, X35, X18, X5, X12]:((class_Orderings_Oorder(X5)&class_Orderings_Oorder(X12))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),hAPP(X18,X35)),hAPP(X18,X38)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X35),X38)))<=c_Orderings_Oorder__class_Ostrict__mono(X5,X12,X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_strict__monoD)). 6.97/7.20 fof(fact_strict__mono__less, axiom, ![X38, X35, X18, X5, X12]:((class_Orderings_Olinorder(X5)&class_Orderings_Oorder(X12))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12),hAPP(X18,X35)),hAPP(X18,X38)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X35),X38)))<=c_Orderings_Oorder__class_Ostrict__mono(X5,X12,X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_strict__mono__less)). 6.97/7.20 fof(fact_monoD, axiom, ![X38, X35, X18, X5, X12]:((c_Orderings_Oorder__class_Omono(X5,X12,X18)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),hAPP(X18,X35)),hAPP(X18,X38)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),X38))))<=(class_Orderings_Oorder(X5)&class_Orderings_Oorder(X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_monoD)). 6.97/7.20 fof(fact_strict__mono__less__eq, axiom, ![X38, X35, X18, X5, X12]:((class_Orderings_Oorder(X12)&class_Orderings_Olinorder(X5))=>(c_Orderings_Oorder__class_Ostrict__mono(X5,X12,X18)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),X38))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),hAPP(X18,X35)),hAPP(X18,X38)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_strict__mono__less__eq)). 6.97/7.20 fof(fact_frac__eq__eq, axiom, ![X9, X35, X14, X38, X5]:((((hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X38)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X35),X14)<=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X9),X14)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X35),X38))<=c_Groups_Ozero__class_Ozero(X5)!=X14)<=X38!=c_Groups_Ozero__class_Ozero(X5))<=class_Fields_Ofield(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_frac__eq__eq)). 6.97/7.20 fof(fact_finite__maxlen, axiom, ![X94, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X5)),X94))=>?[X48]:![X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X22)),X48))<=hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X22),X94)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__maxlen)). 6.97/7.20 fof(fact_max__less__iff__conj, axiom, ![X14, X38, X35, X5]:(class_Orderings_Olinorder(X5)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X38),X14))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X35),X14)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X35),X38)),X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__less__iff__conj)). 6.97/7.20 fof(fact_min__max_Ole__sup__iff, axiom, ![X14, X38, X35, X5]:(class_Orderings_Olinorder(X5)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X38),X14))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),X14)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X35),X38)),X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ole__sup__iff)). 6.97/7.20 fof(fact_min__less__iff__conj, axiom, ![X38, X35, X14, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X14),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X35),X38)))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X14),X38))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X14),X35))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__less__iff__conj)). 6.97/7.20 fof(fact_abs__div__pos, axiom, ![X6, X7, X8]:(class_Fields_Olinordered__field__inverse__zero(X8)=>(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),X6)),X7)=hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X6),X7))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__div__pos)). 6.97/7.20 fof(fact_InterE, axiom, ![X56, X65, X4, X5]:((hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X56),X65))=>hBOOL(hAPP(hAPP(c_member(X5),X4),X56)))<=hBOOL(hAPP(hAPP(c_member(X5),X4),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X65)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_InterE)). 6.97/7.20 fof(fact_of__nat__add, axiom, ![X25, X36, X8]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),X36)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),X25))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X25))<=class_Rings_Osemiring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__add)). 6.97/7.20 fof(fact_min__max_Ole__inf__iff, axiom, ![X14, X38, X35, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X38),X14)))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),X14))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),X38))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ole__inf__iff)). 6.97/7.20 fof(fact_finite__Plus__UNIV__iff, axiom, ![X12, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X5,X12)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X5,X12),tc_HOL_Obool))))<=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))&hBOOL(hAPP(c_Finite__Set_Ofinite(X12),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Plus__UNIV__iff)). 6.97/7.20 fof(fact_finite__Prod__UNIV, axiom, ![X12, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X12)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X5,X12),tc_HOL_Obool))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X12),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Prod__UNIV)). 6.97/7.20 fof(fact_int__div__less__self, axiom, ![X19, X6]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6),X19)),X6))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X19)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__div__less__self)). 6.97/7.20 fof(fact_min__max_OSup__fin_Oin__idem, axiom, ![X35, X4, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hBOOL(hAPP(hAPP(c_member(X5),X35),X4))=>c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X4)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X35),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Oin__idem)). 6.97/7.20 fof(fact_min__max_OInf__fin_Oin__idem, axiom, ![X35, X4, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X4)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X35),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X4))<=hBOOL(hAPP(hAPP(c_member(X5),X35),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Oin__idem)). 6.97/7.20 fof(fact_folding__image__simple_Oeq__fold__g, axiom, ![X4, X55, X50, X14, X18, X12, X5]:(c_Finite__Set_Ofolding__image__simple(X5,X12,X18,X14,X50,X55)=>(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X12,X18),X50),X14),X4)=hAPP(X55,X4)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple_Oeq__fold__g)). 6.97/7.20 fof(fact_div__less__dividend, axiom, ![X36, X25]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X36))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X36),X25)),X36)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__less__dividend)). 6.97/7.20 fof(fact_diff__less, axiom, ![X36, X25]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),X25)),X36))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X36)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__less)). 6.97/7.20 fof(fact_Inf__less__iff, axiom, ![X2, X44, X5]:((class_Orderings_Olinorder(X5)&class_Complete__Lattice_Ocomplete__lattice(X5))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Complete__Lattice_OInf__class_OInf(X5,X44)),X2))<=>?[X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X44))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X22),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__less__iff)). 6.97/7.20 fof(fact_less__Sup__iff, axiom, ![X44, X2, X5]:((class_Orderings_Olinorder(X5)&class_Complete__Lattice_Ocomplete__lattice(X5))=>(?[X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),X22))&hBOOL(hAPP(hAPP(c_member(X5),X22),X44)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),c_Complete__Lattice_OSup__class_OSup(X5,X44))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__Sup__iff)). 6.97/7.20 fof(fact_insort__remove1, axiom, ![X23, X2, X5]:((hBOOL(hAPP(hAPP(c_member(X5),X2),hAPP(c_List_Oset(X5),X23)))=>(X23=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X2),c_List_Oremove1(X5,X2,X23))<=c_List_Olinorder__class_Osorted(X5,X23)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__remove1)). 6.97/7.20 fof(fact_InterI, axiom, ![X4, X65, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X4),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X65)))<=![X241]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X241),X65))=>hBOOL(hAPP(hAPP(c_member(X5),X4),X241)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_InterI)). 6.97/7.20 fof(fact_of__nat__mult, axiom, ![X25, X36, X8]:(hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X25))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),X36)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),X25))<=class_Rings_Osemiring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__mult)). 6.97/7.20 fof(fact_lessThan__strict__subset__iff, axiom, ![X32, X34, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X34),X32))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X34)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lessThan__strict__subset__iff)). 6.97/7.20 fof(fact_number__of__diff, axiom, ![X39, X40, X8]:(hAPP(c_Int_Onumber__class_Onumber__of(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X40),X39))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),X40)),hAPP(c_Int_Onumber__class_Onumber__of(X8),X39))<=class_Int_Onumber__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__diff)). 6.97/7.20 fof(fact_greaterThan__subset__iff, axiom, ![X38, X35, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X38),X35))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X35)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X38))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_greaterThan__subset__iff)). 6.97/7.20 fof(fact_lessThan__subset__iff, axiom, ![X38, X35, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X35)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X38)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),X38)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lessThan__subset__iff)). 6.97/7.20 fof(fact_atLeast__subset__iff, axiom, ![X38, X35, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X38),X35))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X35)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X38))))<=class_Orderings_Oorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeast__subset__iff)). 6.97/7.20 fof(fact_atMost__subset__iff, axiom, ![X38, X35, X5]:(class_Orderings_Oorder(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X35)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X38)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),X38)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atMost__subset__iff)). 6.97/7.20 fof(fact_mod__add__left__eq, axiom, ![X31, X29, X30, X8]:(c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),c_Divides_Odiv__class_Omod(X8,X30,X31)),X29),X31)=c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29),X31)<=class_Divides_Osemiring__div(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__add__left__eq)). 6.97/7.20 fof(fact_mod__diff__left__eq, axiom, ![X31, X29, X30, X8]:(class_Divides_Oring__div(X8)=>c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X30),X29),X31)=c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),c_Divides_Odiv__class_Omod(X8,X30,X31)),X29),X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__diff__left__eq)). 6.97/7.20 fof(fact_zmod__simps_I4_J, axiom, ![X29, X31, X30, X8]:(class_Divides_Osemiring__div(X8)=>c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29),X31)=c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Divides_Odiv__class_Omod(X8,X30,X31)),X29),X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__simps_I4_J)). 6.97/7.20 fof(fact_number__of__add, axiom, ![X39, X40, X8]:(class_Int_Onumber__ring(X8)=>hAPP(c_Int_Onumber__class_Onumber__of(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X40),X39))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),X40)),hAPP(c_Int_Onumber__class_Onumber__of(X8),X39))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__add)). 6.97/7.20 fof(fact_Powp__mono, axiom, ![X11, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(X5,X4)),c_Predicate_OPowp(X5,X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Powp__mono)). 6.97/7.20 fof(fact_Max__eqI, axiom, ![X35, X4, X5]:(class_Orderings_Olinorder(X5)=>(((c_Big__Operators_Olinorder__class_OMax(X5,X4)=X35<=hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))<=![X72]:(hBOOL(hAPP(hAPP(c_member(X5),X72),X4))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X72),X35))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max__eqI)). 6.97/7.20 fof(fact_min__max_Osup__assoc, axiom, ![X26, X7, X6, X8]:(class_Orderings_Olinorder(X8)=>hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X6),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X7),X26))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X6),X7)),X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__assoc)). 6.97/7.20 fof(fact_mod__diff__right__eq, axiom, ![X31, X29, X30, X8]:(c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X30),c_Divides_Odiv__class_Omod(X8,X29,X31)),X31)=c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X30),X29),X31)<=class_Divides_Oring__div(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__diff__right__eq)). 6.97/7.20 fof(fact_mod__add__right__eq, axiom, ![X31, X29, X30, X8]:(class_Divides_Osemiring__div(X8)=>c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29),X31)=c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),c_Divides_Odiv__class_Omod(X8,X29,X31)),X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__add__right__eq)). 6.97/7.20 fof(fact_min__max_Oinf_Oassoc, axiom, ![X31, X29, X30, X8]:(class_Orderings_Olinorder(X8)=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X30),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X29),X31))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X30),X29)),X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf_Oassoc)). 6.97/7.20 fof(fact_number__of__mult, axiom, ![X39, X40, X8]:(hAPP(c_Int_Onumber__class_Onumber__of(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X40),X39))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),X40)),hAPP(c_Int_Onumber__class_Onumber__of(X8),X39))<=class_Int_Onumber__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__mult)). 6.97/7.20 fof(fact_Min__eqI, axiom, ![X35, X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(![X72]:(hBOOL(hAPP(hAPP(c_member(X5),X72),X4))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),X72)))=>(X35=c_Big__Operators_Olinorder__class_OMin(X5,X4)<=hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min__eqI)). 6.97/7.20 fof(fact_distinct_Osimps_I2_J, axiom, ![X23, X35, X5]:(hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23)))<=>(~(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23))))&hBOOL(hAPP(c_List_Odistinct(X5),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct_Osimps_I2_J)). 6.97/7.20 fof(fact_atLeastAtMostSuc__conv, axiom, ![X32, X34]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),hAPP(c_Nat_OSuc,X32)))=>c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X34,hAPP(c_Nat_OSuc,X32))=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X32)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X34,X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastAtMostSuc__conv)). 6.97/7.20 fof(fact_mod__mult__right__eq, axiom, ![X31, X29, X30, X8]:(class_Divides_Osemiring__div(X8)=>c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29),X31)=c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),c_Divides_Odiv__class_Omod(X8,X29,X31)),X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__right__eq)). 6.97/7.20 fof(fact_nat__power__less__imp__less, axiom, ![X25, X36, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X28))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X28),X36)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X28),X25)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X36),X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__power__less__imp__less)). 6.97/7.20 fof(fact_power__dvd__imp__le, axiom, ![X25, X36, X28]:(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X28),X36)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X28),X25)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X36),X25))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X28)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__dvd__imp__le)). 6.97/7.20 fof(fact_filter__insort__triv, axiom, ![X23, X18, X5, X35, X17, X12]:(class_Orderings_Olinorder(X12)=>(~(hBOOL(hAPP(X17,X35)))=>hAPP(c_List_Ofilter(X5,X17),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X12,X18),X35),X23))=hAPP(c_List_Ofilter(X5,X17),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__insort__triv)). 6.97/7.20 fof(fact_inv__o__cancel, axiom, ![X18, X12, X5]:(hAPP(c_Fun_Ocomp(X12,X5,X5,c_Hilbert__Choice_Oinv__into(X5,X12,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X18)),X18)=c_Fun_Oid(X5)<=c_Fun_Oinj__on(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inv__o__cancel)). 6.97/7.20 fof(fact_takeWhile__tail, axiom, ![X52, X23, X5, X35, X17]:(~(hBOOL(hAPP(X17,X35)))=>c_List_OtakeWhile(X5,X17,X23)=c_List_OtakeWhile(X5,X17,hAPP(hAPP(c_List_Oappend(X5),X23),hAPP(hAPP(c_List_Olist_OCons(X5),X35),X52)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__tail)). 6.97/7.20 fof(fact_unique__remainder, axiom, ![X100, X101, X70, X53, X29, X30]:(((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X29=>X70=X100)<=hBOOL(hAPP(c_Divides_Odivmod__int__rel(X30,X29),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X101),X100))))<=hBOOL(hAPP(c_Divides_Odivmod__int__rel(X30,X29),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X53),X70)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_unique__remainder)). 6.97/7.20 fof(fact_unique__quotient, axiom, ![X100, X101, X70, X53, X29, X30]:(hBOOL(hAPP(c_Divides_Odivmod__int__rel(X30,X29),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X53),X70)))=>(hBOOL(hAPP(c_Divides_Odivmod__int__rel(X30,X29),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X101),X100)))=>(X29!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=>X53=X101))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_unique__quotient)). 6.97/7.20 fof(fact_zmod__zminus2__eq__if, axiom, ![X29, X30]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X29)=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X29)),X29)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X29)))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X29)=>c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zminus2__eq__if)). 6.97/7.20 fof(fact_abs__power__minus, axiom, ![X25, X30, X8]:(hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25))=hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X30)),X25))<=class_Rings_Olinordered__idom(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__power__minus)). 6.97/7.20 fof(fact_listsum__append, axiom, ![X45, X41, X8]:(hAPP(c_List_Omonoid__add__class_Olistsum(X8),hAPP(hAPP(c_List_Oappend(X8),X41),X45))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(c_List_Omonoid__add__class_Olistsum(X8),X41)),hAPP(c_List_Omonoid__add__class_Olistsum(X8),X45))<=class_Groups_Omonoid__add(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__append)). 6.97/7.20 fof(fact_abs__mult, axiom, ![X29, X30, X8]:(hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),X30)),hAPP(c_Groups_Oabs__class_Oabs(X8),X29))<=class_Rings_Olinordered__idom(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__mult)). 6.97/7.20 fof(fact_zmod__zminus1__eq__if, axiom, ![X29, X30]:((c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X29)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=>c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X30),X29)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X29),c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X29))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X30),X29)<=c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X29)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zminus1__eq__if)). 6.97/7.20 fof(fact_abs__divide, axiom, ![X29, X30, X8]:(class_Fields_Olinordered__field__inverse__zero(X8)=>hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X30),X29))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),X30)),hAPP(c_Groups_Oabs__class_Oabs(X8),X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__divide)). 6.97/7.20 fof(fact_of__int__diff, axiom, ![X26, X39, X8]:(class_Rings_Oring__1(X8)=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),hAPP(c_Int_Oring__1__class_Oof__int(X8),X39)),hAPP(c_Int_Oring__1__class_Oof__int(X8),X26))=hAPP(c_Int_Oring__1__class_Oof__int(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X39),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__diff)). 6.97/7.20 fof(fact_of__int__add, axiom, ![X26, X39, X8]:(hAPP(c_Int_Oring__1__class_Oof__int(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X39),X26))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(c_Int_Oring__1__class_Oof__int(X8),X39)),hAPP(c_Int_Oring__1__class_Oof__int(X8),X26))<=class_Rings_Oring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__add)). 6.97/7.20 fof(fact_of__int__mult, axiom, ![X26, X39, X8]:(class_Rings_Oring__1(X8)=>hAPP(c_Int_Oring__1__class_Oof__int(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X39),X26))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(c_Int_Oring__1__class_Oof__int(X8),X39)),hAPP(c_Int_Oring__1__class_Oof__int(X8),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__mult)). 6.97/7.20 fof(fact_setprod__zero, axiom, ![X18, X4, X5, X12]:(class_Rings_Ocomm__semiring__1(X12)=>((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X18),X4)=c_Groups_Ozero__class_Ozero(X12)<=?[X22]:(hAPP(X18,X22)=c_Groups_Ozero__class_Ozero(X12)&hBOOL(hAPP(hAPP(c_member(X5),X22),X4))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__zero)). 6.97/7.20 fof(fact_mult__right__less__imp__less, axiom, ![X29, X31, X30, X8]:(class_Rings_Olinordered__semiring(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X31)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),X29))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X31))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__right__less__imp__less)). 6.97/7.20 fof(fact_mult__less__imp__less__right, axiom, ![X29, X31, X30, X8]:(class_Rings_Olinordered__semiring__strict(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X31)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),X29))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X31))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__less__imp__less__right)). 6.97/7.20 fof(fact_in__set__remove1, axiom, ![X23, X5, X1, X2]:((hBOOL(hAPP(hAPP(c_member(X5),X2),hAPP(c_List_Oset(X5),X23)))<=>hBOOL(hAPP(hAPP(c_member(X5),X2),hAPP(c_List_Oset(X5),c_List_Oremove1(X5,X1,X23)))))<=X2!=X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__remove1)). 6.97/7.20 fof(fact_disjoint__eq__subset__Compl, axiom, ![X11, X4, X5]:(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_disjoint__eq__subset__Compl)). 6.97/7.20 fof(fact_mult__left__less__imp__less, axiom, ![X29, X30, X31, X8]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X31))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),X29)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X30)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X29))))<=class_Rings_Olinordered__semiring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__left__less__imp__less)). 6.97/7.20 fof(fact_mult__less__imp__less__left, axiom, ![X29, X30, X31, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X30)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X29)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X31))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),X29))))<=class_Rings_Olinordered__semiring__strict(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__less__imp__less__left)). 6.97/7.20 fof(fact_mult__right__le__imp__le, axiom, ![X29, X31, X30, X8]:(class_Rings_Olinordered__semiring__strict(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X31)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X31))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),X29))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__right__le__imp__le)). 6.97/7.20 fof(fact_length__pos__if__in__set, axiom, ![X23, X35, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23)))=>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(X5)),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__pos__if__in__set)). 6.97/7.20 fof(fact_mult__left__le__imp__le, axiom, ![X29, X30, X31, X8]:(class_Rings_Olinordered__semiring__strict(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X30)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X29)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),X29))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X31))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__left__le__imp__le)). 6.97/7.20 fof(fact_mult__less__cancel__left__neg, axiom, ![X1, X2, X10, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),c_Groups_Ozero__class_Ozero(X5)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X1)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X1),X2))))<=class_Rings_Olinordered__ring__strict(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__less__cancel__left__neg)). 6.97/7.20 fof(fact_inj__map, axiom, ![X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))<=>c_Fun_Oinj__on(tc_List_Olist(X5),tc_List_Olist(X12),hAPP(c_List_Omap(X5,X12),X18),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__map)). 6.97/7.20 fof(fact_image__constant__conv, axiom, ![X10, X12, X5, X4]:((X4=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>hAPP(c_Set_Oimage(X5,X12,hAPP(c_COMBK(X12,X5),X10)),X4)=c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool)))&(hAPP(c_Set_Oimage(X5,X12,hAPP(c_COMBK(X12,X5),X10)),X4)=hAPP(hAPP(c_Set_Oinsert(X12),X10),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool)))<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__constant__conv)). 6.97/7.20 fof(fact_semiring__1__class_Oof__nat__code, axiom, ![X32, X5]:(c_Nat_Osemiring__1__class_Oof__nat__aux(X5,hAPP(hAPP(c_COMBC(X5,X5,X5),c_Groups_Oplus__class_Oplus(X5)),c_Groups_Oone__class_Oone(X5)),X32,c_Groups_Ozero__class_Ozero(X5))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X32)<=class_Rings_Osemiring__1(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_semiring__1__class_Oof__nat__code)). 6.97/7.20 fof(fact_union__fold__insert, axiom, ![X11, X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hAPP(hAPP(c_Finite__Set_Ofold(X5,tc_fun(X5,tc_HOL_Obool),c_Set_Oinsert(X5)),X11),X4)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_union__fold__insert)). 6.97/7.20 fof(fact_ivl__disj__int_I9_J, axiom, ![X51, X34, X52, X5]:(class_Orderings_Oorder(X5)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X52,X34)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X34),X51))=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I9_J)). 6.97/7.20 fof(fact_ivl__disj__int_I15_J, axiom, ![X51, X34, X52, X5]:(class_Orderings_Oorder(X5)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X52),X34)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X34,X51))=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I15_J)). 6.97/7.20 fof(fact_ivl__disj__int_I8_J, axiom, ![X51, X52, X5]:(class_Orderings_Oorder(X5)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X52),X51)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X51))=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I8_J)). 6.97/7.20 fof(fact_INTER__UNIV__conv_I1_J, axiom, ![X11, X4, X12, X5]:(![X22]:(hBOOL(hAPP(hAPP(c_member(X12),X22),X4))=>c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))=hAPP(X11,X22))<=>c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),X4),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INTER__UNIV__conv_I1_J)). 6.97/7.20 fof(fact_UNION__empty__conv_I1_J, axiom, ![X11, X4, X12, X5]:(![X22]:(hAPP(X11,X22)=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))<=hBOOL(hAPP(hAPP(c_member(X12),X22),X4)))<=>c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X4),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UNION__empty__conv_I1_J)). 6.97/7.20 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H, axiom, ![X2, X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Set_Oinsert(X5),X2),X4))=hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X2),X4))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Oeq__fold__idem_H)). 6.97/7.20 fof(fact_ivl__disj__int_I2_J, axiom, ![X51, X52, X5]:(class_Orderings_Oorder(X5)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X52)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X52),X51))=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I2_J)). 6.97/7.20 fof(fact_in__set__conv__nth, axiom, ![X23, X35, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23)))<=>?[X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)))&hAPP(hAPP(c_List_Onth(X5),X23),X42)=X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__conv__nth)). 6.97/7.20 fof(fact_setsum__SucD, axiom, ![X32, X4, X18, X5]:(?[X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X18,X22))))<=hAPP(c_Nat_OSuc,X32)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X18),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__SucD)). 6.97/7.20 fof(fact_INTER__UNIV__conv_I2_J, axiom, ![X11, X4, X5, X12]:(![X22]:(c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))=hAPP(X11,X22)<=hBOOL(hAPP(hAPP(c_member(X12),X22),X4)))<=>c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),X4),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INTER__UNIV__conv_I2_J)). 6.97/7.20 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H, axiom, ![X2, X4, X5]:((hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X2),X4)=c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Set_Oinsert(X5),X2),X4))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Oeq__fold__idem_H)). 6.97/7.20 fof(fact_insert__ident, axiom, ![X11, X4, X35, X5]:(~(hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))=>((hAPP(hAPP(c_Set_Oinsert(X5),X35),X4)=hAPP(hAPP(c_Set_Oinsert(X5),X35),X11)<=>X11=X4)<=~(hBOOL(hAPP(hAPP(c_member(X5),X35),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__ident)). 6.97/7.20 fof(fact_list__all2__dropI, axiom, ![X32, X159, X160, X17, X12, X5]:(c_List_Olist__all2(X5,X12,X17,hAPP(hAPP(c_List_Odrop(X5),X32),X160),hAPP(hAPP(c_List_Odrop(X12),X32),X159))<=c_List_Olist__all2(X5,X12,X17,X160,X159)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__dropI)). 6.97/7.20 fof(fact_less__number__of, axiom, ![X38, X35, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X35),X38))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X35)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X38))))<=(class_Rings_Olinordered__idom(X5)&class_Int_Onumber__ring(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__number__of)). 6.97/7.20 fof(fact_le__number__of, axiom, ![X38, X35, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X35)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X38)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X35),X38)))<=(class_Rings_Olinordered__idom(X5)&class_Int_Onumber__ring(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__number__of)). 6.97/7.20 fof(fact_less__trans__Suc, axiom, ![X19, X27, X28]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X28)),X19))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X27),X19)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28),X27))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__trans__Suc)). 6.97/7.20 fof(fact_UNION__empty__conv_I2_J, axiom, ![X11, X4, X5, X12]:(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X4),X11)<=>![X22]:(hBOOL(hAPP(hAPP(c_member(X12),X22),X4))=>c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(X11,X22))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UNION__empty__conv_I2_J)). 6.97/7.20 fof(fact_list__all2__takeI, axiom, ![X32, X84, X23, X17, X12, X5]:(c_List_Olist__all2(X5,X12,X17,X23,X84)=>c_List_Olist__all2(X5,X12,X17,hAPP(hAPP(c_List_Otake(X5),X32),X23),hAPP(hAPP(c_List_Otake(X12),X32),X84))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__takeI)). 6.97/7.20 fof(fact_listsp__infI, axiom, ![X11, X52, X4, X5]:(hBOOL(hAPP(c_List_Olistsp(X5,X4),X52))=>(hBOOL(hAPP(c_List_Olistsp(X5,X11),X52))=>hBOOL(hAPP(c_List_Olistsp(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)),X52)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsp__infI)). 6.97/7.20 fof(fact_mod__induct__0, axiom, ![X47, X17, X24]:(![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),X24))=>(hBOOL(hAPP(X17,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X42),X24)))<=hBOOL(hAPP(X17,X42))))=>(hBOOL(hAPP(X17,X47))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X47),X24))=>hBOOL(hAPP(X17,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__induct__0)). 6.97/7.20 fof(fact_INT__constant, axiom, ![X10, X12, X5, X4]:((hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),X4),hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X5),X10))=c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=X4)&(X4!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>X10=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),X4),hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X5),X10)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__constant)). 6.97/7.20 fof(fact_sort__key__simps_I2_J, axiom, ![X23, X35, X18, X5, X12]:(class_Orderings_Olinorder(X12)=>c_List_Olinorder__class_Osort__key(X5,X12,X18,hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X12,X18),X35),c_List_Olinorder__class_Osort__key(X5,X12,X18,X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sort__key__simps_I2_J)). 6.97/7.20 fof(fact_abs__less__iff, axiom, ![X1, X2, X5]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X2)),X1))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),X1)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Groups_Oabs__class_Oabs(X5),X2)),X1)))<=class_Rings_Olinordered__idom(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__less__iff)). 6.97/7.20 fof(fact_abs__leI, axiom, ![X29, X30, X8]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),X30)),X29))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X30)),X29)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),X29)))<=class_Groups_Oordered__ab__group__add__abs(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__leI)). 6.97/7.20 fof(fact_ex__bij__betw__nat__finite, axiom, ![X94, X5]:(?[X205]:c_Fun_Obij__betw(tc_Nat_Onat,X5,X205,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X5),X94)),X94)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X94))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ex__bij__betw__nat__finite)). 6.97/7.20 fof(fact_ex__bij__betw__finite__nat, axiom, ![X94, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X94))=>?[X205]:c_Fun_Obij__betw(X5,tc_Nat_Onat,X205,X94,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X5),X94)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ex__bij__betw__finite__nat)). 6.97/7.20 fof(fact_minus1__divide, axiom, ![X6, X8]:((class_Int_Onumber__ring(X8)&class_Fields_Ofield__inverse__zero(X8))=>hAPP(c_Groups_Ouminus__class_Ouminus(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),c_Groups_Oone__class_Oone(X8)),X6))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OMin)),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus1__divide)). 6.97/7.20 fof(fact_sublist__singleton, axiom, ![X35, X5, X4]:((c_List_Osublist(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X35),c_List_Olist_ONil(X5)),X4)=hAPP(hAPP(c_List_Olist_OCons(X5),X35),c_List_Olist_ONil(X5))<=hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4)))&(c_List_Olist_ONil(X5)=c_List_Osublist(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X35),c_List_Olist_ONil(X5)),X4)<=~(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublist__singleton)). 6.97/7.20 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J, axiom, ![X7, X6]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6))=>(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,X6,X7)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Divides_Otransfer__nat__int__function__closures_I2_J)). 6.97/7.20 fof(fact_less__than__iff, axiom, ![X38, X35]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X35),X38))<=>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),X35),X38)),c_Wellfounded_Oless__than))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__than__iff)). 6.97/7.20 fof(fact_min__max_Ofold1__belowI, axiom, ![X2, X4, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X4)),X2))<=hBOOL(hAPP(hAPP(c_member(X5),X2),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ofold1__belowI)). 6.97/7.20 fof(fact_fold1__belowI, axiom, ![X2, X4, X5]:(class_Lattices_Osemilattice__inf(X5)=>((hBOOL(hAPP(hAPP(c_member(X5),X2),X4))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X4)),X2)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__belowI)). 6.97/7.20 fof(fact_finite__cartesian__productD2, axiom, ![X11, X4, X12, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X11))<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4)<=hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X4),hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X5),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__cartesian__productD2)). 6.97/7.20 fof(fact_finite__cartesian__productD1, axiom, ![X11, X4, X12, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X4),hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X5),X11))))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))<=c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool))!=X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__cartesian__productD1)). 6.97/7.20 fof(fact_div__pos__pos, axiom, ![X29, X30]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X29))=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),X29)=hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X30,X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__pos__pos)). 6.97/7.20 fof(fact_div__neg__pos, axiom, ![X29, X30]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>(hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X30,X29))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),X29)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__neg__pos)). 6.97/7.20 fof(fact_nth__take, axiom, ![X41, X8, X25, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28),X25))=>hAPP(hAPP(c_List_Onth(X8),X41),X28)=hAPP(hAPP(c_List_Onth(X8),hAPP(hAPP(c_List_Otake(X8),X25),X41)),X28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__take)). 6.97/7.20 fof(fact_Id__onE, axiom, ![X4, X10, X5]:(~(![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))=>hAPP(hAPP(c_Product__Type_OPair(X5,X5),X22),X22)!=X10))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X10),c_Relation_OId__on(X5,X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Id__onE)). 6.97/7.20 fof(fact_power__less__imp__less__base, axiom, ![X29, X25, X30, X8]:(class_Rings_Olinordered__semidom(X8)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),X29))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X29)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X29),X25))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__less__imp__less__base)). 6.97/7.20 fof(fact_listsp__mono, axiom, ![X11, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),c_List_Olistsp(X5,X4)),c_List_Olistsp(X5,X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsp__mono)). 6.97/7.20 fof(fact_lists__mono, axiom, ![X11, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),c_List_Olists(X5,X4)),c_List_Olists(X5,X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists__mono)). 6.97/7.20 fof(fact_UnE, axiom, ![X11, X4, X10, X5]:((hBOOL(hAPP(hAPP(c_member(X5),X10),X11))<=~(hBOOL(hAPP(hAPP(c_member(X5),X10),X4))))<=hBOOL(hAPP(hAPP(c_member(X5),X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UnE)). 6.97/7.20 fof(fact_finite__Inter, axiom, ![X94, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X94)))<=?[X22]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X22),X94))&hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X22)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Inter)). 6.97/7.20 fof(fact_subset__insertI2, axiom, ![X1, X11, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X1),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__insertI2)). 6.97/7.20 fof(fact_folding_Oeq__fold, axiom, ![X66, X4, X55, X18, X12, X5]:(c_Finite__Set_Ofolding(X5,X12,X18,X55)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hAPP(hAPP(X55,X4),X66)=hAPP(hAPP(c_Finite__Set_Ofold(X5,X12,X18),X66),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Oeq__fold)). 6.97/7.20 fof(fact_o__eq__dest, axiom, ![X60, X97, X10, X92, X1, X2, X5, X12, X62]:(hAPP(X10,hAPP(X97,X60))=hAPP(X2,hAPP(X1,X60))<=hAPP(c_Fun_Ocomp(X92,X12,X5,X10),X97)=hAPP(c_Fun_Ocomp(X62,X12,X5,X2),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_o__eq__dest)). 6.97/7.20 fof(fact_mod__mult__self1, axiom, ![X29, X31, X30, X8]:(class_Divides_Osemiring__div(X8)=>c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X31),X29)),X29)=c_Divides_Odiv__class_Omod(X8,X30,X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__self1)). 6.97/7.20 fof(fact_mod__mult__self2, axiom, ![X31, X29, X30, X8]:(c_Divides_Odiv__class_Omod(X8,X30,X29)=c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X31)),X29)<=class_Divides_Osemiring__div(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__self2)). 6.97/7.20 fof(fact_f__the__inv__into__f, axiom, ![X38, X4, X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,X4)=>(hAPP(X18,hAPP(c_Fun_Othe__inv__into(X5,X12,X4,X18),X38))=X38<=hBOOL(hAPP(hAPP(c_member(X12),X38),hAPP(c_Set_Oimage(X5,X12,X18),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_f__the__inv__into__f)). 6.97/7.20 fof(fact_double__add__less__zero__iff__single__add__less__zero, axiom, ![X2, X5]:(class_Groups_Olinordered__ab__group__add(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X2),X2)),c_Groups_Ozero__class_Ozero(X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),c_Groups_Ozero__class_Ozero(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_double__add__less__zero__iff__single__add__less__zero)). 6.97/7.20 fof(fact_even__less__0__iff, axiom, ![X2, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),c_Groups_Ozero__class_Ozero(X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X2),X2)),c_Groups_Ozero__class_Ozero(X5))))<=class_Rings_Olinordered__idom(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_even__less__0__iff)). 6.97/7.20 fof(fact_double__add__le__zero__iff__single__add__le__zero, axiom, ![X2, X5]:(class_Groups_Olinordered__ab__group__add(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X2),X2)),c_Groups_Ozero__class_Ozero(X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X2),c_Groups_Ozero__class_Ozero(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_double__add__le__zero__iff__single__add__le__zero)). 6.97/7.20 fof(fact_Suc__mult__le__cancel1, axiom, ![X32, X34, X33]:(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,X33)),X34)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X33)),X32)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__mult__le__cancel1)). 6.97/7.20 fof(fact_zero__less__power, axiom, ![X25, X30, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X30)))<=class_Rings_Olinordered__semidom(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__power)). 6.97/7.20 fof(fact_zero__less__double__add__iff__zero__less__single__add, axiom, ![X2, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X2),X2)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X2)))<=class_Groups_Olinordered__ab__group__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__double__add__iff__zero__less__single__add)). 6.97/7.20 fof(fact_one__le__power, axiom, ![X25, X30, X8]:(class_Rings_Olinordered__semidom(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Oone__class_Oone(X8)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Oone__class_Oone(X8)),X30)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__le__power)). 6.97/7.20 fof(fact_zero__le__power, axiom, ![X25, X30, X8]:(class_Rings_Olinordered__semidom(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X30))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__power)). 6.97/7.20 fof(fact_sorted__insort__insert__key, axiom, ![X35, X23, X18, X12, X5]:((c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X12,X5),X18),X23))=>c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X12,X5),X18),c_List_Olinorder__class_Oinsort__insert__key(X12,X5,X18,X35,X23))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__insort__insert__key)). 6.97/7.20 fof(fact_image__iff, axiom, ![X4, X18, X12, X14, X5]:(?[X22]:(hBOOL(hAPP(hAPP(c_member(X12),X22),X4))&X14=hAPP(X18,X22))<=>hBOOL(hAPP(hAPP(c_member(X5),X14),hAPP(c_Set_Oimage(X12,X5,X18),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__iff)). 6.97/7.20 fof(fact_zero__le__double__add__iff__zero__le__single__add, axiom, ![X2, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X2))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X2),X2))))<=class_Groups_Olinordered__ab__group__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__double__add__iff__zero__le__single__add)). 6.97/7.20 fof(fact_acc__subset, axiom, ![X129, X130, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Wellfounded_Oacc(X5,X129)),c_Wellfounded_Oacc(X5,X130)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X130),X129))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acc__subset)). 6.97/7.20 fof(fact_accp__subset, axiom, ![X129, X130, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Wellfounded_Oaccp(X5,X129)),c_Wellfounded_Oaccp(X5,X130)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X130),X129))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_accp__subset)). 6.97/7.20 fof(fact_imageE, axiom, ![X4, X18, X12, X1, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X1),hAPP(c_Set_Oimage(X12,X5,X18),X4)))=>~(![X22]:(X1=hAPP(X18,X22)=>~(hBOOL(hAPP(hAPP(c_member(X12),X22),X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_imageE)). 6.97/7.20 fof(fact_lists__accI, axiom, ![X3, X23, X5]:(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X23),c_Wellfounded_Oacc(tc_List_Olist(X5),c_List_Olistrel1(X5,X3))))=>hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X23),c_List_Olists(X5,c_Wellfounded_Oacc(X5,X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists__accI)). 6.97/7.20 fof(fact_setprod__eq__1__iff, axiom, ![X18, X55, X5]:((![X22]:(hAPP(X18,X22)=c_Groups_Oone__class_Oone(tc_Nat_Onat)<=hBOOL(hAPP(hAPP(c_member(X5),X22),X55)))<=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,tc_Nat_Onat),X18),X55)=c_Groups_Oone__class_Oone(tc_Nat_Onat))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X55))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__eq__1__iff)). 6.97/7.20 fof(fact_le__fun__def, axiom, ![X50, X18, X5, X12]:(class_Orderings_Oord(X12)=>(![X22]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),hAPP(X18,X22)),hAPP(X50,X22)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X12)),X18),X50)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__fun__def)). 6.97/7.20 fof(fact_folding__one__idem_Oin__idem, axiom, ![X35, X4, X55, X18, X5]:(c_Finite__Set_Ofolding__one__idem(X5,X18,X55)=>((hBOOL(hAPP(hAPP(c_member(X5),X35),X4))=>hAPP(X55,X4)=hAPP(hAPP(X18,X35),hAPP(X55,X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one__idem_Oin__idem)). 6.97/7.20 fof(fact_setsum__eq__0__iff, axiom, ![X18, X55, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X55))=>(![X22]:(hAPP(X18,X22)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<=hBOOL(hAPP(hAPP(c_member(X5),X22),X55)))<=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X18),X55))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__eq__0__iff)). 6.97/7.20 fof(fact_surj__f__inv__f, axiom, ![X38, X18, X5, X12]:(X38=hAPP(X18,hAPP(c_Hilbert__Choice_Oinv__into(X12,X5,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)),X18),X38))<=c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))=hAPP(c_Set_Oimage(X12,X5,X18),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_surj__f__inv__f)). 6.97/7.20 fof(fact_List_Oinsert__def, axiom, ![X23, X35, X5]:((hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23)))=>c_List_Oinsert(X5,X35,X23)=X23)&(c_List_Oinsert(X5,X35,X23)=hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23)<=~(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_List_Oinsert__def)). 6.97/7.20 fof(fact_SigmaD2, axiom, ![X11, X4, X1, X2, X12, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X2),X1)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X4),X11)))=>hBOOL(hAPP(hAPP(c_member(X12),X1),hAPP(X11,X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SigmaD2)). 6.97/7.20 fof(fact_distinct__map, axiom, ![X23, X18, X12, X5]:(hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Omap(X12,X5),X18),X23)))<=>(hBOOL(hAPP(c_List_Odistinct(X12),X23))&c_Fun_Oinj__on(X12,X5,X18,hAPP(c_List_Oset(X12),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__map)). 6.97/7.20 fof(fact_setprod__zero__iff, axiom, ![X18, X4, X5, X12]:((class_Rings_Ocomm__semiring__1(X12)&class_Rings_Ono__zero__divisors(X12))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(?[X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))&c_Groups_Ozero__class_Ozero(X12)=hAPP(X18,X22))<=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X12),X18),X4)=c_Groups_Ozero__class_Ozero(X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__zero__iff)). 6.97/7.20 fof(fact_inj__on__diff__nat, axiom, ![X33, X20]:(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)),X33),X20)<=![X22]:(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X22),X20))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X22)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__diff__nat)). 6.97/7.20 fof(fact_set__insort, axiom, ![X23, X35, X18, X5, X12]:(class_Orderings_Olinorder(X12)=>hAPP(hAPP(c_Set_Oinsert(X5),X35),hAPP(c_List_Oset(X5),X23))=hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X12,X18),X35),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__insort)). 6.97/7.20 fof(fact_wf__not__sym, axiom, ![X35, X2, X3, X5]:(c_Wellfounded_Owf(X5,X3)=>(~(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X2)),X3)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X35)),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__not__sym)). 6.97/7.20 fof(fact_surj__iff__all, axiom, ![X18, X5, X12]:(![X22]:hAPP(X18,hAPP(c_Hilbert__Choice_Oinv__into(X12,X5,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)),X18),X22))=X22<=>hAPP(c_Set_Oimage(X12,X5,X18),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_surj__iff__all)). 6.97/7.20 fof(fact_sup2CI, axiom, ![X12, X5, X4, X38, X35, X11]:(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X12,tc_HOL_Obool))),X4),X11),X35),X38))<=(~(hBOOL(hAPP(hAPP(X11,X35),X38)))=>hBOOL(hAPP(hAPP(X4,X35),X38)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup2CI)). 6.97/7.20 fof(fact_refl__onD1, axiom, ![X38, X35, X3, X4, X5]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),X3))=>hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))<=c_Relation_Orefl__on(X5,X4,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__onD1)). 6.97/7.20 fof(fact_refl__onD2, axiom, ![X38, X35, X3, X4, X5]:((hBOOL(hAPP(hAPP(c_member(X5),X38),X4))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),X3)))<=c_Relation_Orefl__on(X5,X4,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__onD2)). 6.97/7.20 fof(fact_dvd__div__mult__self, axiom, ![X29, X30, X8]:((X29=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),X29),X30)),X30)<=hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X8),X30),X29)))<=class_Divides_Osemiring__div(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dvd__div__mult__self)). 6.97/7.20 fof(fact_dvd__mult__div__cancel, axiom, ![X29, X30, X8]:((hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X8),X30),X29))=>X29=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),X29),X30)))<=class_Divides_Osemiring__div(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dvd__mult__div__cancel)). 6.97/7.20 fof(fact_minus__less__iff, axiom, ![X1, X2, X5]:(class_Groups_Oordered__ab__group__add(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X2)),X1))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X1)),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__less__iff)). 6.97/7.20 fof(fact_finite__compl, axiom, ![X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X4)))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__compl)). 6.97/7.20 fof(fact_pos__imp__zdiv__neg__iff, axiom, ![X2, X1]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(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))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__imp__zdiv__neg__iff)). 6.97/7.20 fof(fact_minus__le__iff, axiom, ![X1, X2, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X2)),X1))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X1)),X2)))<=class_Groups_Oordered__ab__group__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__le__iff)). 6.97/7.20 fof(fact_less__minus__iff, axiom, ![X1, X2, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X1),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X2)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X1))))<=class_Groups_Oordered__ab__group__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__minus__iff)). 6.97/7.20 fof(fact_nonneg1__imp__zdiv__pos__iff, axiom, ![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))&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_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nonneg1__imp__zdiv__pos__iff)). 6.97/7.20 fof(fact_diff__Suc__less, axiom, ![X28, X25]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),hAPP(c_Nat_OSuc,X28))),X25))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__Suc__less)). 6.97/7.20 fof(fact_le__minus__iff, axiom, ![X1, X2, X5]:(class_Groups_Oordered__ab__group__add(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X1),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X2)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__minus__iff)). 6.97/7.20 fof(fact_finite__UNIV__card__ge__0, axiom, ![X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,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(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__UNIV__card__ge__0)). 6.97/7.20 fof(fact_le__imp__0__less, axiom, ![X26]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))=>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)),X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__imp__0__less)). 6.97/7.20 fof(fact_nth__list__update__eq, axiom, ![X6, X41, X8, X28]:(hAPP(hAPP(c_List_Onth(X8),hAPP(hAPP(c_List_Olist__update(X8,X41),X28),X6)),X28)=X6<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__list__update__eq)). 6.97/7.20 fof(fact_less__iff__diff__less__0, axiom, ![X1, X2, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),X1))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X2),X1)),c_Groups_Ozero__class_Ozero(X5))))<=class_Groups_Oordered__ab__group__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__iff__diff__less__0)). 6.97/7.20 fof(fact_le__iff__diff__le__0, axiom, ![X1, X2, X5]:(class_Groups_Oordered__ab__group__add(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X2),X1)),c_Groups_Ozero__class_Ozero(X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X2),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__iff__diff__le__0)). 6.97/7.20 fof(fact_length__insort, axiom, ![X23, X35, X18, X5, X12]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X12,X18),X35),X23))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23))<=class_Orderings_Olinorder(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__insort)). 6.97/7.20 fof(fact_neg__less__iff__less, axiom, ![X2, X1, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),X1))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X1)),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X2))))<=class_Groups_Oordered__ab__group__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__less__iff__less)). 6.97/7.20 fof(fact_the__inv__into__onto, axiom, ![X4, X18, X12, X5]:(hAPP(c_Set_Oimage(X12,X5,c_Fun_Othe__inv__into(X5,X12,X4,X18)),hAPP(c_Set_Oimage(X5,X12,X18),X4))=X4<=c_Fun_Oinj__on(X5,X12,X18,X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__inv__into__onto)). 6.97/7.20 fof(fact_min__less__iff__disj, axiom, ![X14, X38, X35, X5]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X38),X14))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X35),X14)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X35),X38)),X14)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__less__iff__disj)). 6.97/7.20 fof(fact_min__le__iff__disj, axiom, ![X14, X38, X35, X5]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X38),X14))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),X14)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X35),X38)),X14)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__le__iff__disj)). 6.97/7.20 fof(fact_less__max__iff__disj, axiom, ![X38, X35, X14, X5]:(class_Orderings_Olinorder(X5)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X14),X38))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X14),X35)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X14),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X35),X38))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__max__iff__disj)). 6.97/7.20 fof(fact_compl__mono, axiom, ![X7, X6, X8]:(class_Lattices_Oboolean__algebra(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),X7))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X7)),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X6))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__mono)). 6.97/7.20 fof(fact_neg__le__iff__le, axiom, ![X2, X1, X5]:(class_Groups_Oordered__ab__group__add(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X1)),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X2)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X2),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__le__iff__le)). 6.97/7.20 fof(fact_le__max__iff__disj, axiom, ![X38, X35, X14, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X14),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X35),X38)))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X14),X38))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X14),X35))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__max__iff__disj)). 6.97/7.20 fof(fact_image__uminus__greaterThanAtMost, axiom, ![X38, X35, X5]:(class_Groups_Oordered__ab__group__add(X5)=>hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X35,X38))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,hAPP(c_Groups_Ouminus__class_Ouminus(X5),X38)),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__uminus__greaterThanAtMost)). 6.97/7.20 fof(fact_take__Cons__number__of, axiom, ![X41, X6, X8, X40]:((hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>hAPP(hAPP(c_List_Otake(X8),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)),hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41))=hAPP(hAPP(c_List_Olist_OCons(X8),X6),hAPP(hAPP(c_List_Otake(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X41)))&(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>hAPP(hAPP(c_List_Otake(X8),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)),hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41))=c_List_Olist_ONil(X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__Cons__number__of)). 6.97/7.20 fof(fact_ivl__disj__int_I13_J, axiom, ![X51, X34, X52, X5]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X52,X34)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X34,X51))=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))<=class_Orderings_Oorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I13_J)). 6.97/7.20 fof(fact_ivl__disj__int_I12_J, axiom, ![X51, X34, X52, X5]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X52,X34)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X34,X51))=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))<=class_Orderings_Oorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I12_J)). 6.97/7.20 fof(fact_ivl__disj__int_I10_J, axiom, ![X51, X34, X52, X5]:(class_Orderings_Oorder(X5)=>c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X52,X34)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X34,X51))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I10_J)). 6.97/7.20 fof(fact_ivl__disj__int_I14_J, axiom, ![X51, X34, X52, X5]:(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X52,X34)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X34,X51))<=class_Orderings_Oorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I14_J)). 6.97/7.20 fof(fact_pred__comp_Oequations, axiom, ![X102, X103, X66, X3, X62, X12, X5]:(?[X96]:(hBOOL(hAPP(hAPP(X3,X103),X96))&hBOOL(hAPP(hAPP(X66,X96),X102)))<=>hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X5,X12,X62,X3,X66),X103),X102))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pred__comp_Oequations)). 6.97/7.20 fof(fact_lexn__length, axiom, ![X32, X3, X84, X23, X5]:((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X84)=X32&hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)=X32)<=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)),X23),X84)),hAPP(c_List_Olexn(X5,X3),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexn__length)). 6.97/7.20 fof(fact_abs__minus__commute, axiom, ![X29, X30, X8]:(class_Groups_Oordered__ab__group__add__abs(X8)=>hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X29),X30))=hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X30),X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__minus__commute)). 6.97/7.20 fof(fact_ivl__disj__int_I16_J, axiom, ![X51, X34, X52, X5]:(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X52,X34)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X34,X51))<=class_Orderings_Oorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I16_J)). 6.97/7.20 fof(fact_ivl__disj__int_I6_J, axiom, ![X51, X52, X5]:(class_Orderings_Oorder(X5)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X52,X51)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X51))=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I6_J)). 6.97/7.20 fof(fact_ivl__disj__int_I5_J, axiom, ![X51, X52, X5]:(class_Orderings_Oorder(X5)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X52,X51)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X51))=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I5_J)). 6.97/7.20 fof(fact_ivl__disj__int_I7_J, axiom, ![X51, X52, X5]:(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X52,X51)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X51))<=class_Orderings_Oorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I7_J)). 6.97/7.20 fof(fact_bij__betw__imp__surj, axiom, ![X4, X18, X12, X5]:(c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))=hAPP(c_Set_Oimage(X5,X12,X18),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))<=c_Fun_Obij__betw(X5,X12,X18,X4,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bij__betw__imp__surj)). 6.97/7.20 fof(fact_sorted__filter, axiom, ![X17, X23, X18, X12, X5]:(class_Orderings_Olinorder(X5)=>(c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X12,X5),X18),hAPP(c_List_Ofilter(X12,X17),X23)))<=c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X12,X5),X18),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__filter)). 6.97/7.20 fof(fact_ivl__disj__int_I4_J, axiom, ![X51, X52, X5]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X52)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X52,X51))=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))<=class_Orderings_Oorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I4_J)). 6.97/7.20 fof(fact_ivl__disj__int_I1_J, axiom, ![X51, X52, X5]:(class_Orderings_Oorder(X5)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X52)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X52,X51))=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I1_J)). 6.97/7.20 fof(fact_ivl__disj__int_I3_J, axiom, ![X51, X52, X5]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X52)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X52,X51))=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))<=class_Orderings_Oorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I3_J)). 6.97/7.20 fof(fact_Ints__power, axiom, ![X32, X2, X5]:(class_Rings_Oring__1(X5)=>(hBOOL(hAPP(hAPP(c_member(X5),X2),c_Int_Oring__1__class_OInts(X5)))=>hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X2),X32)),c_Int_Oring__1__class_OInts(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__power)). 6.97/7.20 fof(fact_Inf__le__Sup, axiom, ![X4, X5]:(class_Lattices_Olattice(X5)=>((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Big__Operators_Olattice__class_OInf__fin(X5,X4)),c_Big__Operators_Olattice__class_OSup__fin(X5,X4))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__le__Sup)). 6.97/7.20 fof(fact_less__diff__conv, axiom, ![X33, X46, X47]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X47),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X46),X33)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X47),X33)),X46))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__diff__conv)). 6.97/7.20 fof(fact_le__diff__conv, axiom, ![X47, X33, X46]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X46),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X47),X33)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X46),X33)),X47))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__diff__conv)). 6.97/7.20 fof(fact_lfp__induct, axiom, ![X17, X18, X5]:((c_Orderings_Oorder__class_Omono(X5,X5,X18)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Inductive_Ocomplete__lattice__class_Olfp(X5,X18)),X17))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X18,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Inductive_Ocomplete__lattice__class_Olfp(X5,X18)),X17))),X17))))<=class_Complete__Lattice_Ocomplete__lattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lfp__induct)). 6.97/7.20 fof(fact_coinduct, axiom, ![X56, X18, X5]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X56),c_Inductive_Ocomplete__lattice__class_Ogfp(X5,X18)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X56),hAPP(X18,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X56),c_Inductive_Ocomplete__lattice__class_Ogfp(X5,X18))))))<=c_Orderings_Oorder__class_Omono(X5,X5,X18))<=class_Complete__Lattice_Ocomplete__lattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_coinduct)). 6.97/7.20 fof(fact_ex__bij__betw__nat__finite__1, axiom, ![X94, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X94))=>?[X205]:c_Fun_Obij__betw(tc_Nat_Onat,X5,X205,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X94)),X94)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ex__bij__betw__nat__finite__1)). 6.97/7.20 fof(fact_zero__less__mult__pos2, axiom, ![X30, X29, X8]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X29))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X30)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X30))))<=class_Rings_Olinordered__semiring__strict(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__mult__pos2)). 6.97/7.20 fof(fact_zero__less__mult__pos, axiom, ![X29, X30, X8]:(class_Rings_Olinordered__semiring__strict(X8)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X29))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X30)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__mult__pos)). 6.97/7.20 fof(fact_of__nat__power, axiom, ![X25, X36, X8]:(class_Rings_Osemiring__1(X8)=>hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),X36)),X25)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X36),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__power)). 6.97/7.20 fof(fact_listsum__0, axiom, ![X23, X12, X5]:(class_Groups_Omonoid__add(X5)=>c_Groups_Ozero__class_Ozero(X5)=hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X12,X5),hAPP(c_COMBK(X5,X12),c_Groups_Ozero__class_Ozero(X5))),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__0)). 6.97/7.20 fof(fact_of__int__power, axiom, ![X25, X26, X8]:(hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(c_Int_Oring__1__class_Oof__int(X8),X26)),X25)=hAPP(c_Int_Oring__1__class_Oof__int(X8),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),X25))<=class_Rings_Oring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__power)). 6.97/7.20 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J, axiom, ![X7, X6]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X6,X7)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7)))<=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__function__closures_I3_J)). 6.97/7.20 fof(fact_start__le__sum, axiom, ![X186, X32, X34]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),X32))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X186)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_start__le__sum)). 6.97/7.20 fof(fact_imageI, axiom, ![X18, X12, X4, X35, X5]:(hBOOL(hAPP(hAPP(c_member(X12),hAPP(X18,X35)),hAPP(c_Set_Oimage(X5,X12,X18),X4)))<=hBOOL(hAPP(hAPP(c_member(X5),X35),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_imageI)). 6.97/7.20 fof(fact_transpose__empty, axiom, ![X23, X5]:(![X22]:(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X22),hAPP(c_List_Oset(tc_List_Olist(X5)),X23)))=>c_List_Olist_ONil(X5)=X22)<=>c_List_Olist_ONil(tc_List_Olist(X5))=c_List_Otranspose(X5,X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__empty)). 6.97/7.20 fof(fact_inv__into__inv__into__eq, axiom, ![X2, X107, X4, X18, X12, X5]:(c_Fun_Obij__betw(X5,X12,X18,X4,X107)=>(hBOOL(hAPP(hAPP(c_member(X5),X2),X4))=>hAPP(c_Hilbert__Choice_Oinv__into(X12,X5,X107,c_Hilbert__Choice_Oinv__into(X5,X12,X4,X18)),X2)=hAPP(X18,X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inv__into__inv__into__eq)). 6.97/7.20 fof(fact_comp__inj__on__iff, axiom, ![X138, X62, X4, X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,X4)=>(c_Fun_Oinj__on(X12,X62,X138,hAPP(c_Set_Oimage(X5,X12,X18),X4))<=>c_Fun_Oinj__on(X5,X62,hAPP(c_Fun_Ocomp(X12,X62,X5,X138),X18),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comp__inj__on__iff)). 6.97/7.20 fof(fact_UnCI, axiom, ![X4, X11, X10, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11)))<=(~(hBOOL(hAPP(hAPP(c_member(X5),X10),X11)))=>hBOOL(hAPP(hAPP(c_member(X5),X10),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UnCI)). 6.97/7.20 fof(fact_filter__empty__conv, axiom, ![X23, X17, X5]:(hAPP(c_List_Ofilter(X5,X17),X23)=c_List_Olist_ONil(X5)<=>![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X23)))=>~(hBOOL(hAPP(X17,X22))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__empty__conv)). 6.97/7.20 fof(fact_Sup__le__iff, axiom, ![X1, X4, X5]:(class_Complete__Lattice_Ocomplete__lattice(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Complete__Lattice_OSup__class_OSup(X5,X4)),X1))<=>![X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X22),X1))<=hBOOL(hAPP(hAPP(c_member(X5),X22),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__le__iff)). 6.97/7.20 fof(fact_le__Inf__iff, axiom, ![X4, X1, X5]:((![X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X1),X22))<=hBOOL(hAPP(hAPP(c_member(X5),X22),X4)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X1),c_Complete__Lattice_OInf__class_OInf(X5,X4))))<=class_Complete__Lattice_Ocomplete__lattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__Inf__iff)). 6.97/7.20 fof(fact_power__Suc, axiom, ![X25, X30, X8]:(class_Power_Opower(X8)=>hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),hAPP(c_Nat_OSuc,X25))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__Suc)). 6.97/7.20 fof(fact_le__funI, axiom, ![X5, X50, X18, X12]:((![X22]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12),hAPP(X18,X22)),hAPP(X50,X22)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X12)),X18),X50)))<=class_Orderings_Oord(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__funI)). 6.97/7.20 fof(fact_of__nat__less__iff, axiom, ![X32, X34, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34),X32))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X34)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X32))))<=class_Rings_Olinordered__semidom(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__less__iff)). 6.97/7.20 fof(fact_of__int__less__iff, axiom, ![X14, X9, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Oring__1__class_Oof__int(X5),X9)),hAPP(c_Int_Oring__1__class_Oof__int(X5),X14)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9),X14)))<=class_Rings_Olinordered__idom(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__less__iff)). 6.97/7.20 fof(fact_of__nat__le__iff, axiom, ![X32, X34, X5]:(class_Rings_Olinordered__semidom(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X34)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X32)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__le__iff)). 6.97/7.20 fof(fact_of__int__le__iff, axiom, ![X14, X9, X5]:(class_Rings_Olinordered__idom(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Oring__1__class_Oof__int(X5),X9)),hAPP(c_Int_Oring__1__class_Oof__int(X5),X14)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9),X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__le__iff)). 6.97/7.20 fof(fact_bij__betw__comp__iff, axiom, ![X137, X138, X62, X107, X4, X18, X12, X5]:((c_Fun_Obij__betw(X12,X62,X138,X107,X137)<=>c_Fun_Obij__betw(X5,X62,hAPP(c_Fun_Ocomp(X12,X62,X5,X138),X18),X4,X137))<=c_Fun_Obij__betw(X5,X12,X18,X4,X107)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bij__betw__comp__iff)). 6.97/7.20 fof(fact_congruentD, axiom, ![X14, X38, X18, X3, X12, X5]:(c_Equiv__Relations_Ocongruent(X5,X12,X3,X18)=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X38),X14)),X3))=>hAPP(X18,X38)=hAPP(X18,X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_congruentD)). 6.97/7.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J, axiom, ![X53, X6, X8]:(class_Rings_Ocomm__semiring__1(X8)=>hAPP(hAPP(c_Power_Opower__class_Opower(X8),X6),hAPP(c_Nat_OSuc,X53))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X6),X53))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J)). 6.97/7.20 fof(fact_Nitpick_Orefl_H__def, axiom, ![X3, X5]:(![X22]:hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X22),X22)),X3))<=>c_Nitpick_Orefl_H(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Orefl_H__def)). 6.97/7.20 fof(fact_in__listsp__conv__set, axiom, ![X23, X4, X5]:(![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X23)))=>hBOOL(hAPP(X4,X22)))<=>hBOOL(hAPP(c_List_Olistsp(X5,X4),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__listsp__conv__set)). 6.97/7.20 fof(fact_Inter__lower, axiom, ![X4, X11, X5]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X11),X4))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X4)),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__lower)). 6.97/7.20 fof(fact_Union__upper, axiom, ![X4, X11, X5]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X11),X4))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__upper)). 6.97/7.20 fof(fact_wf__same__fst, axiom, ![X5, X67, X12, X17]:(![X22]:(c_Wellfounded_Owf(X12,hAPP(X67,X22))<=hBOOL(hAPP(X17,X22)))=>c_Wellfounded_Owf(tc_prod(X5,X12),c_Recdef_Osame__fst(X5,X12,X17,X67))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__same__fst)). 6.97/7.20 fof(fact_nth__Cons__number__of, axiom, ![X41, X6, X8, X40]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)=>hAPP(hAPP(c_List_Onth(X8),hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40))=X6)&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)=>hAPP(hAPP(c_List_Onth(X8),X41),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_List_Onth(X8),hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__Cons__number__of)). 6.97/7.20 fof(fact_Sup__least, axiom, ![X14, X4, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Complete__Lattice_OSup__class_OSup(X5,X4)),X14))<=![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X22),X14))))<=class_Complete__Lattice_Ocomplete__lattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__least)). 6.97/7.20 fof(fact_card__insert__if, axiom, ![X35, X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>((hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))=hAPP(c_Finite__Set_Ocard(X5),X4)<=hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))&(hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))=hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X5),X4))<=~(hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__insert__if)). 6.97/7.20 fof(fact_partition__P, axiom, ![X171, X172, X23, X17, X5]:((![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X171)))=>~(hBOOL(hAPP(X17,X22))))&![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X172)))=>hBOOL(hAPP(X17,X22))))<=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X172),X171)=c_List_Opartition(X5,X17,X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_partition__P)). 6.97/7.20 fof(fact_nonzero__minus__divide__divide, axiom, ![X30, X29, X8]:(class_Rings_Odivision__ring(X8)=>(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X30)),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X29))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X30),X29)<=c_Groups_Ozero__class_Ozero(X8)!=X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nonzero__minus__divide__divide)). 6.97/7.20 fof(fact_Inf__greatest, axiom, ![X14, X4, X5]:(class_Complete__Lattice_Ocomplete__lattice(X5)=>(![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X14),X22)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X14),c_Complete__Lattice_OInf__class_OInf(X5,X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__greatest)). 6.97/7.20 fof(fact_image__uminus__greaterThanLessThan, axiom, ![X38, X35, X5]:(class_Groups_Oordered__ab__group__add(X5)=>c_SetInterval_Oord__class_OgreaterThanLessThan(X5,hAPP(c_Groups_Ouminus__class_Ouminus(X5),X38),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X35))=hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X35,X38))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__uminus__greaterThanLessThan)). 6.97/7.20 fof(fact_image__uminus__atLeastAtMost, axiom, ![X38, X35, X5]:(class_Groups_Oordered__ab__group__add(X5)=>c_SetInterval_Oord__class_OatLeastAtMost(X5,hAPP(c_Groups_Ouminus__class_Ouminus(X5),X38),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X35))=hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X35,X38))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__uminus__atLeastAtMost)). 6.97/7.20 fof(fact_sup2E, axiom, ![X38, X35, X11, X4, X12, X5]:(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X12,tc_HOL_Obool))),X4),X11),X35),X38))=>(hBOOL(hAPP(hAPP(X11,X35),X38))<=~(hBOOL(hAPP(hAPP(X4,X35),X38))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup2E)). 6.97/7.20 fof(fact_UnionE, axiom, ![X65, X4, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X4),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X65)))=>~(![X241]:(hBOOL(hAPP(hAPP(c_member(X5),X4),X241))=>~(hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X241),X65)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UnionE)). 6.97/7.20 fof(fact_Image__closed__trancl, axiom, ![X56, X3, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X3),X56)),X56))=>X56=hAPP(c_Relation_OImage(X5,X5,c_Transitive__Closure_Ortrancl(X5,X3)),X56)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__closed__trancl)). 6.97/7.20 fof(fact_inj__image__mem__iff, axiom, ![X4, X2, X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))=>(hBOOL(hAPP(hAPP(c_member(X5),X2),X4))<=>hBOOL(hAPP(hAPP(c_member(X12),hAPP(X18,X2)),hAPP(c_Set_Oimage(X5,X12,X18),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__image__mem__iff)). 6.97/7.20 fof(fact_zero__le__power__abs, axiom, ![X25, X30, X8]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),X30)),X25)))<=class_Rings_Olinordered__idom(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__power__abs)). 6.97/7.20 fof(fact_zdiv__eq__0__iff, axiom, ![X33, X47]:(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X47),X33)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)<=>(X33=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)),X47))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X47),X33)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33),X47))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X47),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__eq__0__iff)). 6.97/7.20 fof(fact_INF1__E, axiom, ![X2, X1, X11, X4, X12, X5]:(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X12,tc_HOL_Obool)),X4),X11),X1))=>(~(hBOOL(hAPP(hAPP(X11,X2),X1)))=>~(hBOOL(hAPP(hAPP(c_member(X5),X2),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF1__E)). 6.97/7.20 fof(fact_Max_Oeq__fold__idem_H, axiom, ![X2, X4, X5]:(class_Orderings_Olinorder(X5)=>(hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X2),X4)=c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X2),X4))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max_Oeq__fold__idem_H)). 6.97/7.20 fof(fact_mod__pos__pos, axiom, ![X29, X30]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X29))=>c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X29)=hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X30,X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__pos__pos)). 6.97/7.20 fof(fact_Min_Oeq__fold__idem_H, axiom, ![X2, X4, X5]:(class_Orderings_Olinorder(X5)=>(c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X2),X4))=hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X2),X4)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min_Oeq__fold__idem_H)). 6.97/7.20 fof(fact_sup__Sup__fold__sup, axiom, ![X11, X4, X5]:(class_Complete__Lattice_Ocomplete__lattice(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X11),X4)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X11),c_Complete__Lattice_OSup__class_OSup(X5,X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__Sup__fold__sup)). 6.97/7.20 fof(fact_min__max_Oinf__Sup__absorb, axiom, ![X2, X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hBOOL(hAPP(hAPP(c_member(X5),X2),X4))=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X2),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X4))=X2))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__Sup__absorb)). 6.97/7.20 fof(fact_min__max_Osup__Inf__absorb, axiom, ![X2, X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(X2=hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X2),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X4))<=hBOOL(hAPP(hAPP(c_member(X5),X2),X4))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__Inf__absorb)). 6.97/7.20 fof(fact_mod__neg__pos, axiom, ![X29, X30]:((hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X30,X29))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X29)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X29)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__neg__pos)). 6.97/7.20 fof(fact_distinct__listsum__conv__Setsum, axiom, ![X23, X5]:(class_Groups_Ocomm__monoid__add(X5)=>(hBOOL(hAPP(c_List_Odistinct(X5),X23))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X5),c_COMBI(X5)),hAPP(c_List_Oset(X5),X23))=hAPP(c_List_Omonoid__add__class_Olistsum(X5),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__listsum__conv__Setsum)). 6.97/7.20 fof(fact_nth__list__update__neq, axiom, ![X6, X41, X8, X27, X28]:(X28!=X27=>hAPP(hAPP(c_List_Onth(X8),hAPP(hAPP(c_List_Olist__update(X8,X41),X28),X6)),X27)=hAPP(hAPP(c_List_Onth(X8),X41),X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__list__update__neq)). 6.97/7.20 fof(fact_SUP1__E, axiom, ![X1, X11, X4, X12, X5]:(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X12,tc_HOL_Obool)),X4),X11),X1))=>~(![X22]:(~(hBOOL(hAPP(hAPP(X11,X22),X1)))<=hBOOL(hAPP(hAPP(c_member(X5),X22),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP1__E)). 6.97/7.20 fof(fact_divmod__int__rel__0, axiom, ![X29]:(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X29),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))))<=X29!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__rel__0)). 6.97/7.20 fof(fact_takeWhile__nth, axiom, ![X23, X17, X5, X46]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X17,X23))))=>hAPP(hAPP(c_List_Onth(X5),c_List_OtakeWhile(X5,X17,X23)),X46)=hAPP(hAPP(c_List_Onth(X5),X23),X46)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__nth)). 6.97/7.20 fof(fact_mod__pos__neg__trivial, axiom, ![X29, X30]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X30),X29)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X29)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X30),X29)),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)),X30))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__pos__neg__trivial)). 6.97/7.20 fof(fact_abs__mult__self, axiom, ![X30, X8]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),X30)),hAPP(c_Groups_Oabs__class_Oabs(X8),X30))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X30)<=class_Rings_Olinordered__idom(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__mult__self)). 6.97/7.20 fof(fact_field__le__mult__one__interval, axiom, ![X7, X6, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),X7))<=![X116]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X116))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X116),c_Groups_Oone__class_Oone(X8)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X116),X6)),X7)))))<=class_Fields_Olinordered__field__inverse__zero(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_field__le__mult__one__interval)). 6.97/7.20 fof(fact_field__le__epsilon, axiom, ![X7, X6, X8]:(class_Fields_Olinordered__field(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),X7))<=![X269]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X7),X269)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X269))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_field__le__epsilon)). 6.97/7.20 fof(fact_ord_OgreaterThanAtMost__iff, axiom, ![X51, X52, X192, X228, X47, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X47),c_SetInterval_Oord_OgreaterThanAtMost(X5,X228,X192,X52,X51)))<=>(hBOOL(hAPP(hAPP(X192,X52),X47))&hBOOL(hAPP(hAPP(X228,X47),X51)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ord_OgreaterThanAtMost__iff)). 6.97/7.20 fof(fact_ord_OatLeastLessThan__iff, axiom, ![X51, X52, X192, X228, X47, X5]:((hBOOL(hAPP(hAPP(X228,X52),X47))&hBOOL(hAPP(hAPP(X192,X47),X51)))<=>hBOOL(hAPP(hAPP(c_member(X5),X47),c_SetInterval_Oord_OatLeastLessThan(X5,X228,X192,X52,X51)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ord_OatLeastLessThan__iff)). 6.97/7.20 fof(fact_minus__mult__minus, axiom, ![X29, X30, X8]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X30)),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X29))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29)<=class_Rings_Oring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__mult__minus)). 6.97/7.20 fof(fact_mono__iff__le__Suc, axiom, ![X18, X5]:((c_Orderings_Oorder__class_Omono(tc_Nat_Onat,X5,X18)<=>![X48]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X18,X48)),hAPP(X18,hAPP(c_Nat_OSuc,X48)))))<=class_Orderings_Oorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mono__iff__le__Suc)). 6.97/7.20 fof(fact_nat__zero__less__power__iff, axiom, ![X32, X35]:(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),X35),X32)))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X35))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__zero__less__power__iff)). 6.97/7.20 fof(fact_psubsetD, axiom, ![X10, X11, X4, X5]:((hBOOL(hAPP(hAPP(c_member(X5),X10),X4))=>hBOOL(hAPP(hAPP(c_member(X5),X10),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X4),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_psubsetD)). 6.97/7.20 fof(fact_minus__divide__divide, axiom, ![X29, X30, X8]:(class_Fields_Ofield__inverse__zero(X8)=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X30),X29)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X30)),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__divide__divide)). 6.97/7.20 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J, axiom, ![X25, X6]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6))=>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),X6),X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J)). 6.97/7.20 fof(fact_card__gt__0__iff, axiom, ![X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X5),X4)))<=>(X4!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))&hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__gt__0__iff)). 6.97/7.20 fof(fact_take__butlast, axiom, ![X41, X8, X25]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)))=>hAPP(hAPP(c_List_Otake(X8),X25),c_List_Obutlast(X8,X41))=hAPP(hAPP(c_List_Otake(X8),X25),X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__butlast)). 6.97/7.20 fof(fact_all__interval__nat__def, axiom, ![X46, X47, X17]:(![X22]:(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X22),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X47),X46)))=>hBOOL(hAPP(X17,X22)))<=>c_List_Oall__interval__nat(X17,X47,X46)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_all__interval__nat__def)). 6.97/7.20 fof(fact_less__infI1, axiom, ![X29, X6, X30, X8]:(class_Lattices_Osemilattice__inf(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),X6))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X30),X29)),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__infI1)). 6.97/7.20 fof(fact_list__all__length, axiom, ![X23, X17, X5]:(![X48]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X48),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)))=>hBOOL(hAPP(X17,hAPP(hAPP(c_List_Onth(X5),X23),X48))))<=>c_List_Olist__all(X5,X17,X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all__length)). 6.97/7.20 fof(fact_mult__less__cancel1, axiom, ![X32, X34, X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X34)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X32)))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34),X32))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__less__cancel1)). 6.97/7.20 fof(fact_less__infI2, axiom, ![X30, X6, X29, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X30),X29)),X6))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X29),X6)))<=class_Lattices_Osemilattice__inf(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__infI2)). 6.97/7.20 fof(fact_le__infI1, axiom, ![X29, X6, X30, X8]:(class_Lattices_Osemilattice__inf(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),X6))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X30),X29)),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__infI1)). 6.97/7.20 fof(fact_le__infI2, axiom, ![X30, X6, X29, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X29),X6))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X30),X29)),X6)))<=class_Lattices_Osemilattice__inf(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__infI2)). 6.97/7.20 fof(fact_dvd__mult2, axiom, ![X31, X29, X30, X8]:(class_Rings_Ocomm__semiring__1(X8)=>(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X8),X30),X29))=>hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X8),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X31))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dvd__mult2)). 6.97/7.20 fof(fact_ComplI, axiom, ![X4, X10, X5]:(~(hBOOL(hAPP(hAPP(c_member(X5),X10),X4)))=>hBOOL(hAPP(hAPP(c_member(X5),X10),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ComplI)). 6.97/7.20 fof(fact_filter__id__conv, axiom, ![X23, X17, X5]:(hAPP(c_List_Ofilter(X5,X17),X23)=X23<=>![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X23)))=>hBOOL(hAPP(X17,X22)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__id__conv)). 6.97/7.20 fof(fact_nonzero__minus__divide__right, axiom, ![X30, X29, X8]:(class_Rings_Odivision__ring(X8)=>(c_Groups_Ozero__class_Ozero(X8)!=X29=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X30),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X29))=hAPP(c_Groups_Ouminus__class_Ouminus(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X30),X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nonzero__minus__divide__right)). 6.97/7.20 fof(fact_dvd__mult, axiom, ![X29, X31, X30, X8]:(class_Rings_Ocomm__semiring__1(X8)=>(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X8),X30),X31))=>hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X8),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X31))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dvd__mult)). 6.97/7.20 fof(fact_less__supI1, axiom, ![X29, X30, X6, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X6),X30))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X30),X29))))<=class_Lattices_Osemilattice__sup(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__supI1)). 6.97/7.20 fof(fact_less__supI2, axiom, ![X30, X29, X6, X8]:(class_Lattices_Osemilattice__sup(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X30),X29)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X6),X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__supI2)). 6.97/7.20 fof(fact_le__supI1, axiom, ![X29, X30, X6, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),X30))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X30),X29))))<=class_Lattices_Osemilattice__sup(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__supI1)). 6.97/7.20 fof(fact_insort__insert__key__triv, axiom, ![X23, X12, X35, X18, X5]:((hBOOL(hAPP(hAPP(c_member(X5),hAPP(X18,X35)),hAPP(c_Set_Oimage(X12,X5,X18),hAPP(c_List_Oset(X12),X23))))=>X23=c_List_Olinorder__class_Oinsort__insert__key(X12,X5,X18,X35,X23))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__insert__key__triv)). 6.97/7.20 fof(fact_le__supI2, axiom, ![X30, X29, X6, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),X29))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X30),X29))))<=class_Lattices_Osemilattice__sup(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__supI2)). 6.97/7.20 fof(fact_set__insort__insert, axiom, ![X23, X35, X5]:(class_Orderings_Olinorder(X5)=>hAPP(hAPP(c_Set_Oinsert(X5),X35),hAPP(c_List_Oset(X5),X23))=hAPP(c_List_Oset(X5),c_List_Olinorder__class_Oinsort__insert__key(X5,X5,c_COMBI(X5),X35,X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__insort__insert)). 6.97/7.20 fof(fact_finite__Un, axiom, ![X117, X55, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X55),X117)))<=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X117))&hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X55)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Un)). 6.97/7.20 fof(fact_Suc__diff__le, axiom, ![X36, X25]:(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),X25))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X36)),X25)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X36))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__diff__le)). 6.97/7.20 fof(fact_SigmaD1, axiom, ![X11, X4, X1, X2, X12, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X2),X1)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X4),X11)))=>hBOOL(hAPP(hAPP(c_member(X5),X2),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SigmaD1)). 6.97/7.20 fof(fact_f__inv__into__f, axiom, ![X4, X18, X12, X38, X5]:(hAPP(X18,hAPP(c_Hilbert__Choice_Oinv__into(X12,X5,X4,X18),X38))=X38<=hBOOL(hAPP(hAPP(c_member(X5),X38),hAPP(c_Set_Oimage(X12,X5,X18),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_f__inv__into__f)). 6.97/7.20 fof(fact_zero__less__two, axiom, ![X8]:(class_Rings_Olinordered__semidom(X8)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),c_Groups_Oone__class_Oone(X8)),c_Groups_Oone__class_Oone(X8))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__two)). 6.97/7.20 fof(fact_order__less__trans, axiom, ![X26, X7, X6, X8]:(class_Orderings_Opreorder(X8)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X6),X26))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X7),X26)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X6),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__less__trans)). 6.97/7.20 fof(fact_order__le__less__trans, axiom, ![X26, X7, X6, X8]:(class_Orderings_Opreorder(X8)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X7),X26))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X6),X26)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__le__less__trans)). 6.97/7.20 fof(fact_order__less__le__trans, axiom, ![X26, X7, X6, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X6),X7))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X7),X26))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X6),X26))))<=class_Orderings_Opreorder(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__less__le__trans)). 6.97/7.20 fof(fact_xt1_I10_J, axiom, ![X26, X6, X7, X8]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X26),X7))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X26),X6)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X7),X6)))<=class_Orderings_Oorder(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_xt1_I10_J)). 6.97/7.20 fof(fact_xt1_I8_J, axiom, ![X26, X6, X7, X8]:(class_Orderings_Oorder(X8)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X26),X6))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X26),X7)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X7),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_xt1_I8_J)). 6.97/7.20 fof(fact_the__inv__f__f, axiom, ![X35, X18, X12, X5]:(hAPP(c_Fun_Othe__inv__into(X5,X12,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X18),hAPP(X18,X35))=X35<=c_Fun_Oinj__on(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__inv__f__f)). 6.97/7.20 fof(fact_inv__f__f, axiom, ![X35, X18, X12, X5]:(hAPP(c_Hilbert__Choice_Oinv__into(X5,X12,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X18),hAPP(X18,X35))=X35<=c_Fun_Oinj__on(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inv__f__f)). 6.97/7.20 fof(fact_tl__append2, axiom, ![X45, X8, X41]:(hAPP(c_List_Otl(X8),hAPP(hAPP(c_List_Oappend(X8),X41),X45))=hAPP(hAPP(c_List_Oappend(X8),hAPP(c_List_Otl(X8),X41)),X45)<=c_List_Olist_ONil(X8)!=X41), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tl__append2)). 6.97/7.20 fof(fact_xt1_I7_J, axiom, ![X26, X6, X7, X8]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X26),X7))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X26),X6)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X7),X6)))<=class_Orderings_Oorder(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_xt1_I7_J)). 6.97/7.20 fof(fact_order__trans, axiom, ![X26, X7, X6, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),X7))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X7),X26))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),X26))))<=class_Orderings_Opreorder(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__trans)). 6.97/7.20 fof(fact_xt1_I6_J, axiom, ![X26, X6, X7, X8]:(class_Orderings_Oorder(X8)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X26),X7))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X26),X6)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X7),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_xt1_I6_J)). 6.97/7.20 fof(fact_less__le__not__le, axiom, ![X38, X35, X5]:(class_Orderings_Opreorder(X5)=>((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X38),X35)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),X38)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X35),X38)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__le__not__le)). 6.97/7.20 fof(fact_less__bin__lemma, axiom, ![X52, X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33),X52))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X33),X52)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__bin__lemma)). 6.97/7.20 fof(fact_minus__divide__left, axiom, ![X29, X30, X8]:(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X30)),X29)=hAPP(c_Groups_Ouminus__class_Ouminus(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X30),X29))<=class_Rings_Odivision__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__divide__left)). 6.97/7.20 fof(fact_minus__mult__left, axiom, ![X29, X30, X8]:(class_Rings_Oring(X8)=>hAPP(c_Groups_Ouminus__class_Ouminus(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X30)),X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__mult__left)). 6.97/7.20 fof(fact_minus__mult__commute, axiom, ![X29, X30, X8]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X30)),X29)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X29))<=class_Rings_Oring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__mult__commute)). 6.97/7.20 fof(fact_linorder__cases, axiom, ![X7, X6, X8]:(class_Orderings_Olinorder(X8)=>(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X6),X7)))=>(X7!=X6=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X7),X6))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_linorder__cases)). 6.97/7.20 fof(fact_transfer__int__nat__relations_I2_J, axiom, ![X38, X35]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X35),X38))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X35)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X38)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__relations_I2_J)). 6.97/7.20 fof(fact_transfer__int__nat__relations_I3_J, axiom, ![X38, X35]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X35)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X38)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X35),X38))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__relations_I3_J)). 6.97/7.20 fof(fact_distinct__conv__nth, axiom, ![X23, X5]:(hBOOL(hAPP(c_List_Odistinct(X5),X23))<=>![X42]:(![X43]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)))=>(hAPP(hAPP(c_List_Onth(X5),X23),X42)!=hAPP(hAPP(c_List_Onth(X5),X23),X43)<=X43!=X42))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__conv__nth)). 6.97/7.20 fof(fact_zero__less__diff, axiom, ![X34, X32]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34),X32))<=>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),X32),X34)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__diff)). 6.97/7.20 fof(fact_lists__accD, axiom, ![X3, X23, X5]:(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X23),c_List_Olists(X5,c_Wellfounded_Oacc(X5,X3))))=>hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X23),c_Wellfounded_Oacc(tc_List_Olist(X5),c_List_Olistrel1(X5,X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists__accD)). 6.97/7.20 fof(fact_linorder__neqE__linordered__idom, axiom, ![X7, X6, X8]:((X6!=X7=>(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X6),X7)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X7),X6))))<=class_Rings_Olinordered__idom(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_linorder__neqE__linordered__idom)). 6.97/7.20 fof(fact_transfer__int__nat__quantifiers_I2_J, axiom, ![X17]:(?[X22]:(hBOOL(hAPP(X17,X22))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22)))<=>?[X22]:hBOOL(hAPP(X17,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__quantifiers_I2_J)). 6.97/7.20 fof(fact_sgn__times, axiom, ![X29, X30, X8]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Osgn__class_Osgn(X8,X30)),c_Groups_Osgn__class_Osgn(X8,X29))=c_Groups_Osgn__class_Osgn(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29))<=class_Rings_Olinordered__idom(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__times)). 6.97/7.20 fof(fact_sorted__map__remove1, axiom, ![X35, X23, X18, X12, X5]:((c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X12,X5),X18),c_List_Oremove1(X12,X35,X23)))<=c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X12,X5),X18),X23)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__map__remove1)). 6.97/7.20 fof(fact_append__in__listsp__conv, axiom, ![X84, X23, X4, X5]:((hBOOL(hAPP(c_List_Olistsp(X5,X4),X84))&hBOOL(hAPP(c_List_Olistsp(X5,X4),X23)))<=>hBOOL(hAPP(c_List_Olistsp(X5,X4),hAPP(hAPP(c_List_Oappend(X5),X23),X84)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__in__listsp__conv)). 6.97/7.20 fof(fact_zle__trans, axiom, ![X19, X27, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X28),X27))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X27),X19))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X28),X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zle__trans)). 6.97/7.20 fof(fact_le__trans, axiom, ![X19, X27, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28),X27))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X27),X19))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28),X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__trans)). 6.97/7.20 fof(fact_min__max_Ole__infI2, axiom, ![X30, X6, X29, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X30),X29)),X6))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X29),X6)))<=class_Orderings_Olinorder(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ole__infI2)). 6.97/7.20 fof(fact_minus__mult__right, axiom, ![X29, X30, X8]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X29))=hAPP(c_Groups_Ouminus__class_Ouminus(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29))<=class_Rings_Oring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__mult__right)). 6.97/7.20 fof(fact_min__max_Oless__supI1, axiom, ![X29, X30, X6, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X6),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X30),X29)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X6),X30)))<=class_Orderings_Olinorder(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oless__supI1)). 6.97/7.20 fof(fact_min__max_Oless__supI2, axiom, ![X30, X29, X6, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X6),X29))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X6),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X30),X29))))<=class_Orderings_Olinorder(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oless__supI2)). 6.97/7.20 fof(fact_BIJ, axiom, ![X11, X12, X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X11))=>(?[X185]:c_Fun_Obij__betw(X5,X12,X185,X4,X11)<=>hAPP(c_Finite__Set_Ocard(X12),X11)=hAPP(c_Finite__Set_Ocard(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_BIJ)). 6.97/7.20 fof(fact_takeWhile_Osimps_I2_J, axiom, ![X23, X5, X35, X17]:((hBOOL(hAPP(X17,X35))=>hAPP(hAPP(c_List_Olist_OCons(X5),X35),c_List_OtakeWhile(X5,X17,X23))=c_List_OtakeWhile(X5,X17,hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23)))&(~(hBOOL(hAPP(X17,X35)))=>c_List_OtakeWhile(X5,X17,hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23))=c_List_Olist_ONil(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile_Osimps_I2_J)). 6.97/7.20 fof(fact_minus__divide__right, axiom, ![X29, X30, X8]:(class_Fields_Ofield__inverse__zero(X8)=>hAPP(c_Groups_Ouminus__class_Ouminus(X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X30),X29))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X30),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__divide__right)). 6.97/7.20 fof(fact_min__max_Ole__supI2, axiom, ![X30, X29, X6, X8]:(class_Orderings_Olinorder(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),X29))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X30),X29))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ole__supI2)). 6.97/7.20 fof(fact_PowI, axiom, ![X11, X4, X5]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Set_OPow(X5),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_PowI)). 6.97/7.20 fof(fact_subsetI, axiom, ![X11, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))<=![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X4))=>hBOOL(hAPP(hAPP(c_member(X5),X22),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subsetI)). 6.97/7.20 fof(fact_z3div__def, axiom, ![X19, X93]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X93))=>c_SMT_Oz3div(X19,X93)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19),X93))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X93)))=>c_SMT_Oz3div(X19,X93)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X93))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_z3div__def)). 6.97/7.20 fof(fact_mod__geq, axiom, ![X25, X36]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X36),X25)))=>c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),X25),X25)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X36,X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__geq)). 6.97/7.20 fof(fact_add__diff__inverse, axiom, ![X25, X36]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X36),X25)))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),X25))=X36), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__diff__inverse)). 6.97/7.20 fof(fact_list__all2__append, axiom, ![X217, X218, X17, X84, X12, X23, X5]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12)),X84)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)=>((c_List_Olist__all2(X5,X12,X17,X23,X84)&c_List_Olist__all2(X5,X12,X17,X218,X217))<=>c_List_Olist__all2(X5,X12,X17,hAPP(hAPP(c_List_Oappend(X5),X23),X218),hAPP(hAPP(c_List_Oappend(X12),X84),X217)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__append)). 6.97/7.20 fof(fact_takeWhile__eq__all__conv, axiom, ![X23, X17, X5]:(![X22]:(hBOOL(hAPP(X17,X22))<=hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X23))))<=>c_List_OtakeWhile(X5,X17,X23)=X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__eq__all__conv)). 6.97/7.20 fof(fact_mult__left__idem, axiom, ![X29, X30, X8]:(class_Lattices_Oab__semigroup__idem__mult(X8)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__left__idem)). 6.97/7.20 fof(fact_inj__on__Int, axiom, ![X11, X4, X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,X4)=>(c_Fun_Oinj__on(X5,X12,X18,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11))<=c_Fun_Oinj__on(X5,X12,X18,X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__Int)). 6.97/7.20 fof(fact_finite__UNIV__inj__surj, axiom, ![X18, X5]:((hAPP(c_Set_Oimage(X5,X5,X18),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))<=c_Fun_Oinj__on(X5,X5,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__UNIV__inj__surj)). 6.97/7.20 fof(fact_finite__UNIV__surj__inj, axiom, ![X18, X5]:((c_Fun_Oinj__on(X5,X5,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))<=hAPP(c_Set_Oimage(X5,X5,X18),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__UNIV__surj__inj)). 6.97/7.20 fof(fact_add__minus__cancel, axiom, ![X29, X30, X8]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X30)),X29))=X29<=class_Groups_Ogroup__add(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__minus__cancel)). 6.97/7.20 fof(fact_minus__add__cancel, axiom, ![X29, X30, X8]:(class_Groups_Ogroup__add(X8)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X30)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29))=X29), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__add__cancel)). 6.97/7.20 fof(fact_bex__reg__eqv, axiom, ![X17, X67, X5]:((?[X76]:hBOOL(hAPP(X17,X76))<=>?[X22]:(hBOOL(hAPP(X17,X22))&hBOOL(hAPP(hAPP(c_member(X5),X22),c_Quotient_ORespects(X5,X67)))))<=c_Equiv__Relations_Oequivp(X5,X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bex__reg__eqv)). 6.97/7.20 fof(fact_finite__induct, axiom, ![X17, X55, X5]:((hBOOL(hAPP(X17,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))=>(hBOOL(hAPP(X17,X55))<=![X22, X234]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X234))=>((hBOOL(hAPP(X17,X234))=>hBOOL(hAPP(X17,hAPP(hAPP(c_Set_Oinsert(X5),X22),X234))))<=~(hBOOL(hAPP(hAPP(c_member(X5),X22),X234)))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X55))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__induct)). 6.97/7.20 fof(fact_sup_Oleft__idem, axiom, ![X29, X30, X8]:(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X30),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X30),X29))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X30),X29)<=class_Lattices_Osemilattice__sup(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup_Oleft__idem)). 6.97/7.20 fof(fact_neg__less__0__iff__less, axiom, ![X2, X5]:(class_Groups_Oordered__ab__group__add(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X2)),c_Groups_Ozero__class_Ozero(X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__less__0__iff__less)). 6.97/7.20 fof(fact_neg__le__0__iff__le, axiom, ![X2, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X2)),c_Groups_Ozero__class_Ozero(X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X2)))<=class_Groups_Oordered__ab__group__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__le__0__iff__le)). 6.97/7.20 fof(fact_neg__0__less__iff__less, axiom, ![X2, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X2)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),c_Groups_Ozero__class_Ozero(X5))))<=class_Groups_Oordered__ab__group__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__0__less__iff__less)). 6.97/7.20 fof(fact_neg__0__le__iff__le, axiom, ![X2, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X2),c_Groups_Ozero__class_Ozero(X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X2))))<=class_Groups_Oordered__ab__group__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__0__le__iff__le)). 6.97/7.20 fof(fact_congruent2__implies__congruent, axiom, ![X2, X18, X151, X62, X12, X153, X4, X5]:((c_Equiv__Relations_Ocongruent2(X5,X12,X62,X153,X151,X18)=>(hBOOL(hAPP(hAPP(c_member(X5),X2),X4))=>c_Equiv__Relations_Ocongruent(X12,X62,X151,hAPP(X18,X2))))<=c_Equiv__Relations_Oequiv(X5,X4,X153)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_congruent2__implies__congruent)). 6.97/7.20 fof(fact_endo__inj__surj, axiom, ![X18, X4, X5]:(((X4=hAPP(c_Set_Oimage(X5,X5,X18),X4)<=c_Fun_Oinj__on(X5,X5,X18,X4))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X5,X18),X4)),X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_endo__inj__surj)). 6.97/7.20 fof(fact_rtrancl__subset, axiom, ![X44, X67, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X67),X44))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X44),c_Transitive__Closure_Ortrancl(X5,X67)))=>c_Transitive__Closure_Ortrancl(X5,X67)=c_Transitive__Closure_Ortrancl(X5,X44))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__subset)). 6.97/7.20 fof(fact_inf__sup__aci_I8_J, axiom, ![X7, X6, X8]:(class_Lattices_Olattice(X8)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),X7))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__aci_I8_J)). 6.97/7.20 fof(fact_of__nat__0__less__iff, axiom, ![X32, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X32))))<=class_Rings_Olinordered__semidom(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__0__less__iff)). 6.97/7.20 fof(fact_sorted__nth__monoI, axiom, ![X41, X8]:((c_List_Olinorder__class_Osorted(X8,X41)<=![X42, X43]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_List_Onth(X8),X41),X42)),hAPP(hAPP(c_List_Onth(X8),X41),X43)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X43))))<=class_Orderings_Olinorder(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__nth__monoI)). 6.97/7.20 fof(fact_ord_OatLeastAtMost__iff, axiom, ![X51, X52, X228, X47, X5]:((hBOOL(hAPP(hAPP(X228,X47),X51))&hBOOL(hAPP(hAPP(X228,X52),X47)))<=>hBOOL(hAPP(hAPP(c_member(X5),X47),c_SetInterval_Oord_OatLeastAtMost(X5,X228,X52,X51)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ord_OatLeastAtMost__iff)). 6.97/7.20 fof(fact_ord_OgreaterThanLessThan__iff, axiom, ![X51, X52, X192, X47, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X47),c_SetInterval_Oord_OgreaterThanLessThan(X5,X192,X52,X51)))<=>(hBOOL(hAPP(hAPP(X192,X47),X51))&hBOOL(hAPP(hAPP(X192,X52),X47)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ord_OgreaterThanLessThan__iff)). 6.97/7.20 fof(fact_rev__predicate2D, axiom, ![X104, X12, X5, X38, X35, X17]:(hBOOL(hAPP(hAPP(X17,X35),X38))=>(hBOOL(hAPP(hAPP(X104,X35),X38))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X12,tc_HOL_Obool))),X17),X104)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__predicate2D)). 6.97/7.20 fof(fact_inf__left__idem, axiom, ![X7, X6, X8]:(class_Lattices_Osemilattice__inf(X8)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),X7)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__left__idem)). 6.97/7.20 fof(fact_Max_Oin__idem, axiom, ![X35, X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(c_Big__Operators_Olinorder__class_OMax(X5,X4)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X35),c_Big__Operators_Olinorder__class_OMax(X5,X4))<=hBOOL(hAPP(hAPP(c_member(X5),X35),X4))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max_Oin__idem)). 6.97/7.20 fof(fact_Sup__fin_Oin__idem, axiom, ![X35, X4, X5]:(((hBOOL(hAPP(hAPP(c_member(X5),X35),X4))=>c_Big__Operators_Olattice__class_OSup__fin(X5,X4)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X35),c_Big__Operators_Olattice__class_OSup__fin(X5,X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Lattices_Olattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Oin__idem)). 6.97/7.20 fof(fact_Min_Oin__idem, axiom, ![X35, X4, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(c_Big__Operators_Olinorder__class_OMin(X5,X4)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X35),c_Big__Operators_Olinorder__class_OMin(X5,X4))<=hBOOL(hAPP(hAPP(c_member(X5),X35),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min_Oin__idem)). 6.97/7.20 fof(fact_inf__sup__aci_I4_J, axiom, ![X7, X6, X8]:(class_Lattices_Olattice(X8)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),X7)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__aci_I4_J)). 6.97/7.20 fof(fact_Suc__times__mod__eq, axiom, ![X36, X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X19))=>c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X36)),X19)=c_Groups_Oone__class_Oone(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__times__mod__eq)). 6.97/7.20 fof(fact_power__abs, axiom, ![X25, X30, X8]:(class_Rings_Olinordered__idom(X8)=>hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25))=hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),X30)),X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__abs)). 6.97/7.20 fof(fact_Inf__fin_Oin__idem, axiom, ![X35, X4, X5]:(class_Lattices_Olattice(X5)=>((hBOOL(hAPP(hAPP(c_member(X5),X35),X4))=>c_Big__Operators_Olattice__class_OInf__fin(X5,X4)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X35),c_Big__Operators_Olattice__class_OInf__fin(X5,X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Oin__idem)). 6.97/7.20 fof(fact_listsum__simps_I2_J, axiom, ![X41, X6, X8]:(class_Groups_Omonoid__add(X8)=>hAPP(c_List_Omonoid__add__class_Olistsum(X8),hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X6),hAPP(c_List_Omonoid__add__class_Olistsum(X8),X41))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__simps_I2_J)). 6.97/7.20 fof(fact_min__max_Osup_Oleft__idem, axiom, ![X29, X30, X8]:(hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X30),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X30),X29))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X30),X29)<=class_Orderings_Olinorder(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup_Oleft__idem)). 6.97/7.20 fof(fact_in__set__dropD, axiom, ![X23, X32, X35, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Odrop(X5),X32),X23))))=>hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__dropD)). 6.97/7.20 fof(fact_in__set__takeD, axiom, ![X23, X32, X35, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Otake(X5),X32),X23))))=>hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__takeD)). 6.97/7.20 fof(fact_transfer__int__nat__quantifiers_I1_J, axiom, ![X17]:(![X22]:hBOOL(hAPP(X17,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22)))<=>![X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22))=>hBOOL(hAPP(X17,X22)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__quantifiers_I1_J)). 6.97/7.20 fof(fact_min__max_Oinf_Oleft__idem, axiom, ![X29, X30, X8]:(class_Orderings_Olinorder(X8)=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X30),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X30),X29))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X30),X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf_Oleft__idem)). 6.97/7.20 fof(fact_list__ex__length, axiom, ![X23, X17, X5]:(c_List_Olist__ex(X5,X17,X23)<=>?[X48]:(hBOOL(hAPP(X17,hAPP(hAPP(c_List_Onth(X5),X23),X48)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X48),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex__length)). 6.97/7.20 fof(fact_nth__length__takeWhile, axiom, ![X23, X17, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X17,X23))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)))=>~(hBOOL(hAPP(X17,hAPP(hAPP(c_List_Onth(X5),X23),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X17,X23))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__length__takeWhile)). 6.97/7.20 fof(fact_lfp__lemma2, axiom, ![X18, X5]:((c_Orderings_Oorder__class_Omono(X5,X5,X18)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X18,c_Inductive_Ocomplete__lattice__class_Olfp(X5,X18))),c_Inductive_Ocomplete__lattice__class_Olfp(X5,X18))))<=class_Complete__Lattice_Ocomplete__lattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lfp__lemma2)). 6.97/7.20 fof(fact_gfp__lemma3, axiom, ![X18, X5]:(class_Complete__Lattice_Ocomplete__lattice(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X18,c_Inductive_Ocomplete__lattice__class_Ogfp(X5,X18))),c_Inductive_Ocomplete__lattice__class_Ogfp(X5,X18)))<=c_Orderings_Oorder__class_Omono(X5,X5,X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_gfp__lemma3)). 6.97/7.20 fof(fact_lfp__lemma3, axiom, ![X18, X5]:(class_Complete__Lattice_Ocomplete__lattice(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Inductive_Ocomplete__lattice__class_Olfp(X5,X18)),hAPP(X18,c_Inductive_Ocomplete__lattice__class_Olfp(X5,X18))))<=c_Orderings_Oorder__class_Omono(X5,X5,X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lfp__lemma3)). 6.97/7.20 fof(fact_gfp__lemma2, axiom, ![X18, X5]:(class_Complete__Lattice_Ocomplete__lattice(X5)=>(c_Orderings_Oorder__class_Omono(X5,X5,X18)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Inductive_Ocomplete__lattice__class_Ogfp(X5,X18)),hAPP(X18,c_Inductive_Ocomplete__lattice__class_Ogfp(X5,X18)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_gfp__lemma2)). 6.97/7.20 fof(fact_all__interval__int__def, axiom, ![X46, X47, X17]:(![X22]:(hBOOL(hAPP(X17,X22))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X22),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X47,X46))))<=>c_List_Oall__interval__int(X17,X47,X46)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_all__interval__int__def)). 6.97/7.20 fof(fact_Abs__Integ__induct, axiom, ![X35, X17]:(![X72]:(hBOOL(hAPP(X17,hAPP(c_Int_OAbs__Integ,X72)))<=hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X72),c_Int_OInteg)))=>hBOOL(hAPP(X17,X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Abs__Integ__induct)). 6.97/7.20 fof(fact_Ball__set__list__all, axiom, ![X17, X23, X5]:(c_List_Olist__all(X5,X17,X23)<=>![X22]:(hBOOL(hAPP(X17,X22))<=hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X23))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ball__set__list__all)). 6.97/7.20 fof(fact_add__le__imp__le__left, axiom, ![X29, X30, X31, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),X29))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X31),X30)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X31),X29))))<=class_Groups_Oordered__ab__semigroup__add__imp__le(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__le__imp__le__left)). 6.97/7.20 fof(fact_folding__idem_Oidem__comp, axiom, ![X35, X55, X18, X12, X5]:(c_Finite__Set_Ofolding__idem(X5,X12,X18,X55)=>hAPP(X18,X35)=hAPP(c_Fun_Ocomp(X12,X12,X12,hAPP(X18,X35)),hAPP(X18,X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__idem_Oidem__comp)). 6.97/7.20 fof(fact_list__all__iff__raw, axiom, ![X23, X17, X5]:(c_List_Olist__all(X5,X17,X23)<=>![X22]:(hBOOL(hAPP(X17,X22))<=hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X23))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all__iff__raw)). 6.97/7.20 fof(fact_list__all__iff, axiom, ![X23, X17, X5]:(c_List_Olist__all(X5,X17,X23)<=>![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X23)))=>hBOOL(hAPP(X17,X22)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all__iff)). 6.97/7.20 fof(fact_mod__minus__eq, axiom, ![X29, X30, X8]:(class_Divides_Oring__div(X8)=>c_Divides_Odiv__class_Omod(X8,hAPP(c_Groups_Ouminus__class_Ouminus(X8),X30),X29)=c_Divides_Odiv__class_Omod(X8,hAPP(c_Groups_Ouminus__class_Ouminus(X8),c_Divides_Odiv__class_Omod(X8,X30,X29)),X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__minus__eq)). 6.97/7.20 fof(fact_wf__no__infinite__down__chainE, axiom, ![X18, X3, X5]:(~(![X145]:hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(X18,hAPP(c_Nat_OSuc,X145))),hAPP(X18,X145))),X3)))<=c_Wellfounded_Owf(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__no__infinite__down__chainE)). 6.97/7.20 fof(fact_SUP__const, axiom, ![X94, X5, X4, X12]:((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4=>X94=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X12),X4),hAPP(c_COMBK(X12,X5),X94)))<=class_Complete__Lattice_Ocomplete__lattice(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP__const)). 6.97/7.20 fof(fact_finite__nonempty__imp__fold1Set, axiom, ![X18, X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4=>?[X76]:hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X18,X4),X76)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__nonempty__imp__fold1Set)). 6.97/7.20 fof(fact_diff__eq__diff__less, axiom, ![X97, X10, X1, X2, X5]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X2),X1)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X10),X97)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),X97))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),X1))))<=class_Groups_Oordered__ab__group__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__eq__diff__less)). 6.97/7.20 fof(fact_diff__eq__diff__less__eq, axiom, ![X97, X10, X1, X2, X5]:(class_Groups_Oordered__ab__group__add(X5)=>(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X10),X97)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X2),X1)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X10),X97))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X2),X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__eq__diff__less__eq)). 6.97/7.20 fof(fact_INF__const, axiom, ![X94, X5, X4, X12]:(class_Complete__Lattice_Ocomplete__lattice(X12)=>(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X12),X4),hAPP(c_COMBK(X12,X5),X94))=X94<=X4!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF__const)). 6.97/7.20 fof(fact_image__uminus__greaterThan, axiom, ![X35, X5]:(hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X35))=hAPP(c_SetInterval_Oord__class_OlessThan(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X35))<=class_Groups_Oordered__ab__group__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__uminus__greaterThan)). 6.97/7.20 fof(fact_image__uminus__lessThan, axiom, ![X35, X5]:(hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X35))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X35))<=class_Groups_Oordered__ab__group__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__uminus__lessThan)). 6.97/7.20 fof(fact_image__uminus__atLeast, axiom, ![X35, X5]:(class_Groups_Oordered__ab__group__add(X5)=>hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X35))=hAPP(c_SetInterval_Oord__class_OatMost(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__uminus__atLeast)). 6.97/7.20 fof(fact_image__uminus__atMost, axiom, ![X35, X5]:(class_Groups_Oordered__ab__group__add(X5)=>hAPP(c_SetInterval_Oord__class_OatLeast(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X35))=hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__uminus__atMost)). 6.97/7.20 fof(fact_compl__unique, axiom, ![X7, X6, X8]:(((X7=hAPP(c_Groups_Ouminus__class_Ouminus(X8),X6)<=c_Orderings_Otop__class_Otop(X8)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),X7))<=c_Orderings_Obot__class_Obot(X8)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),X7))<=class_Lattices_Oboolean__algebra(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__unique)). 6.97/7.20 fof(fact_hd__map, axiom, ![X18, X12, X5, X23]:(hAPP(c_List_Ohd(X12),hAPP(hAPP(c_List_Omap(X5,X12),X18),X23))=hAPP(X18,hAPP(c_List_Ohd(X5),X23))<=X23!=c_List_Olist_ONil(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__map)). 6.97/7.20 fof(fact_Ints__minus, axiom, ![X2, X5]:((hBOOL(hAPP(hAPP(c_member(X5),X2),c_Int_Oring__1__class_OInts(X5)))=>hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X2)),c_Int_Oring__1__class_OInts(X5))))<=class_Rings_Oring__1(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__minus)). 6.97/7.20 fof(fact_listsp_Oequations_I2_J, axiom, ![X125, X103, X4, X5]:((hBOOL(hAPP(c_List_Olistsp(X5,X4),X125))&hBOOL(hAPP(X4,X103)))<=>hBOOL(hAPP(c_List_Olistsp(X5,X4),hAPP(hAPP(c_List_Olist_OCons(X5),X103),X125)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsp_Oequations_I2_J)). 6.97/7.20 fof(fact_of__int__less__0__iff, axiom, ![X14, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Oring__1__class_Oof__int(X5),X14)),c_Groups_Ozero__class_Ozero(X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))<=class_Rings_Olinordered__idom(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__less__0__iff)). 6.97/7.20 fof(fact_of__int__le__0__iff, axiom, ![X14, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Oring__1__class_Oof__int(X5),X14)),c_Groups_Ozero__class_Ozero(X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X14),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))<=class_Rings_Olinordered__idom(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__le__0__iff)). 6.97/7.20 fof(fact_of__int__0__less__iff, axiom, ![X14, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Oring__1__class_Oof__int(X5),X14))))<=class_Rings_Olinordered__idom(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__0__less__iff)). 6.97/7.20 fof(fact_of__int__0__le__iff, axiom, ![X14, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Oring__1__class_Oof__int(X5),X14)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14)))<=class_Rings_Olinordered__idom(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__0__le__iff)). 6.97/7.20 fof(fact_Max__in, axiom, ![X4, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hBOOL(hAPP(hAPP(c_member(X5),c_Big__Operators_Olinorder__class_OMax(X5,X4)),X4))<=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max__in)). 6.97/7.20 fof(fact_Min__in, axiom, ![X4, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(X4!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>hBOOL(hAPP(hAPP(c_member(X5),c_Big__Operators_Olinorder__class_OMin(X5,X4)),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min__in)). 6.97/7.20 fof(fact_lfp__lowerbound, axiom, ![X4, X18, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Inductive_Ocomplete__lattice__class_Olfp(X5,X18)),X4))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X18,X4)),X4)))<=class_Complete__Lattice_Ocomplete__lattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lfp__lowerbound)). 6.97/7.20 fof(fact_gfp__upperbound, axiom, ![X18, X56, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X56),hAPP(X18,X56)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X56),c_Inductive_Ocomplete__lattice__class_Ogfp(X5,X18))))<=class_Complete__Lattice_Ocomplete__lattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_gfp__upperbound)). 6.97/7.20 fof(fact_map__eq__imp__length__eq, axiom, ![X84, X50, X62, X23, X18, X5, X12]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12)),X23)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X62)),X84)<=hAPP(hAPP(c_List_Omap(X62,X5),X50),X84)=hAPP(hAPP(c_List_Omap(X12,X5),X18),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__eq__imp__length__eq)). 6.97/7.20 fof(fact_linorder__le__cases, axiom, ![X7, X6, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X7),X6))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),X7))))<=class_Orderings_Olinorder(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_linorder__le__cases)). 6.97/7.20 fof(fact_rangeE, axiom, ![X18, X12, X1, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X1),hAPP(c_Set_Oimage(X12,X5,X18),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))))=>~(![X22]:hAPP(X18,X22)!=X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rangeE)). 6.97/7.20 fof(fact_zless__linear, axiom, ![X7, X6]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7),X6))|X6=X7|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zless__linear)). 6.97/7.20 fof(fact_abs__minus__le__zero, axiom, ![X30, X8]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),X30))),c_Groups_Ozero__class_Ozero(X8)))<=class_Groups_Oordered__ab__group__add__abs(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__minus__le__zero)). 6.97/7.20 fof(fact_equiv__comp__eq, axiom, ![X3, X4, X5]:(c_Equiv__Relations_Oequiv(X5,X4,X3)=>X3=hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(c_Relation_Oconverse(X5,X5),X3)),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__comp__eq)). 6.97/7.20 fof(fact_type__definition_OAbs__inject, axiom, ![X38, X35, X4, X90, X91, X12, X5]:(((hBOOL(hAPP(hAPP(c_member(X12),X38),X4))=>(X38=X35<=>hAPP(X90,X35)=hAPP(X90,X38)))<=hBOOL(hAPP(hAPP(c_member(X12),X35),X4)))<=c_Typedef_Otype__definition(X5,X12,X91,X90,X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_type__definition_OAbs__inject)). 6.97/7.20 fof(fact_distinct__zipI1, axiom, ![X45, X5, X41, X8]:(hBOOL(hAPP(c_List_Odistinct(X8),X41))=>hBOOL(hAPP(c_List_Odistinct(tc_prod(X8,X5)),hAPP(hAPP(c_List_Ozip(X8,X5),X41),X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__zipI1)). 6.97/7.20 fof(fact_distinct__zipI2, axiom, ![X41, X5, X45, X8]:(hBOOL(hAPP(c_List_Odistinct(X8),X45))=>hBOOL(hAPP(c_List_Odistinct(tc_prod(X5,X8)),hAPP(hAPP(c_List_Ozip(X5,X8),X41),X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__zipI2)). 6.97/7.20 fof(fact_div__mult__self1__is__m, axiom, ![X36, X25]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X36)),X25)=X36), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__self1__is__m)). 6.97/7.20 fof(fact_div__mult__self__is__m, axiom, ![X36, X25]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X25)),X25)=X36), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__self__is__m)). 6.97/7.20 fof(fact_linorder__neqE__nat, axiom, ![X7, X6]:(X7!=X6=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7),X6))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_linorder__neqE__nat)). 6.97/7.20 fof(fact_less__imp__diff__less, axiom, ![X25, X19, X27]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X27),X25)),X19))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X27),X19))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__imp__diff__less)). 6.97/7.20 fof(fact_inj__on__the__inv__into, axiom, ![X4, X18, X12, X5]:(c_Fun_Oinj__on(X12,X5,c_Fun_Othe__inv__into(X5,X12,X4,X18),hAPP(c_Set_Oimage(X5,X12,X18),X4))<=c_Fun_Oinj__on(X5,X12,X18,X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__the__inv__into)). 6.97/7.20 fof(fact_distinct__product, axiom, ![X45, X5, X41, X8]:((hBOOL(hAPP(c_List_Odistinct(X5),X45))=>hBOOL(hAPP(c_List_Odistinct(tc_prod(X8,X5)),c_Enum_Oproduct(X8,X5,X41,X45))))<=hBOOL(hAPP(c_List_Odistinct(X8),X41))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__product)). 6.97/7.20 fof(fact_sgn__if, axiom, ![X6, X8]:(((c_Groups_Ozero__class_Ozero(X8)=c_Groups_Osgn__class_Osgn(X8,X6)<=X6=c_Groups_Ozero__class_Ozero(X8))&(((c_Groups_Osgn__class_Osgn(X8,X6)=hAPP(c_Groups_Ouminus__class_Ouminus(X8),c_Groups_Oone__class_Oone(X8))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X6))))&(c_Groups_Osgn__class_Osgn(X8,X6)=c_Groups_Oone__class_Oone(X8)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X6))))<=X6!=c_Groups_Ozero__class_Ozero(X8)))<=class_Groups_Osgn__if(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__if)). 6.97/7.20 fof(fact_finite__Plus__iff, axiom, ![X11, X4, X12, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X5,X12)),c_Sum__Type_OPlus(X5,X12,X4,X11)))<=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))&hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Plus__iff)). 6.97/7.20 fof(fact_transfer__nat__int__set__relations_I2_J, axiom, ![X4, X35]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X35)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X4)))<=>hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X35),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__set__relations_I2_J)). 6.97/7.20 fof(fact_insert__iff, axiom, ![X4, X1, X2, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X2),hAPP(hAPP(c_Set_Oinsert(X5),X1),X4)))<=>(hBOOL(hAPP(hAPP(c_member(X5),X2),X4))|X1=X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__iff)). 6.97/7.20 fof(fact_termination__basic__simps_I1_J, axiom, ![X26, X7, X6]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X7))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7),X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_termination__basic__simps_I1_J)). 6.97/7.20 fof(fact_tl__replicate, axiom, ![X6, X8, X25]:(hAPP(c_List_Otl(X8),c_List_Oreplicate(X8,X25,X6))=c_List_Oreplicate(X8,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X6)<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tl__replicate)). 6.97/7.20 fof(fact_inj__on__imageI, axiom, ![X4, X18, X50, X62, X12, X5]:(c_Fun_Oinj__on(X5,X12,hAPP(c_Fun_Ocomp(X62,X12,X5,X50),X18),X4)=>c_Fun_Oinj__on(X62,X12,X50,hAPP(c_Set_Oimage(X5,X62,X18),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__imageI)). 6.97/7.20 fof(fact_fun__left__comm__idem_Ofun__comp__idem, axiom, ![X35, X18, X12, X5]:(c_Finite__Set_Ofun__left__comm__idem(X5,X12,X18)=>hAPP(X18,X35)=hAPP(c_Fun_Ocomp(X12,X12,X12,hAPP(X18,X35)),hAPP(X18,X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem_Ofun__comp__idem)). 6.97/7.20 fof(fact_trans__less__add2, axiom, ![X36, X27, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28),X27))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X27)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trans__less__add2)). 6.97/7.20 fof(fact_trans__le__add1, axiom, ![X36, X27, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27),X36)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28),X27))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trans__le__add1)). 6.97/7.20 fof(fact_append1__eq__conv, axiom, ![X38, X84, X35, X23, X5]:(hAPP(hAPP(c_List_Oappend(X5),X84),hAPP(hAPP(c_List_Olist_OCons(X5),X38),c_List_Olist_ONil(X5)))=hAPP(hAPP(c_List_Oappend(X5),X23),hAPP(hAPP(c_List_Olist_OCons(X5),X35),c_List_Olist_ONil(X5)))<=>(X35=X38&X84=X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append1__eq__conv)). 6.97/7.20 fof(fact_equivp__def, axiom, ![X67, X5]:(![X22, X72]:(hAPP(X67,X72)=hAPP(X67,X22)<=>hBOOL(hAPP(hAPP(X67,X22),X72)))<=>c_Equiv__Relations_Oequivp(X5,X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equivp__def)). 6.97/7.20 fof(fact_termination__basic__simps_I4_J, axiom, ![X7, X26, X6]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7),X26)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_termination__basic__simps_I4_J)). 6.97/7.20 fof(fact_Inf__fold__inf, axiom, ![X4, X5]:((hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),c_Orderings_Otop__class_Otop(X5)),X4)=c_Complete__Lattice_OInf__class_OInf(X5,X4)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Complete__Lattice_Ocomplete__lattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fold__inf)). 6.97/7.20 fof(fact_Sup__fold__sup, axiom, ![X4, X5]:(class_Complete__Lattice_Ocomplete__lattice(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>c_Complete__Lattice_OSup__class_OSup(X5,X4)=hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),c_Orderings_Obot__class_Obot(X5)),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fold__sup)). 6.97/7.20 fof(fact_posDivAlg__correct, axiom, ![X29, X30]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30))=>(hBOOL(hAPP(c_Divides_Odivmod__int__rel(X30,X29),c_Divides_OposDivAlg(X30,X29)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_posDivAlg__correct)). 6.97/7.20 fof(fact_negDivAlg__correct, axiom, ![X29, X30]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X29))=>hBOOL(hAPP(c_Divides_Odivmod__int__rel(X30,X29),c_Divides_OnegDivAlg(X30,X29))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negDivAlg__correct)). 6.97/7.20 fof(fact_rel__pow__0__E, axiom, ![X67, X38, X35, X5]:(X35=X38<=hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X67)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__0__E)). 6.97/7.20 fof(fact_abs__power__minus__one, axiom, ![X25, X8]:(hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OMin)),X25))=c_Groups_Oone__class_Oone(X8)<=(class_Rings_Olinordered__idom(X8)&class_Int_Onumber__ring(X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__power__minus__one)). 6.97/7.20 fof(fact_r__into__rtrancl, axiom, ![X3, X24, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X24),X3))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X24),c_Transitive__Closure_Ortrancl(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_r__into__rtrancl)). 6.97/7.20 fof(fact_less__Suc__eq__0__disj, axiom, ![X32, X34]:((X34=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|?[X43]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),X32))&hAPP(c_Nat_OSuc,X43)=X34))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34),hAPP(c_Nat_OSuc,X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__Suc__eq__0__disj)). 6.97/7.20 fof(fact_hd__in__set, axiom, ![X5, X23]:(hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_List_Ohd(X5),X23)),hAPP(c_List_Oset(X5),X23)))<=c_List_Olist_ONil(X5)!=X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__in__set)). 6.97/7.20 fof(fact_comm__monoid__big_Oinfinite, axiom, ![X50, X4, X55, X14, X18, X12, X5]:(c_Big__Operators_Ocomm__monoid__big(X5,X12,X18,X14,X55)=>(hAPP(hAPP(X55,X50),X4)=X14<=~(hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__monoid__big_Oinfinite)). 6.97/7.20 fof(fact_Min__le, axiom, ![X35, X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Big__Operators_Olinorder__class_OMin(X5,X4)),X35))<=hBOOL(hAPP(hAPP(c_member(X5),X35),X4))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min__le)). 6.97/7.20 fof(fact_Max__ge, axiom, ![X35, X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(hBOOL(hAPP(hAPP(c_member(X5),X35),X4))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),c_Big__Operators_Olinorder__class_OMax(X5,X4)))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max__ge)). 6.97/7.20 fof(fact_div__mult__self1__is__id, axiom, ![X30, X29, X8]:(class_Divides_Osemiring__div(X8)=>(hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X30)),X29)=X30<=X29!=c_Groups_Ozero__class_Ozero(X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__self1__is__id)). 6.97/7.20 fof(fact_div__mult__self2__is__id, axiom, ![X30, X29, X8]:(class_Divides_Osemiring__div(X8)=>(X29!=c_Groups_Ozero__class_Ozero(X8)=>X30=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29)),X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__self2__is__id)). 6.97/7.20 fof(fact_neg__less__nonneg, axiom, ![X2, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X2))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X2)),X2)))<=class_Groups_Olinordered__ab__group__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__less__nonneg)). 6.97/7.20 fof(fact_inj__on__def, axiom, ![X4, X18, X12, X5]:(![X22]:(![X115]:((X22=X115<=hAPP(X18,X115)=hAPP(X18,X22))<=hBOOL(hAPP(hAPP(c_member(X5),X115),X4)))<=hBOOL(hAPP(hAPP(c_member(X5),X22),X4)))<=>c_Fun_Oinj__on(X5,X12,X18,X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__def)). 6.97/7.20 fof(fact_minus__le__self__iff, axiom, ![X2, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X2))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X2)),X2)))<=class_Groups_Olinordered__ab__group__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__le__self__iff)). 6.97/7.20 fof(fact_less__minus__self__iff, axiom, ![X2, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),c_Groups_Ozero__class_Ozero(X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X2))))<=class_Rings_Olinordered__idom(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__minus__self__iff)). 6.97/7.20 fof(fact_le__minus__self__iff, axiom, ![X2, X5]:(class_Groups_Olinordered__ab__group__add(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X2),c_Groups_Ozero__class_Ozero(X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__minus__self__iff)). 6.97/7.20 fof(fact_of__nat__aux_Osimps_I2_J, axiom, ![X47, X32, X266, X5]:(c_Nat_Osemiring__1__class_Oof__nat__aux(X5,X266,X32,hAPP(X266,X47))=c_Nat_Osemiring__1__class_Oof__nat__aux(X5,X266,hAPP(c_Nat_OSuc,X32),X47)<=class_Rings_Osemiring__1(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__aux_Osimps_I2_J)). 6.97/7.20 fof(fact_last__drop, axiom, ![X41, X8, X25]:(c_List_Olast(X8,hAPP(hAPP(c_List_Odrop(X8),X25),X41))=c_List_Olast(X8,X41)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__drop)). 6.97/7.20 fof(fact_butlast__append, axiom, ![X41, X8, X45]:((c_List_Olist_ONil(X8)!=X45=>c_List_Obutlast(X8,hAPP(hAPP(c_List_Oappend(X8),X41),X45))=hAPP(hAPP(c_List_Oappend(X8),X41),c_List_Obutlast(X8,X45)))&(c_List_Olist_ONil(X8)=X45=>c_List_Obutlast(X8,X41)=c_List_Obutlast(X8,hAPP(hAPP(c_List_Oappend(X8),X41),X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_butlast__append)). 6.97/7.20 fof(fact_listrel__Nil1, axiom, ![X3, X23, X5]:(X23=c_List_Olist_ONil(X5)<=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)),c_List_Olist_ONil(X5)),X23)),c_List_Olistrel(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__Nil1)). 6.97/7.20 fof(fact_Bex__set__list__ex, axiom, ![X17, X23, X5]:(?[X22]:(hBOOL(hAPP(X17,X22))&hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X23))))<=>c_List_Olist__ex(X5,X17,X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Bex__set__list__ex)). 6.97/7.20 fof(fact_list__ex__iff, axiom, ![X23, X17, X5]:(c_List_Olist__ex(X5,X17,X23)<=>?[X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X23)))&hBOOL(hAPP(X17,X22)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex__iff)). 6.97/7.20 fof(fact_list__ex__iff__raw, axiom, ![X23, X17, X5]:(?[X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),hAPP(c_List_Oset(X5),X23)))&hBOOL(hAPP(X17,X22)))<=>c_List_Olist__ex(X5,X17,X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex__iff__raw)). 6.97/7.20 fof(fact_listrel__Nil2, axiom, ![X3, X23, X5]:(c_List_Olist_ONil(X5)=X23<=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)),X23),c_List_Olist_ONil(X5))),c_List_Olistrel(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__Nil2)). 6.97/7.20 fof(fact_filter__sort, axiom, ![X23, X18, X17, X5, X12]:(class_Orderings_Olinorder(X12)=>hAPP(c_List_Ofilter(X5,X17),c_List_Olinorder__class_Osort__key(X5,X12,X18,X23))=c_List_Olinorder__class_Osort__key(X5,X12,X18,hAPP(c_List_Ofilter(X5,X17),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__sort)). 6.97/7.20 fof(fact_Suc__lessI, axiom, ![X25, X36]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X36)),X25))<=hAPP(c_Nat_OSuc,X36)!=X25)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X36),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__lessI)). 6.97/7.20 fof(fact_le__mod__geq, axiom, ![X36, X25]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X36))=>c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),X25),X25)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X36,X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__mod__geq)). 6.97/7.20 fof(fact_diff__diff__cancel, axiom, ![X25, X28]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X28))=X28<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__diff__cancel)). 6.97/7.20 fof(fact_sup__Inf__absorb, axiom, ![X2, X4, X5]:(((hBOOL(hAPP(hAPP(c_member(X5),X2),X4))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X2),c_Big__Operators_Olattice__class_OInf__fin(X5,X4))=X2)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Lattices_Olattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__Inf__absorb)). 6.97/7.20 fof(fact_inf__Sup__absorb, axiom, ![X2, X4, X5]:(((X2=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X2),c_Big__Operators_Olattice__class_OSup__fin(X5,X4))<=hBOOL(hAPP(hAPP(c_member(X5),X2),X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Lattices_Olattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__Sup__absorb)). 6.97/7.20 fof(fact_trans__Int, axiom, ![X66, X3, X5]:(c_Relation_Otrans(X5,X3)=>(c_Relation_Otrans(X5,X66)=>c_Relation_Otrans(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),X66)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trans__Int)). 6.97/7.20 fof(fact_sym__Int, axiom, ![X66, X3, X5]:((c_Relation_Osym(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),X66))<=c_Relation_Osym(X5,X66))<=c_Relation_Osym(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sym__Int)). 6.97/7.20 fof(fact_sym__Un, axiom, ![X66, X3, X5]:((c_Relation_Osym(X5,X66)=>c_Relation_Osym(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),X66)))<=c_Relation_Osym(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sym__Un)). 6.97/7.20 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply, axiom, ![X50, X62, X18, X12, X5]:(c_Finite__Set_Ofun__left__comm__idem(X62,X12,hAPP(hAPP(c_COMBB(X5,tc_fun(X12,X12),X62),X18),X50))<=c_Finite__Set_Ofun__left__comm__idem(X5,X12,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem_Ofun__left__comm__idem__apply)). 6.97/7.20 fof(fact_fun__left__comm_Ofun__left__comm__apply, axiom, ![X50, X62, X18, X12, X5]:(c_Finite__Set_Ofun__left__comm(X62,X12,hAPP(hAPP(c_COMBB(X5,tc_fun(X12,X12),X62),X18),X50))<=c_Finite__Set_Ofun__left__comm(X5,X12,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofun__left__comm__apply)). 6.97/7.20 fof(fact_set__replicate, axiom, ![X35, X5, X32]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X32=>hAPP(c_List_Oset(X5),c_List_Oreplicate(X5,X32,X35))=hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__replicate)). 6.97/7.20 fof(fact_of__nat__Suc, axiom, ![X36, X8]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),c_Groups_Oone__class_Oone(X8)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),X36))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),hAPP(c_Nat_OSuc,X36))<=class_Rings_Osemiring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__Suc)). 6.97/7.20 fof(fact_remove1__idem, axiom, ![X23, X35, X5]:(~(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23))))=>X23=c_List_Oremove1(X5,X35,X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remove1__idem)). 6.97/7.20 fof(fact_fun__left__comm__idem_Ofun__left__idem, axiom, ![X14, X35, X18, X12, X5]:(hAPP(hAPP(X18,X35),X14)=hAPP(hAPP(X18,X35),hAPP(hAPP(X18,X35),X14))<=c_Finite__Set_Ofun__left__comm__idem(X5,X12,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem_Ofun__left__idem)). 6.97/7.20 fof(fact_in__set__sublistD, axiom, ![X15, X23, X35, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23)))<=hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),c_List_Osublist(X5,X23,X15))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__sublistD)). 6.97/7.20 fof(fact_divmod__int__rel__div, axiom, ![X70, X53, X29, X30]:(hBOOL(hAPP(c_Divides_Odivmod__int__rel(X30,X29),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X53),X70)))=>(X53=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),X29)<=X29!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__rel__div)). 6.97/7.20 fof(fact_inf1I, axiom, ![X5, X11, X35, X4]:(hBOOL(hAPP(X4,X35))=>(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11),X35))<=hBOOL(hAPP(X11,X35)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf1I)). 6.97/7.20 fof(fact_notin__set__remove1, axiom, ![X38, X23, X35, X5]:(~(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23))))=>~(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),c_List_Oremove1(X5,X38,X23)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_notin__set__remove1)). 6.97/7.20 fof(fact_set__takeWhileD, axiom, ![X23, X17, X35, X5]:((hBOOL(hAPP(X17,X35))&hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23))))<=hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),c_List_OtakeWhile(X5,X17,X23))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__takeWhileD)). 6.97/7.20 fof(fact_neg__mod__sign, axiom, ![X30, X29]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X29)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X29),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__mod__sign)). 6.97/7.20 fof(fact_pos__mod__sign, axiom, ![X30, X29]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X29))=>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,X30,X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__mod__sign)). 6.97/7.20 fof(fact_zero__less__int__conv, axiom, ![X32]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32))<=>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),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__int__conv)). 6.97/7.20 fof(fact_insort__key_Osimps_I1_J, axiom, ![X35, X18, X5, X12]:(class_Orderings_Olinorder(X12)=>hAPP(hAPP(c_List_Olist_OCons(X5),X35),c_List_Olist_ONil(X5))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X12,X18),X35),c_List_Olist_ONil(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__key_Osimps_I1_J)). 6.97/7.20 fof(fact_min__max_OSup__fin_Osingleton, axiom, ![X35, X5]:(class_Orderings_Olinorder(X5)=>X35=c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Osingleton)). 6.97/7.20 fof(fact_min__max_OInf__fin_Osingleton, axiom, ![X35, X5]:(X35=c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Osingleton)). 6.97/7.20 fof(fact_sgn__less, axiom, ![X2, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),c_Groups_Ozero__class_Ozero(X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Osgn__class_Osgn(X5,X2)),c_Groups_Ozero__class_Ozero(X5))))<=class_Rings_Olinordered__idom(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__less)). 6.97/7.20 fof(fact_Id__on__iff, axiom, ![X4, X38, X35, X5]:((hBOOL(hAPP(hAPP(c_member(X5),X35),X4))&X38=X35)<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),c_Relation_OId__on(X5,X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Id__on__iff)). 6.97/7.20 fof(fact_sgn__greater, axiom, ![X2, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X2))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),c_Groups_Osgn__class_Osgn(X5,X2))))<=class_Rings_Olinordered__idom(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__greater)). 6.97/7.20 fof(fact_card__seteq, axiom, ![X4, X11, X5]:(((X4=X11<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X11)),hAPP(c_Finite__Set_Ocard(X5),X4))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__seteq)). 6.97/7.20 fof(fact_abs__ge__minus__self, axiom, ![X30, X8]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X30)),hAPP(c_Groups_Oabs__class_Oabs(X8),X30)))<=class_Groups_Oordered__ab__group__add__abs(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__ge__minus__self)). 6.97/7.20 fof(fact_zero__le__square, axiom, ![X30, X8]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X30)))<=class_Rings_Olinordered__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__square)). 6.97/7.20 fof(fact_override__on__apply__notin, axiom, ![X50, X18, X12, X4, X2, X5]:(~(hBOOL(hAPP(hAPP(c_member(X5),X2),X4)))=>hAPP(X18,X2)=hAPP(c_Fun_Ooverride__on(X5,X12,X18,X50,X4),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_override__on__apply__notin)). 6.97/7.20 fof(fact_split__paired__All, axiom, ![X12, X5, X17]:(![X76]:hBOOL(hAPP(X17,X76))<=>![X13, X96]:hBOOL(hAPP(X17,hAPP(hAPP(c_Product__Type_OPair(X5,X12),X13),X96)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__paired__All)). 6.97/7.20 fof(fact_less__add__one, axiom, ![X30, X8]:(class_Rings_Olinordered__semidom(X8)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),c_Groups_Oone__class_Oone(X8))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__add__one)). 6.97/7.20 fof(fact_part__equivp__transp, axiom, ![X14, X38, X35, X67, X5]:(c_Equiv__Relations_Opart__equivp(X5,X67)=>((hBOOL(hAPP(hAPP(X67,X38),X14))=>hBOOL(hAPP(hAPP(X67,X35),X14)))<=hBOOL(hAPP(hAPP(X67,X35),X38)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_part__equivp__transp)). 6.97/7.20 fof(fact_transpE, axiom, ![X14, X38, X35, X3, X5]:(((hBOOL(hAPP(hAPP(X3,X35),X14))<=hBOOL(hAPP(hAPP(X3,X38),X14)))<=hBOOL(hAPP(hAPP(X3,X35),X38)))<=c_Predicate_Otransp(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpE)). 6.97/7.20 fof(fact_equivp__transp, axiom, ![X14, X38, X35, X67, X5]:(((hBOOL(hAPP(hAPP(X67,X35),X14))<=hBOOL(hAPP(hAPP(X67,X38),X14)))<=hBOOL(hAPP(hAPP(X67,X35),X38)))<=c_Equiv__Relations_Oequivp(X5,X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equivp__transp)). 6.97/7.20 fof(fact_list__all2__rev, axiom, ![X84, X23, X17, X12, X5]:(c_List_Olist__all2(X5,X12,X17,hAPP(c_List_Orev(X5),X23),hAPP(c_List_Orev(X12),X84))<=>c_List_Olist__all2(X5,X12,X17,X23,X84)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__rev)). 6.97/7.20 fof(fact_listsum__eq__0__nat__iff__nat, axiom, ![X186]:(![X22]:(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X22),hAPP(c_List_Oset(tc_Nat_Onat),X186)))=>X22=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<=>hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X186)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__eq__0__nat__iff__nat)). 6.97/7.20 fof(fact_folding__one_Osingleton, axiom, ![X35, X55, X18, X5]:(c_Finite__Set_Ofolding__one(X5,X18,X55)=>X35=hAPP(X55,hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one_Osingleton)). 6.97/7.20 fof(fact_inv__into__f__f, axiom, ![X35, X4, X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,X4)=>(hBOOL(hAPP(hAPP(c_member(X5),X35),X4))=>hAPP(c_Hilbert__Choice_Oinv__into(X5,X12,X4,X18),hAPP(X18,X35))=X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inv__into__f__f)). 6.97/7.20 fof(fact_minus__diff__eq, axiom, ![X29, X30, X8]:(hAPP(c_Groups_Ouminus__class_Ouminus(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X30),X29))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X29),X30)<=class_Groups_Oab__group__add(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__diff__eq)). 6.97/7.20 fof(fact_atLeastAtMost__singleton, axiom, ![X2, X5]:(class_Orderings_Oorder(X5)=>c_SetInterval_Oord__class_OatLeastAtMost(X5,X2,X2)=hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastAtMost__singleton)). 6.97/7.20 fof(fact_inj__on__diff, axiom, ![X11, X4, X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11))<=c_Fun_Oinj__on(X5,X12,X18,X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__diff)). 6.97/7.20 fof(fact_the__inv__into__f__f, axiom, ![X35, X4, X18, X12, X5]:((hBOOL(hAPP(hAPP(c_member(X5),X35),X4))=>X35=hAPP(c_Fun_Othe__inv__into(X5,X12,X4,X18),hAPP(X18,X35)))<=c_Fun_Oinj__on(X5,X12,X18,X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__inv__into__f__f)). 6.97/7.20 fof(fact_eq__diff__iff, axiom, ![X32, X34, X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X34))=>((X32=X34<=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X32),X33)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X34),X33))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__diff__iff)). 6.97/7.20 fof(fact_finite__Diff, axiom, ![X11, X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Diff)). 6.97/7.20 fof(fact_finite__Int, axiom, ![X117, X55, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X55),X117)))<=(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X117))|hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X55)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Int)). 6.97/7.20 fof(fact_sgn__1__neg, axiom, ![X2, X5]:((hAPP(c_Groups_Ouminus__class_Ouminus(X5),c_Groups_Oone__class_Oone(X5))=c_Groups_Osgn__class_Osgn(X5,X2)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),c_Groups_Ozero__class_Ozero(X5))))<=class_Rings_Olinordered__idom(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__1__neg)). 6.97/7.20 fof(fact_sgn__neg, axiom, ![X30, X8]:(class_Rings_Olinordered__idom(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),c_Groups_Ozero__class_Ozero(X8)))=>c_Groups_Osgn__class_Osgn(X8,X30)=hAPP(c_Groups_Ouminus__class_Ouminus(X8),c_Groups_Oone__class_Oone(X8)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__neg)). 6.97/7.20 fof(fact_setprod__1, axiom, ![X4, X12, X5]:(class_Groups_Ocomm__monoid__mult(X5)=>c_Groups_Oone__class_Oone(X5)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12,X5),hAPP(c_COMBK(X5,X12),c_Groups_Oone__class_Oone(X5))),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__1)). 6.97/7.20 fof(fact_setsum__0, axiom, ![X4, X12, X5]:(c_Groups_Ozero__class_Ozero(X5)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5),hAPP(c_COMBK(X5,X12),c_Groups_Ozero__class_Ozero(X5))),X4)<=class_Groups_Ocomm__monoid__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__0)). 6.97/7.20 fof(fact_abs__le__iff, axiom, ![X1, X2, X5]:(class_Groups_Oordered__ab__group__add__abs(X5)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X2),X1))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X2)),X1)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Oabs__class_Oabs(X5),X2)),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__le__iff)). 6.97/7.20 fof(fact_negD, axiom, ![X6]:(?[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,X48)))=X6<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negD)). 6.97/7.20 fof(fact_Inf__insert, axiom, ![X4, X2, X5]:(class_Complete__Lattice_Ocomplete__lattice(X5)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X2),c_Complete__Lattice_OInf__class_OInf(X5,X4))=c_Complete__Lattice_OInf__class_OInf(X5,hAPP(hAPP(c_Set_Oinsert(X5),X2),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__insert)). 6.97/7.20 fof(fact_Sup__insert, axiom, ![X4, X2, X5]:(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X2),c_Complete__Lattice_OSup__class_OSup(X5,X4))=c_Complete__Lattice_OSup__class_OSup(X5,hAPP(hAPP(c_Set_Oinsert(X5),X2),X4))<=class_Complete__Lattice_Ocomplete__lattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__insert)). 6.97/7.20 fof(fact_finite__converse, axiom, ![X3, X12, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X12)),hAPP(c_Relation_Oconverse(X12,X5),X3)))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X12,X5)),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__converse)). 6.97/7.20 fof(fact_in__set__butlastD, axiom, ![X23, X35, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),c_List_Obutlast(X5,X23))))=>hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__butlastD)). 6.97/7.20 fof(fact_less__code__numeral__def, axiom, ![X34, X32]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X32),X34))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X32)),hAPP(c_Code__Numeral_Onat__of,X34)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__code__numeral__def)). 6.97/7.20 fof(fact_Suc__mono, axiom, ![X25, X36]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X36),X25))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X36)),hAPP(c_Nat_OSuc,X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__mono)). 6.97/7.20 fof(fact_in__inv__imagep, axiom, ![X38, X35, X18, X3, X12, X5]:(c_Predicate_Oinv__imagep(X5,X12,X3,X18,X35,X38)<=>hBOOL(hAPP(hAPP(X3,hAPP(X18,X35)),hAPP(X18,X38)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__inv__imagep)). 6.97/7.20 fof(fact_not__sum__squares__lt__zero, axiom, ![X7, X6, X8]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X6),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X7))),c_Groups_Ozero__class_Ozero(X8))))<=class_Rings_Olinordered__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__sum__squares__lt__zero)). 6.97/7.20 fof(fact_less__eq__code__numeral__def, axiom, ![X34, X32]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X32),X34))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X32)),hAPP(c_Code__Numeral_Onat__of,X34)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__eq__code__numeral__def)). 6.97/7.20 fof(fact_nat__set__def, axiom, ![X44]:(c_Nat__Transfer_Onat__set(X44)<=>![X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X22),X44)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__set__def)). 6.97/7.20 fof(fact_lessThan__iff, axiom, ![X33, X47, X5]:(class_Orderings_Oord(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X47),X33))<=>hBOOL(hAPP(hAPP(c_member(X5),X47),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X33))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lessThan__iff)). 6.97/7.20 fof(fact_zle__linear, axiom, ![X39, X26]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X39),X26))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26),X39))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zle__linear)). 6.97/7.20 fof(fact_power__inject__exp, axiom, ![X32, X34, X2, X5]:(((X34=X32<=>hAPP(hAPP(c_Power_Opower__class_Opower(X5),X2),X34)=hAPP(hAPP(c_Power_Opower__class_Opower(X5),X2),X32))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Oone__class_Oone(X5)),X2)))<=class_Rings_Olinordered__semidom(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__inject__exp)). 6.97/7.20 fof(fact_inj__iff, axiom, ![X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))<=>hAPP(c_Fun_Ocomp(X12,X5,X5,c_Hilbert__Choice_Oinv__into(X5,X12,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X18)),X18)=c_Fun_Oid(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__iff)). 6.97/7.20 fof(fact_nat__le__linear, axiom, ![X25, X36]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X36))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X36),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__le__linear)). 6.97/7.20 fof(fact_atMost__iff, axiom, ![X33, X47, X5]:(class_Orderings_Oord(X5)=>(hBOOL(hAPP(hAPP(c_member(X5),X47),hAPP(c_SetInterval_Oord__class_OatMost(X5),X33)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X47),X33)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atMost__iff)). 6.97/7.20 fof(fact_greaterThan__iff, axiom, ![X33, X47, X5]:(class_Orderings_Oord(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X33),X47))<=>hBOOL(hAPP(hAPP(c_member(X5),X47),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X33))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_greaterThan__iff)). 6.97/7.20 fof(fact_atLeast__iff, axiom, ![X33, X47, X5]:((hBOOL(hAPP(hAPP(c_member(X5),X47),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X33)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X33),X47)))<=class_Orderings_Oord(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeast__iff)). 6.97/7.20 fof(fact_list__ex__iff__not__all__inverval__int, axiom, ![X46, X47, X17]:(c_List_Olist__ex(tc_Int_Oint,X17,c_List_Oupto(X47,X46))<=>~(c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),X17),X47,X46))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex__iff__not__all__inverval__int)). 6.97/7.20 fof(fact_card__eq__UNIV__imp__eq__UNIV, axiom, ![X4, X5]:((hAPP(c_Finite__Set_Ocard(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))=hAPP(c_Finite__Set_Ocard(X5),X4)=>X4=c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__eq__UNIV__imp__eq__UNIV)). 6.97/7.20 fof(fact_list__update__same__conv, axiom, ![X35, X23, X5, X47]:((X35=hAPP(hAPP(c_List_Onth(X5),X23),X47)<=>X23=hAPP(hAPP(c_List_Olist__update(X5,X23),X47),X35))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X47),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__same__conv)). 6.97/7.20 fof(fact_Powp__def, axiom, ![X11, X4, X5]:(![X22]:(hBOOL(hAPP(hAPP(c_member(X5),X22),X11))=>hBOOL(hAPP(X4,X22)))<=>hBOOL(hAPP(c_Predicate_OPowp(X5,X4),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Powp__def)). 6.97/7.20 fof(fact_div__pos__pos__trivial, axiom, ![X29, X30]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),X29))=>c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__pos__pos__trivial)). 6.97/7.20 fof(fact_mod__Suc, axiom, ![X25, X36]:((hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X36,X25))=X25=>c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X36),X25)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X36,X25))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X36),X25)<=hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X36,X25))!=X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__Suc)). 6.97/7.20 fof(fact_type__definition_ORep__range, axiom, ![X4, X90, X91, X12, X5]:(c_Typedef_Otype__definition(X5,X12,X91,X90,X4)=>X4=hAPP(c_Set_Oimage(X5,X12,X91),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_type__definition_ORep__range)). 6.97/7.20 fof(fact_inj__on__inv__into, axiom, ![X4, X18, X12, X11, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(c_Set_Oimage(X12,X5,X18),X4)))=>c_Fun_Oinj__on(X5,X12,c_Hilbert__Choice_Oinv__into(X12,X5,X4,X18),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__inv__into)). 6.97/7.20 fof(fact_PowD, axiom, ![X11, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))<=hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Set_OPow(X5),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_PowD)). 6.97/7.20 fof(fact_single__valued__rel__comp, axiom, ![X66, X62, X3, X12, X5]:((c_Relation_Osingle__valued(X12,X62,X66)=>c_Relation_Osingle__valued(X5,X62,hAPP(hAPP(c_Relation_Orel__comp(X5,X12,X62),X3),X66)))<=c_Relation_Osingle__valued(X5,X12,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_single__valued__rel__comp)). 6.97/7.20 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J, axiom, ![X6, X8]:(hAPP(c_Groups_Ouminus__class_Ouminus(X8),X6)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),c_Groups_Oone__class_Oone(X8))),X6)<=class_Rings_Ocomm__ring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J)). 6.97/7.20 fof(fact_sorted__sort__key, axiom, ![X23, X18, X12, X5]:(class_Orderings_Olinorder(X5)=>c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X12,X5),X18),c_List_Olinorder__class_Osort__key(X12,X5,X18,X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__sort__key)). 6.97/7.20 fof(fact_nat__mult__eq__cancel1, axiom, ![X32, X34, X33]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))=>(X32=X34<=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X32)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X34))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__eq__cancel1)). 6.97/7.20 fof(fact_card__image, axiom, ![X4, X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,X4)=>hAPP(c_Finite__Set_Ocard(X5),X4)=hAPP(c_Finite__Set_Ocard(X12),hAPP(c_Set_Oimage(X5,X12,X18),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__image)). 6.97/7.20 fof(fact_minus__shift__def, axiom, ![X70, X93, X19]:((c_Random_Ominus__shift(X70,X19,X93)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X19),X93)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X19),X93))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X19),X93))=>c_Random_Ominus__shift(X70,X19,X93)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X70),X19)),X93))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__shift__def)). 6.97/7.20 fof(fact_small__lazy__prod__def, axiom, ![X74, X5, X8]:(c_Lazy__Sequence_Oproduct(X8,X5,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X8,X74),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X5,X74))=c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(X8,X5),X74)<=(class_Lazy__Sequence_Osmall__lazy(X5)&class_Lazy__Sequence_Osmall__lazy(X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_small__lazy__prod__def)). 6.97/7.20 fof(fact_Sup__set__fold, axiom, ![X23, X5]:(c_Complete__Lattice_OSup__class_OSup(X5,hAPP(c_List_Oset(X5),X23))=hAPP(c_List_Ofoldl(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5),c_Orderings_Obot__class_Obot(X5)),X23)<=class_Complete__Lattice_Ocomplete__lattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__set__fold)). 6.97/7.20 fof(fact_Inf__set__fold, axiom, ![X23, X5]:(c_Complete__Lattice_OInf__class_OInf(X5,hAPP(c_List_Oset(X5),X23))=hAPP(c_List_Ofoldl(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Orderings_Otop__class_Otop(X5)),X23)<=class_Complete__Lattice_Ocomplete__lattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__set__fold)). 6.97/7.20 fof(fact_single__valued__rel__pow, axiom, ![X32, X67, X5]:(c_Relation_Osingle__valued(X5,X5,X67)=>c_Relation_Osingle__valued(X5,X5,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X32),X67))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_single__valued__rel__pow)). 6.97/7.20 fof(fact_sorted__distinct__set__unique, axiom, ![X84, X23, X5]:((c_List_Olinorder__class_Osorted(X5,X23)=>(hBOOL(hAPP(c_List_Odistinct(X5),X23))=>(c_List_Olinorder__class_Osorted(X5,X84)=>((X23=X84<=hAPP(c_List_Oset(X5),X23)=hAPP(c_List_Oset(X5),X84))<=hBOOL(hAPP(c_List_Odistinct(X5),X84))))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__distinct__set__unique)). 6.97/7.20 fof(fact_THE__default__def, axiom, ![X97, X5, X17]:((c_FunDef_OTHE__default(X5,X97,X17)=X97<=~(?[X22]:(![X72]:(X72=X22<=hBOOL(hAPP(X17,X72)))&hBOOL(hAPP(X17,X22)))))&(c_HOL_OThe(X5,X17)=c_FunDef_OTHE__default(X5,X97,X17)<=?[X22]:(hBOOL(hAPP(X17,X22))&![X72]:(X72=X22<=hBOOL(hAPP(X17,X72)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_THE__default__def)). 6.97/7.20 fof(fact_last__in__set, axiom, ![X5, X160]:(X160!=c_List_Olist_ONil(X5)=>hBOOL(hAPP(hAPP(c_member(X5),c_List_Olast(X5,X160)),hAPP(c_List_Oset(X5),X160)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__in__set)). 6.97/7.20 fof(fact_list__all2__rev1, axiom, ![X84, X23, X17, X12, X5]:(c_List_Olist__all2(X5,X12,X17,hAPP(c_List_Orev(X5),X23),X84)<=>c_List_Olist__all2(X5,X12,X17,X23,hAPP(c_List_Orev(X12),X84))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__rev1)). 6.97/7.20 fof(fact_atLeastLessThan__empty__iff, axiom, ![X1, X2, X5]:(class_Orderings_Oorder(X5)=>(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X2),X1)<=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThan__empty__iff)). 6.97/7.20 fof(fact_last__map, axiom, ![X18, X12, X5, X23]:(hAPP(X18,c_List_Olast(X5,X23))=c_List_Olast(X12,hAPP(hAPP(c_List_Omap(X5,X12),X18),X23))<=X23!=c_List_Olist_ONil(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__map)). 6.97/7.20 fof(fact_length__greater__0__conv, axiom, ![X23, X5]:(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(X5)),X23)))<=>c_List_Olist_ONil(X5)!=X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__greater__0__conv)). 6.97/7.20 fof(fact_pos__mod__bound, axiom, ![X30, X29]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X29))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X29)),X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__mod__bound)). 6.97/7.20 fof(fact_mod__less__divisor, axiom, ![X36, X25]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X36,X25)),X25))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__less__divisor)). 6.97/7.20 fof(fact_zmod__le__nonneg__dividend, axiom, ![X19, 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_Divides_Odiv__class_Omod(tc_Int_Oint,X36,X19)),X36))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__le__nonneg__dividend)). 6.97/7.20 fof(fact_mod__le__divisor, axiom, ![X36, X25]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X36,X25)),X25))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__le__divisor)). 6.97/7.20 fof(fact_neg__mod__bound, axiom, ![X30, X29]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X29),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X29),c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__mod__bound)). 6.97/7.20 fof(fact_compl__le__compl__iff, axiom, ![X38, X35, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X38),X35))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X35)),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X38))))<=class_Lattices_Oboolean__algebra(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__le__compl__iff)). 6.97/7.20 fof(fact_diff__minus__eq__add, axiom, ![X29, X30, X8]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X30),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X29))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29)<=class_Groups_Ogroup__add(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__minus__eq__add)). 6.97/7.20 fof(fact_finite__option__UNIV, axiom, ![X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X5)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X5),tc_HOL_Obool))))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__option__UNIV)). 6.97/7.20 fof(fact_rev__finite__subset, axiom, ![X4, X11, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__finite__subset)). 6.97/7.20 fof(fact_remove1__insort, axiom, ![X23, X35, X5]:(c_List_Oremove1(X5,X35,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X35),X23))=X23<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remove1__insort)). 6.97/7.20 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J, axiom, ![X7, X6, X8]:(class_Rings_Ocomm__ring__1(X8)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X6),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X7))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X6),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J)). 6.97/7.20 fof(fact_finite__nat__set__iff__bounded, axiom, ![X20]:(?[X21]:![X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),X21))<=hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X22),X20)))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__nat__set__iff__bounded)). 6.97/7.20 fof(fact_finite__nat__set__iff__bounded__le, axiom, ![X20]:(?[X21]:![X22]:(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X22),X20))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X21)))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__nat__set__iff__bounded__le)). 6.97/7.20 fof(fact_inf__le1, axiom, ![X7, X6, X8]:(class_Lattices_Osemilattice__inf(X8)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),X7)),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__le1)). 6.97/7.20 fof(fact_diff__def, axiom, ![X29, X30, X8]:(class_Groups_Ogroup__add(X8)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X29))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X30),X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__def)). 6.97/7.20 fof(fact_inf__sup__ord_I1_J, axiom, ![X7, X6, X8]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),X7)),X6))<=class_Lattices_Olattice(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__ord_I1_J)). 6.97/7.20 fof(fact_inf__le2, axiom, ![X7, X6, X8]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),X7)),X7))<=class_Lattices_Osemilattice__inf(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__le2)). 6.97/7.20 fof(fact_inf__sup__ord_I2_J, axiom, ![X7, X6, X8]:(class_Lattices_Olattice(X8)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),X7)),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__ord_I2_J)). 6.97/7.20 fof(fact_dvd__triv__left, axiom, ![X29, X30, X8]:(class_Rings_Ocomm__semiring__1(X8)=>hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X8),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dvd__triv__left)). 6.97/7.20 fof(fact_not__less__eq, axiom, ![X32, X34]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34),X32)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32),hAPP(c_Nat_OSuc,X34)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__less__eq)). 6.97/7.20 fof(fact_map__injective, axiom, ![X84, X23, X18, X5, X12]:(hAPP(hAPP(c_List_Omap(X12,X5),X18),X84)=hAPP(hAPP(c_List_Omap(X12,X5),X18),X23)=>(X84=X23<=c_Fun_Oinj__on(X12,X5,X18,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__injective)). 6.97/7.20 fof(fact_ab__diff__minus, axiom, ![X29, X30, X8]:(class_Groups_Oab__group__add(X8)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X29))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X30),X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ab__diff__minus)). 6.97/7.20 fof(fact_dvd__triv__right, axiom, ![X29, X30, X8]:(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X8),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X30)))<=class_Rings_Ocomm__semiring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dvd__triv__right)). 6.97/7.20 fof(fact_sup__ge1, axiom, ![X7, X6, X8]:(class_Lattices_Osemilattice__sup(X8)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__ge1)). 6.97/7.20 fof(fact_inf__sup__ord_I3_J, axiom, ![X7, X6, X8]:(class_Lattices_Olattice(X8)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__ord_I3_J)). 6.97/7.20 fof(fact_sup__ge2, axiom, ![X6, X7, X8]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),X7)))<=class_Lattices_Osemilattice__sup(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__ge2)). 6.97/7.20 fof(fact_diff__eq, axiom, ![X7, X6, X8]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X6),X7)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X7))<=class_Lattices_Oboolean__algebra(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__eq)). 6.97/7.20 fof(fact_inf__sup__ord_I4_J, axiom, ![X6, X7, X8]:(class_Lattices_Olattice(X8)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__ord_I4_J)). 6.97/7.20 fof(fact_wf__Int1, axiom, ![X37, X3, X5]:(c_Wellfounded_Owf(X5,X3)=>c_Wellfounded_Owf(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),X37))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__Int1)). 6.97/7.20 fof(fact_wf__Int2, axiom, ![X37, X3, X5]:(c_Wellfounded_Owf(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X37),X3))<=c_Wellfounded_Owf(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__Int2)). 6.97/7.20 fof(fact_divmod__int__rel__neg, axiom, ![X119, X29, X30]:(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X30),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X29)),X119))=>hBOOL(hAPP(c_Divides_Odivmod__int__rel(X30,X29),hAPP(c_Divides_OnegateSnd,X119)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__rel__neg)). 6.97/7.20 fof(fact_of__nat__less__imp__less, axiom, ![X25, X36, X8]:(class_Rings_Olinordered__semidom(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),X36)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),X25)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X36),X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__less__imp__less)). 6.97/7.20 fof(fact_abs__if, axiom, ![X30, X8]:(((hAPP(c_Groups_Ouminus__class_Ouminus(X8),X30)=hAPP(c_Groups_Oabs__class_Oabs(X8),X30)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),c_Groups_Ozero__class_Ozero(X8))))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),c_Groups_Ozero__class_Ozero(X8))))=>hAPP(c_Groups_Oabs__class_Oabs(X8),X30)=X30))<=class_Groups_Oabs__if(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__if)). 6.97/7.20 fof(fact_fun__left__comm_Ofold__graph__determ, axiom, ![X38, X35, X4, X14, X18, X12, X5]:(c_Finite__Set_Ofun__left__comm(X5,X12,X18)=>((X38=X35<=hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X12,X18,X14,X4),X38)))<=hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X12,X18,X14,X4),X35)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__graph__determ)). 6.97/7.20 fof(fact_finite__surj, axiom, ![X18, X11, X12, X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X11))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12,tc_HOL_Obool)),X11),hAPP(c_Set_Oimage(X5,X12,X18),X4))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__surj)). 6.97/7.20 fof(fact_finite__fun__UNIVD2, axiom, ![X12, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X12),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,X12)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X5,X12),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__fun__UNIVD2)). 6.97/7.20 fof(fact_le__SucE, axiom, ![X25, X36]:((hAPP(c_Nat_OSuc,X25)=X36<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X36),X25))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X36),hAPP(c_Nat_OSuc,X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__SucE)). 6.97/7.20 fof(fact_divmod__int__rel__mod, axiom, ![X70, X53, X29, X30]:((X70=c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X29)<=X29!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))<=hBOOL(hAPP(c_Divides_Odivmod__int__rel(X30,X29),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X53),X70)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__rel__mod)). 6.97/7.20 fof(fact_uminus__apply, axiom, ![X35, X4, X12, X5]:(class_Groups_Ouminus(X5)=>hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X12,X5)),X4),X35)=hAPP(c_Groups_Ouminus__class_Ouminus(X5),hAPP(X4,X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_uminus__apply)). 6.97/7.20 fof(fact_sorted__insort, axiom, ![X23, X35, X5]:((c_List_Olinorder__class_Osorted(X5,X23)<=>c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X35),X23)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__insort)). 6.97/7.20 fof(fact_DiffD1, axiom, ![X11, X4, X10, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X10),X4))<=hBOOL(hAPP(hAPP(c_member(X5),X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_DiffD1)). 6.97/7.20 fof(fact_length__sort, axiom, ![X23, X18, X5, X12]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Olinorder__class_Osort__key(X5,X12,X18,X23))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)<=class_Orderings_Olinorder(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__sort)). 6.97/7.20 fof(fact_Suc__pred_H, axiom, ![X25]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))=>X25=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__pred_H)). 6.97/7.20 fof(fact_IntD2, axiom, ![X11, X4, X10, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X10),X11))<=hBOOL(hAPP(hAPP(c_member(X5),X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_IntD2)). 6.97/7.20 fof(fact_length__n__lists__elem, axiom, ![X23, X32, X84, X5]:(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X84),hAPP(c_List_Oset(tc_List_Olist(X5)),c_Enum_On__lists(X5,X32,X23))))=>hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X84)=X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__n__lists__elem)). 6.97/7.20 fof(fact_linorder__not__less, axiom, ![X38, X35, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X38),X35))<=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X35),X38))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_linorder__not__less)). 6.97/7.20 fof(fact_Inf__lower, axiom, ![X4, X35, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Complete__Lattice_OInf__class_OInf(X5,X4)),X35))<=hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))<=class_Complete__Lattice_Ocomplete__lattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__lower)). 6.97/7.20 fof(fact_Sup__upper, axiom, ![X4, X35, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),c_Complete__Lattice_OSup__class_OSup(X5,X4)))<=hBOOL(hAPP(hAPP(c_member(X5),X35),X4)))<=class_Complete__Lattice_Ocomplete__lattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__upper)). 6.97/7.20 fof(fact_in__respects, axiom, ![X67, X35, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X35),c_Quotient_ORespects(X5,X67)))<=>hBOOL(hAPP(hAPP(X67,X35),X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__respects)). 6.97/7.20 fof(fact_atLeastLessThan__inj_I1_J, axiom, ![X97, X10, X1, X2, X5]:(class_Orderings_Olinorder(X5)=>(((X10=X2<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),X97)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),X1)))<=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X10),X97)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X2),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThan__inj_I1_J)). 6.97/7.20 fof(fact_atLeastLessThan__inj_I2_J, axiom, ![X97, X10, X1, X2, X5]:((hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X2),X1)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X10),X97)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),X97))=>X97=X1)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X2),X1))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThan__inj_I2_J)). 6.97/7.20 fof(fact_add__diff__cancel, axiom, ![X29, X30, X8]:(class_Groups_Ogroup__add(X8)=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29)),X29)=X30), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__diff__cancel)). 6.97/7.20 fof(fact_fun__left__comm_Ofold__equality, axiom, ![X38, X4, X14, X18, X12, X5]:(c_Finite__Set_Ofun__left__comm(X5,X12,X18)=>(X38=hAPP(hAPP(c_Finite__Set_Ofold(X5,X12,X18),X14),X4)<=hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X12,X18,X14,X4),X38)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__equality)). 6.97/7.20 fof(fact_distinct__insort__insert, axiom, ![X35, X18, X23, X5, X12]:((hBOOL(hAPP(c_List_Odistinct(X5),X23))=>hBOOL(hAPP(c_List_Odistinct(X5),c_List_Olinorder__class_Oinsort__insert__key(X5,X12,X18,X35,X23))))<=class_Orderings_Olinorder(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__insort__insert)). 6.97/7.20 fof(fact_type__definition_OAbs__inverse, axiom, ![X38, X4, X90, X91, X12, X5]:((hBOOL(hAPP(hAPP(c_member(X12),X38),X4))=>X38=hAPP(X91,hAPP(X90,X38)))<=c_Typedef_Otype__definition(X5,X12,X91,X90,X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_type__definition_OAbs__inverse)). 6.97/7.20 fof(fact_diff__add__cancel, axiom, ![X29, X30, X8]:(class_Groups_Ogroup__add(X8)=>X30=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X30),X29)),X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__add__cancel)). 6.97/7.20 fof(fact_mod__add__self2, axiom, ![X29, X30, X8]:(c_Divides_Odiv__class_Omod(X8,X30,X29)=c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29),X29)<=class_Divides_Osemiring__div(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__add__self2)). 6.97/7.20 fof(fact_mod__add__self1, axiom, ![X30, X29, X8]:(class_Divides_Osemiring__div(X8)=>c_Divides_Odiv__class_Omod(X8,X30,X29)=c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X29),X30),X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__add__self1)). 6.97/7.20 fof(fact_inf__sup__absorb, axiom, ![X7, X6, X8]:(class_Lattices_Olattice(X8)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),X7))=X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__absorb)). 6.97/7.20 fof(fact_wfE__pf, axiom, ![X4, X67, X5]:((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=X4<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Relation_OImage(X5,X5,X67),X4))))<=c_Wellfounded_Owf(X5,X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wfE__pf)). 6.97/7.20 fof(fact_dvd__mult__left, axiom, ![X31, X29, X30, X8]:(class_Rings_Ocomm__semiring__1(X8)=>(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X8),X30),X31))<=hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29)),X31)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dvd__mult__left)). 6.97/7.20 fof(fact_dvd__mult__right, axiom, ![X31, X29, X30, X8]:((hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29)),X31))=>hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X8),X29),X31)))<=class_Rings_Ocomm__semiring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dvd__mult__right)). 6.97/7.20 fof(fact_divide__minus1, axiom, ![X6, X8]:(hAPP(c_Groups_Ouminus__class_Ouminus(X8),X6)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X6),hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OMin))<=(class_Fields_Ofield__inverse__zero(X8)&class_Int_Onumber__ring(X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__minus1)). 6.97/7.20 fof(fact_sup__inf__absorb, axiom, ![X7, X6, X8]:(class_Lattices_Olattice(X8)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),X7))=X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__inf__absorb)). 6.97/7.20 fof(fact_mult__minus1, axiom, ![X26, X8]:(hAPP(c_Groups_Ouminus__class_Ouminus(X8),X26)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OMin)),X26)<=class_Int_Onumber__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__minus1)). 6.97/7.20 fof(fact_min__max_Oinf__le1, axiom, ![X7, X6, X8]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X6),X7)),X6))<=class_Orderings_Olinorder(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__le1)). 6.97/7.20 fof(fact_min__max_Oinf__le2, axiom, ![X7, X6, X8]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X6),X7)),X7))<=class_Orderings_Olinorder(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__le2)). 6.97/7.20 fof(fact_le__maxI1, axiom, ![X7, X6, X8]:(class_Orderings_Olinorder(X8)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X6),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__maxI1)). 6.97/7.20 fof(fact_hd__append, axiom, ![X45, X8, X41]:((X41!=c_List_Olist_ONil(X8)=>hAPP(c_List_Ohd(X8),X41)=hAPP(c_List_Ohd(X8),hAPP(hAPP(c_List_Oappend(X8),X41),X45)))&(hAPP(c_List_Ohd(X8),hAPP(hAPP(c_List_Oappend(X8),X41),X45))=hAPP(c_List_Ohd(X8),X45)<=c_List_Olist_ONil(X8)=X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__append)). 6.97/7.20 fof(fact_le__infE, axiom, ![X29, X30, X6, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X30),X29)))=>~((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),X30))=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),X29))))))<=class_Lattices_Osemilattice__inf(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__infE)). 6.97/7.20 fof(fact_accp_Oequations, axiom, ![X2, X3, X5]:(hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X3),X2))<=>![X22]:(hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X3),X22))<=hBOOL(hAPP(hAPP(X3,X22),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_accp_Oequations)). 6.97/7.20 fof(fact_of__int__minus, axiom, ![X26, X8]:(hAPP(c_Groups_Ouminus__class_Ouminus(X8),hAPP(c_Int_Oring__1__class_Oof__int(X8),X26))=hAPP(c_Int_Oring__1__class_Oof__int(X8),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26))<=class_Rings_Oring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__minus)). 6.97/7.20 fof(fact_le__maxI2, axiom, ![X6, X7, X8]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X7),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X6),X7)))<=class_Orderings_Olinorder(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__maxI2)). 6.97/7.20 fof(fact_accp_Osimps, axiom, ![X2, X3, X5]:(hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X3),X2))<=>![X22]:(hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X3),X22))<=hBOOL(hAPP(hAPP(X3,X22),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_accp_Osimps)). 6.97/7.20 fof(fact_accp__downward, axiom, ![X2, X1, X3, X5]:(hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X3),X1))=>(hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X3),X2))<=hBOOL(hAPP(hAPP(X3,X2),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_accp__downward)). 6.97/7.20 fof(fact_arith__simps_I30_J, axiom, ![X39, X8]:(class_Int_Onumber__ring(X8)=>hAPP(c_Groups_Ouminus__class_Ouminus(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),X39))=hAPP(c_Int_Onumber__class_Onumber__of(X8),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X39))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_arith__simps_I30_J)). 6.97/7.20 fof(fact_mult__minus1__right, axiom, ![X26, X8]:(hAPP(c_Groups_Ouminus__class_Ouminus(X8),X26)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OMin))<=class_Int_Onumber__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__minus1__right)). 6.97/7.20 fof(fact_linorder__antisym__conv1, axiom, ![X38, X35, X5]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X35),X38)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),X38))<=>X38=X35))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_linorder__antisym__conv1)). 6.97/7.20 fof(fact_order__neq__le__trans, axiom, ![X29, X30, X8]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),X29))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),X29)))<=X29!=X30)<=class_Orderings_Oorder(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__neq__le__trans)). 6.97/7.20 fof(fact_finite__surj__inj, axiom, ![X18, X4, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X5,X5,X18),X4)))=>c_Fun_Oinj__on(X5,X5,X18,X4))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__surj__inj)). 6.97/7.20 fof(fact_Ints__odd__nonzero, axiom, ![X2, X5]:(class_Int_Oring__char__0(X5)=>(hBOOL(hAPP(hAPP(c_member(X5),X2),c_Int_Oring__1__class_OInts(X5)))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oone__class_Oone(X5)),X2)),X2)!=c_Groups_Ozero__class_Ozero(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__odd__nonzero)). 6.97/7.20 fof(fact_sorted__list__of__set__sort__remdups, axiom, ![X23, X5]:(class_Orderings_Olinorder(X5)=>c_List_Olinorder__class_Osort__key(X5,X5,c_COMBI(X5),c_List_Oremdups(X5,X23))=c_List_Olinorder__class_Osorted__list__of__set(X5,hAPP(c_List_Oset(X5),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__list__of__set__sort__remdups)). 6.97/7.20 fof(fact_min__max_Osup_Ocommute, axiom, ![X29, X30, X8]:(class_Orderings_Olinorder(X8)=>hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X30),X29)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X29),X30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup_Ocommute)). 6.97/7.20 fof(fact_Diff__triv, axiom, ![X11, X4, X5]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=>X4=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__triv)). 6.97/7.20 fof(fact_min__max_Oinf__commute, axiom, ![X7, X6, X8]:(class_Orderings_Olinorder(X8)=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X7),X6)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X6),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__commute)). 6.97/7.20 fof(fact_sup1CI, axiom, ![X5, X4, X35, X11]:((hBOOL(hAPP(X4,X35))<=~(hBOOL(hAPP(X11,X35))))=>hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11),X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup1CI)). 6.97/7.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, axiom, ![X31, X30, X8]:(class_Rings_Ocomm__semiring__1(X8)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X31)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X31),X30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J)). 6.97/7.20 fof(fact_nth__replicate, axiom, ![X6, X8, X25, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28),X25))=>hAPP(hAPP(c_List_Onth(X8),c_List_Oreplicate(X8,X25,X6)),X28)=X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__replicate)). 6.97/7.20 fof(fact_ord_OatMost__iff, axiom, ![X33, X228, X47, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X47),c_SetInterval_Oord_OatMost(X5,X228,X33)))<=>hBOOL(hAPP(hAPP(X228,X47),X33))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ord_OatMost__iff)). 6.97/7.20 fof(fact_ord_OlessThan__iff, axiom, ![X33, X192, X47, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X47),c_SetInterval_Oord_OlessThan(X5,X192,X33)))<=>hBOOL(hAPP(hAPP(X192,X47),X33))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ord_OlessThan__iff)). 6.97/7.20 fof(fact_inf2D1, axiom, ![X38, X35, X11, X4, X12, X5]:(hBOOL(hAPP(hAPP(X4,X35),X38))<=hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X12,tc_HOL_Obool))),X4),X11),X35),X38))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf2D1)). 6.97/7.20 fof(fact_inf2D2, axiom, ![X38, X35, X11, X4, X12, X5]:(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X12,tc_HOL_Obool))),X4),X11),X35),X38))=>hBOOL(hAPP(hAPP(X11,X35),X38))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf2D2)). 6.97/7.20 fof(fact_ord_OgreaterThan__iff, axiom, ![X33, X192, X47, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X47),c_SetInterval_Oord_OgreaterThan(X5,X192,X33)))<=>hBOOL(hAPP(hAPP(X192,X33),X47))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ord_OgreaterThan__iff)). 6.97/7.20 fof(fact_ord_OatLeast__iff, axiom, ![X33, X228, X47, X5]:(hBOOL(hAPP(hAPP(X228,X33),X47))<=>hBOOL(hAPP(hAPP(c_member(X5),X47),c_SetInterval_Oord_OatLeast(X5,X228,X33)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ord_OatLeast__iff)). 6.97/7.20 fof(fact_type__definition_ORep, axiom, ![X35, X4, X90, X91, X12, X5]:(c_Typedef_Otype__definition(X5,X12,X91,X90,X4)=>hBOOL(hAPP(hAPP(c_member(X12),hAPP(X91,X35)),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_type__definition_ORep)). 6.97/7.20 fof(fact_inf__commute, axiom, ![X7, X6, X8]:(class_Lattices_Osemilattice__inf(X8)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X7),X6)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__commute)). 6.97/7.20 fof(fact_inf__sup__aci_I1_J, axiom, ![X7, X6, X8]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X7),X6)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),X7)<=class_Lattices_Olattice(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__aci_I1_J)). 6.97/7.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, axiom, ![X29, X30, X8]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X30)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29)<=class_Rings_Ocomm__semiring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J)). 6.97/7.20 fof(fact_atLeastatMost__empty__iff2, axiom, ![X1, X2, X5]:((c_SetInterval_Oord__class_OatLeastAtMost(X5,X2,X1)=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))<=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X2),X1))))<=class_Orderings_Oorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastatMost__empty__iff2)). 6.97/7.20 fof(fact_pos__zmult__eq__1__iff, axiom, ![X32, X34]:(((c_Groups_Oone__class_Oone(tc_Int_Oint)=X32&c_Groups_Oone__class_Oone(tc_Int_Oint)=X34)<=>c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34),X32))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__zmult__eq__1__iff)). 6.97/7.20 fof(fact_abs__of__neg, axiom, ![X30, X8]:(class_Groups_Oordered__ab__group__add__abs(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),c_Groups_Ozero__class_Ozero(X8)))=>hAPP(c_Groups_Oabs__class_Oabs(X8),X30)=hAPP(c_Groups_Ouminus__class_Ouminus(X8),X30))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__of__neg)). 6.97/7.20 fof(fact_abs__of__nonpos, axiom, ![X30, X8]:(class_Groups_Oordered__ab__group__add__abs(X8)=>(hAPP(c_Groups_Ouminus__class_Ouminus(X8),X30)=hAPP(c_Groups_Oabs__class_Oabs(X8),X30)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),c_Groups_Ozero__class_Ozero(X8))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__of__nonpos)). 6.97/7.20 fof(fact_sup__commute, axiom, ![X7, X6, X8]:(class_Lattices_Osemilattice__sup(X8)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),X7)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X7),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__commute)). 6.97/7.20 fof(fact_setsum_Oempty, axiom, ![X50, X12, X5]:(class_Groups_Ocomm__monoid__add(X5)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12,X5),X50),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool)))=c_Groups_Ozero__class_Ozero(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum_Oempty)). 6.97/7.20 fof(fact_Int__absorb1, axiom, ![X4, X11, X5]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)=X11<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__absorb1)). 6.97/7.20 fof(fact_int__zle__neg, axiom, ![X34, X32]:((X32=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X34)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X32)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X34))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__zle__neg)). 6.97/7.20 fof(fact_folding__one_Oeq__fold, axiom, ![X4, X55, X18, X5]:(c_Finite__Set_Ofolding__one(X5,X18,X55)=>(hAPP(X55,X4)=hAPP(c_Finite__Set_Ofold1(X5,X18),X4)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one_Oeq__fold)). 6.97/7.20 fof(fact_z3mod__def, axiom, ![X19, X93]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X93))=>c_SMT_Oz3mod(X19,X93)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X19,X93))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X93)))=>c_Divides_Odiv__class_Omod(tc_Int_Oint,X19,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X93))=c_SMT_Oz3mod(X19,X93))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_z3mod__def)). 6.97/7.20 fof(fact_inf__sup__aci_I5_J, axiom, ![X7, X6, X8]:(class_Lattices_Olattice(X8)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X7),X6)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__aci_I5_J)). 6.97/7.20 fof(fact_Un__absorb2, axiom, ![X4, X11, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X4))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11)=X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__absorb2)). 6.97/7.20 fof(fact_Int__absorb2, axiom, ![X11, X4, X5]:(X4=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__absorb2)). 6.97/7.20 fof(fact_Un__absorb1, axiom, ![X11, X4, X5]:(X11=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__absorb1)). 6.97/7.20 fof(fact_zero__less__imp__eq__int, axiom, ![X19]:(?[X48]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X48))&hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X48)=X19)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__imp__eq__int)). 6.97/7.20 fof(fact_semilattice__big_OF__eq, axiom, ![X4, X55, X18, X5]:((hAPP(X55,X4)=hAPP(c_Finite__Set_Ofold1(X5,X18),X4)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=c_Big__Operators_Osemilattice__big(X5,X18,X55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_semilattice__big_OF__eq)). 6.97/7.20 fof(fact_list__update__beyond, axiom, ![X6, X28, X41, X8]:(X41=hAPP(hAPP(c_List_Olist__update(X8,X41),X28),X6)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)),X28))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__beyond)). 6.97/7.20 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J, axiom, ![X4]:(c_Nat__Transfer_Onat__set(X4)=>hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X4))=hAPP(c_Finite__Set_Ocard(tc_Int_Oint),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J)). 6.97/7.20 fof(fact_Max_Osingleton, axiom, ![X35, X5]:(class_Orderings_Olinorder(X5)=>c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))=X35), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max_Osingleton)). 6.97/7.20 fof(fact_Sup__fin_Osingleton, axiom, ![X35, X5]:(c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))=X35<=class_Lattices_Olattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Osingleton)). 6.97/7.20 fof(fact_add__lessD1, axiom, ![X19, X27, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),X27)),X19))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28),X19))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__lessD1)). 6.97/7.20 fof(fact_Sup__singleton, axiom, ![X2, X5]:(class_Complete__Lattice_Ocomplete__lattice(X5)=>c_Complete__Lattice_OSup__class_OSup(X5,hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))=X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__singleton)). 6.97/7.20 fof(fact_Inf__fin_Osingleton, axiom, ![X35, X5]:(c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))=X35<=class_Lattices_Olattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Osingleton)). 6.97/7.20 fof(fact_Min_Osingleton, axiom, ![X35, X5]:(X35=c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min_Osingleton)). 6.97/7.20 fof(fact_Inf__singleton, axiom, ![X2, X5]:(X2=c_Complete__Lattice_OInf__class_OInf(X5,hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))<=class_Complete__Lattice_Ocomplete__lattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__singleton)). 6.97/7.20 fof(fact_add__leD1, axiom, ![X25, X19, X36]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X36),X25))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X19)),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__leD1)). 6.97/7.20 fof(fact_power__0__Suc, axiom, ![X25, X8]:((class_Power_Opower(X8)&class_Rings_Osemiring__0(X8))=>c_Groups_Ozero__class_Ozero(X8)=hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(c_Nat_OSuc,X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__0__Suc)). 6.97/7.20 fof(fact_min__max_Oinf__sup__absorb, axiom, ![X7, X6, X8]:(class_Orderings_Olinorder(X8)=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X6),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X6),X7))=X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__sup__absorb)). 6.97/7.20 fof(fact_min__max_Osup__inf__absorb, axiom, ![X7, X6, X8]:(X6=hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X6),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X6),X7))<=class_Orderings_Olinorder(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__inf__absorb)). 6.97/7.20 fof(fact_distinct__card, axiom, ![X23, X5]:(hBOOL(hAPP(c_List_Odistinct(X5),X23))=>hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)=hAPP(c_Finite__Set_Ocard(X5),hAPP(c_List_Oset(X5),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__card)). 6.97/7.20 fof(fact_mult__sgn__abs, axiom, ![X6, X8]:(class_Rings_Olinordered__idom(X8)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Osgn__class_Osgn(X8,X6)),hAPP(c_Groups_Oabs__class_Oabs(X8),X6))=X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__sgn__abs)). 6.97/7.20 fof(fact_Compl__greaterThan, axiom, ![X33, X5]:(class_Orderings_Olinorder(X5)=>hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X33))=hAPP(c_SetInterval_Oord__class_OatMost(X5),X33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__greaterThan)). 6.97/7.20 fof(fact_Compl__atMost, axiom, ![X33, X5]:(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X33))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X33)<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__atMost)). 6.97/7.20 fof(fact_Compl__atLeast, axiom, ![X33, X5]:(hAPP(c_SetInterval_Oord__class_OlessThan(X5),X33)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X33))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__atLeast)). 6.97/7.20 fof(fact_Compl__lessThan, axiom, ![X33, X5]:(hAPP(c_SetInterval_Oord__class_OatLeast(X5),X33)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X33))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__lessThan)). 6.97/7.20 fof(fact_Union__quotient, axiom, ![X3, X4, X5]:(c_Equiv__Relations_Oequiv(X5,X4,X3)=>c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X4),X3))=X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__quotient)). 6.97/7.20 fof(fact_abs__ge__zero, axiom, ![X30, X8]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(c_Groups_Oabs__class_Oabs(X8),X30)))<=class_Groups_Oordered__ab__group__add__abs(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__ge__zero)). 6.97/7.20 fof(fact_zero__le__imp__of__nat, axiom, ![X36, X8]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),X36)))<=class_Rings_Olinordered__semidom(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__imp__of__nat)). 6.97/7.20 fof(fact_finite__imageI, axiom, ![X71, X12, X55, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X12),hAPP(c_Set_Oimage(X5,X12,X71),X55)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X55))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__imageI)). 6.97/7.20 fof(fact_override__on__apply__in, axiom, ![X50, X18, X12, X4, X2, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X2),X4))=>hAPP(X50,X2)=hAPP(c_Fun_Ooverride__on(X5,X12,X18,X50,X4),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_override__on__apply__in)). 6.97/7.20 fof(fact_distinct__drop, axiom, ![X28, X41, X8]:(hBOOL(hAPP(c_List_Odistinct(X8),X41))=>hBOOL(hAPP(c_List_Odistinct(X8),hAPP(hAPP(c_List_Odrop(X8),X28),X41)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__drop)). 6.97/7.20 fof(fact_distinct__take, axiom, ![X28, X41, X8]:(hBOOL(hAPP(c_List_Odistinct(X8),X41))=>hBOOL(hAPP(c_List_Odistinct(X8),hAPP(hAPP(c_List_Otake(X8),X28),X41)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__take)). 6.97/7.20 fof(fact_finite__insert, axiom, ![X4, X2, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Set_Oinsert(X5),X2),X4)))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__insert)). 6.97/7.20 fof(fact_finite__Diff2, axiom, ![X4, X11, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Diff2)). 6.97/7.20 fof(fact_div__eq, axiom, ![X70, X53, X25, X36]:(X53=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X36),X25)<=hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X36,X25),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X53),X70)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__eq)). 6.97/7.20 fof(fact_Least__equality, axiom, ![X35, X17, X5]:((hBOOL(hAPP(X17,X35))=>(c_Orderings_Oord__class_OLeast(X5,X17)=X35<=![X72]:(hBOOL(hAPP(X17,X72))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),X72)))))<=class_Orderings_Oorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Least__equality)). 6.97/7.20 fof(fact_finite__Pow__iff, axiom, ![X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OPow(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Pow__iff)). 6.97/7.20 fof(fact_greaterThanAtMost__empty__iff2, axiom, ![X52, X33, X5]:((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X33,X52)<=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X33),X52))))<=class_Orderings_Oorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_greaterThanAtMost__empty__iff2)). 6.97/7.20 fof(fact_drop__eq__Nil, axiom, ![X23, X32, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)),X32))<=>hAPP(hAPP(c_List_Odrop(X5),X32),X23)=c_List_Olist_ONil(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__eq__Nil)). 6.97/7.20 fof(fact_ex__in__conv, axiom, ![X4, X5]:(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4<=>?[X22]:hBOOL(hAPP(hAPP(c_member(X5),X22),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ex__in__conv)). 6.97/7.20 fof(fact_insort__insert__triv, axiom, ![X23, X35, X5]:(class_Orderings_Olinorder(X5)=>(X23=c_List_Olinorder__class_Oinsort__insert__key(X5,X5,c_COMBI(X5),X35,X23)<=hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__insert__triv)). 6.97/7.20 fof(fact_all__not__in__conv, axiom, ![X4, X5]:(X4=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))<=>![X22]:~(hBOOL(hAPP(hAPP(c_member(X5),X22),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_all__not__in__conv)). 6.97/7.20 fof(fact_drop__all, axiom, ![X25, X41, X8]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)),X25))=>hAPP(hAPP(c_List_Odrop(X8),X25),X41)=c_List_Olist_ONil(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__all)). 6.97/7.20 fof(fact_setprod__empty, axiom, ![X18, X12, X5]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12,X5),X18),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool)))=c_Groups_Oone__class_Oone(X5)<=class_Groups_Ocomm__monoid__mult(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__empty)). 6.97/7.20 fof(fact_finite__Domain, axiom, ![X3, X12, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X12)),X3))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Relation_ODomain(X5,X12),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Domain)). 6.97/7.20 fof(fact_subset__Compl__self__eq, axiom, ![X4, X5]:(X4=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__Compl__self__eq)). 6.97/7.20 fof(fact_finite__Range, axiom, ![X3, X12, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X12)),X3))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X12),hAPP(c_Relation_ORange(X5,X12),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Range)). 6.97/7.20 fof(fact_less__Suc__eq, axiom, ![X32, X34]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34),hAPP(c_Nat_OSuc,X32)))<=>(X32=X34|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__Suc__eq)). 6.97/7.20 fof(fact_less__Suc__eq__le, axiom, ![X32, X34]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),X32))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34),hAPP(c_Nat_OSuc,X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__Suc__eq__le)). 6.97/7.20 fof(fact_inj__on__Un__image__eq__iff, axiom, ![X11, X4, X18, X12, X5]:((hAPP(c_Set_Oimage(X5,X12,X18),X4)=hAPP(c_Set_Oimage(X5,X12,X18),X11)<=>X4=X11)<=c_Fun_Oinj__on(X5,X12,X18,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__Un__image__eq__iff)). 6.97/7.20 fof(fact_subset__inj__on, axiom, ![X4, X11, X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,X11)=>(c_Fun_Oinj__on(X5,X12,X18,X4)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__inj__on)). 6.97/7.20 fof(fact_le__SucI, axiom, ![X25, X36]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X36),hAPP(c_Nat_OSuc,X25)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X36),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__SucI)). 6.97/7.20 fof(fact_RangeP_Oequations, axiom, ![X125, X3, X12, X5]:(hBOOL(hAPP(c_Predicate_ORangeP(X5,X12,X3),X125))<=>?[X13]:hBOOL(hAPP(hAPP(X3,X13),X125))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_RangeP_Oequations)). 6.97/7.20 fof(fact_DomainP_Oequations, axiom, ![X103, X3, X12, X5]:(hBOOL(hAPP(c_Predicate_ODomainP(X5,X12,X3),X103))<=>?[X76]:hBOOL(hAPP(hAPP(X3,X103),X76))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_DomainP_Oequations)). 6.97/7.20 fof(fact_inj__image__eq__iff, axiom, ![X11, X4, X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))=>(X4=X11<=>hAPP(c_Set_Oimage(X5,X12,X18),X4)=hAPP(c_Set_Oimage(X5,X12,X18),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__image__eq__iff)). 6.97/7.20 fof(fact_singleton__inject, axiom, ![X1, X2, X5]:(hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))=hAPP(hAPP(c_Set_Oinsert(X5),X1),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))=>X2=X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_singleton__inject)). 6.97/7.20 fof(fact_list__all__simps_I1_J, axiom, ![X23, X35, X17, X5]:((hBOOL(hAPP(X17,X35))&c_List_Olist__all(X5,X17,X23))<=>c_List_Olist__all(X5,X17,hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all__simps_I1_J)). 6.97/7.20 fof(fact_less__SucE, axiom, ![X25, X36]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X36),hAPP(c_Nat_OSuc,X25)))=>(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X36),X25)))=>X36=X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__SucE)). 6.97/7.20 fof(fact_filter__replicate, axiom, ![X32, X5, X35, X17]:((~(hBOOL(hAPP(X17,X35)))=>c_List_Olist_ONil(X5)=hAPP(c_List_Ofilter(X5,X17),c_List_Oreplicate(X5,X32,X35)))&(hAPP(c_List_Ofilter(X5,X17),c_List_Oreplicate(X5,X32,X35))=c_List_Oreplicate(X5,X32,X35)<=hBOOL(hAPP(X17,X35)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__replicate)). 6.97/7.20 fof(fact_Suc__less__eq, axiom, ![X32, X34]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34),X32))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X34)),hAPP(c_Nat_OSuc,X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__less__eq)). 6.97/7.20 fof(fact_nth__via__drop, axiom, ![X45, X7, X41, X25, X8]:(X7=hAPP(hAPP(c_List_Onth(X8),X41),X25)<=hAPP(hAPP(c_List_Odrop(X8),X25),X41)=hAPP(hAPP(c_List_Olist_OCons(X8),X7),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__via__drop)). 6.97/7.20 fof(fact_self__quotient, axiom, ![X70, X53, X30]:((c_Groups_Oone__class_Oone(tc_Int_Oint)=X53<=c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X30)<=hBOOL(hAPP(c_Divides_Odivmod__int__rel(X30,X30),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X53),X70)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_self__quotient)). 6.97/7.20 fof(fact_self__remainder, axiom, ![X70, X53, X30]:(hBOOL(hAPP(c_Divides_Odivmod__int__rel(X30,X30),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X53),X70)))=>(X70=c_Groups_Ozero__class_Ozero(tc_Int_Oint)<=c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_self__remainder)). 6.97/7.20 fof(fact_single__valued__subset, axiom, ![X66, X3, X12, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),X3),X66))=>(c_Relation_Osingle__valued(X5,X12,X66)=>c_Relation_Osingle__valued(X5,X12,X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_single__valued__subset)). 6.97/7.20 fof(fact_distinct__sort, axiom, ![X23, X18, X5, X12]:((hBOOL(hAPP(c_List_Odistinct(X5),c_List_Olinorder__class_Osort__key(X5,X12,X18,X23)))<=>hBOOL(hAPP(c_List_Odistinct(X5),X23)))<=class_Orderings_Olinorder(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__sort)). 6.97/7.20 fof(fact_list__all__append, axiom, ![X84, X23, X17, X5]:(c_List_Olist__all(X5,X17,hAPP(hAPP(c_List_Oappend(X5),X23),X84))<=>(c_List_Olist__all(X5,X17,X84)&c_List_Olist__all(X5,X17,X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all__append)). 6.97/7.20 fof(fact_of__nat__in__Nats, axiom, ![X32, X5]:(class_Rings_Osemiring__1(X5)=>hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X32)),c_Nat_Osemiring__1__class_ONats(X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__in__Nats)). 6.97/7.20 fof(fact_Ints__of__nat, axiom, ![X32, X5]:(hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X32)),c_Int_Oring__1__class_OInts(X5)))<=class_Rings_Oring__1(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__of__nat)). 6.97/7.20 fof(fact_Rep__Integ__induct, axiom, ![X17, X38]:((hBOOL(hAPP(X17,X38))<=![X22]:hBOOL(hAPP(X17,hAPP(c_Int_ORep__Integ,X22))))<=hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X38),c_Int_OInteg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Rep__Integ__induct)). 6.97/7.20 fof(fact_sup1E, axiom, ![X35, X11, X4, X5]:(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11),X35))=>(~(hBOOL(hAPP(X4,X35)))=>hBOOL(hAPP(X11,X35)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup1E)). 6.97/7.20 fof(fact_Ints__of__int, axiom, ![X14, X5]:(class_Rings_Oring__1(X5)=>hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Int_Oring__1__class_Oof__int(X5),X14)),c_Int_Oring__1__class_OInts(X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__of__int)). 6.97/7.20 fof(fact_Ints__number__of, axiom, ![X9, X5]:(hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X9)),c_Int_Oring__1__class_OInts(X5)))<=class_Int_Onumber__ring(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__number__of)). 6.97/7.20 fof(fact_sgn__1__pos, axiom, ![X2, X5]:(class_Rings_Olinordered__idom(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X2))<=>c_Groups_Oone__class_Oone(X5)=c_Groups_Osgn__class_Osgn(X5,X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__1__pos)). 6.97/7.20 fof(fact_set__eq__subset, axiom, ![X5, X11, X4]:(X4=X11<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__eq__subset)). 6.97/7.20 fof(fact_subset__Un__eq, axiom, ![X11, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X11))<=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11)=X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__Un__eq)). 6.97/7.20 fof(fact_Least__le, axiom, ![X33, X17, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Orderings_Oord__class_OLeast(X5,X17)),X33))<=hBOOL(hAPP(X17,X33)))<=class_Orderings_Owellorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Least__le)). 6.97/7.20 fof(fact_mod__div__trivial, axiom, ![X29, X30, X8]:(hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),c_Divides_Odiv__class_Omod(X8,X30,X29)),X29)=c_Groups_Ozero__class_Ozero(X8)<=class_Divides_Osemiring__div(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__div__trivial)). 6.97/7.20 fof(fact_mod__mult__self1__is__0, axiom, ![X30, X29, X8]:(c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X30),X29)=c_Groups_Ozero__class_Ozero(X8)<=class_Divides_Osemiring__div(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__self1__is__0)). 6.97/7.20 fof(fact_mod__mult__self2__is__0, axiom, ![X29, X30, X8]:(c_Groups_Ozero__class_Ozero(X8)=c_Divides_Odiv__class_Omod(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29),X29)<=class_Divides_Osemiring__div(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__self2__is__0)). 6.97/7.20 fof(fact_left__minus, axiom, ![X30, X8]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X30)),X30)=c_Groups_Ozero__class_Ozero(X8)<=class_Groups_Ogroup__add(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_left__minus)). 6.97/7.20 fof(fact_ab__left__minus, axiom, ![X30, X8]:(class_Groups_Oab__group__add(X8)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X30)),X30)=c_Groups_Ozero__class_Ozero(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ab__left__minus)). 6.97/7.20 fof(fact_compl__sup__top, axiom, ![X6, X8]:(c_Orderings_Otop__class_Otop(X8)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X6)),X6)<=class_Lattices_Oboolean__algebra(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__sup__top)). 6.97/7.20 fof(fact_compl__inf__bot, axiom, ![X6, X8]:(c_Orderings_Obot__class_Obot(X8)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X6)),X6)<=class_Lattices_Oboolean__algebra(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__inf__bot)). 6.97/7.20 fof(fact_last__appendR, axiom, ![X41, X8, X45]:(c_List_Olast(X8,hAPP(hAPP(c_List_Oappend(X8),X41),X45))=c_List_Olast(X8,X45)<=X45!=c_List_Olist_ONil(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__appendR)). 6.97/7.20 fof(fact_right__minus, axiom, ![X30, X8]:(class_Groups_Ogroup__add(X8)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X30))=c_Groups_Ozero__class_Ozero(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_right__minus)). 6.97/7.20 fof(fact_inf__compl__bot, axiom, ![X6, X8]:(class_Lattices_Oboolean__algebra(X8)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X6))=c_Orderings_Obot__class_Obot(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__compl__bot)). 6.97/7.20 fof(fact_sup__compl__top, axiom, ![X6, X8]:(c_Orderings_Otop__class_Otop(X8)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X6))<=class_Lattices_Oboolean__algebra(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__compl__top)). 6.97/7.20 fof(fact_last_Osimps, axiom, ![X6, X8, X41]:((X6=c_List_Olast(X8,hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41))<=c_List_Olist_ONil(X8)=X41)&(X41!=c_List_Olist_ONil(X8)=>c_List_Olast(X8,X41)=c_List_Olast(X8,hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last_Osimps)). 6.97/7.20 fof(fact_atLeastLessThan__empty, axiom, ![X2, X1, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X1),X2))=>hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X2),X1)=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))<=class_Orderings_Oorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThan__empty)). 6.97/7.20 fof(fact_pigeonhole, axiom, ![X4, X18, X12, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(c_Set_Oimage(X12,X5,X18),X4))),hAPP(c_Finite__Set_Ocard(X12),X4)))=>~(c_Fun_Oinj__on(X12,X5,X18,X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pigeonhole)). 6.97/7.20 fof(fact_weaken, axiom, ![X174, X216, X117, X5]:(c_Hoare__Mirabelle_Ohoare__derivs(X5,X117,X216)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)),X174),X216))=>c_Hoare__Mirabelle_Ohoare__derivs(X5,X117,X174))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_weaken)). 6.97/7.20 fof(fact_Babs__def, axiom, ![X34, X12, X24, X35, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X35),X24))=>hAPP(c_Quotient_OBabs(X5,X12,X24,X34),X35)=hAPP(X34,X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Babs__def)). 6.97/7.20 fof(fact_int__one__le__iff__zero__less, axiom, ![X14]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__one__le__iff__zero__less)). 6.97/7.20 fof(fact_conversep__iff, axiom, ![X1, X2, X3, X12, X5]:(hBOOL(hAPP(hAPP(X3,X1),X2))<=>hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X5,X12,X3),X2),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_conversep__iff)). 6.97/7.20 fof(fact_take__all, axiom, ![X25, X41, X8]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)),X25))=>hAPP(hAPP(c_List_Otake(X8),X25),X41)=X41), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__all)). 6.97/7.20 fof(fact_set__sort, axiom, ![X23, X18, X5, X12]:(hAPP(c_List_Oset(X5),c_List_Olinorder__class_Osort__key(X5,X12,X18,X23))=hAPP(c_List_Oset(X5),X23)<=class_Orderings_Olinorder(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__sort)). 6.97/7.20 fof(fact_abs__sgn, axiom, ![X19, X8]:(hAPP(c_Groups_Oabs__class_Oabs(X8),X19)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X19),c_Groups_Osgn__class_Osgn(X8,X19))<=class_Rings_Olinordered__idom(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__sgn)). 6.97/7.20 fof(fact_rev__predicate1D, axiom, ![X104, X5, X35, X17]:(hBOOL(hAPP(X17,X35))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X17),X104))=>hBOOL(hAPP(X104,X35)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__predicate1D)). 6.97/7.20 fof(fact_nat__less__le, axiom, ![X32, X34]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),X32))&X34!=X32)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__less__le)). 6.97/7.20 fof(fact_min__max_OInf__fin_OF__eq, axiom, ![X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X4)=c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X4))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_OF__eq)). 6.97/7.20 fof(fact_Sup__fin__Sup, axiom, ![X4, X5]:(((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4=>c_Big__Operators_Olattice__class_OSup__fin(X5,X4)=c_Complete__Lattice_OSup__class_OSup(X5,X4))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Complete__Lattice_Ocomplete__lattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin__Sup)). 6.97/7.20 fof(fact_Inf__fin__Inf, axiom, ![X4, X5]:(class_Complete__Lattice_Ocomplete__lattice(X5)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=X4=>c_Complete__Lattice_OInf__class_OInf(X5,X4)=c_Big__Operators_Olattice__class_OInf__fin(X5,X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin__Inf)). 6.97/7.20 fof(fact_min__max_OSup__fin_OF__eq, axiom, ![X4, X5]:((c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X4)=hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omax(X5)),X4)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_OF__eq)). 6.97/7.20 fof(fact_remove1__remdups, axiom, ![X6, X41, X8]:(c_List_Oremove1(X8,X6,c_List_Oremdups(X8,X41))=c_List_Oremdups(X8,c_List_Oremove1(X8,X6,X41))<=hBOOL(hAPP(c_List_Odistinct(X8),X41))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remove1__remdups)). 6.97/7.20 fof(fact_abs__ge__self, axiom, ![X30, X8]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),hAPP(c_Groups_Oabs__class_Oabs(X8),X30)))<=class_Groups_Oordered__ab__group__add__abs(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__ge__self)). 6.97/7.20 fof(fact_part__equivpE, axiom, ![X67, X5]:(c_Equiv__Relations_Opart__equivp(X5,X67)=>~(((c_Predicate_Osymp(X5,X67)=>~(c_Predicate_Otransp(X5,X67)))<=?[X22]:hBOOL(hAPP(hAPP(X67,X22),X22))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_part__equivpE)). 6.97/7.20 fof(fact_part__equivp__refl__symp__transp, axiom, ![X67, X5]:(c_Equiv__Relations_Opart__equivp(X5,X67)<=>((c_Predicate_Otransp(X5,X67)&c_Predicate_Osymp(X5,X67))&?[X22]:hBOOL(hAPP(hAPP(X67,X22),X22)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_part__equivp__refl__symp__transp)). 6.97/7.20 fof(fact_mod__pos__pos__trivial, axiom, ![X29, X30]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),X29))=>c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X29)=X30)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__pos__pos__trivial)). 6.97/7.20 fof(fact_mod__neg__neg__trivial, axiom, ![X29, X30]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X29),X30))=>c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X29)=X30)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X30),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__neg__neg__trivial)). 6.97/7.20 fof(fact_mult__cancel2, axiom, ![X32, X33, X34]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X33)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X33)<=>(X34=X32|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__cancel2)). 6.97/7.20 fof(fact_transfer__int__nat__set__relations_I3_J, axiom, ![X11, X4]:(((hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X4)=hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X11)<=>X11=X4)<=c_Nat__Transfer_Onat__set(X11))<=c_Nat__Transfer_Onat__set(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__set__relations_I3_J)). 6.97/7.20 fof(fact_Suc__mult__cancel1, axiom, ![X32, X34, X33]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X33)),X34)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X33)),X32)<=>X34=X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__mult__cancel1)). 6.97/7.20 fof(fact_bij__betw__the__inv__into, axiom, ![X11, X4, X18, X12, X5]:(c_Fun_Obij__betw(X12,X5,c_Fun_Othe__inv__into(X5,X12,X4,X18),X11,X4)<=c_Fun_Obij__betw(X5,X12,X18,X4,X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bij__betw__the__inv__into)). 6.97/7.20 fof(fact_bij__betw__inv__into, axiom, ![X11, X4, X18, X12, X5]:(c_Fun_Obij__betw(X5,X12,X18,X4,X11)=>c_Fun_Obij__betw(X12,X5,c_Hilbert__Choice_Oinv__into(X5,X12,X4,X18),X11,X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bij__betw__inv__into)). 6.97/7.20 fof(fact_nat__mult__eq__cancel__disj, axiom, ![X32, X34, X33]:((X33=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X34=X32)<=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X32)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X34)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__eq__cancel__disj)). 6.97/7.20 fof(fact_wf__comp__self, axiom, ![X67, X5]:(c_Wellfounded_Owf(X5,hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X67),X67))<=>c_Wellfounded_Owf(X5,X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__comp__self)). 6.97/7.20 fof(fact_subset__empty, axiom, ![X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))<=>c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__empty)). 6.97/7.20 fof(fact_distinct__n__lists, axiom, ![X25, X41, X8]:(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X8)),c_Enum_On__lists(X8,X25,X41)))<=hBOOL(hAPP(c_List_Odistinct(X8),X41))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__n__lists)). 6.97/7.20 fof(fact_distinct__filter, axiom, ![X17, X23, X5]:(hBOOL(hAPP(c_List_Odistinct(X5),hAPP(c_List_Ofilter(X5,X17),X23)))<=hBOOL(hAPP(c_List_Odistinct(X5),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__filter)). 6.97/7.20 fof(fact_distinct__butlast, axiom, ![X8, X41]:(X41!=c_List_Olist_ONil(X8)=>(hBOOL(hAPP(c_List_Odistinct(X8),X41))=>hBOOL(hAPP(c_List_Odistinct(X8),c_List_Obutlast(X8,X41))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__butlast)). 6.97/7.20 fof(fact_mk__less__def, axiom, ![X38, X35, X67, X5]:((~(hBOOL(hAPP(hAPP(X67,X38),X35)))&hBOOL(hAPP(hAPP(X67,X35),X38)))<=>c_Partial__Function_Omk__less(X5,X67,X35,X38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mk__less__def)). 6.97/7.20 fof(fact_diff__0, axiom, ![X30, X8]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),c_Groups_Ozero__class_Ozero(X8)),X30)=hAPP(c_Groups_Ouminus__class_Ouminus(X8),X30)<=class_Groups_Ogroup__add(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__0)). 6.97/7.20 fof(fact_dual__min, axiom, ![X5]:(c_Orderings_Oord_Omin(X5,hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X5)))=c_Orderings_Oord__class_Omax(X5)<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dual__min)). 6.97/7.20 fof(fact_dual__max, axiom, ![X5]:(class_Orderings_Olinorder(X5)=>c_Orderings_Oord__class_Omin(X5)=c_Orderings_Oord_Omax(X5,hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dual__max)). 6.97/7.20 fof(fact_part__equivp__symp, axiom, ![X38, X35, X67, X5]:(c_Equiv__Relations_Opart__equivp(X5,X67)=>(hBOOL(hAPP(hAPP(X67,X38),X35))<=hBOOL(hAPP(hAPP(X67,X35),X38)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_part__equivp__symp)). 6.97/7.20 fof(fact_sympE, axiom, ![X38, X35, X3, X5]:(c_Predicate_Osymp(X5,X3)=>(hBOOL(hAPP(hAPP(X3,X38),X35))<=hBOOL(hAPP(hAPP(X3,X35),X38)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sympE)). 6.97/7.20 fof(fact_finite__Field, axiom, ![X3, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Relation_OField(X5),X3)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X5)),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Field)). 6.97/7.20 fof(fact_equivp__symp, axiom, ![X38, X35, X67, X5]:((hBOOL(hAPP(hAPP(X67,X38),X35))<=hBOOL(hAPP(hAPP(X67,X35),X38)))<=c_Equiv__Relations_Oequivp(X5,X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equivp__symp)). 6.97/7.20 fof(fact_inf__absorb2, axiom, ![X6, X7, X8]:(class_Lattices_Osemilattice__inf(X8)=>(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),X7)=X7<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X7),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__absorb2)). 6.97/7.20 fof(fact_sup__absorb2, axiom, ![X7, X6, X8]:(class_Lattices_Osemilattice__sup(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),X7))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),X7)=X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__absorb2)). 6.97/7.20 fof(fact_le__iff__inf, axiom, ![X38, X35, X5]:(class_Lattices_Osemilattice__inf(X5)=>(X35=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X35),X38)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),X38)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__iff__inf)). 6.97/7.20 fof(fact_sup__absorb1, axiom, ![X6, X7, X8]:((X6=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),X7)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X7),X6)))<=class_Lattices_Osemilattice__sup(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__absorb1)). 6.97/7.20 fof(fact_Nitpick_Owf_H__def, axiom, ![X3, X5]:(c_Nitpick_Owf_H(X5,X3)<=>((hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X5)),X3))|c_Nitpick_Ounknown(tc_HOL_Obool))&c_Wellfounded_Oacyclic(X5,X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Owf_H__def)). 6.97/7.20 fof(fact_inj__on__iff__eq__card, axiom, ![X18, X12, X4, X5]:((c_Fun_Oinj__on(X5,X12,X18,X4)<=>hAPP(c_Finite__Set_Ocard(X12),hAPP(c_Set_Oimage(X5,X12,X18),X4))=hAPP(c_Finite__Set_Ocard(X5),X4))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__iff__eq__card)). 6.97/7.20 fof(fact_trans__lex__prod, axiom, ![X129, X12, X130, X5]:((c_Relation_Otrans(X12,X129)=>c_Relation_Otrans(tc_prod(X5,X12),c_Wellfounded_Olex__prod(X5,X12,X130,X129)))<=c_Relation_Otrans(X5,X130)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trans__lex__prod)). 6.97/7.20 fof(fact_Sup__fin_OF__eq, axiom, ![X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>hAPP(c_Finite__Set_Ofold1(X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X4)=c_Big__Operators_Olattice__class_OSup__fin(X5,X4))<=class_Lattices_Olattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_OF__eq)). 6.97/7.20 fof(fact_Max_OF__eq, axiom, ![X4, X5]:((c_Big__Operators_Olinorder__class_OMax(X5,X4)=hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omax(X5)),X4)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max_OF__eq)). 6.97/7.20 fof(fact_Min_OF__eq, axiom, ![X4, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))=>c_Big__Operators_Olinorder__class_OMin(X5,X4)=hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X4))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min_OF__eq)). 6.97/7.20 fof(fact_Inf__fin_OF__eq, axiom, ![X4, X5]:(class_Lattices_Olattice(X5)=>(c_Big__Operators_Olattice__class_OInf__fin(X5,X4)=hAPP(c_Finite__Set_Ofold1(X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X4)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_OF__eq)). 6.97/7.20 fof(fact_wf__lex__prod, axiom, ![X214, X12, X215, X5]:((c_Wellfounded_Owf(X12,X214)=>c_Wellfounded_Owf(tc_prod(X5,X12),c_Wellfounded_Olex__prod(X5,X12,X215,X214)))<=c_Wellfounded_Owf(X5,X215)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__lex__prod)). 6.97/7.20 fof(fact_abs__of__pos, axiom, ![X30, X8]:((hAPP(c_Groups_Oabs__class_Oabs(X8),X30)=X30<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X30)))<=class_Groups_Oordered__ab__group__add__abs(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__of__pos)). 6.97/7.20 fof(fact_abs__of__nonneg, axiom, ![X30, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X30))=>X30=hAPP(c_Groups_Oabs__class_Oabs(X8),X30))<=class_Groups_Oordered__ab__group__add__abs(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__of__nonneg)). 6.97/7.20 fof(fact_minus__unique, axiom, ![X29, X30, X8]:((hAPP(c_Groups_Ouminus__class_Ouminus(X8),X30)=X29<=c_Groups_Ozero__class_Ozero(X8)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29))<=class_Groups_Ogroup__add(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__unique)). 6.97/7.20 fof(fact_eq__neg__iff__add__eq__0, axiom, ![X1, X2, X5]:((c_Groups_Ozero__class_Ozero(X5)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X2),X1)<=>hAPP(c_Groups_Ouminus__class_Ouminus(X5),X1)=X2)<=class_Groups_Ogroup__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__neg__iff__add__eq__0)). 6.97/7.20 fof(fact_transfer__int__nat__set__relations_I1_J, axiom, ![X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X4))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X4))))<=c_Nat__Transfer_Onat__set(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__set__relations_I1_J)). 6.97/7.20 fof(fact_finite__acyclic__wf__converse, axiom, ![X3, X5]:((c_Wellfounded_Owf(X5,hAPP(c_Relation_Oconverse(X5,X5),X3))<=c_Wellfounded_Oacyclic(X5,X3))<=hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X5)),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__acyclic__wf__converse)). 6.97/7.20 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J, axiom, ![X11, X4]:((c_Nat__Transfer_Onat__set(X11)=>c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X4),X11)))<=c_Nat__Transfer_Onat__set(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J)). 6.97/7.20 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J, axiom, ![X11, X4]:((c_Nat__Transfer_Onat__set(X11)=>c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X4),X11)))<=c_Nat__Transfer_Onat__set(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J)). 6.97/7.20 fof(fact_sorted__insort__insert, axiom, ![X35, X23, X5]:(class_Orderings_Olinorder(X5)=>(c_List_Olinorder__class_Osorted(X5,c_List_Olinorder__class_Oinsort__insert__key(X5,X5,c_COMBI(X5),X35,X23))<=c_List_Olinorder__class_Osorted(X5,X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__insort__insert)). 6.97/7.20 fof(fact_acyclic__subset, axiom, ![X3, X66, X5]:(c_Wellfounded_Oacyclic(X5,X66)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),X66))=>c_Wellfounded_Oacyclic(X5,X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acyclic__subset)). 6.97/7.20 fof(fact_antisym__subset, axiom, ![X66, X3, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),X66))=>(c_Relation_Oantisym(X5,X66)=>c_Relation_Oantisym(X5,X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_antisym__subset)). 6.97/7.20 fof(fact_wf__subset, axiom, ![X24, X3, X5]:(c_Wellfounded_Owf(X5,X3)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X24),X3))=>c_Wellfounded_Owf(X5,X24))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__subset)). 6.97/7.20 fof(fact_list__ex__simps_I1_J, axiom, ![X23, X35, X17, X5]:((hBOOL(hAPP(X17,X35))|c_List_Olist__ex(X5,X17,X23))<=>c_List_Olist__ex(X5,X17,hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex__simps_I1_J)). 6.97/7.20 fof(fact_wfP__subset, axiom, ![X24, X3, X5]:((c_Wellfounded_OwfP(X5,X24)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X24),X3)))<=c_Wellfounded_OwfP(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wfP__subset)). 6.97/7.20 fof(fact_mod__eq, axiom, ![X70, X53, X25, X36]:(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X36,X25)=X70<=hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X36,X25),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X53),X70)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__eq)). 6.97/7.20 fof(fact_transfer__nat__int__set__relations_I1_J, axiom, ![X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X4))<=>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)),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__set__relations_I1_J)). 6.97/7.20 fof(fact_fun__upd__def, axiom, ![X1, X18, X12, X5, X2, X35]:((hAPP(X18,X35)=hAPP(c_Fun_Ofun__upd(X5,X12,X18,X2,X1),X35)<=X35!=X2)&(X2=X35=>X1=hAPP(c_Fun_Ofun__upd(X5,X12,X18,X2,X1),X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upd__def)). 6.97/7.20 fof(fact_list__ex__append, axiom, ![X84, X23, X17, X5]:((c_List_Olist__ex(X5,X17,X23)|c_List_Olist__ex(X5,X17,X84))<=>c_List_Olist__ex(X5,X17,hAPP(hAPP(c_List_Oappend(X5),X23),X84))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex__append)). 6.97/7.20 fof(fact_Suc__lessD, axiom, ![X25, X36]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X36),X25))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X36)),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__lessD)). 6.97/7.20 fof(fact_listrel__refl__on, axiom, ![X3, X4, X5]:(c_Relation_Orefl__on(tc_List_Olist(X5),c_List_Olists(X5,X4),c_List_Olistrel(X5,X3))<=c_Relation_Orefl__on(X5,X4,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__refl__on)). 6.97/7.20 fof(fact_equiv__listrel, axiom, ![X3, X4, X5]:(c_Equiv__Relations_Oequiv(X5,X4,X3)=>c_Equiv__Relations_Oequiv(tc_List_Olist(X5),c_List_Olists(X5,X4),c_List_Olistrel(X5,X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__listrel)). 6.97/7.20 fof(fact_prod__eqI, axiom, ![X53, X81, X5, X8]:((hAPP(c_Product__Type_Osnd(X8,X5),X53)=hAPP(c_Product__Type_Osnd(X8,X5),X81)=>X81=X53)<=hAPP(c_Product__Type_Ofst(X8,X5),X53)=hAPP(c_Product__Type_Ofst(X8,X5),X81)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_prod__eqI)). 6.97/7.20 fof(fact_finite__imageD, axiom, ![X4, X18, X12, X5]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X4))<=c_Fun_Oinj__on(X12,X5,X18,X4))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_Oimage(X12,X5,X18),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__imageD)). 6.97/7.20 fof(fact_power__0__left, axiom, ![X25, X8]:((class_Power_Opower(X8)&class_Rings_Osemiring__0(X8))=>((hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Groups_Ozero__class_Ozero(X8)),X25)=c_Groups_Oone__class_Oone(X8)<=X25=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Groups_Ozero__class_Ozero(X8)),X25)=c_Groups_Ozero__class_Ozero(X8)<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__0__left)). 6.97/7.20 fof(fact_min__max_Ole__iff__inf, axiom, ![X38, X35, X5]:((hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X35),X38)=X35<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),X38)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ole__iff__inf)). 6.97/7.20 fof(fact_min__max_Oinf__absorb2, axiom, ![X6, X7, X8]:(class_Orderings_Olinorder(X8)=>(X7=hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X6),X7)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X7),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__absorb2)). 6.97/7.20 fof(fact_abs__minus__cancel, axiom, ![X30, X8]:(hAPP(c_Groups_Oabs__class_Oabs(X8),X30)=hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X30))<=class_Groups_Oordered__ab__group__add__abs(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__minus__cancel)). 6.97/7.20 fof(fact_min__max_Osup__absorb2, axiom, ![X7, X6, X8]:(class_Orderings_Olinorder(X8)=>(X7=hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X6),X7)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__absorb2)). 6.97/7.20 fof(fact_min__max_Osup__absorb1, axiom, ![X6, X7, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X7),X6))=>X6=hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X6),X7))<=class_Orderings_Olinorder(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__absorb1)). 6.97/7.20 fof(fact_list__all2__lengthD, axiom, ![X84, X23, X17, X12, X5]:(c_List_Olist__all2(X5,X12,X17,X23,X84)=>hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12)),X84)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__lengthD)). 6.97/7.20 fof(fact_zmod__zminus1__not__zero, axiom, ![X93, X19]:(c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19),X93)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=>c_Divides_Odiv__class_Omod(tc_Int_Oint,X19,X93)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zminus1__not__zero)). 6.97/7.20 fof(fact_DiffD2, axiom, ![X11, X4, X10, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11)))=>~(hBOOL(hAPP(hAPP(c_member(X5),X10),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_DiffD2)). 6.97/7.20 fof(fact_RangeP_Ointros, axiom, ![X12, X5, X1, X2, X3]:(hBOOL(hAPP(c_Predicate_ORangeP(X5,X12,X3),X1))<=hBOOL(hAPP(hAPP(X3,X2),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_RangeP_Ointros)). 6.97/7.20 fof(fact_in__set__insert, axiom, ![X23, X35, X5]:(X23=c_List_Oinsert(X5,X35,X23)<=hBOOL(hAPP(hAPP(c_member(X5),X35),hAPP(c_List_Oset(X5),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__insert)). 6.97/7.20 fof(fact_abs__of__nat, axiom, ![X25, X8]:(class_Rings_Olinordered__idom(X8)=>hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),X25))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__of__nat)). 6.97/7.20 fof(fact_listsum__rev, axiom, ![X41, X8]:(hAPP(c_List_Omonoid__add__class_Olistsum(X8),X41)=hAPP(c_List_Omonoid__add__class_Olistsum(X8),hAPP(c_List_Orev(X8),X41))<=class_Groups_Ocomm__monoid__add(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__rev)). 6.97/7.20 fof(fact_abs__idempotent, axiom, ![X30, X8]:(hAPP(c_Groups_Oabs__class_Oabs(X8),X30)=hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),X30))<=class_Groups_Oordered__ab__group__add__abs(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__idempotent)). 6.97/7.20 fof(fact_atLeastatMost__empty, axiom, ![X2, X1, X5]:((c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=c_SetInterval_Oord__class_OatLeastAtMost(X5,X2,X1)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X1),X2)))<=class_Orderings_Oorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastatMost__empty)). 6.97/7.20 fof(fact_mod__mod__trivial, axiom, ![X29, X30, X8]:(class_Divides_Osemiring__div(X8)=>c_Divides_Odiv__class_Omod(X8,c_Divides_Odiv__class_Omod(X8,X30,X29),X29)=c_Divides_Odiv__class_Omod(X8,X30,X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mod__trivial)). 6.97/7.20 fof(fact_transfer__nat__int__set__relations_I3_J, axiom, ![X11, X4]:(X4=X11<=>hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X4)=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__set__relations_I3_J)). 6.97/7.20 fof(fact_of__int__of__nat__eq, axiom, ![X25, X8]:(class_Rings_Oring__1(X8)=>hAPP(c_Int_Oring__1__class_Oof__int(X8),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__of__nat__eq)). 6.97/7.20 fof(fact_diff__is__0__eq, axiom, ![X32, X34]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X34),X32)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__is__0__eq)). 6.97/7.20 fof(fact_div__less, axiom, ![X25, X36]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X36),X25))=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X36),X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__less)). 6.97/7.20 fof(fact_inj__of__nat, axiom, ![X5]:(c_Fun_Oinj__on(tc_Nat_Onat,X5,c_Nat_Osemiring__1__class_Oof__nat(X5),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))<=class_Nat_Osemiring__char__0(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__of__nat)). 6.97/7.20 fof(fact_type__definition_OAbs__image, axiom, ![X4, X90, X91, X12, X5]:(c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))=hAPP(c_Set_Oimage(X12,X5,X90),X4)<=c_Typedef_Otype__definition(X5,X12,X91,X90,X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_type__definition_OAbs__image)). 6.97/7.20 fof(fact_abs__zmult__eq__1, axiom, ![X25, X36]:(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),X36),X25))=>c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X36)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__zmult__eq__1)). 6.97/7.20 fof(fact_zero__less__one, axiom, ![X8]:(class_Rings_Olinordered__semidom(X8)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),c_Groups_Oone__class_Oone(X8)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__one)). 6.97/7.20 fof(fact_zero__le__one, axiom, ![X8]:(class_Rings_Olinordered__semidom(X8)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),c_Groups_Oone__class_Oone(X8)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__one)). 6.97/7.20 fof(fact_order__antisym, axiom, ![X7, X6, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),X7))=>(X7=X6<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X7),X6))))<=class_Orderings_Oorder(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__antisym)). 6.97/7.20 fof(fact_card__ge__0__finite, axiom, ![X4, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__ge__0__finite)). 6.97/7.20 fof(fact_rp__inv__image__rp, axiom, ![X18, X12, X17, X5]:(c_FunDef_Oreduction__pair(X5,X17)=>c_FunDef_Oreduction__pair(X12,hAPP(hAPP(c_FunDef_Orp__inv__image(X5,X12),X17),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rp__inv__image__rp)). 6.97/7.20 fof(fact_trans__inv__image, axiom, ![X18, X12, X3, X5]:(c_Relation_Otrans(X5,X3)=>c_Relation_Otrans(X12,hAPP(hAPP(c_Relation_Oinv__image(X5,X12),X3),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trans__inv__image)). 6.97/7.20 fof(fact_sym__inv__image, axiom, ![X18, X12, X3, X5]:(c_Relation_Osym(X5,X3)=>c_Relation_Osym(X12,hAPP(hAPP(c_Relation_Oinv__image(X5,X12),X3),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sym__inv__image)). 6.97/7.20 fof(fact_diffs0__imp__equal, axiom, ![X25, X36]:((X25=X36<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X36))<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diffs0__imp__equal)). 6.97/7.20 fof(fact_wf__inv__image, axiom, ![X18, X12, X3, X5]:(c_Wellfounded_Owf(X5,X3)=>c_Wellfounded_Owf(X12,hAPP(hAPP(c_Relation_Oinv__image(X5,X12),X3),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__inv__image)). 6.97/7.20 fof(fact_acc__wfD, axiom, ![X35, X3, X5]:(c_Wellfounded_Owf(X5,X3)=>hBOOL(hAPP(hAPP(c_member(X5),X35),c_Wellfounded_Oacc(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acc__wfD)). 6.97/7.20 fof(fact_hd__rev, axiom, ![X8, X41]:(c_List_Olast(X8,X41)=hAPP(c_List_Ohd(X8),hAPP(c_List_Orev(X8),X41))<=c_List_Olist_ONil(X8)!=X41), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__rev)). 6.97/7.20 fof(fact_listsum__foldl, axiom, ![X5]:(c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),c_Groups_Ozero__class_Ozero(X5))=c_List_Omonoid__add__class_Olistsum(X5)<=class_Groups_Omonoid__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__foldl)). 6.97/7.20 fof(fact_sorted__drop, axiom, ![X25, X41, X8]:(class_Orderings_Olinorder(X8)=>(c_List_Olinorder__class_Osorted(X8,X41)=>c_List_Olinorder__class_Osorted(X8,hAPP(hAPP(c_List_Odrop(X8),X25),X41)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__drop)). 6.97/7.20 fof(fact_sorted__take, axiom, ![X25, X41, X8]:((c_List_Olinorder__class_Osorted(X8,hAPP(hAPP(c_List_Otake(X8),X25),X41))<=c_List_Olinorder__class_Osorted(X8,X41))<=class_Orderings_Olinorder(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__take)). 6.97/7.20 fof(fact_distinct__sublistI, axiom, ![X15, X23, X5]:(hBOOL(hAPP(c_List_Odistinct(X5),c_List_Osublist(X5,X23,X15)))<=hBOOL(hAPP(c_List_Odistinct(X5),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__sublistI)). 6.97/7.20 fof(fact_distinct__remove1, axiom, ![X6, X41, X8]:(hBOOL(hAPP(c_List_Odistinct(X8),X41))=>hBOOL(hAPP(c_List_Odistinct(X8),c_List_Oremove1(X8,X6,X41)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__remove1)). 6.97/7.20 fof(fact_distinct__insert, axiom, ![X6, X41, X8]:(hBOOL(hAPP(c_List_Odistinct(X8),c_List_Oinsert(X8,X6,X41)))<=hBOOL(hAPP(c_List_Odistinct(X8),X41))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__insert)). 6.97/7.20 fof(fact_singletonE, axiom, ![X2, X1, X5]:(X1=X2<=hBOOL(hAPP(hAPP(c_member(X5),X1),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_singletonE)). 6.97/7.20 fof(fact_distinct__takeWhile, axiom, ![X17, X23, X5]:(hBOOL(hAPP(c_List_Odistinct(X5),X23))=>hBOOL(hAPP(c_List_Odistinct(X5),c_List_OtakeWhile(X5,X17,X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__takeWhile)). 6.97/7.20 fof(fact_distinct__tl, axiom, ![X41, X8]:(hBOOL(hAPP(c_List_Odistinct(X8),hAPP(c_List_Otl(X8),X41)))<=hBOOL(hAPP(c_List_Odistinct(X8),X41))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__tl)). 6.97/7.20 fof(fact_distinct1__rotate, axiom, ![X23, X5]:(hBOOL(hAPP(c_List_Odistinct(X5),hAPP(c_List_Orotate1(X5),X23)))<=>hBOOL(hAPP(c_List_Odistinct(X5),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct1__rotate)). 6.97/7.20 fof(fact_distinct__rev, axiom, ![X23, X5]:(hBOOL(hAPP(c_List_Odistinct(X5),X23))<=>hBOOL(hAPP(c_List_Odistinct(X5),hAPP(c_List_Orev(X5),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__rev)). 6.97/7.20 fof(fact_Un__empty, axiom, ![X11, X4, X5]:((X11=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))&c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=X4)<=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11)=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__empty)). 6.97/7.20 fof(fact_greaterThanLessThan__empty, axiom, ![X33, X52, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X52),X33))=>c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X33,X52))<=class_Orderings_Oorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_greaterThanLessThan__empty)). 6.97/7.20 fof(fact_greaterThanAtMost__empty, axiom, ![X33, X52, X5]:(class_Orderings_Oorder(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X52),X33))=>c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X33,X52))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_greaterThanAtMost__empty)). 6.97/7.20 fof(fact_zabs__def, axiom, ![X28]:((hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X28)=X28<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X28),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X28),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X28)=hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X28))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zabs__def)). 6.97/7.20 fof(fact_sorted__list__of__set, axiom, ![X4, X5]:(class_Orderings_Olinorder(X5)=>(((hBOOL(hAPP(c_List_Odistinct(X5),c_List_Olinorder__class_Osorted__list__of__set(X5,X4)))&c_List_Olinorder__class_Osorted(X5,c_List_Olinorder__class_Osorted__list__of__set(X5,X4)))&X4=hAPP(c_List_Oset(X5),c_List_Olinorder__class_Osorted__list__of__set(X5,X4)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__list__of__set)). 6.97/7.20 fof(fact_abs__minus__one, axiom, ![X8]:(c_Groups_Oone__class_Oone(X8)=hAPP(c_Groups_Oabs__class_Oabs(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OMin))<=(class_Int_Onumber__ring(X8)&class_Rings_Olinordered__idom(X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__minus__one)). 6.97/7.20 fof(fact_atLeastAtMost__singleton__iff, axiom, ![X10, X1, X2, X5]:(class_Orderings_Oorder(X5)=>(hAPP(hAPP(c_Set_Oinsert(X5),X10),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))=c_SetInterval_Oord__class_OatLeastAtMost(X5,X2,X1)<=>(X1=X2&X1=X10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastAtMost__singleton__iff)). 6.97/7.20 fof(fact_no__zero__divisors, axiom, ![X29, X30, X8]:(((X29!=c_Groups_Ozero__class_Ozero(X8)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29)!=c_Groups_Ozero__class_Ozero(X8))<=c_Groups_Ozero__class_Ozero(X8)!=X30)<=class_Rings_Ono__zero__divisors(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_no__zero__divisors)). 6.97/7.20 fof(fact_rotate1__length01, axiom, ![X41, X8]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=>hAPP(c_List_Orotate1(X8),X41)=X41), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate1__length01)). 6.97/7.20 fof(fact_hd__conv__nth, axiom, ![X8, X41]:(hAPP(c_List_Ohd(X8),X41)=hAPP(hAPP(c_List_Onth(X8),X41),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<=X41!=c_List_Olist_ONil(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__conv__nth)). 6.97/7.20 fof(fact_le__iff__sup, axiom, ![X38, X35, X5]:((hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X35),X38)=X38<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),X38)))<=class_Lattices_Osemilattice__sup(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__iff__sup)). 6.97/7.20 fof(fact_last__rev, axiom, ![X8, X41]:(hAPP(c_List_Ohd(X8),X41)=c_List_Olast(X8,hAPP(c_List_Orev(X8),X41))<=X41!=c_List_Olist_ONil(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__rev)). 6.97/7.20 fof(fact_sgn__pos, axiom, ![X30, X8]:(class_Rings_Olinordered__idom(X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X30))=>c_Groups_Oone__class_Oone(X8)=c_Groups_Osgn__class_Osgn(X8,X30))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__pos)). 6.97/7.20 fof(fact_fun__left__comm__insort, axiom, ![X5]:(c_Finite__Set_Ofun__left__comm(X5,tc_List_Olist(X5),c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__insort)). 6.97/7.20 fof(fact_Nats__1, axiom, ![X5]:(class_Rings_Osemiring__1(X5)=>hBOOL(hAPP(hAPP(c_member(X5),c_Groups_Oone__class_Oone(X5)),c_Nat_Osemiring__1__class_ONats(X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nats__1)). 6.97/7.20 fof(fact_Ints__1, axiom, ![X5]:(hBOOL(hAPP(hAPP(c_member(X5),c_Groups_Oone__class_Oone(X5)),c_Int_Oring__1__class_OInts(X5)))<=class_Rings_Oring__1(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__1)). 6.97/7.20 fof(fact_Nats__0, axiom, ![X5]:(hBOOL(hAPP(hAPP(c_member(X5),c_Groups_Ozero__class_Ozero(X5)),c_Nat_Osemiring__1__class_ONats(X5)))<=class_Rings_Osemiring__1(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nats__0)). 6.97/7.20 fof(fact_Ints__0, axiom, ![X5]:(class_Rings_Oring__1(X5)=>hBOOL(hAPP(hAPP(c_member(X5),c_Groups_Ozero__class_Ozero(X5)),c_Int_Oring__1__class_OInts(X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__0)). 6.97/7.20 fof(fact_tsub__def, axiom, ![X6, X7]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7),X6))=>c_Nat__Transfer_Otsub(X6,X7)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X6),X7))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Nat__Transfer_Otsub(X6,X7)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7),X6))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tsub__def)). 6.97/7.20 fof(fact_sorted__single, axiom, ![X6, X8]:(c_List_Olinorder__class_Osorted(X8,hAPP(hAPP(c_List_Olist_OCons(X8),X6),c_List_Olist_ONil(X8)))<=class_Orderings_Olinorder(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__single)). 6.97/7.20 fof(fact_zle__antisym, axiom, ![X39, X26]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26),X39))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X39),X26))=>X26=X39)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zle__antisym)). 6.97/7.20 fof(fact_le__antisym, axiom, ![X25, X36]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X36),X25))=>(X36=X25<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X36)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__antisym)). 6.97/7.20 fof(fact_wf__not__refl, axiom, ![X2, X3, X5]:(~(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X2)),X3)))<=c_Wellfounded_Owf(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__not__refl)). 6.97/7.20 fof(fact_insert__absorb, axiom, ![X4, X2, X5]:(hBOOL(hAPP(hAPP(c_member(X5),X2),X4))=>X4=hAPP(hAPP(c_Set_Oinsert(X5),X2),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__absorb)). 6.97/7.20 fof(fact_le__less__Suc__eq, axiom, ![X32, X34]:((X34=X32<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32),hAPP(c_Nat_OSuc,X34))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__less__Suc__eq)). 6.97/7.20 fof(fact_Respects__def, axiom, ![X35, X67, X5]:(hBOOL(hAPP(hAPP(X67,X35),X35))<=>hBOOL(hAPP(c_Quotient_ORespects(X5,X67),X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Respects__def)). 6.97/7.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, axiom, ![X30, X8]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ozero__class_Ozero(X8)),X30)=c_Groups_Ozero__class_Ozero(X8)<=class_Rings_Ocomm__semiring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J)). 6.97/7.20 fof(fact_divide__zero__left, axiom, ![X30, X8]:(class_Rings_Odivision__ring(X8)=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),c_Groups_Ozero__class_Ozero(X8)),X30)=c_Groups_Ozero__class_Ozero(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__zero__left)). 6.97/7.20 fof(fact_sup__top__left, axiom, ![X6, X8]:(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),c_Orderings_Otop__class_Otop(X8)),X6)=c_Orderings_Otop__class_Otop(X8)<=class_Lattices_Obounded__lattice__top(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__top__left)). 6.97/7.20 fof(fact_power__one, axiom, ![X25, X8]:(class_Groups_Omonoid__mult(X8)=>c_Groups_Oone__class_Oone(X8)=hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Groups_Oone__class_Oone(X8)),X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__one)). 6.97/7.20 fof(fact_LeastI__ex, axiom, ![X17, X5]:(class_Orderings_Owellorder(X5)=>(hBOOL(hAPP(X17,c_Orderings_Oord__class_OLeast(X5,X17)))<=?[X76]:hBOOL(hAPP(X17,X76)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_LeastI__ex)). 6.97/7.20 fof(fact_divmod__int__correct, axiom, ![X30, X29]:(hBOOL(hAPP(c_Divides_Odivmod__int__rel(X30,X29),c_Divides_Odivmod__int(X30,X29)))<=X29!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__correct)). 6.97/7.20 fof(fact_div__0, axiom, ![X30, X8]:(class_Divides_Osemiring__div(X8)=>c_Groups_Ozero__class_Ozero(X8)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),c_Groups_Ozero__class_Ozero(X8)),X30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__0)). 6.97/7.20 fof(fact_mult__zero__left, axiom, ![X30, X8]:(class_Rings_Omult__zero(X8)=>c_Groups_Ozero__class_Ozero(X8)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ozero__class_Ozero(X8)),X30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__zero__left)). 6.97/7.20 fof(fact_inf__bot__left, axiom, ![X6, X8]:(class_Lattices_Obounded__lattice__bot(X8)=>c_Orderings_Obot__class_Obot(X8)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),c_Orderings_Obot__class_Obot(X8)),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__bot__left)). 6.97/7.20 fof(fact_div__by__0, axiom, ![X30, X8]:(class_Divides_Osemiring__div(X8)=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),X30),c_Groups_Ozero__class_Ozero(X8))=c_Groups_Ozero__class_Ozero(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__by__0)). 6.97/7.20 fof(fact_min__max_Ole__iff__sup, axiom, ![X38, X35, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),X38))<=>X38=hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X35),X38))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ole__iff__sup)). 6.97/7.20 fof(fact_mult__zero__right, axiom, ![X30, X8]:(class_Rings_Omult__zero(X8)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),c_Groups_Ozero__class_Ozero(X8))=c_Groups_Ozero__class_Ozero(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__zero__right)). 6.97/7.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, axiom, ![X30, X8]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),c_Groups_Ozero__class_Ozero(X8))=c_Groups_Ozero__class_Ozero(X8)<=class_Rings_Ocomm__semiring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J)). 6.97/7.20 fof(fact_sup__top__right, axiom, ![X6, X8]:(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),c_Orderings_Otop__class_Otop(X8))=c_Orderings_Otop__class_Otop(X8)<=class_Lattices_Obounded__lattice__top(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__top__right)). 6.97/7.20 fof(fact_divide__zero, axiom, ![X30, X8]:(c_Groups_Ozero__class_Ozero(X8)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X30),c_Groups_Ozero__class_Ozero(X8))<=class_Rings_Odivision__ring__inverse__zero(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__zero)). 6.97/7.20 fof(fact_inf__bot__right, axiom, ![X6, X8]:(class_Lattices_Obounded__lattice__bot(X8)=>c_Orderings_Obot__class_Obot(X8)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),c_Orderings_Obot__class_Obot(X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__bot__right)). 6.97/7.20 fof(fact_finite__PlusD_I1_J, axiom, ![X11, X4, X12, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X5,X12)),c_Sum__Type_OPlus(X5,X12,X4,X11)))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__PlusD_I1_J)). 6.97/7.20 fof(fact_finite__PlusD_I2_J, axiom, ![X11, X4, X12, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X5,X12)),c_Sum__Type_OPlus(X5,X12,X4,X11)))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__PlusD_I2_J)). 6.97/7.20 fof(fact_folding__image__simple__idem_Oidem, axiom, ![X35, X55, X50, X14, X18, X12, X5]:(c_Finite__Set_Ofolding__image__simple__idem(X5,X12,X18,X14,X50,X55)=>X35=hAPP(hAPP(X18,X35),X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple__idem_Oidem)). 6.97/7.20 fof(fact_divide__self__if, axiom, ![X30, X8]:(((hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X30),X30)=c_Groups_Ozero__class_Ozero(X8)<=c_Groups_Ozero__class_Ozero(X8)=X30)&(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X30),X30)=c_Groups_Oone__class_Oone(X8)<=c_Groups_Ozero__class_Ozero(X8)!=X30))<=class_Rings_Odivision__ring__inverse__zero(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__self__if)). 6.97/7.20 fof(fact_ComplD, axiom, ![X4, X10, X5]:(~(hBOOL(hAPP(hAPP(c_member(X5),X10),X4)))<=hBOOL(hAPP(hAPP(c_member(X5),X10),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ComplD)). 6.97/7.20 fof(fact_total__on__converse, axiom, ![X3, X4, X5]:(c_Relation_Ototal__on(X5,X4,X3)<=>c_Relation_Ototal__on(X5,X4,hAPP(c_Relation_Oconverse(X5,X5),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_total__on__converse)). 6.97/7.20 fof(fact_Rep__Integ__cases, axiom, ![X38]:(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X38),c_Int_OInteg))=>~(![X22]:X38!=hAPP(c_Int_ORep__Integ,X22))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Rep__Integ__cases)). 6.97/7.20 fof(fact_refl__on__converse, axiom, ![X3, X4, X5]:(c_Relation_Orefl__on(X5,X4,hAPP(c_Relation_Oconverse(X5,X5),X3))<=>c_Relation_Orefl__on(X5,X4,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__on__converse)). 6.97/7.20 fof(fact_add__right__cancel, axiom, ![X10, X2, X1, X5]:((X1=X10<=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X1),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X10),X2))<=class_Groups_Ocancel__semigroup__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__right__cancel)). 6.97/7.20 fof(fact_div__self, axiom, ![X30, X8]:((c_Groups_Oone__class_Oone(X8)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),X30),X30)<=c_Groups_Ozero__class_Ozero(X8)!=X30)<=class_Divides_Osemiring__div(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__self)). 6.97/7.20 fof(fact_bot__least, axiom, ![X6, X8]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Orderings_Obot__class_Obot(X8)),X6))<=class_Orderings_Obot(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bot__least)). 6.97/7.20 fof(fact_not__neg__eq__ge__0, axiom, ![X35]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X35))<=>~(hBOOL(hAPP(c_Nat__Numeral_Oneg,X35)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__neg__eq__ge__0)). 6.97/7.20 fof(fact_add__imp__eq, axiom, ![X31, X29, X30, X8]:(class_Groups_Ocancel__ab__semigroup__add(X8)=>(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X31)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29)=>X31=X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__imp__eq)). 6.97/7.20 fof(fact_add__left__imp__eq, axiom, ![X31, X29, X30, X8]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X31)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),X29)=>X31=X29)<=class_Groups_Ocancel__semigroup__add(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__left__imp__eq)). 6.97/7.20 fof(fact_divide__self, axiom, ![X30, X8]:(class_Rings_Odivision__ring(X8)=>(c_Groups_Ozero__class_Ozero(X8)!=X30=>c_Groups_Oone__class_Oone(X8)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X30),X30))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__self)). 6.97/7.20 fof(fact_dvd__0__right, axiom, ![X30, X8]:(class_Rings_Ocomm__semiring__1(X8)=>hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X8),X30),c_Groups_Ozero__class_Ozero(X8)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dvd__0__right)). 6.97/7.20 fof(fact_top__greatest, axiom, ![X6, X8]:(class_Orderings_Otop(X8)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),c_Orderings_Otop__class_Otop(X8)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_top__greatest)). 6.97/7.20 fof(fact_mult__eq__self__implies__10, axiom, ![X25, X36]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X36|c_Groups_Oone__class_Oone(tc_Nat_Onat)=X25)<=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X25)=X36), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__eq__self__implies__10)). 6.97/7.20 fof(fact_hd__replicate, axiom, ![X6, X8, X25]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X25=>X6=hAPP(c_List_Ohd(X8),c_List_Oreplicate(X8,X25,X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__replicate)). 6.97/7.20 fof(fact_wf__lexn, axiom, ![X32, X3, X5]:(c_Wellfounded_Owf(tc_List_Olist(X5),hAPP(c_List_Olexn(X5,X3),X32))<=c_Wellfounded_Owf(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__lexn)). 6.97/7.20 fof(fact_card__distinct, axiom, ![X23, X5]:(hBOOL(hAPP(c_List_Odistinct(X5),X23))<=hAPP(c_Finite__Set_Ocard(X5),hAPP(c_List_Oset(X5),X23))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__distinct)). 6.97/7.20 fof(fact_injD, axiom, ![X38, X35, X18, X12, X5]:(c_Fun_Oinj__on(X5,X12,X18,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))=>(hAPP(X18,X38)=hAPP(X18,X35)=>X35=X38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_injD)). 6.97/7.20 fof(fact_less__or__eq__imp__le, axiom, ![X25, X36]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X36),X25))|X36=X25)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X36),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__or__eq__imp__le)). 6.97/7.20 fof(fact_int__le__0__conv, axiom, ![X32]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X32)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=>X32=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__le__0__conv)). 6.97/7.20 fof(fact_Pair__inject, axiom, ![X68, X69, X29, X30, X5, X8]:(hAPP(hAPP(c_Product__Type_OPair(X8,X5),X30),X29)=hAPP(hAPP(c_Product__Type_OPair(X8,X5),X69),X68)=>~((X69=X30=>X29!=X68))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pair__inject)). 6.97/7.20 fof(fact_Pair__eq, axiom, ![X259, X165, X1, X2, X12, X5]:((X259=X1&X2=X165)<=>hAPP(hAPP(c_Product__Type_OPair(X5,X12),X2),X1)=hAPP(hAPP(c_Product__Type_OPair(X5,X12),X165),X259)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pair__eq)). 6.97/7.20 fof(fact_power__0, axiom, ![X30, X8]:(class_Power_Opower(X8)=>hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__0)). 6.97/7.20 fof(fact_sorted__butlast, axiom, ![X41, X8]:(class_Orderings_Olinorder(X8)=>(c_List_Olist_ONil(X8)!=X41=>(c_List_Olinorder__class_Osorted(X8,X41)=>c_List_Olinorder__class_Osorted(X8,c_List_Obutlast(X8,X41))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__butlast)). 6.97/7.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, axiom, ![X6, X8]:(class_Rings_Ocomm__semiring__1(X8)=>c_Groups_Oone__class_Oone(X8)=hAPP(hAPP(c_Power_Opower__class_Opower(X8),X6),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J)). 6.97/7.20 fof(fact_right__inverse__eq, axiom, ![X2, X1, X5]:(class_Rings_Odivision__ring(X5)=>(X1!=c_Groups_Ozero__class_Ozero(X5)=>(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X2),X1)=c_Groups_Oone__class_Oone(X5)<=>X1=X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_right__inverse__eq)). 6.97/7.20 fof(fact_wf__no__loop, axiom, ![X67, X5]:(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))=hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X67),X67)=>c_Wellfounded_Owf(X5,X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__no__loop)). 6.97/7.20 fof(fact_negative__eq__positive, axiom, ![X34, X32]:(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X32))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X34)<=>(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X34&X32=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negative__eq__positive)). 6.97/7.20 fof(fact_inf1D1, axiom, ![X35, X11, X4, X5]:(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11),X35))=>hBOOL(hAPP(X4,X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf1D1)). 6.97/7.20 fof(fact_inf1D2, axiom, ![X35, X11, X4, X5]:(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11),X35))=>hBOOL(hAPP(X11,X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf1D2)). 6.97/7.20 fof(fact_type__definition_ORep__inverse, axiom, ![X35, X4, X90, X91, X12, X5]:(c_Typedef_Otype__definition(X5,X12,X91,X90,X4)=>X35=hAPP(X90,hAPP(X91,X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_type__definition_ORep__inverse)). 6.97/7.20 fof(fact_conversepD, axiom, ![X1, X2, X3, X12, X5]:(hBOOL(hAPP(hAPP(X3,X1),X2))<=hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X5,X12,X3),X2),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_conversepD)). 6.97/7.20 fof(fact_enum__ex, axiom, ![X17, X5]:(class_Enum_Oenum(X5)=>(?[X76]:hBOOL(hAPP(X17,X76))<=>hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X5),X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__ex)). 6.97/7.20 fof(fact_exists__code, axiom, ![X17, X5]:((?[X76]:hBOOL(hAPP(X17,X76))<=>hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X5),X17)))<=class_Enum_Oenum(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_exists__code)). 6.97/7.20 fof(fact_bij__betw__same__card, axiom, ![X11, X4, X18, X12, X5]:(hAPP(c_Finite__Set_Ocard(X12),X11)=hAPP(c_Finite__Set_Ocard(X5),X4)<=c_Fun_Obij__betw(X5,X12,X18,X4,X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bij__betw__same__card)). 6.97/7.20 fof(fact_bij__betw__empty2, axiom, ![X4, X18, X12, X5]:(c_Fun_Obij__betw(X5,X12,X18,X4,c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool)))=>c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bij__betw__empty2)). 6.97/7.20 fof(fact_add__0__left, axiom, ![X30, X8]:(class_Groups_Omonoid__add(X8)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),c_Groups_Ozero__class_Ozero(X8)),X30)=X30), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__0__left)). 6.97/7.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, axiom, ![X30, X8]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),c_Groups_Ozero__class_Ozero(X8)),X30)=X30<=class_Rings_Ocomm__semiring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J)). 6.97/7.20 fof(fact_add__0, axiom, ![X30, X8]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),c_Groups_Ozero__class_Ozero(X8)),X30)=X30<=class_Groups_Ocomm__monoid__add(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__0)). 6.97/7.20 fof(fact_inf__top__left, axiom, ![X6, X8]:(class_Lattices_Obounded__lattice__top(X8)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),c_Orderings_Otop__class_Otop(X8)),X6)=X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__top__left)). 6.97/7.20 fof(fact_bij__betw__empty1, axiom, ![X4, X18, X12, X5]:(c_Fun_Obij__betw(X5,X12,X18,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),X4)=>X4=c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bij__betw__empty1)). 6.97/7.20 fof(fact_folding__image__simple_Oempty, axiom, ![X55, X50, X14, X18, X12, X5]:(c_Finite__Set_Ofolding__image__simple(X5,X12,X18,X14,X50,X55)=>X14=hAPP(X55,c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple_Oempty)). 6.97/7.20 fof(fact_mult__1__left, axiom, ![X30, X8]:(class_Groups_Omonoid__mult(X8)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oone__class_Oone(X8)),X30)=X30), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__1__left)). 6.97/7.20 fof(fact_mult__1, axiom, ![X30, X8]:(class_Groups_Ocomm__monoid__mult(X8)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oone__class_Oone(X8)),X30)=X30), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__1)). 6.97/7.20 fof(fact_sup__bot__left, axiom, ![X6, X8]:(class_Lattices_Obounded__lattice__bot(X8)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),c_Orderings_Obot__class_Obot(X8)),X6)=X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__bot__left)). 6.97/7.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, axiom, ![X30, X8]:(X30=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oone__class_Oone(X8)),X30)<=class_Rings_Ocomm__semiring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J)). 6.97/7.20 fof(fact_order__less__asym, axiom, ![X7, X6, X8]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X6),X7))=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X7),X6))))<=class_Orderings_Opreorder(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__less__asym)). 6.97/7.20 fof(fact_xt1_I9_J, axiom, ![X30, X29, X8]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),X29)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X29),X30)))<=class_Orderings_Oorder(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_xt1_I9_J)). 6.97/7.20 fof(fact_div__by__1, axiom, ![X30, X8]:(hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8),X30),c_Groups_Oone__class_Oone(X8))=X30<=class_Divides_Osemiring__div(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__by__1)). 6.97/7.20 fof(fact_mult__1__right, axiom, ![X30, X8]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),c_Groups_Oone__class_Oone(X8))=X30<=class_Groups_Omonoid__mult(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__1__right)). 6.97/7.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, axiom, ![X30, X8]:(class_Rings_Ocomm__semiring__1(X8)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),c_Groups_Oone__class_Oone(X8))=X30), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J)). 6.97/7.20 fof(fact_not__less__iff__gr__or__eq, axiom, ![X38, X35, X5]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X35),X38)))<=>(X38=X35|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X38),X35))))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__less__iff__gr__or__eq)). 6.97/7.20 fof(fact_divmod__nat__rel__unique, axiom, ![X118, X119, X25, X36]:((hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X36,X25),X118))=>X119=X118)<=hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X36,X25),X119))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__rel__unique)). 6.97/7.20 fof(fact_Compl__eq__Compl__iff, axiom, ![X11, X4, X5]:(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X4)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X11)<=>X4=X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__eq__Compl__iff)). 6.97/7.20 fof(fact_double__compl, axiom, ![X6, X8]:(hAPP(c_Groups_Ouminus__class_Ouminus(X8),hAPP(c_Groups_Ouminus__class_Ouminus(X8),X6))=X6<=class_Lattices_Oboolean__algebra(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_double__compl)). 6.97/7.20 fof(fact_diff__0__right, axiom, ![X30, X8]:(class_Groups_Ogroup__add(X8)=>X30=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X30),c_Groups_Ozero__class_Ozero(X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__0__right)). 6.97/7.20 fof(fact_add__0__right, axiom, ![X30, X8]:(class_Groups_Omonoid__add(X8)=>X30=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),c_Groups_Ozero__class_Ozero(X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__0__right)). 6.97/7.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, axiom, ![X30, X8]:(X30=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),c_Groups_Ozero__class_Ozero(X8))<=class_Rings_Ocomm__semiring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J)). 6.97/7.20 fof(fact_nat__add__right__cancel, axiom, ![X32, X33, X34]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X33)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34),X33)<=>X34=X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__add__right__cancel)). 6.97/7.20 fof(fact_nat__add__left__cancel, axiom, ![X32, X34, X33]:(X32=X34<=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X34)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__add__left__cancel)). 6.97/7.20 fof(fact_add_Ocomm__neutral, axiom, ![X30, X8]:(X30=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X30),c_Groups_Ozero__class_Ozero(X8))<=class_Groups_Ocomm__monoid__add(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add_Ocomm__neutral)). 6.97/7.20 fof(fact_inf__top__right, axiom, ![X6, X8]:(X6=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),c_Orderings_Otop__class_Otop(X8))<=class_Lattices_Obounded__lattice__top(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__top__right)). 6.97/7.20 fof(fact_mult_Ocomm__neutral, axiom, ![X30, X8]:(X30=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),c_Groups_Oone__class_Oone(X8))<=class_Groups_Ocomm__monoid__mult(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult_Ocomm__neutral)). 6.97/7.20 fof(fact_divide__1, axiom, ![X30, X8]:(X30=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),X30),c_Groups_Oone__class_Oone(X8))<=class_Rings_Odivision__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__1)). 6.97/7.20 fof(fact_beyond__def, axiom, ![X93, X19]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X19),X93))=>X93=c_Quickcheck_Obeyond(X19,X93))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X19),X93)))=>c_Quickcheck_Obeyond(X19,X93)=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_beyond__def)). 6.97/7.20 fof(fact_sup__bot__right, axiom, ![X6, X8]:(X6=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),c_Orderings_Obot__class_Obot(X8))<=class_Lattices_Obounded__lattice__bot(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__bot__right)). 6.97/7.20 fof(fact_power__one__right, axiom, ![X30, X8]:(class_Groups_Omonoid__mult(X8)=>X30=hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),c_Groups_Oone__class_Oone(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__one__right)). 6.97/7.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, axiom, ![X6, X8]:(class_Rings_Ocomm__semiring__1(X8)=>X6=hAPP(hAPP(c_Power_Opower__class_Opower(X8),X6),c_Groups_Oone__class_Oone(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J)). 6.97/7.20 fof(fact_babs__reg__eqv, axiom, ![X17, X12, X67, X5]:(c_Quotient_OBabs(X5,X12,c_Quotient_ORespects(X5,X67),X17)=X17<=c_Equiv__Relations_Oequivp(X5,X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_babs__reg__eqv)). 6.97/7.20 fof(fact_sorted__sort, axiom, ![X23, X5]:(c_List_Olinorder__class_Osorted(X5,c_List_Olinorder__class_Osort__key(X5,X5,c_COMBI(X5),X23))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__sort)). 6.97/7.20 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J, axiom, ![X7, X6]:(c_Nat__Transfer_Ois__nat(X6)=>(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6),X7))<=c_Nat__Transfer_Ois__nat(X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Divides_Otransfer__int__nat__function__closures_I1_J)). 6.97/7.20 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J, axiom, ![X7, X6]:((c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6),X7))<=c_Nat__Transfer_Ois__nat(X7))<=c_Nat__Transfer_Ois__nat(X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J)). 6.97/7.20 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J, axiom, ![X7, X6]:(c_Nat__Transfer_Ois__nat(X6)=>(c_Nat__Transfer_Ois__nat(X7)=>c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X6),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J)). 6.97/7.20 fof(fact_take__eq__Nil, axiom, ![X23, X32, X5]:(c_List_Olist_ONil(X5)=hAPP(hAPP(c_List_Otake(X5),X32),X23)<=>(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X32|c_List_Olist_ONil(X5)=X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__eq__Nil)). 6.97/7.20 fof(fact_mult__is__0, axiom, ![X32, X34]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X32)<=>(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X32|X34=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__is__0)). 6.97/7.20 fof(fact_n__lists__Nil, axiom, ![X8, X25]:((X25!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>c_List_Olist_ONil(tc_List_Olist(X8))=c_Enum_On__lists(X8,X25,c_List_Olist_ONil(X8)))&(hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X8)),c_List_Olist_ONil(X8)),c_List_Olist_ONil(tc_List_Olist(X8)))=c_Enum_On__lists(X8,X25,c_List_Olist_ONil(X8))<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_n__lists__Nil)). 6.97/7.20 fof(fact_list__all__rev, axiom, ![X23, X17, X5]:(c_List_Olist__all(X5,X17,hAPP(c_List_Orev(X5),X23))<=>c_List_Olist__all(X5,X17,X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all__rev)). 6.97/7.20 fof(fact_list__ex__rev, axiom, ![X23, X17, X5]:(c_List_Olist__ex(X5,X17,hAPP(c_List_Orev(X5),X23))<=>c_List_Olist__ex(X5,X17,X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex__rev)). 6.97/7.20 fof(fact_mem__def, axiom, ![X4, X35, X5]:(hBOOL(hAPP(X4,X35))<=>hBOOL(hAPP(hAPP(c_member(X5),X35),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mem__def)). 6.97/7.20 fof(fact_someI, axiom, ![X5, X35, X17]:(hBOOL(hAPP(X17,X35))=>hBOOL(hAPP(X17,c_Hilbert__Choice_OEps(X5,X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_someI)). 6.97/7.20 fof(fact_some__eq__ex, axiom, ![X5, X17]:(?[X76]:hBOOL(hAPP(X17,X76))<=>hBOOL(hAPP(X17,c_Hilbert__Choice_OEps(X5,X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_some__eq__ex)). 6.97/7.20 fof(fact_folding_Oempty, axiom, ![X55, X18, X12, X5]:(c_Fun_Oid(X12)=hAPP(X55,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))<=c_Finite__Set_Ofolding(X5,X12,X18,X55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Oempty)). 6.97/7.20 fof(fact_inj__on__imageI2, axiom, ![X4, X18, X138, X62, X12, X5]:(c_Fun_Oinj__on(X5,X62,X18,X4)<=c_Fun_Oinj__on(X5,X12,hAPP(c_Fun_Ocomp(X62,X12,X5,X138),X18),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__imageI2)). 6.97/7.20 fof(fact_bot__apply, axiom, ![X35, X12, X5]:(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X12,X5)),X35)=c_Orderings_Obot__class_Obot(X5)<=class_Orderings_Obot(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bot__apply)). 6.97/7.20 fof(fact_top__apply, axiom, ![X35, X12, X5]:(c_Orderings_Otop__class_Otop(X5)=hAPP(c_Orderings_Otop__class_Otop(tc_fun(X12,X5)),X35)<=class_Orderings_Otop(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_top__apply)). 6.97/7.20 fof(fact_diff__self, axiom, ![X30, X8]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X30),X30)=c_Groups_Ozero__class_Ozero(X8)<=class_Groups_Ogroup__add(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__self)). 6.97/7.20 fof(fact_replicate__eq__replicate, axiom, ![X38, X32, X35, X34, X5]:((X34=X32&(X35=X38<=X34!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))<=>c_List_Oreplicate(X5,X34,X35)=c_List_Oreplicate(X5,X32,X38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_replicate__eq__replicate)). 6.97/7.20 fof(fact_bij__betw__finite, axiom, ![X11, X4, X18, X12, X5]:(c_Fun_Obij__betw(X5,X12,X18,X4,X11)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X12),X11))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bij__betw__finite)). 6.97/7.20 fof(fact_not__square__less__zero, axiom, ![X30, X8]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X30)),c_Groups_Ozero__class_Ozero(X8))))<=class_Rings_Olinordered__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__square__less__zero)). 6.97/7.20 fof(fact_asm, axiom, ![X117, X174, X5]:(c_Hoare__Mirabelle_Ohoare__derivs(X5,X117,X174)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)),X174),X117))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_asm)). 6.97/7.20 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures, axiom, ![X38, X35]:(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X35,X38))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SetInterval_Otransfer__nat__int__set__function__closures)). 6.97/7.20 fof(fact_last__replicate, axiom, ![X6, X8, X25]:(X25!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>X6=c_List_Olast(X8,c_List_Oreplicate(X8,X25,X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__replicate)). 6.97/7.20 fof(fact_list_Oinject, axiom, ![X257, X165, X253, X2, X5]:(hAPP(hAPP(c_List_Olist_OCons(X5),X165),X257)=hAPP(hAPP(c_List_Olist_OCons(X5),X2),X253)<=>(X2=X165&X257=X253)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list_Oinject)). 6.97/7.20 fof(fact_lfp__const, axiom, ![X82, X5]:(class_Complete__Lattice_Ocomplete__lattice(X5)=>X82=c_Inductive_Ocomplete__lattice__class_Olfp(X5,hAPP(c_COMBK(X5,X5),X82))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lfp__const)). 6.97/7.20 fof(fact_order__refl, axiom, ![X6, X8]:(class_Orderings_Opreorder(X8)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X6),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__refl)). 6.97/7.20 fof(fact_min__ext__wf, axiom, ![X3, X5]:(c_Wellfounded_Owf(X5,X3)=>c_Wellfounded_Owf(tc_fun(X5,tc_HOL_Obool),c_Wellfounded_Omin__ext(X5,X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__ext__wf)). 6.97/7.20 fof(fact_max__ext__wf, axiom, ![X3, X5]:(c_Wellfounded_Owf(X5,X3)=>c_Wellfounded_Owf(tc_fun(X5,tc_HOL_Obool),c_Wellfounded_Omax__ext(X5,X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__ext__wf)). 6.97/7.20 fof(fact_append__same__eq, axiom, ![X83, X23, X84, X5]:(hAPP(hAPP(c_List_Oappend(X5),X83),X23)=hAPP(hAPP(c_List_Oappend(X5),X84),X23)<=>X83=X84), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__same__eq)). 6.97/7.20 fof(fact_same__append__eq, axiom, ![X83, X84, X23, X5]:(X83=X84<=>hAPP(hAPP(c_List_Oappend(X5),X23),X83)=hAPP(hAPP(c_List_Oappend(X5),X23),X84)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_same__append__eq)). 6.97/7.20 fof(fact_acyclic__converse, axiom, ![X3, X5]:(c_Wellfounded_Oacyclic(X5,hAPP(c_Relation_Oconverse(X5,X5),X3))<=>c_Wellfounded_Oacyclic(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acyclic__converse)). 6.97/7.20 fof(fact_antisym__converse, axiom, ![X3, X5]:(c_Relation_Oantisym(X5,hAPP(c_Relation_Oconverse(X5,X5),X3))<=>c_Relation_Oantisym(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_antisym__converse)). 6.97/7.20 fof(fact_trans__converse, axiom, ![X3, X5]:(c_Relation_Otrans(X5,hAPP(c_Relation_Oconverse(X5,X5),X3))<=>c_Relation_Otrans(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trans__converse)). 6.97/7.20 fof(fact_sym__converse, axiom, ![X3, X5]:(c_Relation_Osym(X5,X3)<=>c_Relation_Osym(X5,hAPP(c_Relation_Oconverse(X5,X5),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sym__converse)). 6.97/7.20 fof(fact_sort__key__simps_I1_J, axiom, ![X18, X5, X12]:(c_List_Olist_ONil(X5)=c_List_Olinorder__class_Osort__key(X5,X12,X18,c_List_Olist_ONil(X5))<=class_Orderings_Olinorder(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sort__key__simps_I1_J)). 6.97/7.20 fof(fact_strict__mono__eq, axiom, ![X38, X35, X18, X5, X12]:(((X38=X35<=>hAPP(X18,X38)=hAPP(X18,X35))<=c_Orderings_Oorder__class_Ostrict__mono(X5,X12,X18))<=(class_Orderings_Olinorder(X5)&class_Orderings_Oorder(X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_strict__mono__eq)). 6.97/7.20 fof(fact_fold__graph__imp__finite, axiom, ![X35, X4, X14, X18, X12, X5]:(hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X12,X18,X14,X4),X35))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__graph__imp__finite)). 6.97/7.20 fof(fact_gr0__conv__Suc, axiom, ![X32]:(?[X21]:X32=hAPP(c_Nat_OSuc,X21)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_gr0__conv__Suc)). 6.97/7.20 fof(fact_power__power__power, axiom, ![X5]:(c_Power_Opower__class_Opower(X5)=c_Power_Opower_Opower(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Otimes__class_Otimes(X5))<=class_Power_Opower(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__power__power)). 6.97/7.20 fof(fact_Sup__UNIV, axiom, ![X5]:(c_Complete__Lattice_OSup__class_OSup(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(X5)<=class_Complete__Lattice_Ocomplete__lattice(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__UNIV)). 6.97/7.20 fof(fact_Sup__empty, axiom, ![X5]:(class_Complete__Lattice_Ocomplete__lattice(X5)=>c_Complete__Lattice_OSup__class_OSup(X5,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__empty)). 6.97/7.20 fof(fact_Inf__empty, axiom, ![X5]:(class_Complete__Lattice_Ocomplete__lattice(X5)=>c_Complete__Lattice_OInf__class_OInf(X5,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__empty)). 6.97/7.20 fof(fact_sorted__list__of__set__empty, axiom, ![X5]:(class_Orderings_Olinorder(X5)=>c_List_Olist_ONil(X5)=c_List_Olinorder__class_Osorted__list__of__set(X5,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__list__of__set__empty)). 6.97/7.20 fof(fact_folding__one__idem_Oidem, axiom, ![X35, X55, X18, X5]:(c_Finite__Set_Ofolding__one__idem(X5,X18,X55)=>hAPP(hAPP(X18,X35),X35)=X35), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one__idem_Oidem)). 6.97/7.20 fof(fact_sorted__tl, axiom, ![X41, X8]:(class_Orderings_Olinorder(X8)=>(c_List_Olinorder__class_Osorted(X8,X41)=>c_List_Olinorder__class_Osorted(X8,hAPP(c_List_Otl(X8),X41)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__tl)). 6.97/7.20 fof(fact_Inf__UNIV, axiom, ![X5]:(class_Complete__Lattice_Ocomplete__lattice(X5)=>c_Orderings_Obot__class_Obot(X5)=c_Complete__Lattice_OInf__class_OInf(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__UNIV)). 6.97/7.20 fof(fact_inf__eq__top__iff, axiom, ![X38, X35, X5]:((hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X35),X38)=c_Orderings_Otop__class_Otop(X5)<=>(X38=c_Orderings_Otop__class_Otop(X5)&c_Orderings_Otop__class_Otop(X5)=X35))<=class_Lattices_Obounded__lattice__top(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__eq__top__iff)). 6.97/7.20 fof(fact_neg__def, axiom, ![X258]:(hBOOL(hAPP(c_Nat__Numeral_Oneg,X258))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X258),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__def)). 6.97/7.20 fof(fact_strict__mono__imp__inj__on, axiom, ![X4, X18, X5, X12]:((c_Orderings_Oorder__class_Ostrict__mono(X5,X12,X18)=>c_Fun_Oinj__on(X5,X12,X18,X4))<=(class_Orderings_Oorder(X12)&class_Orderings_Olinorder(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_strict__mono__imp__inj__on)). 6.97/7.20 fof(fact_empty__fold__graphE, axiom, ![X35, X14, X18, X12, X5]:(hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X12,X18,X14,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X35))=>X35=X14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__fold__graphE)). 6.97/7.20 fof(fact_wf__exp, axiom, ![X67, X32, X5]:(c_Wellfounded_Owf(X5,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X32),X67))=>c_Wellfounded_Owf(X5,X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__exp)). 6.97/7.20 fof(fact_wf__acc__iff, axiom, ![X3, X5]:(![X22]:hBOOL(hAPP(hAPP(c_member(X5),X22),c_Wellfounded_Oacc(X5,X3)))<=>c_Wellfounded_Owf(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__acc__iff)). 6.97/7.20 fof(fact_eq__number__of, axiom, ![X38, X35, X5]:((class_Int_Oring__char__0(X5)&class_Int_Onumber__ring(X5))=>(X35=X38<=>hAPP(c_Int_Onumber__class_Onumber__of(X5),X35)=hAPP(c_Int_Onumber__class_Onumber__of(X5),X38))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__number__of)). 6.97/7.20 fof(fact_accp__wfPD, axiom, ![X35, X3, X5]:(c_Wellfounded_OwfP(X5,X3)=>hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X3),X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_accp__wfPD)). 6.97/7.20 fof(fact_zdiv__self, axiom, ![X30]:(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),X30)=c_Groups_Oone__class_Oone(tc_Int_Oint)<=X30!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__self)). 6.97/7.20 fof(fact_Inf__fin_Oidem, axiom, ![X6, X8]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),X6)=X6<=class_Lattices_Olattice(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Oidem)). 6.97/7.20 fof(fact_reflpE, axiom, ![X35, X3, X5]:(hBOOL(hAPP(hAPP(X3,X35),X35))<=c_Predicate_Oreflp(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_reflpE)). 6.97/7.20 fof(fact_equivp__reflp, axiom, ![X35, X67, X5]:(c_Equiv__Relations_Oequivp(X5,X67)=>hBOOL(hAPP(hAPP(X67,X35),X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equivp__reflp)). 6.97/7.20 fof(fact_Sup__fin_Oidem, axiom, ![X6, X8]:(class_Lattices_Olattice(X8)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X6),X6)=X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Oidem)). 6.97/7.20 fof(fact_inf__idem, axiom, ![X6, X8]:(X6=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X6),X6)<=class_Lattices_Osemilattice__inf(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__idem)). 6.97/7.20 fof(fact_mult__idem, axiom, ![X6, X8]:(X6=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X6),X6)<=class_Lattices_Oab__semigroup__idem__mult(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__idem)). 6.97/7.20 fof(fact_enum__all, axiom, ![X17, X5]:((![X76]:hBOOL(hAPP(X17,X76))<=>hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X5),X17)))<=class_Enum_Oenum(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__all)). 6.97/7.20 fof(fact_arith__simps_I31_J, axiom, ![X8]:(hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OMin)=hAPP(c_Groups_Ouminus__class_Ouminus(X8),c_Groups_Oone__class_Oone(X8))<=class_Int_Onumber__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_arith__simps_I31_J)). 6.97/7.20 fof(fact_sup_Oidem, axiom, ![X30, X8]:(X30=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X30),X30)<=class_Lattices_Osemilattice__sup(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup_Oidem)). 6.97/7.20 fof(fact_part__equivpI, axiom, ![X5, X67]:(?[X22]:hBOOL(hAPP(hAPP(X67,X22),X22))=>((c_Predicate_Otransp(X5,X67)=>c_Equiv__Relations_Opart__equivp(X5,X67))<=c_Predicate_Osymp(X5,X67))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_part__equivpI)). 6.97/7.20 fof(fact_sorted__remove1, axiom, ![X30, X41, X8]:(class_Orderings_Olinorder(X8)=>(c_List_Olinorder__class_Osorted(X8,c_List_Oremove1(X8,X30,X41))<=c_List_Olinorder__class_Osorted(X8,X41))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__remove1)). 6.97/7.20 fof(fact_sorted__takeWhile, axiom, ![X17, X23, X5]:(class_Orderings_Olinorder(X5)=>(c_List_Olinorder__class_Osorted(X5,c_List_OtakeWhile(X5,X17,X23))<=c_List_Olinorder__class_Osorted(X5,X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__takeWhile)). 6.97/7.20 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J, axiom, ![X25, X6]:(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),X25))<=c_Nat__Transfer_Ois__nat(X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J)). 6.97/7.20 fof(fact_type__definition_ORep__inject, axiom, ![X38, X35, X4, X90, X91, X12, X5]:(c_Typedef_Otype__definition(X5,X12,X91,X90,X4)=>(hAPP(X91,X35)=hAPP(X91,X38)<=>X35=X38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_type__definition_ORep__inject)). 6.97/7.20 fof(fact_all__code, axiom, ![X17, X5]:((![X76]:hBOOL(hAPP(X17,X76))<=>hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X5),X17)))<=class_Enum_Oenum(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_all__code)). 6.97/7.20 fof(fact_nat__le__0, axiom, ![X26]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>hAPP(c_Int_Onat,X26)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__le__0)). 6.97/7.20 fof(fact_sup__eq__bot__iff, axiom, ![X38, X35, X5]:(class_Lattices_Obounded__lattice__bot(X5)=>(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X35),X38)=c_Orderings_Obot__class_Obot(X5)<=>(c_Orderings_Obot__class_Obot(X5)=X38&X35=c_Orderings_Obot__class_Obot(X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__eq__bot__iff)). 6.97/7.20 fof(fact_sgn__sgn, axiom, ![X30, X8]:(class_Rings_Olinordered__idom(X8)=>c_Groups_Osgn__class_Osgn(X8,X30)=c_Groups_Osgn__class_Osgn(X8,c_Groups_Osgn__class_Osgn(X8,X30))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__sgn)). 6.97/7.20 fof(help_c__fconj__1, axiom, ![X104, X17]:(~(hBOOL(X17))|hBOOL(hAPP(hAPP(c_fconj,X17),X104))|~(hBOOL(X104))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fconj__1)). 6.97/7.20 fof(fact_list__all__iff__all__interval__int, axiom, ![X46, X47, X17]:(c_List_Oall__interval__int(X17,X47,X46)<=>c_List_Olist__all(tc_Int_Oint,X17,c_List_Oupto(X47,X46))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all__iff__all__interval__int)). 6.97/7.20 fof(fact_field__power__not__zero, axiom, ![X25, X30, X8]:(class_Rings_Oring__1__no__zero__divisors(X8)=>(X30!=c_Groups_Ozero__class_Ozero(X8)=>c_Groups_Ozero__class_Ozero(X8)!=hAPP(hAPP(c_Power_Opower__class_Opower(X8),X30),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_field__power__not__zero)). 6.97/7.20 fof(fact_mod__if, axiom, ![X25, X36]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X36),X25)))=>c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),X25),X25)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X36,X25))&(X36=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X36,X25)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X36),X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__if)). 6.97/7.20 fof(fact_mod__0, axiom, ![X30, X8]:(c_Divides_Odiv__class_Omod(X8,c_Groups_Ozero__class_Ozero(X8),X30)=c_Groups_Ozero__class_Ozero(X8)<=class_Divides_Osemiring__div(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__0)). 6.97/7.20 fof(fact_mod__by__1, axiom, ![X30, X8]:(class_Divides_Osemiring__div(X8)=>c_Divides_Odiv__class_Omod(X8,X30,c_Groups_Oone__class_Oone(X8))=c_Groups_Ozero__class_Ozero(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__by__1)). 6.97/7.20 fof(fact_sym__conv__converse__eq, axiom, ![X3, X5]:(c_Relation_Osym(X5,X3)<=>hAPP(c_Relation_Oconverse(X5,X5),X3)=X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sym__conv__converse__eq)). 6.97/7.20 fof(fact_linorder__not__le, axiom, ![X38, X35, X5]:(class_Orderings_Olinorder(X5)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X38),X35))<=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X35),X38))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_linorder__not__le)). 6.97/7.20 fof(fact_finite__acyclic__wf, axiom, ![X3, X5]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X5)),X3))=>(c_Wellfounded_Oacyclic(X5,X3)=>c_Wellfounded_Owf(X5,X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__acyclic__wf)). 6.97/7.20 fof(fact_of__nat__less__0__iff, axiom, ![X36, X8]:(class_Rings_Olinordered__semidom(X8)=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),X36)),c_Groups_Ozero__class_Ozero(X8))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__less__0__iff)). 6.97/7.20 fof(fact_abs__not__less__zero, axiom, ![X30, X8]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(c_Groups_Oabs__class_Oabs(X8),X30)),c_Groups_Ozero__class_Ozero(X8))))<=class_Groups_Oordered__ab__group__add__abs(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__not__less__zero)). 6.97/7.20 fof(fact_of__nat__eq__iff, axiom, ![X32, X34, X5]:(class_Nat_Osemiring__char__0(X5)=>(hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X34)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X32)<=>X32=X34)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__eq__iff)). 6.97/7.20 fof(fact_of__nat__aux_Osimps_I1_J, axiom, ![X47, X266, X5]:(c_Nat_Osemiring__1__class_Oof__nat__aux(X5,X266,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X47)=X47<=class_Rings_Osemiring__1(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__aux_Osimps_I1_J)). 6.97/7.20 fof(fact_min__max_Osup_Oidem, axiom, ![X30, X8]:(X30=hAPP(hAPP(c_Orderings_Oord__class_Omax(X8),X30),X30)<=class_Orderings_Olinorder(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup_Oidem)). 6.97/7.20 fof(fact_of__int__eq__iff, axiom, ![X14, X9, X5]:(class_Int_Oring__char__0(X5)=>(X14=X9<=>hAPP(c_Int_Oring__1__class_Oof__int(X5),X9)=hAPP(c_Int_Oring__1__class_Oof__int(X5),X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__eq__iff)). 6.97/7.20 fof(fact_neg__equal__iff__equal, axiom, ![X1, X2, X5]:((X2=X1<=>hAPP(c_Groups_Ouminus__class_Ouminus(X5),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(X5),X1))<=class_Groups_Ogroup__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__equal__iff__equal)). 6.97/7.20 fof(fact_compl__eq__compl__iff, axiom, ![X38, X35, X5]:(class_Lattices_Oboolean__algebra(X5)=>(hAPP(c_Groups_Ouminus__class_Ouminus(X5),X35)=hAPP(c_Groups_Ouminus__class_Ouminus(X5),X38)<=>X35=X38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__eq__compl__iff)). 6.97/7.20 fof(fact_min__max_Oinf_Oidem, axiom, ![X30, X8]:(class_Orderings_Olinorder(X8)=>X30=hAPP(hAPP(c_Orderings_Oord__class_Omin(X8),X30),X30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf_Oidem)). 6.97/7.20 fof(fact_number__of__eq, axiom, ![X19, X8]:(hAPP(c_Int_Oring__1__class_Oof__int(X8),X19)=hAPP(c_Int_Onumber__class_Onumber__of(X8),X19)<=class_Int_Onumber__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__eq)). 6.97/7.20 fof(fact_not__less__Least, axiom, ![X17, X33, X5]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X33),c_Orderings_Oord__class_OLeast(X5,X17)))=>~(hBOOL(hAPP(X17,X33))))<=class_Orderings_Owellorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__less__Least)). 6.97/7.20 fof(fact_upto__empty, axiom, ![X28, X27]:(c_List_Oupto(X28,X27)=c_List_Olist_ONil(tc_Int_Oint)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X27),X28))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upto__empty)). 6.97/7.20 fof(fact_ext, axiom, ![X50, X18]:(![X22]:hAPP(X18,X22)=hAPP(X50,X22)=>X50=X18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ext)). 6.97/7.20 fof(fact_inj__uminus, axiom, ![X4, X5]:(c_Fun_Oinj__on(X5,X5,c_Groups_Ouminus__class_Ouminus(X5),X4)<=class_Groups_Oordered__ab__group__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__uminus)). 6.97/7.20 fof(help_c__fimplies__1, axiom, ![X104, X17]:(hBOOL(X17)|hBOOL(hAPP(hAPP(c_fimplies,X17),X104))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fimplies__1)). 6.97/7.20 fof(fact_listrel__trans, axiom, ![X3, X5]:(c_Relation_Otrans(X5,X3)=>c_Relation_Otrans(tc_List_Olist(X5),c_List_Olistrel(X5,X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__trans)). 6.97/7.20 fof(fact_lexord__transI, axiom, ![X3, X5]:(c_Relation_Otrans(X5,X3)=>c_Relation_Otrans(tc_List_Olist(X5),c_List_Olexord(X5,X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__transI)). 6.97/7.20 fof(fact_compl__top__eq, axiom, ![X8]:(class_Lattices_Oboolean__algebra(X8)=>hAPP(c_Groups_Ouminus__class_Ouminus(X8),c_Orderings_Otop__class_Otop(X8))=c_Orderings_Obot__class_Obot(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__top__eq)). 6.97/7.20 fof(fact_listrel__sym, axiom, ![X3, X5]:(c_Relation_Osym(tc_List_Olist(X5),c_List_Olistrel(X5,X3))<=c_Relation_Osym(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__sym)). 6.97/7.20 fof(fact_wf__lenlex, axiom, ![X3, X5]:(c_Wellfounded_Owf(X5,X3)=>c_Wellfounded_Owf(tc_List_Olist(X5),c_List_Olenlex(X5,X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__lenlex)). 6.97/7.20 fof(fact_wf__lex, axiom, ![X3, X5]:(c_Wellfounded_Owf(X5,X3)=>c_Wellfounded_Owf(tc_List_Olist(X5),c_List_Olex(X5,X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__lex)). 6.97/7.20 fof(fact_equiv__def, axiom, ![X3, X4, X5]:(c_Equiv__Relations_Oequiv(X5,X4,X3)<=>((c_Relation_Osym(X5,X3)&c_Relation_Otrans(X5,X3))&c_Relation_Orefl__on(X5,X4,X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__def)). 6.97/7.20 fof(fact_wf__in__rel, axiom, ![X67, X5]:(c_Wellfounded_Owf(X5,X67)=>c_Wellfounded_OwfP(X5,c_FunDef_Oin__rel(X5,X5,X67))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__in__rel)). 6.97/7.20 fof(fact_wf__mlex, axiom, ![X18, X67, X5]:(c_Wellfounded_Owf(X5,X67)=>c_Wellfounded_Owf(X5,c_Wellfounded_Omlex__prod(X5,X18,X67))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__mlex)). 6.97/7.20 fof(fact_minus__zero, axiom, ![X8]:(class_Groups_Ogroup__add(X8)=>hAPP(c_Groups_Ouminus__class_Ouminus(X8),c_Groups_Ozero__class_Ozero(X8))=c_Groups_Ozero__class_Ozero(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__zero)). 6.97/7.20 fof(fact_cut, axiom, ![X117, X174, X255, X5]:((c_Hoare__Mirabelle_Ohoare__derivs(X5,X117,X255)=>c_Hoare__Mirabelle_Ohoare__derivs(X5,X117,X174))<=c_Hoare__Mirabelle_Ohoare__derivs(X5,X255,X174)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_cut)). 6.97/7.20 fof(fact_le__0__eq, axiom, ![X32]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X32<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__0__eq)). 6.97/7.20 fof(fact_compl__bot__eq, axiom, ![X8]:(class_Lattices_Oboolean__algebra(X8)=>c_Orderings_Otop__class_Otop(X8)=hAPP(c_Groups_Ouminus__class_Ouminus(X8),c_Orderings_Obot__class_Obot(X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__bot__eq)). 6.97/7.20 fof(fact_nat__1__eq__mult__iff, axiom, ![X32, X34]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X32)=c_Groups_Oone__class_Oone(tc_Nat_Onat)<=>(X32=c_Groups_Oone__class_Oone(tc_Nat_Onat)&X34=c_Groups_Oone__class_Oone(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__1__eq__mult__iff)). 6.97/7.20 fof(fact_nat__mult__eq__1__iff, axiom, ![X32, X34]:(c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X32)<=>(X34=c_Groups_Oone__class_Oone(tc_Nat_Onat)&c_Groups_Oone__class_Oone(tc_Nat_Onat)=X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__eq__1__iff)). 6.97/7.20 fof(fact_abs__one, axiom, ![X8]:(class_Rings_Olinordered__idom(X8)=>c_Groups_Oone__class_Oone(X8)=hAPP(c_Groups_Oabs__class_Oabs(X8),c_Groups_Oone__class_Oone(X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__one)). 6.97/7.20 fof(fact_list__update__nonempty, axiom, ![X35, X33, X23, X5]:(hAPP(hAPP(c_List_Olist__update(X5,X23),X33),X35)=c_List_Olist_ONil(X5)<=>c_List_Olist_ONil(X5)=X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__nonempty)). 6.97/7.20 fof(fact_listsum__simps_I1_J, axiom, ![X8]:(c_Groups_Ozero__class_Ozero(X8)=hAPP(c_List_Omonoid__add__class_Olistsum(X8),c_List_Olist_ONil(X8))<=class_Groups_Omonoid__add(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__simps_I1_J)). 6.97/7.20 fof(fact_map__is__Nil__conv, axiom, ![X23, X18, X5, X12]:(X23=c_List_Olist_ONil(X12)<=>hAPP(hAPP(c_List_Omap(X12,X5),X18),X23)=c_List_Olist_ONil(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__is__Nil__conv)). 6.97/7.20 fof(fact_greaterThan__eq__iff, axiom, ![X38, X35, X5]:(class_Orderings_Olinorder(X5)=>(X35=X38<=>hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X35)=hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X38))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_greaterThan__eq__iff)). 6.97/7.20 fof(fact_lessThan__eq__iff, axiom, ![X38, X35, X5]:((X35=X38<=>hAPP(c_SetInterval_Oord__class_OlessThan(X5),X38)=hAPP(c_SetInterval_Oord__class_OlessThan(X5),X35))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lessThan__eq__iff)). 6.97/7.20 fof(fact_abs__zero, axiom, ![X8]:(class_Groups_Oordered__ab__group__add__abs(X8)=>c_Groups_Ozero__class_Ozero(X8)=hAPP(c_Groups_Oabs__class_Oabs(X8),c_Groups_Ozero__class_Ozero(X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__zero)). 6.97/7.20 fof(fact_atLeast__eq__iff, axiom, ![X38, X35, X5]:((X38=X35<=>hAPP(c_SetInterval_Oord__class_OatLeast(X5),X38)=hAPP(c_SetInterval_Oord__class_OatLeast(X5),X35))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeast__eq__iff)). 6.97/7.20 fof(fact_atMost__eq__iff, axiom, ![X38, X35, X5]:(class_Orderings_Olinorder(X5)=>(X38=X35<=>hAPP(c_SetInterval_Oord__class_OatMost(X5),X38)=hAPP(c_SetInterval_Oord__class_OatMost(X5),X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atMost__eq__iff)). 6.97/7.20 fof(fact_sorted__remdups, axiom, ![X93, X8]:((c_List_Olinorder__class_Osorted(X8,c_List_Oremdups(X8,X93))<=c_List_Olinorder__class_Osorted(X8,X93))<=class_Orderings_Olinorder(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__remdups)). 6.97/7.20 fof(fact_mod__by__0, axiom, ![X30, X8]:(class_Divides_Osemiring__div(X8)=>c_Divides_Odiv__class_Omod(X8,X30,c_Groups_Ozero__class_Ozero(X8))=X30), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__by__0)). 6.97/7.20 fof(fact_right__minus__eq, axiom, ![X1, X2, X5]:((X2=X1<=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X2),X1)=c_Groups_Ozero__class_Ozero(X5))<=class_Groups_Ogroup__add(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_right__minus__eq)). 6.97/7.20 fof(help_c__fimplies__2, axiom, ![X17, X104]:(hBOOL(hAPP(hAPP(c_fimplies,X17),X104))|~(hBOOL(X104))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fimplies__2)). 6.97/7.20 fof(help_c__fdisj__1, axiom, ![X104, X17]:(hBOOL(hAPP(hAPP(c_fdisj,X17),X104))|~(hBOOL(X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fdisj__1)). 6.97/7.20 fof(help_c__fdisj__2, axiom, ![X17, X104]:(~(hBOOL(X104))|hBOOL(hAPP(hAPP(c_fdisj,X17),X104))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fdisj__2)). 6.97/7.20 fof(fact_pair__box_Oinject, axiom, ![X259, X165, X1, X2, X12, X5]:(c_Nitpick_Opair__box_OPairBox(X5,X12,X165,X259)=c_Nitpick_Opair__box_OPairBox(X5,X12,X2,X1)<=>(X1=X259&X2=X165)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__box_Oinject)). 6.97/7.20 fof(fact_abs__eq__0, axiom, ![X2, X5]:(class_Groups_Oordered__ab__group__add__abs(X5)=>(c_Groups_Ozero__class_Ozero(X5)=hAPP(c_Groups_Oabs__class_Oabs(X5),X2)<=>c_Groups_Ozero__class_Ozero(X5)=X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__eq__0)). 6.97/7.20 fof(fact_neg__equal__0__iff__equal, axiom, ![X2, X5]:(class_Groups_Ogroup__add(X5)=>(c_Groups_Ozero__class_Ozero(X5)=X2<=>c_Groups_Ozero__class_Ozero(X5)=hAPP(c_Groups_Ouminus__class_Ouminus(X5),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__equal__0__iff__equal)). 6.97/7.20 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J, axiom, ![X7, X6]:((c_Nat__Transfer_Ois__nat(X7)=>c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X6,X7)))<=c_Nat__Transfer_Ois__nat(X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Divides_Otransfer__int__nat__function__closures_I2_J)). 6.97/7.20 fof(fact_wfP__accp__iff, axiom, ![X3, X5]:(![X76]:hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X3),X76))<=>c_Wellfounded_OwfP(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wfP__accp__iff)). 6.97/7.20 fof(fact_append__is__Nil__conv, axiom, ![X84, X23, X5]:((X23=c_List_Olist_ONil(X5)&c_List_Olist_ONil(X5)=X84)<=>c_List_Olist_ONil(X5)=hAPP(hAPP(c_List_Oappend(X5),X23),X84)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__is__Nil__conv)). 6.97/7.20 fof(fact_Nil__is__append__conv, axiom, ![X84, X23, X5]:(c_List_Olist_ONil(X5)=hAPP(hAPP(c_List_Oappend(X5),X23),X84)<=>(c_List_Olist_ONil(X5)=X23&X84=c_List_Olist_ONil(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nil__is__append__conv)). 6.97/7.20 fof(fact_add__is__0, axiom, ![X32, X34]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X32&X34=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__is__0)). 6.97/7.20 fof(help_c__fdisj__3, axiom, ![X104, X17]:(~(hBOOL(hAPP(hAPP(c_fdisj,X17),X104)))|hBOOL(X104)|hBOOL(X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fdisj__3)). 6.97/7.20 fof(fact_is__nat__def, axiom, ![X35]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X35))<=>c_Nat__Transfer_Ois__nat(X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_is__nat__def)). 6.97/7.20 fof(fact_not__one__less__zero, axiom, ![X8]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Oone__class_Oone(X8)),c_Groups_Ozero__class_Ozero(X8))))<=class_Rings_Olinordered__semidom(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__one__less__zero)). 6.97/7.20 fof(fact_not__one__le__zero, axiom, ![X8]:(class_Rings_Olinordered__semidom(X8)=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Oone__class_Oone(X8)),c_Groups_Ozero__class_Ozero(X8))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__one__le__zero)). 6.97/7.20 fof(fact_mod__self, axiom, ![X30, X8]:(class_Divides_Osemiring__div(X8)=>c_Divides_Odiv__class_Omod(X8,X30,X30)=c_Groups_Ozero__class_Ozero(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__self)). 6.97/7.20 fof(fact_rev__is__rev__conv, axiom, ![X84, X23, X5]:(X23=X84<=>hAPP(c_List_Orev(X5),X23)=hAPP(c_List_Orev(X5),X84)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__is__rev__conv)). 6.97/7.20 fof(fact_of__int__1, axiom, ![X8]:(c_Groups_Oone__class_Oone(X8)=hAPP(c_Int_Oring__1__class_Oof__int(X8),c_Groups_Oone__class_Oone(tc_Int_Oint))<=class_Rings_Oring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__1)). 6.97/7.20 fof(fact_int__int__eq, axiom, ![X32, X34]:(X34=X32<=>hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X32)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X34)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__int__eq)). 6.97/7.20 fof(fact_strict__mono__mono, axiom, ![X18, X5, X12]:((c_Orderings_Oorder__class_Ostrict__mono(X5,X12,X18)=>c_Orderings_Oorder__class_Omono(X5,X12,X18))<=(class_Orderings_Oorder(X12)&class_Orderings_Oorder(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_strict__mono__mono)). 6.97/7.20 fof(fact_list__all2__Nil, axiom, ![X84, X17, X12, X5]:(c_List_Olist__all2(X5,X12,X17,c_List_Olist_ONil(X5),X84)<=>c_List_Olist_ONil(X12)=X84), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__Nil)). 6.97/7.20 fof(fact_self__append__conv, axiom, ![X84, X5, X23]:(X23=hAPP(hAPP(c_List_Oappend(X5),X23),X84)<=>c_List_Olist_ONil(X5)=X84), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_self__append__conv)). 6.97/7.20 fof(fact_append__self__conv2, axiom, ![X84, X23, X5]:(X84=hAPP(hAPP(c_List_Oappend(X5),X23),X84)<=>X23=c_List_Olist_ONil(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__self__conv2)). 6.97/7.20 fof(fact_set__empty2, axiom, ![X23, X5]:(X23=c_List_Olist_ONil(X5)<=>c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(c_List_Oset(X5),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__empty2)). 6.97/7.20 fof(fact_add__eq__self__zero, axiom, ![X25, X36]:(X36=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X25)=>X25=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__eq__self__zero)). 6.97/7.20 fof(fact_finite__code, axiom, ![X4, X5]:(class_Finite__Set_Ofinite(X5)=>hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__code)). 6.97/7.20 fof(fact_acyclic__impl__antisym__rtrancl, axiom, ![X3, X5]:(c_Relation_Oantisym(X5,c_Transitive__Closure_Ortrancl(X5,X3))<=c_Wellfounded_Oacyclic(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acyclic__impl__antisym__rtrancl)). 6.97/7.20 fof(fact_lazy__sequence_Oinject, axiom, ![X164, X165, X166, X2, X5]:(c_Lazy__Sequence_Olazy__sequence_OInsert(X5,X165,X164)=c_Lazy__Sequence_Olazy__sequence_OInsert(X5,X2,X166)<=>(X164=X166&X165=X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lazy__sequence_Oinject)). 6.97/7.20 fof(fact_sym__rtrancl, axiom, ![X3, X5]:(c_Relation_Osym(X5,X3)=>c_Relation_Osym(X5,c_Transitive__Closure_Ortrancl(X5,X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sym__rtrancl)). 6.97/7.20 fof(fact_length__0__conv, axiom, ![X23, X5]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23)<=>c_List_Olist_ONil(X5)=X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__0__conv)). 6.97/7.20 fof(fact_min__ord__min, axiom, ![X5]:(class_Orderings_Oord(X5)=>c_Orderings_Oord_Omin(X5,c_Orderings_Oord__class_Oless__eq(X5))=c_Orderings_Oord__class_Omin(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__ord__min)). 6.97/7.20 fof(fact_sgn0, axiom, ![X8]:(c_Groups_Osgn__class_Osgn(X8,c_Groups_Ozero__class_Ozero(X8))=c_Groups_Ozero__class_Ozero(X8)<=class_Groups_Osgn__if(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn0)). 6.97/7.20 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures, axiom, ![X38, X35]:(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X35,X38))<=c_Nat__Transfer_Ois__nat(X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SetInterval_Otransfer__int__nat__set__function__closures)). 6.97/7.20 fof(fact_min__max_Ofun__left__comm__idem__sup, axiom, ![X5]:(class_Orderings_Olinorder(X5)=>c_Finite__Set_Ofun__left__comm__idem(X5,X5,c_Orderings_Oord__class_Omax(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ofun__left__comm__idem__sup)). 6.97/7.20 fof(fact_min__max_Ofun__left__comm__idem__inf, axiom, ![X5]:(c_Finite__Set_Ofun__left__comm__idem(X5,X5,c_Orderings_Oord__class_Omin(X5))<=class_Orderings_Olinorder(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ofun__left__comm__idem__inf)). 6.97/7.20 fof(fact_max__ord__max, axiom, ![X5]:(class_Orderings_Oord(X5)=>c_Orderings_Oord__class_Omax(X5)=c_Orderings_Oord_Omax(X5,c_Orderings_Oord__class_Oless__eq(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__ord__max)). 6.97/7.20 fof(fact_fun__left__comm__idem__inf, axiom, ![X5]:(class_Lattices_Osemilattice__inf(X5)=>c_Finite__Set_Ofun__left__comm__idem(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem__inf)). 6.97/7.20 fof(fact_fun__left__comm__idem, axiom, ![X5]:(c_Finite__Set_Ofun__left__comm__idem(X5,X5,c_Groups_Otimes__class_Otimes(X5))<=class_Lattices_Oab__semigroup__idem__mult(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem)). 6.97/7.20 fof(fact_fun__left__comm__idem__sup, axiom, ![X5]:(c_Finite__Set_Ofun__left__comm__idem(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5))<=class_Lattices_Osemilattice__sup(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem__sup)). 6.97/7.20 fof(fact_fun__left__comm, axiom, ![X5]:(c_Finite__Set_Ofun__left__comm(X5,X5,c_Groups_Otimes__class_Otimes(X5))<=class_Groups_Oab__semigroup__mult(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm)). 6.97/7.20 fof(fact_nat__list__def, axiom, ![X52]:(c_List_Onat__list(X52)<=>c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X52))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__list__def)). 6.97/7.20 fof(fact_remdups__id__iff__distinct, axiom, ![X23, X5]:(hBOOL(hAPP(c_List_Odistinct(X5),X23))<=>X23=c_List_Oremdups(X5,X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remdups__id__iff__distinct)). 6.97/7.20 fof(arity_prod__Lazy__Sequence_Osmall__lazy, axiom, ![X16, X98]:((class_Lazy__Sequence_Osmall__lazy(X98)&class_Lazy__Sequence_Osmall__lazy(X16))=>class_Lazy__Sequence_Osmall__lazy(tc_prod(X98,X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_prod__Lazy__Sequence_Osmall__lazy)). 6.97/7.20 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J, axiom, ![X7, X6]:((c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X6,X7))<=c_Nat__Transfer_Ois__nat(X7))<=c_Nat__Transfer_Ois__nat(X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J)). 6.97/7.20 fof(arity_sum__Finite__Set_Ofinite, axiom, ![X16, X98]:((class_Finite__Set_Ofinite(X16)&class_Finite__Set_Ofinite(X98))=>class_Finite__Set_Ofinite(tc_sum(X98,X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_sum__Finite__Set_Ofinite)). 6.97/7.20 fof(arity_prod__Finite__Set_Ofinite, axiom, ![X16, X98]:(class_Finite__Set_Ofinite(tc_prod(X98,X16))<=(class_Finite__Set_Ofinite(X16)&class_Finite__Set_Ofinite(X98))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_prod__Finite__Set_Ofinite)). 6.97/7.20 fof(arity_fun__Finite__Set_Ofinite, axiom, ![X16, X98]:(class_Finite__Set_Ofinite(tc_fun(X98,X16))<=(class_Finite__Set_Ofinite(X98)&class_Finite__Set_Ofinite(X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Finite__Set_Ofinite)). 6.97/7.20 fof(arity_sum__Enum_Oenum, axiom, ![X16, X98]:(class_Enum_Oenum(tc_sum(X98,X16))<=(class_Enum_Oenum(X98)&class_Enum_Oenum(X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_sum__Enum_Oenum)). 6.97/7.20 fof(arity_prod__Enum_Oenum, axiom, ![X16, X98]:(class_Enum_Oenum(tc_prod(X98,X16))<=(class_Enum_Oenum(X16)&class_Enum_Oenum(X98))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_prod__Enum_Oenum)). 6.97/7.20 fof(arity_fun__Enum_Oenum, axiom, ![X16, X98]:((class_Enum_Oenum(X98)&class_Enum_Oenum(X16))=>class_Enum_Oenum(tc_fun(X98,X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Enum_Oenum)). 6.97/7.20 fof(fact_insort__not__Nil, axiom, ![X23, X2, X18, X5, X12]:(class_Orderings_Olinorder(X12)=>hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X12,X18),X2),X23)!=c_List_Olist_ONil(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__not__Nil)). 6.97/7.20 fof(fact_of__nat__1, axiom, ![X8]:(hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(X8)<=class_Rings_Osemiring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__1)). 6.97/7.20 fof(help_c__fimplies__3, axiom, ![X104, X17]:(hBOOL(X104)|~(hBOOL(X17))|~(hBOOL(hAPP(hAPP(c_fimplies,X17),X104)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fimplies__3)). 6.97/7.20 fof(fact_equivp__reflp__symp__transp, axiom, ![X67, X5]:(((c_Predicate_Oreflp(X5,X67)&c_Predicate_Osymp(X5,X67))&c_Predicate_Otransp(X5,X67))<=>c_Equiv__Relations_Oequivp(X5,X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equivp__reflp__symp__transp)). 6.97/7.20 fof(fact_of__int__0, axiom, ![X8]:(class_Rings_Oring__1(X8)=>hAPP(c_Int_Oring__1__class_Oof__int(X8),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__0)). 6.97/7.20 fof(fact_of__nat__0, axiom, ![X8]:(class_Rings_Osemiring__1(X8)=>c_Groups_Ozero__class_Ozero(X8)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__0)). 6.97/7.20 fof(fact_replicate__empty, axiom, ![X35, X32, X5]:(c_List_Oreplicate(X5,X32,X35)=c_List_Olist_ONil(X5)<=>X32=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_replicate__empty)). 6.97/7.20 fof(fact_rotate1__is__Nil__conv, axiom, ![X23, X5]:(c_List_Olist_ONil(X5)=X23<=>c_List_Olist_ONil(X5)=hAPP(c_List_Orotate1(X5),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate1__is__Nil__conv)). 6.97/7.20 fof(fact_Nil__is__rev__conv, axiom, ![X23, X5]:(hAPP(c_List_Orev(X5),X23)=c_List_Olist_ONil(X5)<=>X23=c_List_Olist_ONil(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nil__is__rev__conv)). 6.97/7.20 fof(fact_int__eq__0__conv, axiom, ![X32]:(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X32)<=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__eq__0__conv)). 6.97/7.20 fof(help_c__fNot__2, axiom, ![X17]:(~(~(hBOOL(X17)))|hBOOL(hAPP(c_fNot,X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fNot__2)). 6.97/7.20 fof(fact_bij__betw__id__iff, axiom, ![X11, X4, X5]:(c_Fun_Obij__betw(X5,X5,c_Fun_Oid(X5),X4,X11)<=>X4=X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bij__betw__id__iff)). 6.97/7.20 fof(fact_code__numeral_Onat__of__inject, axiom, ![X38, X35]:(hAPP(c_Code__Numeral_Onat__of,X38)=hAPP(c_Code__Numeral_Onat__of,X35)<=>X35=X38), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral_Onat__of__inject)). 6.97/7.20 fof(fact_Suc__inject, axiom, ![X7, X6]:(X7=X6<=hAPP(c_Nat_OSuc,X6)=hAPP(c_Nat_OSuc,X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__inject)). 6.97/7.20 fof(fact_Rep__Integ__inject, axiom, ![X38, X35]:(hAPP(c_Int_ORep__Integ,X35)=hAPP(c_Int_ORep__Integ,X38)<=>X38=X35), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Rep__Integ__inject)). 6.97/7.20 fof(help_c__fequal__1, axiom, ![X38, X35]:(X38=X35|~(hBOOL(hAPP(hAPP(c_fequal,X35),X38)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fequal__1)). 6.97/7.20 fof(fact_order__less__irrefl, axiom, ![X6, X8]:(class_Orderings_Opreorder(X8)=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X6),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__less__irrefl)). 6.97/7.20 fof(arity_fun__Orderings_Otop, axiom, ![X98, X16]:(class_Orderings_Otop(tc_fun(X98,X16))<=class_Orderings_Otop(X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Orderings_Otop)). 6.97/7.20 fof(arity_fun__Lattices_Obounded__lattice__bot, axiom, ![X98, X16]:(class_Lattices_Obounded__lattice(X16)=>class_Lattices_Obounded__lattice__bot(tc_fun(X98,X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Lattices_Obounded__lattice__bot)). 6.97/7.20 fof(arity_fun__Groups_Ominus, axiom, ![X98, X16]:(class_Groups_Ominus(X16)=>class_Groups_Ominus(tc_fun(X98,X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Groups_Ominus)). 6.97/7.20 fof(arity_fun__Groups_Ouminus, axiom, ![X98, X16]:(class_Groups_Ouminus(tc_fun(X98,X16))<=class_Groups_Ouminus(X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Groups_Ouminus)). 6.97/7.20 fof(arity_fun__Lattices_Obounded__lattice, axiom, ![X98, X16]:(class_Lattices_Obounded__lattice(X16)=>class_Lattices_Obounded__lattice(tc_fun(X98,X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Lattices_Obounded__lattice)). 6.97/7.20 fof(arity_fun__Orderings_Obot, axiom, ![X98, X16]:(class_Orderings_Obot(tc_fun(X98,X16))<=class_Orderings_Obot(X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Orderings_Obot)). 6.97/7.20 fof(arity_fun__Lattices_Oboolean__algebra, axiom, ![X98, X16]:(class_Lattices_Oboolean__algebra(tc_fun(X98,X16))<=class_Lattices_Oboolean__algebra(X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Lattices_Oboolean__algebra)). 6.97/7.20 fof(arity_fun__Orderings_Oord, axiom, ![X98, X16]:(class_Orderings_Oord(X16)=>class_Orderings_Oord(tc_fun(X98,X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Orderings_Oord)). 6.97/7.20 fof(arity_fun__Lattices_Obounded__lattice__top, axiom, ![X98, X16]:(class_Lattices_Obounded__lattice(X16)=>class_Lattices_Obounded__lattice__top(tc_fun(X98,X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Lattices_Obounded__lattice__top)). 6.97/7.20 fof(arity_fun__Lattices_Osemilattice__inf, axiom, ![X98, X16]:(class_Lattices_Osemilattice__inf(tc_fun(X98,X16))<=class_Lattices_Olattice(X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Lattices_Osemilattice__inf)). 6.97/7.20 fof(arity_fun__Complete__Lattice_Ocomplete__lattice, axiom, ![X98, X16]:(class_Complete__Lattice_Ocomplete__lattice(tc_fun(X98,X16))<=class_Complete__Lattice_Ocomplete__lattice(X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Complete__Lattice_Ocomplete__lattice)). 6.97/7.20 fof(arity_fun__Lattices_Osemilattice__sup, axiom, ![X98, X16]:(class_Lattices_Osemilattice__sup(tc_fun(X98,X16))<=class_Lattices_Olattice(X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Lattices_Osemilattice__sup)). 6.97/7.20 fof(arity_fun__Orderings_Opreorder, axiom, ![X98, X16]:(class_Orderings_Opreorder(tc_fun(X98,X16))<=class_Orderings_Opreorder(X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Orderings_Opreorder)). 6.97/7.20 fof(arity_fun__Orderings_Oorder, axiom, ![X98, X16]:(class_Orderings_Oorder(tc_fun(X98,X16))<=class_Orderings_Oorder(X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Orderings_Oorder)). 6.97/7.20 fof(arity_fun__Lattices_Odistrib__lattice, axiom, ![X98, X16]:(class_Lattices_Odistrib__lattice(X16)=>class_Lattices_Odistrib__lattice(tc_fun(X98,X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Lattices_Odistrib__lattice)). 6.97/7.20 fof(help_c__fconj__2, axiom, ![X104, X17]:(hBOOL(X17)|~(hBOOL(hAPP(hAPP(c_fconj,X17),X104)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fconj__2)). 6.97/7.20 fof(help_c__fconj__3, axiom, ![X104, X17]:(hBOOL(X104)|~(hBOOL(hAPP(hAPP(c_fconj,X17),X104)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fconj__3)). 6.97/7.20 fof(arity_fun__Lattices_Olattice, axiom, ![X98, X16]:(class_Lattices_Olattice(tc_fun(X98,X16))<=class_Lattices_Olattice(X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Lattices_Olattice)). 6.97/7.20 fof(fact_sorted_ONil, axiom, ![X8]:(class_Orderings_Olinorder(X8)=>c_List_Olinorder__class_Osorted(X8,c_List_Olist_ONil(X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted_ONil)). 6.97/7.20 fof(fact_iszero__0, axiom, ![X8]:(c_Int_Oiszero(X8,c_Groups_Ozero__class_Ozero(X8))<=class_Rings_Osemiring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_iszero__0)). 6.97/7.20 fof(fact_iszero__def, axiom, ![X14, X5]:(class_Rings_Osemiring__1(X5)=>(c_Int_Oiszero(X5,X14)<=>c_Groups_Ozero__class_Ozero(X5)=X14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_iszero__def)). 6.97/7.20 fof(fact_remdups__eq__nil__right__iff, axiom, ![X35, X5]:(c_List_Olist_ONil(X5)=c_List_Oremdups(X5,X35)<=>X35=c_List_Olist_ONil(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remdups__eq__nil__right__iff)). 6.97/7.20 fof(fact_nonzero__number__of__Min, axiom, ![X8]:(~(c_Int_Oiszero(X8,hAPP(c_Int_Onumber__class_Onumber__of(X8),c_Int_OMin)))<=class_Int_Onumber__ring(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nonzero__number__of__Min)). 6.97/7.20 fof(fact_sup__max, axiom, ![X5]:(c_Lattices_Osemilattice__sup__class_Osup(X5)=c_Orderings_Oord__class_Omax(X5)<=(class_Orderings_Olinorder(X5)&class_Lattices_Osemilattice__sup(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__max)). 6.97/7.20 fof(fact_inf__min, axiom, ![X5]:((class_Orderings_Olinorder(X5)&class_Lattices_Osemilattice__inf(X5))=>c_Lattices_Osemilattice__inf__class_Oinf(X5)=c_Orderings_Oord__class_Omin(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__min)). 6.97/7.20 fof(fact_equivp__implies__part__equivp, axiom, ![X67, X5]:(c_Equiv__Relations_Opart__equivp(X5,X67)<=c_Equiv__Relations_Oequivp(X5,X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equivp__implies__part__equivp)). 6.97/7.20 fof(fact_equivpE, axiom, ![X67, X5]:(~((c_Predicate_Oreflp(X5,X67)=>(c_Predicate_Osymp(X5,X67)=>~(c_Predicate_Otransp(X5,X67)))))<=c_Equiv__Relations_Oequivp(X5,X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equivpE)). 6.97/7.20 fof(fact_wf__acyclic, axiom, ![X3, X5]:(c_Wellfounded_Owf(X5,X3)=>c_Wellfounded_Oacyclic(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__acyclic)). 6.97/7.20 fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy, axiom, ![X16]:(class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X16))<=class_Lazy__Sequence_Osmall__lazy(X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_List__Olist__Lazy__Sequence_Osmall__lazy)). 6.97/7.20 fof(arity_Option__Ooption__Finite__Set_Ofinite, axiom, ![X16]:(class_Finite__Set_Ofinite(tc_Option_Ooption(X16))<=class_Finite__Set_Ofinite(X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Option__Ooption__Finite__Set_Ofinite)). 6.97/7.20 fof(arity_Option__Ooption__Enum_Oenum, axiom, ![X16]:(class_Enum_Oenum(tc_Option_Ooption(X16))<=class_Enum_Oenum(X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Option__Ooption__Enum_Oenum)). 6.97/7.20 fof(help_c__fNot__1, axiom, ![X17]:(~(hBOOL(X17))|~(hBOOL(hAPP(c_fNot,X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fNot__1)). 6.97/7.20 fof(fact_not__iszero__1, axiom, ![X8]:(~(c_Int_Oiszero(X8,c_Groups_Oone__class_Oone(X8)))<=class_Rings_Osemiring__1(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__iszero__1)). 6.97/7.20 fof(fact_one__neq__zero, axiom, ![X8]:(c_Groups_Ozero__class_Ozero(X8)!=c_Groups_Oone__class_Oone(X8)<=class_Rings_Ozero__neq__one(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__neq__zero)). 6.97/7.20 fof(fact_Nil__notin__lex, axiom, ![X3, X84, X5]:~(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)),c_List_Olist_ONil(X5)),X84)),c_List_Olex(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nil__notin__lex)). 6.97/7.20 fof(fact_not__Nil__listrel1, axiom, ![X3, X23, X5]:~(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)),c_List_Olist_ONil(X5)),X23)),c_List_Olistrel1(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__Nil__listrel1)). 6.97/7.20 fof(fact_Nil2__notin__lex, axiom, ![X3, X23, X5]:~(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)),X23),c_List_Olist_ONil(X5))),c_List_Olex(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nil2__notin__lex)). 6.97/7.20 fof(fact_not__listrel1__Nil, axiom, ![X3, X23, X5]:~(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)),X23),c_List_Olist_ONil(X5))),c_List_Olistrel1(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__listrel1__Nil)). 6.97/7.20 fof(fact_lexord__Nil__right, axiom, ![X3, X35, X5]:~(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)),X35),c_List_Olist_ONil(X5))),c_List_Olexord(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__Nil__right)). 6.97/7.20 fof(fact_in__measures_I1_J, axiom, ![X38, X35, X5]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X38)),c_List_Omeasures(X5,c_List_Olist_ONil(tc_fun(X5,tc_Nat_Onat)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__measures_I1_J)). 6.97/7.20 fof(fact_not__zle__0__negative, axiom, ![X25]:~(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,X25)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__zle__0__negative)). 6.97/7.20 fof(fact_not__int__zless__negative, axiom, ![X36, X25]:~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X36))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__int__zless__negative)). 6.97/7.20 fof(fact_not__add__less1, axiom, ![X27, X28]:~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),X27)),X28))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__add__less1)). 6.97/7.20 fof(fact_not__add__less2, axiom, ![X28, X27]:~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27),X28)),X28))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__add__less2)). 6.97/7.20 fof(fact_not__psubset__empty, axiom, ![X4, X5]:~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X4),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__psubset__empty)). 6.97/7.20 fof(fact_int__less__0__conv, axiom, ![X19]:~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__less__0__conv)). 6.97/7.20 fof(fact_Cantors__paradox, axiom, ![X4, X5]:~(?[X185]:hAPP(c_Set_OPow(X5),X4)=hAPP(c_Set_Oimage(X5,tc_fun(X5,tc_HOL_Obool),X185),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Cantors__paradox)). 6.97/7.20 fof(fact_bot2E, axiom, ![X38, X35, X12, X5]:~(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_fun(X12,tc_HOL_Obool))),X35),X38))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bot2E)). 6.97/7.20 fof(fact_infinite__UNIV__listI, axiom, ![X5]:~(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X5)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X5),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_infinite__UNIV__listI)). 6.97/7.20 fof(fact_empty__fold1SetE, axiom, ![X35, X18, X5]:~(hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X18,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__fold1SetE)). 6.97/7.20 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)). 6.97/7.20 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)). 6.97/7.20 fof(fact_less__zeroE, axiom, ![X25]:~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__zeroE)). 6.97/7.20 fof(fact_insert__not__empty, axiom, ![X4, X2, X5]:hAPP(hAPP(c_Set_Oinsert(X5),X2),X4)!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__not__empty)). 6.97/7.20 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)). 6.97/7.20 fof(fact_Pow__not__empty, axiom, ![X4, X5]:c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))!=hAPP(c_Set_OPow(X5),X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__not__empty)). 6.97/7.20 fof(fact_not__neg__int, axiom, ![X25]:~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__neg__int)). 6.97/7.20 fof(fact_less__irrefl__nat, axiom, ![X25]:~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__irrefl__nat)). 6.97/7.20 fof(fact_list_Osimps_I3_J, axiom, ![X220, X69, X8]:hAPP(hAPP(c_List_Olist_OCons(X8),X69),X220)!=c_List_Olist_ONil(X8), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list_Osimps_I3_J)). 6.97/7.20 fof(fact_UNIV__not__empty, axiom, ![X5]:c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))!=c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UNIV__not__empty)). 6.97/7.20 fof(fact_not__Cons__self, axiom, ![X6, X8, X41]:X41!=hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__Cons__self)). 6.97/7.20 fof(fact_lazy__sequence_Osimps_I2_J, axiom, ![X147, X69, X8]:c_Lazy__Sequence_Olazy__sequence_OEmpty(X8)!=c_Lazy__Sequence_Olazy__sequence_OInsert(X8,X69,X147), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lazy__sequence_Osimps_I2_J)). 6.97/7.20 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)). 6.97/7.20 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)). 6.97/7.20 fof(fact_list__ex1__simps_I1_J, axiom, ![X17, X5]:~(c_List_Olist__ex1(X5,X17,c_List_Olist_ONil(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex1__simps_I1_J)). 6.97/7.20 fof(fact_list__ex__simps_I2_J, axiom, ![X17, X5]:~(c_List_Olist__ex(X5,X17,c_List_Olist_ONil(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex__simps_I2_J)). 6.97/7.20 fof(fact_Suc__not__Zero, axiom, ![X36]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,X36), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__not__Zero)). 6.97/7.20 fof(fact_Suc__n__not__n, axiom, ![X25]:hAPP(c_Nat_OSuc,X25)!=X25, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__n__not__n)). 6.97/7.20 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)). 6.97/7.20 fof(help_c__fFalse__1, axiom, ~(hBOOL(c_fFalse)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fFalse__1)). 6.97/7.20 fof(fact_image__split__eq__Sigma, axiom, ![X4, X50, X18, X12, X5, X62]:hAPP(hAPP(c_Product__Type_OSigma(X5,X12),hAPP(c_Set_Oimage(X62,X5,X18),X4)),hAPP(hAPP(c_COMBB(tc_fun(X62,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool),X5),c_Set_Oimage(X62,X12,X50)),hAPP(hAPP(c_COMBC(X5,tc_fun(X62,tc_HOL_Obool),tc_fun(X62,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X62,tc_HOL_Obool),tc_fun(tc_fun(X62,tc_HOL_Obool),tc_fun(X62,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X62,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X62,tc_HOL_Obool),X5),c_Set_Ovimage(X62,X5,X18)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_Oinsert(X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),X4)))=hAPP(c_Set_Oimage(X62,tc_prod(X5,X12),hAPP(hAPP(c_COMBS(X62,X12,tc_prod(X5,X12)),hAPP(hAPP(c_COMBB(X5,tc_fun(X12,tc_prod(X5,X12)),X62),c_Product__Type_OPair(X5,X12)),X18)),X50)),X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__split__eq__Sigma)). 6.97/7.20 fof(fact_sublist__shift__lemma__Suc, axiom, ![X49, X23, X17, X5]:hAPP(hAPP(c_List_Omap(tc_prod(X5,tc_Nat_Onat),X5),c_Product__Type_Ofst(X5,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X5,tc_Nat_Onat)),X17),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(X5,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(X5,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(X5,tc_Nat_Onat),X23),X49)))=hAPP(hAPP(c_List_Omap(tc_prod(X5,tc_Nat_Onat),X5),c_Product__Type_Ofst(X5,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X5,tc_Nat_Onat)),X17),c_Product__Type_Osnd(X5,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(X5,tc_Nat_Onat),X23),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),X49)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublist__shift__lemma__Suc)). 6.97/7.20 fof(fact_scomp__scomp, axiom, ![X71, X50, X18, X113, X114, X12, X92, X62, X5]:hAPP(hAPP(c_Product__Type_Oscomp(X5,X62,X92,X12),hAPP(hAPP(c_Product__Type_Oscomp(X5,X114,X113,tc_prod(X62,X92)),X18),X50)),X71)=hAPP(hAPP(c_Product__Type_Oscomp(X5,X114,X113,X12),X18),hAPP(hAPP(c_COMBC(X114,tc_fun(X62,tc_fun(X92,X12)),tc_fun(X113,X12)),hAPP(hAPP(c_COMBB(tc_fun(X113,tc_prod(X62,X92)),tc_fun(tc_fun(X62,tc_fun(X92,X12)),tc_fun(X113,X12)),X114),c_Product__Type_Oscomp(X113,X62,X92,X12)),X50)),X71)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_scomp__scomp)). 6.97/7.20 fof(fact_INT__Int__distrib, axiom, ![X11, X4, X15, X5, X12]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),X15),hAPP(hAPP(c_COMBS(X12,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X12),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool))),X4)),X11))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),X15),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),X15),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__Int__distrib)). 6.97/7.20 fof(fact_UN__Un__distrib, axiom, ![X11, X4, X15, X5, X12]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X15),hAPP(hAPP(c_COMBS(X12,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X12),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),X4)),X11))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X15),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X15),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__Un__distrib)). 6.97/7.20 fof(fact_Sigma__Diff__distrib2, axiom, ![X11, X4, X15, X12, X5]:hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X15),hAPP(hAPP(c_COMBS(X5,tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_Groups_Ominus__class_Ominus(tc_fun(X12,tc_HOL_Obool))),X4)),X11))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X15),X4)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X15),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__Diff__distrib2)). 6.97/7.20 fof(fact_Sigma__Int__distrib2, axiom, ![X11, X4, X15, X12, X5]:hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X15),hAPP(hAPP(c_COMBS(X5,tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool))),X4)),X11))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X15),X4)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X15),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__Int__distrib2)). 6.97/7.20 fof(fact_Sigma__Un__distrib2, axiom, ![X11, X4, X15, X12, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X15),X4)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X15),X11))=hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X15),hAPP(hAPP(c_COMBS(X5,tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool))),X4)),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__Un__distrib2)). 6.97/7.20 fof(fact_zip__update, axiom, ![X7, X45, X6, X28, X41, X5, X8]:hAPP(hAPP(c_List_Ozip(X8,X5),hAPP(hAPP(c_List_Olist__update(X8,X41),X28),X6)),hAPP(hAPP(c_List_Olist__update(X5,X45),X28),X7))=hAPP(hAPP(c_List_Olist__update(tc_prod(X8,X5),hAPP(hAPP(c_List_Ozip(X8,X5),X41),X45)),X28),hAPP(hAPP(c_Product__Type_OPair(X8,X5),X6),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__update)). 6.97/7.20 fof(fact_map__pair_Ocompositionality, axiom, ![X244, X47, X71, X113, X114, X50, X18, X12, X92, X5, X62]:hAPP(c_Product__Type_Omap__pair(X62,X5,X92,X12,X18,X50),hAPP(c_Product__Type_Omap__pair(X114,X62,X113,X92,X71,X47),X244))=hAPP(c_Product__Type_Omap__pair(X114,X5,X113,X12,hAPP(c_Fun_Ocomp(X62,X5,X114,X18),X71),hAPP(c_Fun_Ocomp(X92,X12,X113,X50),X47)),X244), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair_Ocompositionality)). 6.97/7.20 fof(fact_zip__Cons__Cons, axiom, ![X45, X7, X41, X6, X5, X8]:hAPP(hAPP(c_List_Ozip(X8,X5),hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41)),hAPP(hAPP(c_List_Olist_OCons(X5),X7),X45))=hAPP(hAPP(c_List_Olist_OCons(tc_prod(X8,X5)),hAPP(hAPP(c_Product__Type_OPair(X8,X5),X6),X7)),hAPP(hAPP(c_List_Ozip(X8,X5),X41),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__Cons__Cons)). 6.97/7.20 fof(fact_image__add__atLeastLessThan, axiom, ![X46, X47, X33]: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)),X33)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X47),X46))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X47),X33)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__add__atLeastLessThan)). 6.97/7.20 fof(fact_INT__simps_I10_J, axiom, ![X11, X4, X18, X62, X5, X12]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X62,tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(X12,tc_fun(X5,tc_HOL_Obool),X62),X11),X18))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X62,X12,X18),X4)),X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__simps_I10_J)). 6.97/7.20 fof(fact_UN__simps_I10_J, axiom, ![X11, X4, X18, X62, X5, X12]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X62,tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(X12,tc_fun(X5,tc_HOL_Obool),X62),X11),X18))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X62,X12,X18),X4)),X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__simps_I10_J)). 6.97/7.20 fof(fact_INT__insert, axiom, ![X11, X4, X2, X5, X12]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(X11,X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X12),X2),X4)),X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__insert)). 6.97/7.20 fof(fact_UN__insert, axiom, ![X11, X4, X2, X5, X12]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(X11,X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X12),X2),X4)),X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__insert)). 6.97/7.20 fof(fact_split__comp, axiom, ![X35, X50, X18, X92, X5, X62, X12]:hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X12,X62,X5),hAPP(c_Fun_Ocomp(X92,tc_fun(X62,X5),X12,X18),X50)),X35)=hAPP(hAPP(X18,hAPP(X50,hAPP(c_Product__Type_Ofst(X12,X62),X35))),hAPP(c_Product__Type_Osnd(X12,X62),X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__comp)). 6.97/7.20 fof(fact_UN__o, axiom, ![X18, X50, X62, X4, X5, X12]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X62,tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X12,X62,X18),X4)),X50)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Fun_Ocomp(X62,tc_fun(X5,tc_HOL_Obool),X12,X50),X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__o)). 6.97/7.20 fof(fact_image__add__atLeastAtMost, axiom, ![X46, X47, X33]: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)),X33)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X47,X46))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X47),X33),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__add__atLeastAtMost)). 6.97/7.20 fof(fact_fst__comp__map__pair, axiom, ![X50, X18, X12, X5, X92, X62]:hAPP(c_Fun_Ocomp(tc_prod(X62,X92),X62,tc_prod(X5,X12),c_Product__Type_Ofst(X62,X92)),c_Product__Type_Omap__pair(X5,X62,X12,X92,X18,X50))=hAPP(c_Fun_Ocomp(X5,X62,tc_prod(X5,X12),X18),c_Product__Type_Ofst(X5,X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fst__comp__map__pair)). 6.97/7.20 fof(fact_snd__comp__map__pair, axiom, ![X50, X18, X12, X5, X62, X92]:hAPP(c_Fun_Ocomp(X12,X62,tc_prod(X5,X12),X50),c_Product__Type_Osnd(X5,X12))=hAPP(c_Fun_Ocomp(tc_prod(X92,X62),X62,tc_prod(X5,X12),c_Product__Type_Osnd(X92,X62)),c_Product__Type_Omap__pair(X5,X92,X12,X62,X18,X50)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_snd__comp__map__pair)). 6.97/7.20 fof(fact_length__filter__map, axiom, ![X23, X18, X12, X17, X5]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,X17),hAPP(hAPP(c_List_Omap(X12,X5),X18),X23)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12)),hAPP(c_List_Ofilter(X12,hAPP(c_Fun_Ocomp(X5,tc_HOL_Obool,X12,X17),X18)),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__filter__map)). 6.97/7.20 fof(fact_transpose__map__map, axiom, ![X23, X18, X12, X5]:c_List_Otranspose(X5,hAPP(hAPP(c_List_Omap(tc_List_Olist(X12),tc_List_Olist(X5)),hAPP(c_List_Omap(X12,X5),X18)),X23))=hAPP(hAPP(c_List_Omap(tc_List_Olist(X12),tc_List_Olist(X5)),hAPP(c_List_Omap(X12,X5),X18)),c_List_Otranspose(X12,X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__map__map)). 6.97/7.20 fof(fact_Int__left__commute, axiom, ![X65, X11, X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X65))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X65)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__left__commute)). 6.97/7.20 fof(fact_Un__left__commute, axiom, ![X65, X11, X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X65))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X65)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__left__commute)). 6.97/7.20 fof(fact_zip__same__conv__map, axiom, ![X23, X5]:hAPP(hAPP(c_List_Omap(X5,tc_prod(X5,X5)),hAPP(hAPP(c_COMBS(X5,X5,tc_prod(X5,X5)),c_Product__Type_OPair(X5,X5)),c_COMBI(X5))),X23)=hAPP(hAPP(c_List_Ozip(X5,X5),X23),X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__same__conv__map)). 6.97/7.20 fof(fact_map__update, axiom, ![X38, X33, X23, X18, X5, X12]:hAPP(hAPP(c_List_Omap(X12,X5),X18),hAPP(hAPP(c_List_Olist__update(X12,X23),X33),X38))=hAPP(hAPP(c_List_Olist__update(X5,hAPP(hAPP(c_List_Omap(X12,X5),X18),X23)),X33),hAPP(X18,X38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__update)). 6.97/7.20 fof(fact_fun__upd__comp, axiom, ![X38, X35, X50, X18, X5, X12, X62]:c_Fun_Ofun__upd(X5,X12,hAPP(c_Fun_Ocomp(X62,X12,X5,X18),X50),X35,hAPP(X18,X38))=hAPP(c_Fun_Ocomp(X62,X12,X5,X18),c_Fun_Ofun__upd(X5,X62,X50,X35,X38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upd__comp)). 6.97/7.20 fof(fact_o__assoc, axiom, ![X71, X50, X92, X18, X5, X12, X62]:hAPP(c_Fun_Ocomp(X92,X12,X5,hAPP(c_Fun_Ocomp(X62,X12,X92,X18),X50)),X71)=hAPP(c_Fun_Ocomp(X62,X12,X5,X18),hAPP(c_Fun_Ocomp(X92,X62,X5,X50),X71)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_o__assoc)). 6.97/7.20 fof(fact_Un__Inter, axiom, ![X11, X4, X5]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X11),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Inter)). 6.97/7.20 fof(fact_Int__Union, axiom, ![X11, X4, X5]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X11),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__Union)). 6.97/7.20 fof(fact_Domain__Union, axiom, ![X44, X12, X5]:hAPP(c_Relation_ODomain(X5,X12),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),X44))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X44),c_Relation_ODomain(X5,X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__Union)). 6.97/7.20 fof(fact_Range__Union, axiom, ![X44, X5, X12]:hAPP(c_Relation_ORange(X12,X5),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X12,X5),tc_HOL_Obool),X44))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X12,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X44),c_Relation_ORange(X12,X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__Union)). 6.97/7.20 fof(fact_map_Osimps_I2_J, axiom, ![X23, X35, X18, X5, X12]:hAPP(hAPP(c_List_Omap(X12,X5),X18),hAPP(hAPP(c_List_Olist_OCons(X12),X35),X23))=hAPP(hAPP(c_List_Olist_OCons(X5),hAPP(X18,X35)),hAPP(hAPP(c_List_Omap(X12,X5),X18),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map_Osimps_I2_J)). 6.97/7.20 fof(fact_image__Union, axiom, ![X44, X18, X5, X12]:hAPP(c_Set_Oimage(X12,X5,X18),c_Complete__Lattice_OSup__class_OSup(tc_fun(X12,tc_HOL_Obool),X44))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X12,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X44),c_Set_Oimage(X12,X5,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__Union)). 6.97/7.20 fof(fact_image__insert, axiom, ![X11, X2, X18, X5, X12]:hAPP(hAPP(c_Set_Oinsert(X5),hAPP(X18,X2)),hAPP(c_Set_Oimage(X12,X5,X18),X11))=hAPP(c_Set_Oimage(X12,X5,X18),hAPP(hAPP(c_Set_Oinsert(X12),X2),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__insert)). 6.97/7.20 fof(fact_Random__Sequence_Osingle__def, axiom, ![X58, X59, X35, X5]:hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(X5),X35))=hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(X5),X35),X59),X58), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Random__Sequence_Osingle__def)). 6.97/7.20 fof(fact_drop__map, axiom, ![X23, X18, X12, X32, X5]:hAPP(hAPP(c_List_Omap(X12,X5),X18),hAPP(hAPP(c_List_Odrop(X12),X32),X23))=hAPP(hAPP(c_List_Odrop(X5),X32),hAPP(hAPP(c_List_Omap(X12,X5),X18),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__map)). 6.97/7.20 fof(fact_take__map, axiom, ![X23, X18, X12, X32, X5]:hAPP(hAPP(c_List_Otake(X5),X32),hAPP(hAPP(c_List_Omap(X12,X5),X18),X23))=hAPP(hAPP(c_List_Omap(X12,X5),X18),hAPP(hAPP(c_List_Otake(X12),X32),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__map)). 6.97/7.20 fof(fact_image__compose, axiom, ![X3, X50, X18, X62, X5, X12]:hAPP(c_Set_Oimage(X62,X5,X18),hAPP(c_Set_Oimage(X12,X62,X50),X3))=hAPP(c_Set_Oimage(X12,X5,hAPP(c_Fun_Ocomp(X62,X5,X12,X18),X50)),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__compose)). 6.97/7.20 fof(fact_foldl__Cons, axiom, ![X23, X35, X2, X18, X12, X5]:hAPP(c_List_Ofoldl(X5,X12,X18,X2),hAPP(hAPP(c_List_Olist_OCons(X12),X35),X23))=hAPP(c_List_Ofoldl(X5,X12,X18,hAPP(hAPP(X18,X2),X35)),X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__Cons)). 6.97/7.20 fof(fact_maps__simps_I1_J, axiom, ![X23, X35, X18, X5, X12]:c_List_Omaps(X12,X5,X18,hAPP(hAPP(c_List_Olist_OCons(X12),X35),X23))=hAPP(hAPP(c_List_Oappend(X5),hAPP(X18,X35)),c_List_Omaps(X12,X5,X18,X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_maps__simps_I1_J)). 6.97/7.20 fof(fact_power_Opower_Opower__Suc, axiom, ![X32, X2, X156, X157, X5]:hAPP(hAPP(X156,X2),hAPP(hAPP(c_Power_Opower_Opower(X5,X157,X156),X2),X32))=hAPP(hAPP(c_Power_Opower_Opower(X5,X157,X156),X2),hAPP(c_Nat_OSuc,X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power_Opower_Opower__Suc)). 6.97/7.20 fof(fact_converse__inv__image, axiom, ![X18, X67, X12, X5]:hAPP(c_Relation_Oconverse(X5,X5),hAPP(hAPP(c_Relation_Oinv__image(X12,X5),X67),X18))=hAPP(hAPP(c_Relation_Oinv__image(X12,X5),hAPP(c_Relation_Oconverse(X12,X12),X67)),X18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__inv__image)). 6.97/7.20 fof(fact_lazy__sequence_Orecs_I2_J, axiom, ![X166, X2, X120, X85, X12, X5]:hAPP(hAPP(hAPP(X120,X2),X166),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X5,X12,X85,X120,X166))=c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X5,X12,X85,X120,c_Lazy__Sequence_Olazy__sequence_OInsert(X12,X2,X166)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lazy__sequence_Orecs_I2_J)). 6.97/7.20 fof(fact_prod__case__beta, axiom, ![X24, X18, X5, X62, X12]:hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X12,X62,X5),X18),X24)=hAPP(hAPP(X18,hAPP(c_Product__Type_Ofst(X12,X62),X24)),hAPP(c_Product__Type_Osnd(X12,X62),X24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_prod__case__beta)). 6.97/7.20 fof(fact_insert__commute, axiom, ![X4, X38, X35, X5]:hAPP(hAPP(c_Set_Oinsert(X5),X35),hAPP(hAPP(c_Set_Oinsert(X5),X38),X4))=hAPP(hAPP(c_Set_Oinsert(X5),X38),hAPP(hAPP(c_Set_Oinsert(X5),X35),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__commute)). 6.97/7.20 fof(fact_list__size__map, axiom, ![X23, X50, X12, X18, X5]:c_List_Olist_Olist__size(X5,X18,hAPP(hAPP(c_List_Omap(X12,X5),X50),X23))=c_List_Olist_Olist__size(X12,hAPP(c_Fun_Ocomp(X5,tc_Nat_Onat,X12,X18),X50),X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__size__map)). 6.97/7.20 fof(fact_rotate__simps, axiom, ![X41, X6, X5, X8]:(hAPP(c_List_Orotate1(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X6),X41))=hAPP(hAPP(c_List_Oappend(X5),X41),hAPP(hAPP(c_List_Olist_OCons(X5),X6),c_List_Olist_ONil(X5)))&hAPP(c_List_Orotate1(X8),c_List_Olist_ONil(X8))=c_List_Olist_ONil(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__simps)). 6.97/7.20 fof(fact_map__tl, axiom, ![X23, X18, X5, X12]:hAPP(c_List_Otl(X5),hAPP(hAPP(c_List_Omap(X12,X5),X18),X23))=hAPP(hAPP(c_List_Omap(X12,X5),X18),hAPP(c_List_Otl(X12),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__tl)). 6.97/7.20 fof(fact_zmult__div__cancel, axiom, ![X36, X25]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X36),X25))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X36),c_Divides_Odiv__class_Omod(tc_Int_Oint,X36,X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult__div__cancel)). 6.97/7.20 fof(fact_mult__div__cancel, axiom, ![X36, X25]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X36,X25))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X36),X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__div__cancel)). 6.97/7.20 fof(fact_map__replicate__const, axiom, ![X169, X33, X5, X12]:hAPP(hAPP(c_List_Omap(X12,X5),hAPP(c_COMBK(X5,X12),X33)),X169)=c_List_Oreplicate(X5,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12)),X169),X33), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__replicate__const)). 6.97/7.20 fof(fact_set__map, axiom, ![X23, X18, X12, X5]:hAPP(c_Set_Oimage(X12,X5,X18),hAPP(c_List_Oset(X12),X23))=hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Omap(X12,X5),X18),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__map)). 6.97/7.20 fof(fact_zadd__left__commute, axiom, ![X26, X7, X6]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6),X26))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7),X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__left__commute)). 6.97/7.20 fof(fact_nat__add__left__commute, axiom, ![X26, X7, X6]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6),X26))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7),X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__add__left__commute)). 6.97/7.20 fof(fact__06, axiom, ![X64, X35, X18, X5, X12]:c_Lazy__Sequence_Omap(X12,X5,X18,c_Lazy__Sequence_Olazy__sequence_OInsert(X12,X35,X64))=c_Lazy__Sequence_Olazy__sequence_OInsert(X5,hAPP(X18,X35),c_Lazy__Sequence_Omap(X12,X5,X18,X64)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact__06)). 6.97/7.20 fof(fact_Random__Sequence_Oempty__def, axiom, ![X58, X59, X5]:c_Random__Sequence_Oempty(X5,X59,X58)=hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Random__Sequence_Oempty__def)). 6.97/7.20 fof(fact_nat__rec__Suc, axiom, ![X128, X120, X85, X5]:hAPP(c_Nat_Onat_Onat__rec(X5,X85,X120),hAPP(c_Nat_OSuc,X128))=hAPP(hAPP(X120,X128),hAPP(c_Nat_Onat_Onat__rec(X5,X85,X120),X128)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__rec__Suc)). 6.97/7.20 fof(fact_map__butlast, axiom, ![X23, X18, X5, X12]:c_List_Obutlast(X5,hAPP(hAPP(c_List_Omap(X12,X5),X18),X23))=hAPP(hAPP(c_List_Omap(X12,X5),X18),c_List_Obutlast(X12,X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__butlast)). 6.97/7.20 fof(fact_mult__Suc, axiom, ![X25, X36]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X36)),X25)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__Suc)). 6.97/7.20 fof(help_c__COMBS__1, axiom, ![X67, X104, X17, X5, X62, X12]:hAPP(hAPP(hAPP(c_COMBS(X12,X62,X5),X17),X104),X67)=hAPP(hAPP(X17,X67),hAPP(X104,X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__COMBS__1)). 6.97/7.20 fof(fact_mult__Suc__right, axiom, ![X25, X36]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),hAPP(c_Nat_OSuc,X25))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__Suc__right)). 6.97/7.20 fof(fact_partition_Osimps_I1_J, axiom, ![X17, X5]:c_List_Opartition(X5,X17,c_List_Olist_ONil(X5))=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_ONil(X5)),c_List_Olist_ONil(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_partition_Osimps_I1_J)). 6.97/7.20 fof(fact_rev__filter, axiom, ![X23, X17, X5]:hAPP(c_List_Orev(X5),hAPP(c_List_Ofilter(X5,X17),X23))=hAPP(c_List_Ofilter(X5,X17),hAPP(c_List_Orev(X5),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__filter)). 6.97/7.20 fof(fact_n__lists_Osimps_I1_J, axiom, ![X41, X8]:c_Enum_On__lists(X8,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X41)=hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X8)),c_List_Olist_ONil(X8)),c_List_Olist_ONil(tc_List_Olist(X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_n__lists_Osimps_I1_J)). 6.97/7.20 fof(fact_remove1__commute, axiom, ![X75, X7, X6, X8]:c_List_Oremove1(X8,X7,c_List_Oremove1(X8,X6,X75))=c_List_Oremove1(X8,X6,c_List_Oremove1(X8,X7,X75)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remove1__commute)). 6.97/7.20 fof(fact_split__Pair, axiom, ![X12, X5]:hAPP(c_Product__Type_Oprod_Oprod__case(X5,X12,tc_prod(X5,X12)),c_Product__Type_OPair(X5,X12))=c_Fun_Oid(tc_prod(X5,X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__Pair)). 6.97/7.20 fof(fact_New__DSequence_Opos__union__def, axiom, ![X47, X63, X64, X5]:hAPP(c_New__DSequence_Opos__union(X5,X64,X63),X47)=c_Lazy__Sequence_Oappend(X5,hAPP(X64,X47),hAPP(X63,X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Opos__union__def)). 6.97/7.20 fof(fact_lexn_Osimps_I1_J, axiom, ![X3, X5]:hAPP(c_List_Olexn(X5,X3),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexn_Osimps_I1_J)). 6.97/7.20 fof(fact_sublists_Osimps_I1_J, axiom, ![X8]:hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X8)),c_List_Olist_ONil(X8)),c_List_Olist_ONil(tc_List_Olist(X8)))=c_Enum_Osublists(X8,c_List_Olist_ONil(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublists_Osimps_I1_J)). 6.97/7.20 fof(fact_rp__inv__image__def, axiom, ![X12, X5]:c_FunDef_Orp__inv__image(X5,X12)=hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X12,X5),tc_prod(tc_fun(tc_prod(X12,X12),tc_HOL_Obool),tc_fun(tc_prod(X12,X12),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X12,X5),tc_fun(tc_prod(X12,X12),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X12,X5),tc_prod(tc_fun(tc_prod(X12,X12),tc_HOL_Obool),tc_fun(tc_prod(X12,X12),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(X12,X5),tc_fun(tc_prod(X12,X12),tc_HOL_Obool)),tc_fun(tc_fun(X12,X5),tc_prod(tc_fun(tc_prod(X12,X12),tc_HOL_Obool),tc_fun(tc_prod(X12,X12),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X12,X5),tc_fun(tc_prod(X12,X12),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X12,X5),tc_prod(tc_fun(tc_prod(X12,X12),tc_HOL_Obool),tc_fun(tc_prod(X12,X12),tc_HOL_Obool))))),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(X12,X5),tc_fun(tc_prod(X12,X12),tc_HOL_Obool)),tc_fun(tc_fun(X12,X5),tc_prod(tc_fun(tc_prod(X12,X12),tc_HOL_Obool),tc_fun(tc_prod(X12,X12),tc_HOL_Obool))),tc_fun(tc_prod(X5,X5),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X12,X5),tc_fun(tc_fun(tc_prod(X12,X12),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X12,X12),tc_HOL_Obool),tc_fun(tc_prod(X12,X12),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(X12,X5),tc_fun(tc_prod(X12,X12),tc_HOL_Obool)),tc_fun(tc_fun(X12,X5),tc_prod(tc_fun(tc_prod(X12,X12),tc_HOL_Obool),tc_fun(tc_prod(X12,X12),tc_HOL_Obool)))),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_COMBS(tc_fun(X12,X5),tc_fun(tc_prod(X12,X12),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X12,X12),tc_HOL_Obool),tc_fun(tc_prod(X12,X12),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X12,X5),tc_fun(tc_prod(X12,X12),tc_HOL_Obool)),tc_fun(tc_fun(X12,X5),tc_fun(tc_fun(tc_prod(X12,X12),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X12,X12),tc_HOL_Obool),tc_fun(tc_prod(X12,X12),tc_HOL_Obool)))),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(X12,X12),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X12,X12),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X12,X12),tc_HOL_Obool),tc_fun(tc_prod(X12,X12),tc_HOL_Obool))),tc_fun(X12,X5)),c_Product__Type_OPair(tc_fun(tc_prod(X12,X12),tc_HOL_Obool),tc_fun(tc_prod(X12,X12),tc_HOL_Obool)))),c_Relation_Oinv__image(X5,X12))))),c_Relation_Oinv__image(X5,X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rp__inv__image__def)). 6.97/7.20 fof(fact_minus__int__def, axiom, ![X14]: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,X14)),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),X14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__int__def)). 6.97/7.20 fof(fact_partition_Osimps_I2_J, axiom, ![X23, X35, X17, X5]:c_List_Opartition(X5,X17,hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23))=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X5),tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))),tc_fun(tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))),tc_List_Olist(X5)),c_COMBS(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),tc_fun(tc_List_Olist(X5),tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))),tc_List_Olist(X5)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),tc_List_Olist(X5)),hAPP(c_If(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(X17,X35)))),hAPP(hAPP(c_COMBB(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),tc_List_Olist(X5)),c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(c_List_Olist_OCons(X5),X35))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),tc_fun(tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))),tc_List_Olist(X5)),c_COMBB(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_List_Olist(X5))),c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)))),hAPP(c_List_Olist_OCons(X5),X35)))),c_List_Opartition(X5,X17,X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_partition_Osimps_I2_J)). 6.97/7.20 fof(fact_Sigma__def, axiom, ![X11, X4, X12, X5]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBS(X5,tc_fun(X12,tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(tc_fun(X12,tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(tc_prod(X5,X12),tc_HOL_Obool))),X11)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X12,tc_fun(tc_prod(X5,X12),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(tc_prod(X5,X12),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X12,tc_fun(tc_prod(X5,X12),tc_HOL_Obool))),X5),c_COMBC(X12,tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(tc_prod(X5,X12),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_prod(X5,X12)),tc_fun(X12,tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(tc_prod(X5,X12),tc_HOL_Obool))),X5),hAPP(c_COMBB(tc_prod(X5,X12),tc_fun(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),X12),c_Set_Oinsert(tc_prod(X5,X12)))),c_Product__Type_OPair(X5,X12)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)))))=hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X4),X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__def)). 6.97/7.21 fof(fact_lazy__sequence__size__code, axiom, ![X64, X66, X5]:c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X5,tc_Lazy__Sequence_Olazy__sequence(X5)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X5,tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat),hAPP(hAPP(c_COMBC(X5,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat)),X5),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),X5),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X5)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat)),X5),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),X5),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X66))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X5,X66))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(X5),X64))=hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X5,X66),X64), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lazy__sequence__size__code)). 6.97/7.21 fof(fact_zip__Cons, axiom, ![X84, X38, X23, X12, X5]:hAPP(hAPP(c_List_Ozip(X5,X12),X23),hAPP(hAPP(c_List_Olist_OCons(X12),X38),X84))=hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X5,X12)),X5,c_List_Olist_ONil(tc_prod(X5,X12)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_List_Olist(X5),tc_List_Olist(tc_prod(X5,X12))),tc_fun(tc_List_Olist(X5),tc_List_Olist(tc_prod(X5,X12)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X5,X12)),tc_List_Olist(tc_prod(X5,X12))),tc_fun(tc_fun(tc_List_Olist(X5),tc_List_Olist(tc_prod(X5,X12))),tc_fun(tc_List_Olist(X5),tc_List_Olist(tc_prod(X5,X12)))),X5),c_COMBB(tc_List_Olist(tc_prod(X5,X12)),tc_List_Olist(tc_prod(X5,X12)),tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_prod(X5,X12),tc_fun(tc_List_Olist(tc_prod(X5,X12)),tc_List_Olist(tc_prod(X5,X12))),X5),c_List_Olist_OCons(tc_prod(X5,X12))),hAPP(hAPP(c_COMBC(X5,X12,tc_prod(X5,X12)),c_Product__Type_OPair(X5,X12)),X38)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(X12),tc_List_Olist(tc_prod(X5,X12))),c_List_Ozip(X5,X12)),X84))),X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__Cons)). 6.97/7.21 fof(fact_UN__Times__distrib, axiom, ![X55, X173, X11, X4, X12, X5, X92, X62]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(X62,X92),tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X62,X92),X4),hAPP(c_COMBK(tc_fun(X92,tc_HOL_Obool),X62),X11))),hAPP(c_Product__Type_Oprod_Oprod__case(X62,X92,tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X62,tc_fun(X92,tc_fun(X5,tc_fun(X12,tc_HOL_Obool))),tc_fun(X92,tc_fun(tc_prod(X5,X12),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_fun(X12,tc_HOL_Obool)),tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),tc_fun(tc_fun(X92,tc_fun(X5,tc_fun(X12,tc_HOL_Obool))),tc_fun(X92,tc_fun(tc_prod(X5,X12),tc_HOL_Obool))),X62),c_COMBB(tc_fun(X5,tc_fun(X12,tc_HOL_Obool)),tc_fun(tc_prod(X5,X12),tc_HOL_Obool),X92)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_fun(X12,tc_HOL_Obool)),tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),X62),c_Product__Type_OSigma(X5,X12)),X173))),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X5,tc_fun(X12,tc_HOL_Obool)),X92),c_COMBK(tc_fun(X12,tc_HOL_Obool),X5)),X55))))=hAPP(hAPP(c_Product__Type_OSigma(X5,X12),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X62,tc_fun(X5,tc_HOL_Obool)),X4),X173)),hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X92,tc_fun(X12,tc_HOL_Obool)),X11),X55))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__Times__distrib)). 6.97/7.21 fof(fact_Int__UN__distrib2, axiom, ![X11, X133, X62, X4, X15, X12, X5]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X15),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X62,tc_fun(X5,tc_HOL_Obool)),X133),X11))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X15),hAPP(hAPP(c_COMBB(tc_fun(X62,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool),X12),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X62,tc_fun(X5,tc_HOL_Obool)),X133)),hAPP(hAPP(c_COMBC(X12,tc_fun(X62,tc_fun(X5,tc_HOL_Obool)),tc_fun(X62,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_fun(tc_fun(X62,tc_fun(X5,tc_HOL_Obool)),tc_fun(X62,tc_fun(X5,tc_HOL_Obool))),X12),c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X62)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X12),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool))),X4))),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__UN__distrib2)). 6.97/7.21 fof(fact_Un__INT__distrib2, axiom, ![X11, X133, X62, X4, X15, X12, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),X15),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X62,tc_fun(X5,tc_HOL_Obool)),X133),X11))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),X15),hAPP(hAPP(c_COMBB(tc_fun(X62,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool),X12),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X62,tc_fun(X5,tc_HOL_Obool)),X133)),hAPP(hAPP(c_COMBC(X12,tc_fun(X62,tc_fun(X5,tc_HOL_Obool)),tc_fun(X62,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_fun(tc_fun(X62,tc_fun(X5,tc_HOL_Obool)),tc_fun(X62,tc_fun(X5,tc_HOL_Obool))),X12),c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X62)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X12),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),X4))),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__INT__distrib2)). 6.97/7.21 fof(fact_zip__Cons1, axiom, ![X84, X23, X35, X12, X5]:hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X5,X12)),X12,c_List_Olist_ONil(tc_prod(X5,X12)),hAPP(hAPP(c_COMBC(X12,tc_fun(tc_List_Olist(X12),tc_List_Olist(tc_prod(X5,X12))),tc_fun(tc_List_Olist(X12),tc_List_Olist(tc_prod(X5,X12)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X5,X12)),tc_List_Olist(tc_prod(X5,X12))),tc_fun(tc_fun(tc_List_Olist(X12),tc_List_Olist(tc_prod(X5,X12))),tc_fun(tc_List_Olist(X12),tc_List_Olist(tc_prod(X5,X12)))),X12),c_COMBB(tc_List_Olist(tc_prod(X5,X12)),tc_List_Olist(tc_prod(X5,X12)),tc_List_Olist(X12))),hAPP(hAPP(c_COMBB(tc_prod(X5,X12),tc_fun(tc_List_Olist(tc_prod(X5,X12)),tc_List_Olist(tc_prod(X5,X12))),X12),c_List_Olist_OCons(tc_prod(X5,X12))),hAPP(c_Product__Type_OPair(X5,X12),X35)))),hAPP(c_List_Ozip(X5,X12),X23))),X84)=hAPP(hAPP(c_List_Ozip(X5,X12),hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23)),X84), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__Cons1)). 6.97/7.21 fof(fact_map__zip__map2, axiom, ![X84, X50, X92, X23, X18, X5, X62, X12]:hAPP(hAPP(c_List_Omap(tc_prod(X12,X62),X5),X18),hAPP(hAPP(c_List_Ozip(X12,X62),X23),hAPP(hAPP(c_List_Omap(X92,X62),X50),X84)))=hAPP(hAPP(c_List_Omap(tc_prod(X12,X92),X5),hAPP(c_Product__Type_Oprod_Oprod__case(X12,X92,X5),hAPP(hAPP(c_COMBB(tc_fun(X92,tc_prod(X12,X62)),tc_fun(X92,X5),X12),hAPP(c_COMBB(tc_prod(X12,X62),X5,X92),X18)),hAPP(hAPP(c_COMBC(X12,tc_fun(X92,X62),tc_fun(X92,tc_prod(X12,X62))),hAPP(hAPP(c_COMBB(tc_fun(X62,tc_prod(X12,X62)),tc_fun(tc_fun(X92,X62),tc_fun(X92,tc_prod(X12,X62))),X12),c_COMBB(X62,tc_prod(X12,X62),X92)),c_Product__Type_OPair(X12,X62))),X50)))),hAPP(hAPP(c_List_Ozip(X12,X92),X23),X84)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__zip__map2)). 6.97/7.21 fof(fact_max__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_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))))=c_FunDef_Omax__weak, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__weak__def)). 6.97/7.21 fof(fact_min__weak__def, axiom, c_FunDef_Omin__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_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)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__weak__def)). 6.97/7.21 fof(fact_zip__map2, axiom, ![X84, X18, X62, X23, X12, X5]:hAPP(hAPP(c_List_Omap(tc_prod(X5,X62),tc_prod(X5,X12)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X62,tc_prod(X5,X12)),hAPP(hAPP(c_COMBC(X5,tc_fun(X62,X12),tc_fun(X62,tc_prod(X5,X12))),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_prod(X5,X12)),tc_fun(tc_fun(X62,X12),tc_fun(X62,tc_prod(X5,X12))),X5),c_COMBB(X12,tc_prod(X5,X12),X62)),c_Product__Type_OPair(X5,X12))),X18))),hAPP(hAPP(c_List_Ozip(X5,X62),X23),X84))=hAPP(hAPP(c_List_Ozip(X5,X12),X23),hAPP(hAPP(c_List_Omap(X62,X12),X18),X84)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__map2)). 6.97/7.21 fof(fact_inj__graph, axiom, ![X12, X5]:c_Fun_Oinj__on(tc_fun(X5,X12),tc_fun(tc_prod(X5,X12),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X5,X12)),c_Set_OCollect(tc_prod(X5,X12))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X12,tc_HOL_Obool)),tc_fun(tc_prod(X5,X12),tc_HOL_Obool),tc_fun(X5,X12)),c_Product__Type_Oprod_Oprod__case(X5,X12,tc_HOL_Obool)),hAPP(c_COMBB(X12,tc_fun(X12,tc_HOL_Obool),X5),hAPP(c_COMBC(X12,X12,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X5,X12),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__graph)). 6.97/7.21 fof(fact_neg__bind__def, axiom, ![X57, X58, X59, X18, X67, X5, X12]:hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(X12,X5,X67,X18),X59),X58),X57)=c_New__DSequence_Oneg__bind(X12,X5,hAPP(hAPP(hAPP(X67,X59),X58),X57),hAPP(hAPP(c_COMBC(X12,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(X5)))),hAPP(hAPP(c_COMBC(X12,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(X5))))),hAPP(hAPP(c_COMBC(X12,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(X5)))))),X18),X59)),X58)),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__bind__def)). 6.97/7.21 fof(fact_map__zip__map, axiom, ![X84, X23, X50, X92, X18, X5, X62, X12]:hAPP(hAPP(c_List_Omap(tc_prod(X92,X62),X5),hAPP(c_Product__Type_Oprod_Oprod__case(X92,X62,X5),hAPP(hAPP(c_COMBB(tc_fun(X62,tc_prod(X12,X62)),tc_fun(X62,X5),X92),hAPP(c_COMBB(tc_prod(X12,X62),X5,X62),X18)),hAPP(hAPP(c_COMBB(X12,tc_fun(X62,tc_prod(X12,X62)),X92),c_Product__Type_OPair(X12,X62)),X50)))),hAPP(hAPP(c_List_Ozip(X92,X62),X23),X84))=hAPP(hAPP(c_List_Omap(tc_prod(X12,X62),X5),X18),hAPP(hAPP(c_List_Ozip(X12,X62),hAPP(hAPP(c_List_Omap(X92,X12),X50),X23)),X84)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__zip__map)). 6.97/7.21 fof(fact_sublists_Osimps_I2_J, axiom, ![X23, X35, X5]:hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(X5)),tc_List_Olist(tc_List_Olist(X5))),c_Enum_Osublists(X5,X23)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(X5)),tc_List_Olist(tc_List_Olist(X5)),tc_List_Olist(tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(X5)),tc_fun(tc_List_Olist(tc_List_Olist(X5)),tc_List_Olist(tc_List_Olist(X5))),tc_List_Olist(tc_List_Olist(X5))),c_List_Oappend(tc_List_Olist(X5))),hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(c_List_Olist_OCons(X5),X35)))),c_COMBI(tc_List_Olist(tc_List_Olist(X5)))))=c_Enum_Osublists(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublists_Osimps_I2_J)). 6.97/7.21 fof(fact_, axiom, ![X277, X278, X12, X5]:c_Lazy__Sequence_Oproduct(X5,X12,X278,X277)=hAPP(c_Lazy__Sequence_Obind(X5,tc_prod(X5,X12),X278),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X5,X12))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X5,X12)),X5),c_Lazy__Sequence_Obind(X12,tc_prod(X5,X12),X277)),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_prod(X5,X12)),tc_fun(X12,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X5,X12))),X5),hAPP(c_COMBB(tc_prod(X5,X12),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X5,X12)),X12),c_Lazy__Sequence_Osingle(tc_prod(X5,X12)))),c_Product__Type_OPair(X5,X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_)). 6.97/7.21 fof(fact_rel__comp__UNION__distrib2, axiom, ![X66, X3, X15, X92, X12, X62, X5]:hAPP(hAPP(c_Relation_Orel__comp(X5,X62,X12),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X92,tc_fun(tc_prod(X5,X62),tc_HOL_Obool)),X15),X3)),X66)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X92,tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),X15),hAPP(hAPP(c_COMBC(X92,tc_fun(tc_prod(X62,X12),tc_HOL_Obool),tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X5,X62),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X62,X12),tc_HOL_Obool),tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),X92),c_Relation_Orel__comp(X5,X62,X12)),X3)),X66)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__comp__UNION__distrib2)). 6.97/7.21 fof(fact_New__Random__Sequence_Oneg__decr__bind__def, axiom, ![X57, X58, X59, X18, X67, X5, X12]:c_New__DSequence_Oneg__decr__bind(X12,X5,hAPP(hAPP(hAPP(X67,X59),X58),X57),hAPP(hAPP(c_COMBC(X12,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(X5)))),hAPP(hAPP(c_COMBC(X12,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(X5))))),hAPP(hAPP(c_COMBC(X12,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(X5)))))),X18),X59)),X58)),X57))=c_New__Random__Sequence_Oneg__decr__bind(X12,X5,X67,X18,X59,X58,X57), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__Random__Sequence_Oneg__decr__bind__def)). 6.97/7.21 fof(fact_pos__bind__def, axiom, ![X57, X58, X59, X18, X67, X5, X12]:c_New__DSequence_Opos__bind(X12,X5,hAPP(hAPP(hAPP(X67,X59),X58),X57),hAPP(hAPP(c_COMBC(X12,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X5))),hAPP(hAPP(c_COMBC(X12,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(X5)))),hAPP(hAPP(c_COMBC(X12,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(X5))))),X18),X59)),X58)),X57))=hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(X12,X5,X67,X18),X59),X58),X57), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__bind__def)). 6.97/7.21 fof(fact_insert__times__insert, axiom, ![X11, X1, X4, X2, X12, X5]:hAPP(hAPP(c_Product__Type_OSigma(X5,X12),hAPP(hAPP(c_Set_Oinsert(X5),X2),X4)),hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X5),hAPP(hAPP(c_Set_Oinsert(X12),X1),X11)))=hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X2),X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X4),hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X5),hAPP(hAPP(c_Set_Oinsert(X12),X1),X11)))),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),hAPP(hAPP(c_Set_Oinsert(X5),X2),X4)),hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X5),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__times__insert)). 6.97/7.21 fof(fact_New__Random__Sequence_Opos__decr__bind__def, axiom, ![X57, X58, X59, X18, X67, X5, X12]:c_New__Random__Sequence_Opos__decr__bind(X12,X5,X67,X18,X59,X58,X57)=c_New__DSequence_Opos__decr__bind(X12,X5,hAPP(hAPP(hAPP(X67,X59),X58),X57),hAPP(hAPP(c_COMBC(X12,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X5))),hAPP(hAPP(c_COMBC(X12,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(X5)))),hAPP(hAPP(c_COMBC(X12,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(X5))))),X18),X59)),X58)),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__Random__Sequence_Opos__decr__bind__def)). 6.97/7.21 fof(fact_Id__on__def_H, axiom, ![X4, X5]:c_Relation_OId__on(X5,X4)=hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj)),c_fequal))),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Id__on__def_H)). 6.97/7.21 fof(fact_INT__extend__simps_I9_J, axiom, ![X65, X11, X62, X4, X5, X12]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X62,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X62,tc_HOL_Obool)),X4),X11)),X65)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBC(X12,tc_fun(X62,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X62,tc_HOL_Obool),tc_fun(tc_fun(X62,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),X12),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X62,tc_fun(X5,tc_HOL_Obool))),X11)),X65)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__extend__simps_I9_J)). 6.97/7.21 fof(fact_measures__def, axiom, ![X121, X5]:hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),X5),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(X5,tc_List_Olist(tc_fun(X5,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(X5,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),X5),c_List_Omap(tc_fun(X5,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(X5,tc_Nat_Onat),X5,tc_Nat_Onat),c_COMBI(tc_fun(X5,tc_Nat_Onat))))),X121))=c_List_Omeasures(X5,X121), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_measures__def)). 6.97/7.21 fof(fact_select__weight__def, axiom, ![X23, X5]: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(X5,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,X5),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X5)),X23)))),hAPP(hAPP(c_COMBB(X5,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X5,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X5,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(X5,X23)))=c_Random_Oselect__weight(X5,X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_select__weight__def)). 6.97/7.21 fof(fact_size__code, axiom, ![X64, X5]:c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X5,tc_Lazy__Sequence_Olazy__sequence(X5)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X5,tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat),X5),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X5),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(X5)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X5)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(X5),X64))=hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X5)),X64), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_size__code)). 6.97/7.21 fof(fact_fun__left__comm__idem__remove, axiom, ![X5]:c_Finite__Set_Ofun__left__comm__idem(X5,tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_Oinsert(X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem__remove)). 6.97/7.21 fof(fact_INT__simps_I6_J, axiom, ![X11, X4, X65, X5, X12]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),X65),hAPP(hAPP(c_COMBC(X12,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X12),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),X4)),X11))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),X65),X4)),X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__simps_I6_J)). 6.97/7.21 fof(fact_UN__simps_I6_J, axiom, ![X11, X4, X65, X5, X12]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X65),X4)),X11)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X65),hAPP(hAPP(c_COMBC(X12,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X12),c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool))),X4)),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__simps_I6_J)). 6.97/7.21 fof(fact_UN__simps_I4_J, axiom, ![X11, X4, X65, X5, X12]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X65),X4)),X11)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X65),hAPP(hAPP(c_COMBC(X12,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X12),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool))),X4)),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__simps_I4_J)). 6.97/7.21 fof(fact_UN__Pow__subset, axiom, ![X11, X4, X12, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),X12),c_Set_OPow(X5)),X11))),hAPP(c_Set_OPow(X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X4),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__Pow__subset)). 6.97/7.21 fof(fact_swap__product, axiom, ![X11, X4, X5, X12]:hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X11),hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X5),X4))=hAPP(c_Set_Oimage(tc_prod(X12,X5),tc_prod(X5,X12),hAPP(c_Product__Type_Oprod_Oprod__case(X12,X5,tc_prod(X5,X12)),hAPP(c_COMBC(X5,X12,tc_prod(X5,X12)),c_Product__Type_OPair(X5,X12)))),hAPP(hAPP(c_Product__Type_OSigma(X12,X5),X4),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X12),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_swap__product)). 6.97/7.21 fof(fact_zip__append2, axiom, ![X75, X45, X41, X5, X8]:hAPP(hAPP(c_List_Oappend(tc_prod(X8,X5)),hAPP(hAPP(c_List_Ozip(X8,X5),hAPP(hAPP(c_List_Otake(X8),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X45)),X41)),X45)),hAPP(hAPP(c_List_Ozip(X8,X5),hAPP(hAPP(c_List_Odrop(X8),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X45)),X41)),X75))=hAPP(hAPP(c_List_Ozip(X8,X5),X41),hAPP(hAPP(c_List_Oappend(X5),X45),X75)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__append2)). 6.97/7.21 fof(fact_zip__append1, axiom, ![X75, X45, X41, X5, X8]:hAPP(hAPP(c_List_Oappend(tc_prod(X8,X5)),hAPP(hAPP(c_List_Ozip(X8,X5),X41),hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)),X75))),hAPP(hAPP(c_List_Ozip(X8,X5),X45),hAPP(hAPP(c_List_Odrop(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)),X75)))=hAPP(hAPP(c_List_Ozip(X8,X5),hAPP(hAPP(c_List_Oappend(X8),X41),X45)),X75), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__append1)). 6.97/7.21 fof(fact_zip__map1, axiom, ![X84, X23, X18, X62, X12, X5]:hAPP(hAPP(c_List_Omap(tc_prod(X62,X12),tc_prod(X5,X12)),hAPP(c_Product__Type_Oprod_Oprod__case(X62,X12,tc_prod(X5,X12)),hAPP(hAPP(c_COMBB(X5,tc_fun(X12,tc_prod(X5,X12)),X62),c_Product__Type_OPair(X5,X12)),X18))),hAPP(hAPP(c_List_Ozip(X62,X12),X23),X84))=hAPP(hAPP(c_List_Ozip(X5,X12),hAPP(hAPP(c_List_Omap(X62,X5),X18),X23)),X84), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__map1)). 6.97/7.21 fof(fact_Image__INT__subset, axiom, ![X11, X4, X62, X3, X12, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X12,X5,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X62,tc_fun(X12,tc_HOL_Obool)),X4),X11))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X62,tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X62),c_Relation_OImage(X12,X5,X3)),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__INT__subset)). 6.97/7.21 fof(fact_rotate1__def, axiom, ![X23, X5]:hAPP(c_List_Orotate1(X5),X23)=hAPP(c_List_Olist_Olist__case(tc_List_Olist(X5),X5,c_List_Olist_ONil(X5),hAPP(hAPP(c_COMBB(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),X5),hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Oappend(X5))),hAPP(hAPP(c_COMBC(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_OCons(X5)),c_List_Olist_ONil(X5)))),X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate1__def)). 6.97/7.21 fof(fact_foldl__map, axiom, ![X23, X18, X62, X2, X50, X12, X5]:hAPP(c_List_Ofoldl(X5,X12,X50,X2),hAPP(hAPP(c_List_Omap(X62,X12),X18),X23))=hAPP(c_List_Ofoldl(X5,X62,hAPP(hAPP(c_COMBC(X5,tc_fun(X62,X12),tc_fun(X62,X5)),hAPP(hAPP(c_COMBB(tc_fun(X12,X5),tc_fun(tc_fun(X62,X12),tc_fun(X62,X5)),X5),c_COMBB(X12,X5,X62)),X50)),X18),X2),X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__map)). 6.97/7.21 fof(fact_rel__comp__UNION__distrib, axiom, ![X3, X15, X92, X66, X12, X62, X5]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X92,tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),X15),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X62,X12),tc_HOL_Obool),tc_fun(tc_prod(X5,X12),tc_HOL_Obool),X92),hAPP(c_Relation_Orel__comp(X5,X62,X12),X66)),X3))=hAPP(hAPP(c_Relation_Orel__comp(X5,X62,X12),X66),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X92,tc_fun(tc_prod(X62,X12),tc_HOL_Obool)),X15),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__comp__UNION__distrib)). 6.97/7.21 fof(fact_split__comp__eq, axiom, ![X50, X18, X92, X62, X12, X5]:hAPP(hAPP(c_COMBS(tc_prod(X5,X12),X12,X62),hAPP(hAPP(c_COMBB(X92,tc_fun(X12,X62),tc_prod(X5,X12)),X18),hAPP(hAPP(c_COMBB(X5,X92,tc_prod(X5,X12)),X50),c_Product__Type_Ofst(X5,X12)))),c_Product__Type_Osnd(X5,X12))=hAPP(c_Product__Type_Oprod_Oprod__case(X5,X12,X62),hAPP(hAPP(c_COMBB(X92,tc_fun(X12,X62),X5),X18),X50)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__comp__eq)). 6.97/7.21 fof(fact_split__twice, axiom, ![X24, X50, X114, X92, X18, X5, X62, X12]:hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X12,X62,X5),X18),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X92,X114,tc_prod(X12,X62)),X50),X24))=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X92,X114,X5),hAPP(hAPP(c_COMBB(tc_fun(X114,tc_prod(X12,X62)),tc_fun(X114,X5),X92),hAPP(c_COMBB(tc_prod(X12,X62),X5,X114),hAPP(c_Product__Type_Oprod_Oprod__case(X12,X62,X5),X18))),X50)),X24), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__twice)). 6.97/7.21 fof(fact_list__update_Osimps_I2_J, axiom, ![X60, X47, X23, X35, X5]:hAPP(hAPP(c_List_Olist__update(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23)),X47),X60)=c_Nat_Onat_Onat__case(tc_List_Olist(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X60),X23),hAPP(hAPP(c_COMBB(tc_List_Olist(X5),tc_List_Olist(X5),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X5),X35)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X5,tc_List_Olist(X5)),c_List_Olist__update(X5,X23)),X60)),X47), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update_Osimps_I2_J)). 6.97/7.21 fof(fact_Sigma__Union, axiom, ![X11, X56, X12, X5]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),X56),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(X12,tc_HOL_Obool)),tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),c_Product__Type_OSigma(X5,X12)),X11))=hAPP(hAPP(c_Product__Type_OSigma(X5,X12),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X56)),X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__Union)). 6.97/7.21 fof(fact_UN__extend__simps_I8_J, axiom, ![X11, X4, X5, X12]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X12,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBC(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool))),X11))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X12,tc_HOL_Obool),X4)),X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__extend__simps_I8_J)). 6.97/7.21 fof(fact_INT__simps_I8_J, axiom, ![X11, X4, X5, X12]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X12,tc_HOL_Obool),X4)),X11)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X12,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBC(tc_fun(X12,tc_HOL_Obool),tc_fun(X12,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool))),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__simps_I8_J)). 6.97/7.21 fof(fact_image__diff__subset, axiom, ![X11, X4, X18, X12, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X12,X5,X18),X4)),hAPP(c_Set_Oimage(X12,X5,X18),X11))),hAPP(c_Set_Oimage(X12,X5,X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12,tc_HOL_Obool)),X4),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__diff__subset)). 6.97/7.21 fof(fact_image__Int__subset, axiom, ![X11, X4, X18, X12, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X12,X5,X18),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),X4),X11))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X12,X5,X18),X4)),hAPP(c_Set_Oimage(X12,X5,X18),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__Int__subset)). 6.97/7.21 fof(fact_Image__Int__subset, axiom, ![X11, X4, X67, X12, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X12,X5,X67),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),X4),X11))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X12,X5,X67),X4)),hAPP(c_Relation_OImage(X12,X5,X67),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__Int__subset)). 6.97/7.21 fof(fact_converse__INTER, axiom, ![X3, X44, X62, X5, X12]:hAPP(c_Relation_Oconverse(X12,X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X62,tc_fun(tc_prod(X12,X5),tc_HOL_Obool)),X44),X3))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X62,tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),X44),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X12,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X12),tc_HOL_Obool),X62),c_Relation_Oconverse(X12,X5)),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__INTER)). 6.97/7.21 fof(fact_converse__UNION, axiom, ![X3, X44, X62, X5, X12]:hAPP(c_Relation_Oconverse(X12,X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X62,tc_fun(tc_prod(X12,X5),tc_HOL_Obool)),X44),X3))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X62,tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),X44),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X12,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X12),tc_HOL_Obool),X62),c_Relation_Oconverse(X12,X5)),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__UNION)). 6.97/7.21 fof(fact_Domain__Int__subset, axiom, ![X11, X4, X12, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5,X12),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),X4),X11))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5,X12),X4)),hAPP(c_Relation_ODomain(X5,X12),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__Int__subset)). 6.97/7.21 fof(fact_Range__Int__subset, axiom, ![X11, X4, X12, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ORange(X12,X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X12,X5),tc_HOL_Obool)),X4),X11))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ORange(X12,X5),X4)),hAPP(c_Relation_ORange(X12,X5),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__Int__subset)). 6.97/7.21 fof(fact_Union__Int__subset, axiom, ![X11, X4, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X4),X11))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X4)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__Int__subset)). 6.97/7.21 fof(fact_Domain__Diff__subset, axiom, ![X11, X4, X12, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5,X12),X4)),hAPP(c_Relation_ODomain(X5,X12),X11))),hAPP(c_Relation_ODomain(X5,X12),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),X4),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__Diff__subset)). 6.97/7.21 fof(fact_Range__Diff__subset, axiom, ![X11, X4, X12, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ORange(X12,X5),X4)),hAPP(c_Relation_ORange(X12,X5),X11))),hAPP(c_Relation_ORange(X12,X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X12,X5),tc_HOL_Obool)),X4),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__Diff__subset)). 6.97/7.21 fof(fact_Inter__Un__subset, axiom, ![X11, X4, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X4)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X11))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X4),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__Un__subset)). 6.97/7.21 fof(fact_update__zip, axiom, ![X279, X28, X45, X41, X5, X8]:hAPP(hAPP(c_List_Ozip(X8,X5),hAPP(hAPP(c_List_Olist__update(X8,X41),X28),hAPP(c_Product__Type_Ofst(X8,X5),X279))),hAPP(hAPP(c_List_Olist__update(X5,X45),X28),hAPP(c_Product__Type_Osnd(X8,X5),X279)))=hAPP(hAPP(c_List_Olist__update(tc_prod(X8,X5),hAPP(hAPP(c_List_Ozip(X8,X5),X41),X45)),X28),X279), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_update__zip)). 6.97/7.21 fof(fact_Compl__Times__UNIV2, axiom, ![X4, X12, X5]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X4),hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X5),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))))=hAPP(hAPP(c_Product__Type_OSigma(X5,X12),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X4)),hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X5),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__Times__UNIV2)). 6.97/7.21 fof(fact_Compl__Times__UNIV1, axiom, ![X4, X12, X5]:hAPP(hAPP(c_Product__Type_OSigma(X5,X12),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X5),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X12,tc_HOL_Obool)),X4)))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__Times__UNIV1)). 6.97/7.21 fof(fact_take__Cons, axiom, ![X23, X35, X32, X5]:hAPP(hAPP(c_List_Otake(X5),X32),hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23))=c_Nat_Onat_Onat__case(tc_List_Olist(X5),c_List_Olist_ONil(X5),hAPP(hAPP(c_COMBB(tc_List_Olist(X5),tc_List_Olist(X5),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X5),X35)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Otake(X5)),X23)),X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__Cons)). 6.97/7.21 fof(fact_zdiv__zmult1__eq, axiom, ![X31, X29, X30]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X29),X31))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),c_Divides_Odiv__class_Omod(tc_Int_Oint,X29,X31))),X31))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X29)),X31), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__zmult1__eq)). 6.97/7.21 fof(fact_div__mult1__eq, axiom, ![X31, X29, X30]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X29),X31))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X29,X31))),X31))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X29)),X31), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult1__eq)). 6.97/7.21 fof(fact_Ex__inj__on__UNION__Sigma, axiom, ![X4, X15, X12, X5]:?[X185]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X12,X5),tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,tc_prod(X12,X5),X185),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X15),X4))),hAPP(hAPP(c_Product__Type_OSigma(X12,X5),X15),X4)))&c_Fun_Oinj__on(X5,tc_prod(X12,X5),X185,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X15),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ex__inj__on__UNION__Sigma)). 6.97/7.21 fof(fact_wmin__emptyI, axiom, ![X56]: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)),X56),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)). 6.97/7.21 fof(fact_Un__Pow__subset, axiom, ![X11, X4, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X5),X4)),hAPP(c_Set_OPow(X5),X11))),hAPP(c_Set_OPow(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Pow__subset)). 6.97/7.21 fof(fact_tl__append, axiom, ![X84, X23, X5]:hAPP(c_List_Otl(X5),hAPP(hAPP(c_List_Oappend(X5),X23),X84))=hAPP(c_List_Olist_Olist__case(tc_List_Olist(X5),X5,hAPP(c_List_Otl(X5),X84),hAPP(c_COMBK(tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),X5),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Oappend(X5)),X84))),X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tl__append)). 6.97/7.21 fof(fact_The__split, axiom, ![X17, X12, X5]:c_HOL_OThe(tc_prod(X5,X12),hAPP(hAPP(c_COMBS(tc_prod(X5,X12),X12,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X5,tc_fun(X12,tc_HOL_Obool),tc_prod(X5,X12)),X17),c_Product__Type_Ofst(X5,X12))),c_Product__Type_Osnd(X5,X12)))=c_HOL_OThe(tc_prod(X5,X12),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X12,tc_HOL_Obool),X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_The__split)). 6.97/7.21 fof(fact_Eps__split, axiom, ![X17, X12, X5]:c_Hilbert__Choice_OEps(tc_prod(X5,X12),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X12,tc_HOL_Obool),X17))=c_Hilbert__Choice_OEps(tc_prod(X5,X12),hAPP(hAPP(c_COMBS(tc_prod(X5,X12),X12,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X5,tc_fun(X12,tc_HOL_Obool),tc_prod(X5,X12)),X17),c_Product__Type_Ofst(X5,X12))),c_Product__Type_Osnd(X5,X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Eps__split)). 6.97/7.21 fof(fact_Int__UN__distrib, axiom, ![X4, X15, X12, X11, X5]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X15),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X12),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11)),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X15),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__UN__distrib)). 6.97/7.21 fof(fact_UN__simps_I7_J, axiom, ![X11, X4, X65, X5, X12]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),X65),X11))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X65),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X12),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4)),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__simps_I7_J)). 6.97/7.21 fof(fact_INT__simps_I7_J, axiom, ![X11, X4, X65, X5, X12]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),X65),X11))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),X65),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X12),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4)),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__simps_I7_J)). 6.97/7.21 fof(fact_rtrancl__Un__subset, axiom, ![X44, X67, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X67)),c_Transitive__Closure_Ortrancl(X5,X44))),c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X67),X44)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__Un__subset)). 6.97/7.21 fof(fact_rel__comp__distrib2, axiom, ![X67, X108, X44, X12, X62, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X62,X12),X44),X67)),hAPP(hAPP(c_Relation_Orel__comp(X5,X62,X12),X108),X67))=hAPP(hAPP(c_Relation_Orel__comp(X5,X62,X12),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X62),tc_HOL_Obool)),X44),X108)),X67), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__comp__distrib2)). 6.97/7.21 fof(fact_rel__comp__distrib, axiom, ![X108, X44, X67, X12, X62, X5]:hAPP(hAPP(c_Relation_Orel__comp(X5,X62,X12),X67),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X62,X12),tc_HOL_Obool)),X44),X108))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X62,X12),X67),X44)),hAPP(hAPP(c_Relation_Orel__comp(X5,X62,X12),X67),X108)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__comp__distrib)). 6.97/7.21 fof(fact_map__pair_Ocomp, axiom, ![X47, X71, X50, X18, X12, X5, X92, X62, X113, X114]:hAPP(c_Fun_Ocomp(tc_prod(X114,X113),tc_prod(X62,X92),tc_prod(X5,X12),c_Product__Type_Omap__pair(X114,X62,X113,X92,X18,X50)),c_Product__Type_Omap__pair(X5,X114,X12,X113,X71,X47))=c_Product__Type_Omap__pair(X5,X62,X12,X92,hAPP(c_Fun_Ocomp(X114,X62,X5,X18),X71),hAPP(c_Fun_Ocomp(X113,X92,X12,X50),X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair_Ocomp)). 6.97/7.21 fof(fact_rtrancl__is__UN__rel__pow, axiom, ![X67, X5]:c_Transitive__Closure_Ortrancl(X5,X67)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X5,X5),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(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool)),X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__is__UN__rel__pow)). 6.97/7.21 fof(fact_Int__Union2, axiom, ![X4, X11, X5]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool))),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X11)),X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__Union2)). 6.97/7.21 fof(fact_INT__Un, axiom, ![X94, X11, X4, X5, X12]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),X4),X94)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),X11),X94))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),X4),X11)),X94), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__Un)). 6.97/7.21 fof(fact_UN__Un, axiom, ![X94, X11, X4, X5, X12]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X4),X94)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X11),X94))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),X4),X11)),X94), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__Un)). 6.97/7.21 fof(fact_Pow__insert, axiom, ![X4, X2, X5]:hAPP(c_Set_OPow(X5),hAPP(hAPP(c_Set_Oinsert(X5),X2),X4))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X5),X4)),hAPP(c_Set_Oimage(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oinsert(X5),X2)),hAPP(c_Set_OPow(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__insert)). 6.97/7.21 fof(fact_Random__Sequence_Omap__def, axiom, ![X17, X18, X5, X12]:c_Random__Sequence_Omap(X12,X5,X18,X17)=c_Random__Sequence_Obind(X12,X5,X17,hAPP(c_Fun_Ocomp(X5,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_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),X12,c_Random__Sequence_Osingle(X5)),X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Random__Sequence_Omap__def)). 6.97/7.21 fof(fact_rel__pow__add, axiom, ![X67, X32, X34, X5]:hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34),X32)),X67)=hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X34),X67)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X32),X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__add)). 6.97/7.21 fof(fact_Pow__INT__eq, axiom, ![X11, X4, X12, X5]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),X12),c_Set_OPow(X5)),X11))=hAPP(c_Set_OPow(X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),X4),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__INT__eq)). 6.97/7.21 fof(fact_image__UN, axiom, ![X11, X4, X62, X18, X5, X12]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X62,tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X62),c_Set_Oimage(X12,X5,X18)),X11))=hAPP(c_Set_Oimage(X12,X5,X18),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X62,tc_fun(X12,tc_HOL_Obool)),X4),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__UN)). 6.97/7.21 fof(fact_Image__UN, axiom, ![X11, X4, X62, X3, X5, X12]:hAPP(c_Relation_OImage(X12,X5,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X62,tc_fun(X12,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X62,tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X62),c_Relation_OImage(X12,X5,X3)),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__UN)). 6.97/7.21 fof(fact_Compl__INT, axiom, ![X11, X4, X12, X5]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X12),c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool))),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__INT)). 6.97/7.21 fof(fact_Compl__UN, axiom, ![X11, X4, X12, X5]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X12),c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool))),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__UN)). 6.97/7.21 fof(fact_INT__simps_I5_J, axiom, ![X11, X2, X65, X5, X12]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),X65),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X12),hAPP(c_Set_Oinsert(X5),X2)),X11))=hAPP(hAPP(c_Set_Oinsert(X5),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),X65),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__simps_I5_J)). 6.97/7.21 fof(fact_drop__append, axiom, ![X45, X41, X25, X8]:hAPP(hAPP(c_List_Oappend(X8),hAPP(hAPP(c_List_Odrop(X8),X25),X41)),hAPP(hAPP(c_List_Odrop(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41))),X45))=hAPP(hAPP(c_List_Odrop(X8),X25),hAPP(hAPP(c_List_Oappend(X8),X41),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__append)). 6.97/7.21 fof(fact_take__append, axiom, ![X45, X41, X25, X8]:hAPP(hAPP(c_List_Otake(X8),X25),hAPP(hAPP(c_List_Oappend(X8),X41),X45))=hAPP(hAPP(c_List_Oappend(X8),hAPP(hAPP(c_List_Otake(X8),X25),X41)),hAPP(hAPP(c_List_Otake(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41))),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__append)). 6.97/7.21 fof(fact_Un__Diff, axiom, ![X65, X11, X4, X5]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11)),X65)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X65)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X65)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Diff)). 6.97/7.21 fof(fact_Int__Un__distrib2, axiom, ![X4, X65, X11, X5]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X65)),X4)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X65),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__Un__distrib2)). 6.97/7.21 fof(fact_Un__Int__distrib2, axiom, ![X4, X65, X11, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X65)),X4)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X65),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Int__distrib2)). 6.97/7.21 fof(fact_Un__Int__distrib, axiom, ![X65, X11, X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X65))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X65)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Int__distrib)). 6.97/7.21 fof(fact_Diff__Int, axiom, ![X65, X11, X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X65))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X11),X65)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__Int)). 6.97/7.21 fof(fact_Int__Un__distrib, axiom, ![X65, X11, X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X65))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X11),X65)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__Un__distrib)). 6.97/7.21 fof(fact_Diff__insert, axiom, ![X11, X2, X4, X5]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X2),X11))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11)),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__insert)). 6.97/7.21 fof(fact_Sigma__Int__distrib1, axiom, ![X65, X133, X15, X12, X5]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X15),X65)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X133),X65))=hAPP(hAPP(c_Product__Type_OSigma(X5,X12),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X15),X133)),X65), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__Int__distrib1)). 6.97/7.21 fof(fact_Sigma__Un__distrib1, axiom, ![X65, X133, X15, X12, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X15),X65)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X133),X65))=hAPP(hAPP(c_Product__Type_OSigma(X5,X12),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X15),X133)),X65), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__Un__distrib1)). 6.97/7.21 fof(fact_Sigma__Diff__distrib1, axiom, ![X65, X133, X15, X12, X5]:hAPP(hAPP(c_Product__Type_OSigma(X5,X12),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X15),X133)),X65)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X15),X65)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X133),X65)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__Diff__distrib1)). 6.97/7.21 fof(fact_pick__drop__zero, axiom, ![X23, X5]:c_Random_Opick(X5,X23)=c_Random_Opick(X5,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X5),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X5)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pick__drop__zero)). 6.97/7.21 fof(fact_select__weigth__drop__zero, axiom, ![X23, X5]:c_Random_Oselect__weight(X5,X23)=c_Random_Oselect__weight(X5,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X5),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X5)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_select__weigth__drop__zero)). 6.97/7.21 fof(fact_the__elem__def, axiom, ![X56, X5]:c_HOL_OThe(X5,hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),hAPP(c_fequal,X56)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_Oinsert(X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))=c_Set_Othe__elem(X5,X56), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__elem__def)). 6.97/7.21 fof(fact_product_Osimps_I2_J, axiom, ![X84, X23, X35, X12, X5]:hAPP(hAPP(c_List_Oappend(tc_prod(X5,X12)),hAPP(hAPP(c_List_Omap(X12,tc_prod(X5,X12)),hAPP(c_Product__Type_OPair(X5,X12),X35)),X84)),c_Enum_Oproduct(X5,X12,X23,X84))=c_Enum_Oproduct(X5,X12,hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23),X84), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_product_Osimps_I2_J)). 6.97/7.21 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J, axiom, ![X11, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X4),X11)=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)),X4)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J)). 6.97/7.21 fof(fact_split__eta, axiom, ![X18, X62, X12, X5]:hAPP(c_Product__Type_Oprod_Oprod__case(X5,X12,X62),hAPP(hAPP(c_COMBB(tc_fun(X12,tc_prod(X5,X12)),tc_fun(X12,X62),X5),hAPP(c_COMBB(tc_prod(X5,X12),X62,X12),X18)),c_Product__Type_OPair(X5,X12)))=X18, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__eta)). 6.97/7.21 fof(fact_zip__takeWhile__fst, axiom, ![X84, X23, X17, X12, X5]:c_List_OtakeWhile(tc_prod(X5,X12),hAPP(c_Fun_Ocomp(X5,tc_HOL_Obool,tc_prod(X5,X12),X17),c_Product__Type_Ofst(X5,X12)),hAPP(hAPP(c_List_Ozip(X5,X12),X23),X84))=hAPP(hAPP(c_List_Ozip(X5,X12),c_List_OtakeWhile(X5,X17,X23)),X84), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__takeWhile__fst)). 6.97/7.21 fof(fact_zip__takeWhile__snd, axiom, ![X84, X17, X23, X12, X5]:hAPP(hAPP(c_List_Ozip(X5,X12),X23),c_List_OtakeWhile(X12,X17,X84))=c_List_OtakeWhile(tc_prod(X5,X12),hAPP(c_Fun_Ocomp(X12,tc_HOL_Obool,tc_prod(X5,X12),X17),c_Product__Type_Osnd(X5,X12)),hAPP(hAPP(c_List_Ozip(X5,X12),X23),X84)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__takeWhile__snd)). 6.97/7.21 fof(fact_list__update__length, axiom, ![X7, X45, X6, X41, X8]:hAPP(hAPP(c_List_Olist__update(X8,hAPP(hAPP(c_List_Oappend(X8),X41),hAPP(hAPP(c_List_Olist_OCons(X8),X6),X45))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)),X7)=hAPP(hAPP(c_List_Oappend(X8),X41),hAPP(hAPP(c_List_Olist_OCons(X8),X7),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__length)). 6.97/7.21 fof(fact_drop__Cons, axiom, ![X23, X35, X32, X5]:hAPP(hAPP(c_List_Odrop(X5),X32),hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23))=c_Nat_Onat_Onat__case(tc_List_Olist(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Odrop(X5)),X23),X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__Cons)). 6.97/7.21 fof(fact_Un__Image, axiom, ![X4, X44, X67, X5, X12]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X12,X5,X67),X4)),hAPP(c_Relation_OImage(X12,X5,X44),X4))=hAPP(c_Relation_OImage(X12,X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X12,X5),tc_HOL_Obool)),X67),X44)),X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Image)). 6.97/7.21 fof(fact_neg__map__def, axiom, ![X17, X18, X5, X12]:c_New__Random__Sequence_Oneg__bind(X12,X5,X17,hAPP(c_Fun_Ocomp(X5,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(X5)))))),X12,c_New__Random__Sequence_Oneg__single(X5)),X18))=c_New__Random__Sequence_Oneg__map(X12,X5,X18,X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__map__def)). 6.97/7.21 fof(fact_image__add__int__atLeastLessThan, axiom, ![X51, X52]: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)),X52)),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),X51),X52)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X52),X51), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__add__int__atLeastLessThan)). 6.97/7.21 fof(fact_converse__Int, axiom, ![X66, X3, X5, X12]:hAPP(c_Relation_Oconverse(X12,X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X12,X5),tc_HOL_Obool)),X3),X66))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X12,X5),X3)),hAPP(c_Relation_Oconverse(X12,X5),X66)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__Int)). 6.97/7.21 fof(fact_converse__Un, axiom, ![X66, X3, X5, X12]:hAPP(c_Relation_Oconverse(X12,X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X12,X5),tc_HOL_Obool)),X3),X66))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X12,X5),X3)),hAPP(c_Relation_Oconverse(X12,X5),X66)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__Un)). 6.97/7.21 fof(fact_funpow__add, axiom, ![X18, X32, X34, X5]:hAPP(hAPP(c_Nat_Ocompow(X5,X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34),X32)),X18)=hAPP(c_Fun_Ocomp(X5,X5,X5,hAPP(hAPP(c_Nat_Ocompow(X5,X5),X34),X18)),hAPP(hAPP(c_Nat_Ocompow(X5,X5),X32),X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_funpow__add)). 6.97/7.21 fof(fact_Image__Un, axiom, ![X11, X4, X67, X5, X12]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X12,X5,X67),X4)),hAPP(c_Relation_OImage(X12,X5,X67),X11))=hAPP(c_Relation_OImage(X12,X5,X67),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),X4),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__Un)). 6.97/7.21 fof(fact_insert__inter__insert, axiom, ![X11, X4, X2, X5]:hAPP(hAPP(c_Set_Oinsert(X5),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X2),X4)),hAPP(hAPP(c_Set_Oinsert(X5),X2),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__inter__insert)). 6.97/7.21 fof(fact_pos__map__def, axiom, ![X17, X18, X5, X12]:c_New__Random__Sequence_Opos__map(X12,X5,X18,X17)=c_New__Random__Sequence_Opos__bind(X12,X5,X17,hAPP(c_Fun_Ocomp(X5,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(X5))))),X12,c_New__Random__Sequence_Opos__single(X5)),X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__map__def)). 6.97/7.21 fof(fact_set__update__subset__insert, axiom, ![X35, X47, X23, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist__update(X5,X23),X47),X35))),hAPP(hAPP(c_Set_Oinsert(X5),X35),hAPP(c_List_Oset(X5),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__update__subset__insert)). 6.97/7.21 fof(fact_zadd__int__left, axiom, ![X26, X25, X36]: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),X36),X25))),X26)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X36)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25)),X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__int__left)). 6.97/7.21 fof(fact_drop__zip, axiom, ![X45, X41, X25, X5, X8]:hAPP(hAPP(c_List_Ozip(X8,X5),hAPP(hAPP(c_List_Odrop(X8),X25),X41)),hAPP(hAPP(c_List_Odrop(X5),X25),X45))=hAPP(hAPP(c_List_Odrop(tc_prod(X8,X5)),X25),hAPP(hAPP(c_List_Ozip(X8,X5),X41),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__zip)). 6.97/7.21 fof(fact_card__cartesian__product, axiom, ![X11, X4, X12, X5]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X4)),hAPP(c_Finite__Set_Ocard(X12),X11))=hAPP(c_Finite__Set_Ocard(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OSigma(X5,X12),X4),hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X5),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__cartesian__product)). 6.97/7.21 fof(fact_partition__filter__conv, axiom, ![X23, X18, X5]:c_List_Opartition(X5,X18,X23)=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,X18),X23)),hAPP(c_List_Ofilter(X5,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X5,c_fNot),X18)),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_partition__filter__conv)). 6.97/7.21 fof(fact_inv__def, axiom, ![X38, X18, X12, X5]:hAPP(c_Hilbert__Choice_Oinv__into(X5,X12,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X18),X38)=c_Hilbert__Choice_OEps(X5,hAPP(hAPP(c_COMBC(X5,X12,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X12,tc_fun(X12,tc_HOL_Obool),X5),c_fequal),X18)),X38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inv__def)). 6.97/7.21 fof(fact_pred__nat__def, axiom, c_Wellfounded_Opred__nat=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))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pred__nat__def)). 6.97/7.21 fof(fact_product__list__set, axiom, ![X84, X23, X12, X5]:hAPP(hAPP(c_Product__Type_OSigma(X5,X12),hAPP(c_List_Oset(X5),X23)),hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X5),hAPP(c_List_Oset(X12),X84)))=hAPP(c_List_Oset(tc_prod(X5,X12)),c_Enum_Oproduct(X5,X12,X23,X84)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_product__list__set)). 6.97/7.21 fof(fact_Id__on__subset__Times, axiom, ![X4, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Relation_OId__on(X5,X4)),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X4),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Id__on__subset__Times)). 6.97/7.21 fof(fact_map__comp__map, axiom, ![X50, X18, X5, X12, X62]:hAPP(c_List_Omap(X5,X12),hAPP(c_Fun_Ocomp(X62,X12,X5,X18),X50))=hAPP(c_Fun_Ocomp(tc_List_Olist(X62),tc_List_Olist(X12),tc_List_Olist(X5),hAPP(c_List_Omap(X62,X12),X18)),hAPP(c_List_Omap(X5,X62),X50)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__comp__map)). 6.97/7.21 fof(fact_swap__inj__on, axiom, ![X4, X12, X5]:c_Fun_Oinj__on(tc_prod(X5,X12),tc_prod(X12,X5),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X12,tc_prod(X12,X5)),hAPP(c_COMBC(X12,X5,tc_prod(X12,X5)),c_Product__Type_OPair(X12,X5))),X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_swap__inj__on)). 6.97/7.21 fof(fact_inj__singleton, axiom, ![X5]:c_Fun_Oinj__on(X5,tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_Oinsert(X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__singleton)). 6.97/7.21 fof(fact_Domain__Un__eq, axiom, ![X11, X4, X12, X5]:hAPP(c_Relation_ODomain(X5,X12),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5,X12),X4)),hAPP(c_Relation_ODomain(X5,X12),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__Un__eq)). 6.97/7.21 fof(fact_Range__Un__eq, axiom, ![X11, X4, X5, X12]:hAPP(c_Relation_ORange(X12,X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X12,X5),tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ORange(X12,X5),X4)),hAPP(c_Relation_ORange(X12,X5),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__Un__eq)). 6.97/7.21 fof(fact_insert__Diff__single, axiom, ![X4, X2, X5]:hAPP(hAPP(c_Set_Oinsert(X5),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))=hAPP(hAPP(c_Set_Oinsert(X5),X2),X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__Diff__single)). 6.97/7.21 fof(fact_converse__meet, axiom, ![X66, X3, X5, X12]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X12,tc_HOL_Obool))),c_Predicate_Oconversep(X12,X5,X3)),c_Predicate_Oconversep(X12,X5,X66))=c_Predicate_Oconversep(X12,X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_fun(X5,tc_HOL_Obool))),X3),X66)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__meet)). 6.97/7.21 fof(fact_converse__join, axiom, ![X66, X3, X5, X12]:c_Predicate_Oconversep(X12,X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_fun(X5,tc_HOL_Obool))),X3),X66))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X12,tc_HOL_Obool))),c_Predicate_Oconversep(X12,X5,X3)),c_Predicate_Oconversep(X12,X5,X66)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__join)). 6.97/7.21 fof(fact_Domain__insert, axiom, ![X3, X1, X2, X12, X5]:hAPP(hAPP(c_Set_Oinsert(X5),X2),hAPP(c_Relation_ODomain(X5,X12),X3))=hAPP(c_Relation_ODomain(X5,X12),hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X12)),hAPP(hAPP(c_Product__Type_OPair(X5,X12),X2),X1)),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__insert)). 6.97/7.21 fof(fact_Range__insert, axiom, ![X3, X1, X2, X5, X12]:hAPP(hAPP(c_Set_Oinsert(X5),X1),hAPP(c_Relation_ORange(X12,X5),X3))=hAPP(c_Relation_ORange(X12,X5),hAPP(hAPP(c_Set_Oinsert(tc_prod(X12,X5)),hAPP(hAPP(c_Product__Type_OPair(X12,X5),X2),X1)),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__insert)). 6.97/7.21 fof(fact_UN__singleton, axiom, ![X4, X5]:X4=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_Oinsert(X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__singleton)). 6.97/7.21 fof(fact_filter__map, axiom, ![X23, X18, X12, X17, X5]:hAPP(c_List_Ofilter(X5,X17),hAPP(hAPP(c_List_Omap(X12,X5),X18),X23))=hAPP(hAPP(c_List_Omap(X12,X5),X18),hAPP(c_List_Ofilter(X12,hAPP(c_Fun_Ocomp(X5,tc_HOL_Obool,X12,X17),X18)),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__map)). 6.97/7.21 fof(fact_rel__pow__0__I, axiom, ![X67, X35, X5]:hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X35),X35)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X67))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__0__I)). 6.97/7.21 fof(fact_rtrancl__Un__rtrancl, axiom, ![X44, X67, X5]:c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X67)),c_Transitive__Closure_Ortrancl(X5,X44)))=c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X67),X44)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__Un__rtrancl)). 6.97/7.21 fof(fact_rev__drop, axiom, ![X41, X28, X8]:hAPP(c_List_Orev(X8),hAPP(hAPP(c_List_Odrop(X8),X28),X41))=hAPP(hAPP(c_List_Otake(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)),X28)),hAPP(c_List_Orev(X8),X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__drop)). 6.97/7.21 fof(fact_rev__take, axiom, ![X41, X28, X8]:hAPP(c_List_Orev(X8),hAPP(hAPP(c_List_Otake(X8),X28),X41))=hAPP(hAPP(c_List_Odrop(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)),X28)),hAPP(c_List_Orev(X8),X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__take)). 6.97/7.21 fof(fact_converse__rel__comp, axiom, ![X66, X3, X62, X5, X12]:hAPP(hAPP(c_Relation_Orel__comp(X5,X62,X12),hAPP(c_Relation_Oconverse(X62,X5),X66)),hAPP(c_Relation_Oconverse(X12,X62),X3))=hAPP(c_Relation_Oconverse(X12,X5),hAPP(hAPP(c_Relation_Orel__comp(X12,X62,X5),X3),X66)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__rel__comp)). 6.97/7.21 fof(fact_nth__append__length__plus, axiom, ![X25, X45, X41, X8]:hAPP(hAPP(c_List_Onth(X8),hAPP(hAPP(c_List_Oappend(X8),X41),X45)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)),X25))=hAPP(hAPP(c_List_Onth(X8),X45),X25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__append__length__plus)). 6.97/7.21 fof(fact_listrel_ONil, axiom, ![X3, X5]: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)),c_List_Olist_ONil(X5)),c_List_Olist_ONil(X5))),c_List_Olistrel(X5,X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel_ONil)). 6.97/7.21 fof(fact_replicate__app__Cons__same, axiom, ![X41, X6, X25, X8]:hAPP(hAPP(c_List_Oappend(X8),c_List_Oreplicate(X8,X25,X6)),hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41))=hAPP(hAPP(c_List_Olist_OCons(X8),X6),hAPP(hAPP(c_List_Oappend(X8),c_List_Oreplicate(X8,X25,X6)),X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_replicate__app__Cons__same)). 6.97/7.21 fof(fact_Pow__Int__eq, axiom, ![X11, X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X5),X4)),hAPP(c_Set_OPow(X5),X11))=hAPP(c_Set_OPow(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__Int__eq)). 6.97/7.21 fof(fact_take__drop, axiom, ![X41, X36, X25, X8]:hAPP(hAPP(c_List_Otake(X8),X25),hAPP(hAPP(c_List_Odrop(X8),X36),X41))=hAPP(hAPP(c_List_Odrop(X8),X36),hAPP(hAPP(c_List_Otake(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X36)),X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__drop)). 6.97/7.21 fof(fact_splice_Osimps_I3_J, axiom, ![X45, X7, X41, X6, X8]:c_List_Osplice(X8,hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41),hAPP(hAPP(c_List_Olist_OCons(X8),X7),X45))=hAPP(hAPP(c_List_Olist_OCons(X8),X6),hAPP(hAPP(c_List_Olist_OCons(X8),X7),c_List_Osplice(X8,X41,X45))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_splice_Osimps_I3_J)). 6.97/7.21 fof(fact_zdiff__zmult__distrib, axiom, ![X39, X182, X183]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X183),X39)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X182),X39))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X183),X182)),X39), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiff__zmult__distrib)). 6.97/7.21 fof(fact_zadd__zmult__distrib, axiom, ![X39, X182, X183]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X183),X39)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X182),X39))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X183),X182)),X39), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__zmult__distrib)). 6.97/7.21 fof(fact_diff__mult__distrib, axiom, ![X19, X25, X36]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),X25)),X19)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X19)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__mult__distrib)). 6.97/7.21 fof(fact_add__mult__distrib, axiom, ![X19, X25, X36]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X25)),X19)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X19)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__mult__distrib)). 6.97/7.21 fof(fact_drop__take, axiom, ![X41, X36, X25, X8]:hAPP(hAPP(c_List_Odrop(X8),X25),hAPP(hAPP(c_List_Otake(X8),X36),X41))=hAPP(hAPP(c_List_Otake(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),X25)),hAPP(hAPP(c_List_Odrop(X8),X25),X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__take)). 6.97/7.21 fof(fact_diff__mult__distrib2, axiom, ![X25, X36, X19]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X36)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X25))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__mult__distrib2)). 6.97/7.21 fof(fact_add__mult__distrib2, axiom, ![X25, X36, X19]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X36)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X25))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__mult__distrib2)). 6.97/7.21 fof(fact_zpower__zadd__distrib, axiom, ![X26, X7, X6]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7),X26))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),X7)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zpower__zadd__distrib)). 6.97/7.21 fof(fact_zdiff__zmult__distrib2, axiom, ![X182, X183, X39]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X39),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X183),X182))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X39),X183)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X39),X182)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiff__zmult__distrib2)). 6.97/7.21 fof(fact_UNIV__Times__UNIV, axiom, ![X12, X5]:hAPP(hAPP(c_Product__Type_OSigma(X5,X12),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X12,tc_HOL_Obool),X5),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))))=c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UNIV__Times__UNIV)). 6.97/7.21 fof(fact_takeWhile__map, axiom, ![X23, X18, X12, X17, X5]:hAPP(hAPP(c_List_Omap(X12,X5),X18),c_List_OtakeWhile(X12,hAPP(c_Fun_Ocomp(X5,tc_HOL_Obool,X12,X17),X18),X23))=c_List_OtakeWhile(X5,X17,hAPP(hAPP(c_List_Omap(X12,X5),X18),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__map)). 6.97/7.21 fof(fact_Un__Diff__Int, axiom, ![X11, X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11))=X4, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Diff__Int)). 6.97/7.21 fof(fact_Field__Un, axiom, ![X66, X3, X5]:hAPP(c_Relation_OField(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),X66))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OField(X5),X3)),hAPP(c_Relation_OField(X5),X66)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Field__Un)). 6.97/7.21 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1, axiom, ![X3, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool)),c_List_Olistrel1(X5,c_Transitive__Closure_Ortrancl(X5,X3))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1__rtrancl__subset__rtrancl__listrel1)). 6.97/7.21 fof(fact_comp__funpow, axiom, ![X18, X32, X12, X5]:c_Fun_Ocomp(X12,X12,X5,hAPP(hAPP(c_Nat_Ocompow(X12,X12),X32),X18))=hAPP(hAPP(c_Nat_Ocompow(tc_fun(X5,X12),tc_fun(X5,X12)),X32),c_Fun_Ocomp(X12,X12,X5,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comp__funpow)). 6.97/7.21 fof(fact_map__pair__simp, axiom, ![X1, X2, X50, X18, X12, X92, X5, X62]:hAPP(hAPP(c_Product__Type_OPair(X5,X12),hAPP(X18,X2)),hAPP(X50,X1))=hAPP(c_Product__Type_Omap__pair(X62,X5,X92,X12,X18,X50),hAPP(hAPP(c_Product__Type_OPair(X62,X92),X2),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair__simp)). 6.97/7.21 fof(fact_list__update__code_I3_J, axiom, ![X7, X28, X41, X6, X8]:hAPP(hAPP(c_List_Olist__update(X8,hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41)),hAPP(c_Nat_OSuc,X28)),X7)=hAPP(hAPP(c_List_Olist_OCons(X8),X6),hAPP(hAPP(c_List_Olist__update(X8,X41),X28),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__code_I3_J)). 6.97/7.21 fof(fact_int__setsum, axiom, ![X4, X18, X5]:hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X5),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X18)),X4)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X18),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__setsum)). 6.97/7.21 fof(fact_int__setprod, axiom, ![X4, X18, X5]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,tc_Nat_Onat),X18),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X5),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X18)),X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__setprod)). 6.97/7.21 fof(fact_funpow__mult, axiom, ![X18, X34, X32, X5]:hAPP(hAPP(c_Nat_Ocompow(X5,X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X32)),X18)=hAPP(hAPP(c_Nat_Ocompow(X5,X5),X32),hAPP(hAPP(c_Nat_Ocompow(X5,X5),X34),X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_funpow__mult)). 6.97/7.21 fof(fact_tl__take, axiom, ![X41, X25, X8]:hAPP(hAPP(c_List_Otake(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(X8),X41))=hAPP(c_List_Otl(X8),hAPP(hAPP(c_List_Otake(X8),X25),X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tl__take)). 6.97/7.21 fof(fact_New__DSequence_Oneg__bind__def, axiom, ![X47, X18, X35, X5, X12]:hAPP(c_New__DSequence_Oneg__bind(X12,X5,X35,X18),X47)=c_Lazy__Sequence_Ohb__bind(X12,X5,hAPP(X35,X47),hAPP(hAPP(c_COMBC(X12,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X5))),X18),X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Oneg__bind__def)). 6.97/7.21 fof(fact_New__DSequence_Opos__bind__def, axiom, ![X47, X18, X35, X5, X12]:hAPP(c_Lazy__Sequence_Obind(X12,X5,hAPP(X35,X47)),hAPP(hAPP(c_COMBC(X12,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X5)),X18),X47))=hAPP(c_New__DSequence_Opos__bind(X12,X5,X35,X18),X47), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Opos__bind__def)). 6.97/7.21 fof(fact_nth__append__length, axiom, ![X45, X6, X41, X8]:hAPP(hAPP(c_List_Onth(X8),hAPP(hAPP(c_List_Oappend(X8),X41),hAPP(hAPP(c_List_Olist_OCons(X8),X6),X45))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41))=X6, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__append__length)). 6.97/7.21 fof(fact_UN__empty2, axiom, ![X4, X5, X12]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12,tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__empty2)). 6.97/7.21 fof(fact_filter__append, axiom, ![X84, X23, X17, X5]:hAPP(c_List_Ofilter(X5,X17),hAPP(hAPP(c_List_Oappend(X5),X23),X84))=hAPP(hAPP(c_List_Oappend(X5),hAPP(c_List_Ofilter(X5,X17),X23)),hAPP(c_List_Ofilter(X5,X17),X84)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__append)). 6.97/7.21 fof(fact_sublists__powset, axiom, ![X23, X5]:hAPP(c_Set_OPow(X5),hAPP(c_List_Oset(X5),X23))=hAPP(c_Set_Oimage(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool),c_List_Oset(X5)),hAPP(c_List_Oset(tc_List_Olist(X5)),c_Enum_Osublists(X5,X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublists__powset)). 6.97/7.21 fof(fact_divmod__nat__rel, axiom, ![X25, X36]:hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X36,X25),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X36),X25)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X36,X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__rel)). 6.97/7.21 fof(fact_listrel__subset__rtrancl__listrel1, axiom, ![X3, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool)),c_List_Olistrel(X5,X3)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__subset__rtrancl__listrel1)). 6.97/7.21 fof(fact_foldl__append, axiom, ![X84, X23, X2, X18, X12, X5]:hAPP(c_List_Ofoldl(X5,X12,X18,hAPP(c_List_Ofoldl(X5,X12,X18,X2),X23)),X84)=hAPP(c_List_Ofoldl(X5,X12,X18,X2),hAPP(hAPP(c_List_Oappend(X12),X23),X84)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__append)). 6.97/7.21 fof(fact_set__drop__subset, axiom, ![X23, X32, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Odrop(X5),X32),X23))),hAPP(c_List_Oset(X5),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__drop__subset)). 6.97/7.21 fof(fact_set__take__subset, axiom, ![X23, X32, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Otake(X5),X32),X23))),hAPP(c_List_Oset(X5),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__take__subset)). 6.97/7.21 fof(fact_Diff__idemp, axiom, ![X11, X4, X5]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11)),X11)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__idemp)). 6.97/7.21 fof(fact_Un__left__absorb, axiom, ![X11, X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__left__absorb)). 6.97/7.21 fof(fact_Int__left__absorb, axiom, ![X11, X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__left__absorb)). 6.97/7.21 fof(fact_Un__Diff__cancel, axiom, ![X11, X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Diff__cancel)). 6.97/7.21 fof(fact_take__Suc__Cons, axiom, ![X41, X6, X25, X8]:hAPP(hAPP(c_List_Olist_OCons(X8),X6),hAPP(hAPP(c_List_Otake(X8),X25),X41))=hAPP(hAPP(c_List_Otake(X8),hAPP(c_Nat_OSuc,X25)),hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__Suc__Cons)). 6.97/7.21 fof(fact_mod__mult__self4, axiom, ![X36, X25, X19]:c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X36),X25)=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),X19),X25)),X36)),X25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__self4)). 6.97/7.21 fof(fact_lex__def, axiom, ![X3, X5]:c_List_Olex(X5,X3)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lex__def)). 6.97/7.21 fof(fact_mod__mult__distrib, axiom, ![X19, X25, X36]:c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X19))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X36,X25)),X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__distrib)). 6.97/7.21 fof(fact_mod__mult__distrib2, axiom, ![X25, X36, X19]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X36,X25))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__distrib2)). 6.97/7.21 fof(fact_diff__cancel, axiom, ![X25, X36, X19]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X36)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X25))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),X25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__cancel)). 6.97/7.21 fof(fact_diff__cancel2, axiom, ![X25, X19, X36]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),X25)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X19)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__cancel2)). 6.97/7.21 fof(fact_rev__foldl__cons, axiom, ![X23, X5]:hAPP(c_List_Orev(X5),X23)=hAPP(c_List_Ofoldl(tc_List_Olist(X5),X5,hAPP(c_COMBC(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_OCons(X5)),c_List_Olist_ONil(X5)),X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__foldl__cons)). 6.97/7.21 fof(fact_listsp__inf__eq, axiom, ![X11, X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),c_List_Olistsp(X5,X4)),c_List_Olistsp(X5,X11))=c_List_Olistsp(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsp__inf__eq)). 6.97/7.21 fof(fact_length__filter__le, axiom, ![X23, X17, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,X17),X23))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__filter__le)). 6.97/7.21 fof(fact_select__weight__cons__zero, axiom, ![X23, X35, X5]:c_Random_Oselect__weight(X5,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X5)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X5),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X35)),X23))=c_Random_Oselect__weight(X5,X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_select__weight__cons__zero)). 6.97/7.21 fof(fact_funpow_Osimps_I2_J, axiom, ![X18, X32, X5]:hAPP(hAPP(c_Nat_Ocompow(X5,X5),hAPP(c_Nat_OSuc,X32)),X18)=hAPP(c_Fun_Ocomp(X5,X5,X5,X18),hAPP(hAPP(c_Nat_Ocompow(X5,X5),X32),X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_funpow_Osimps_I2_J)). 6.97/7.21 fof(fact_replicate__length__filter, axiom, ![X23, X35, X5]:hAPP(c_List_Ofilter(X5,hAPP(c_fequal,X35)),X23)=c_List_Oreplicate(X5,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,hAPP(c_fequal,X35)),X23)),X35), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_replicate__length__filter)). 6.97/7.21 fof(fact_Field__def, axiom, ![X3, X5]:hAPP(c_Relation_OField(X5),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5,X5),X3)),hAPP(c_Relation_ORange(X5,X5),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Field__def)). 6.97/7.21 fof(fact_snd__def, axiom, ![X24, X5, X12]:hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X12,X5,X5),hAPP(c_COMBK(tc_fun(X5,X5),X12),c_COMBI(X5))),X24)=hAPP(c_Product__Type_Osnd(X12,X5),X24), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_snd__def)). 6.97/7.21 fof(fact_set__sublist__subset, axiom, ![X15, X23, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),c_List_Osublist(X5,X23,X15))),hAPP(c_List_Oset(X5),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__sublist__subset)). 6.97/7.21 fof(fact_Diff__Compl, axiom, ![X11, X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__Compl)). 6.97/7.21 fof(fact_set__remove1__subset, axiom, ![X23, X35, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),c_List_Oremove1(X5,X35,X23))),hAPP(c_List_Oset(X5),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__remove1__subset)). 6.97/7.21 fof(fact_length__takeWhile__le, axiom, ![X23, X17, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X17,X23))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__takeWhile__le)). 6.97/7.21 fof(fact_subset__Pow__Union, axiom, ![X4, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_Set_OPow(X5),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__Pow__Union)). 6.97/7.21 fof(fact_negative__zless, axiom, ![X36, X25]: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,X25)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X36))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negative__zless)). 6.97/7.21 fof(fact_append__assoc, axiom, ![X75, X45, X41, X8]:hAPP(hAPP(c_List_Oappend(X8),hAPP(hAPP(c_List_Oappend(X8),X41),X45)),X75)=hAPP(hAPP(c_List_Oappend(X8),X41),hAPP(hAPP(c_List_Oappend(X8),X45),X75)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__assoc)). 6.97/7.21 fof(fact_drop__drop, axiom, ![X41, X36, X25, X8]:hAPP(hAPP(c_List_Odrop(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X36)),X41)=hAPP(hAPP(c_List_Odrop(X8),X25),hAPP(hAPP(c_List_Odrop(X8),X36),X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__drop)). 6.97/7.21 fof(fact_zpower__zpower, axiom, ![X26, X7, X6]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),X7)),X26)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zpower__zpower)). 6.97/7.21 fof(fact_div__mult2__eq, axiom, ![X31, X29, X30]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),X31))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X30),X29)),X31), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult2__eq)). 6.97/7.21 fof(fact_zmult__assoc, axiom, ![X265, X182, X183]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X183),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X182),X265))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X183),X182)),X265), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult__assoc)). 6.97/7.21 fof(fact_nat__mult__assoc, axiom, ![X19, X25, X36]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X19))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X25)),X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__assoc)). 6.97/7.21 fof(fact_funpow__swap1, axiom, ![X35, X32, X5, X18]:hAPP(X18,hAPP(hAPP(hAPP(c_Nat_Ocompow(X5,X5),X32),X18),X35))=hAPP(hAPP(hAPP(c_Nat_Ocompow(X5,X5),X32),X18),hAPP(X18,X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_funpow__swap1)). 6.97/7.21 fof(fact_butlast__conv__take, axiom, ![X41, X8]:c_List_Obutlast(X8,X41)=hAPP(hAPP(c_List_Otake(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X41), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_butlast__conv__take)). 6.97/7.21 fof(fact_zpower__zmod, axiom, ![X7, X36, X6]: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,X6,X36)),X7),X36)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),X7),X36), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zpower__zmod)). 6.97/7.21 fof(fact_zdiff__zmod__left, axiom, ![X7, X36, X6]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X6),X7),X36)=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,X6,X36)),X7),X36), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiff__zmod__left)). 6.97/7.21 fof(fact_Inter__image__eq, axiom, ![X4, X11, X12, X5]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),X4),X11)=c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(X12,tc_fun(X5,tc_HOL_Obool),X11),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__image__eq)). 6.97/7.21 fof(fact_replicate__add, axiom, ![X6, X36, X25, X8]:c_List_Oreplicate(X8,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X36),X6)=hAPP(hAPP(c_List_Oappend(X8),c_List_Oreplicate(X8,X25,X6)),c_List_Oreplicate(X8,X36,X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_replicate__add)). 6.97/7.21 fof(fact_zmod__zmult1__eq, axiom, ![X31, X29, X30]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),c_Divides_Odiv__class_Omod(tc_Int_Oint,X29,X31)),X31)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X29),X31), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zmult1__eq)). 6.97/7.21 fof(fact_zdiff__zmod__right, axiom, ![X36, X7, X6]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X6),X7),X36)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X6),c_Divides_Odiv__class_Omod(tc_Int_Oint,X7,X36)),X36), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiff__zmod__right)). 6.97/7.21 fof(fact_rev__append, axiom, ![X45, X41, X8]:hAPP(c_List_Orev(X8),hAPP(hAPP(c_List_Oappend(X8),X41),X45))=hAPP(hAPP(c_List_Oappend(X8),hAPP(c_List_Orev(X8),X45)),hAPP(c_List_Orev(X8),X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__append)). 6.97/7.21 fof(fact_zdiv__int, axiom, ![X29, X30]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X30)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X29))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X30),X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__int)). 6.97/7.21 fof(fact_zadd__int, axiom, ![X25, X36]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X25))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X36)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__int)). 6.97/7.21 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J, axiom, ![X7, X6]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),X7))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(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),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J)). 6.97/7.21 fof(fact_list__update__overwrite, axiom, ![X7, X6, X28, X41, X8]:hAPP(hAPP(c_List_Olist__update(X8,X41),X28),X7)=hAPP(hAPP(c_List_Olist__update(X8,hAPP(hAPP(c_List_Olist__update(X8,X41),X28),X6)),X28),X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__overwrite)). 6.97/7.21 fof(fact_Diff__disjoint, axiom, ![X11, X4, X5]:c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X11),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__disjoint)). 6.97/7.21 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J, axiom, ![X32, X34]: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),X34),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X32)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X34,X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SetInterval_Otransfer__nat__int__set__functions_I2_J)). 6.97/7.21 fof(fact_snd__prod__fun, axiom, ![X35, X50, X18, X92, X62, X5, X12]:hAPP(c_Product__Type_Osnd(X12,X5),hAPP(c_Product__Type_Omap__pair(X62,X12,X92,X5,X18,X50),X35))=hAPP(X50,hAPP(c_Product__Type_Osnd(X62,X92),X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_snd__prod__fun)). 6.97/7.21 fof(fact_fst__map__pair, axiom, ![X35, X50, X18, X92, X62, X12, X5]:hAPP(c_Product__Type_Ofst(X5,X12),hAPP(c_Product__Type_Omap__pair(X62,X5,X92,X12,X18,X50),X35))=hAPP(X18,hAPP(c_Product__Type_Ofst(X62,X92),X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fst__map__pair)). 6.97/7.21 fof(fact_partition__filter2, axiom, ![X23, X17, X5]:hAPP(c_List_Ofilter(X5,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X5,c_fNot),X17)),X23)=hAPP(c_Product__Type_Osnd(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Opartition(X5,X17,X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_partition__filter2)). 6.97/7.21 fof(fact_rtrancl_Ortrancl__refl, axiom, ![X3, X2, X5]:hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X2),X2)),c_Transitive__Closure_Ortrancl(X5,X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl_Ortrancl__refl)). 6.97/7.21 fof(fact_sorted__transpose, axiom, ![X23, X5]:c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X5))),c_List_Otranspose(X5,X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__transpose)). 6.97/7.21 fof(fact_card__length, axiom, ![X23, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(c_List_Oset(X5),X23))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__length)). 6.97/7.21 fof(fact_scomp__apply, axiom, ![X35, X50, X18, X5, X92, X62, X12]:hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X12,X62,X92,X5),X18),X50),X35)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X62,X92,X5),X50),hAPP(X18,X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_scomp__apply)). 6.97/7.21 fof(fact_le__cube, axiom, ![X36]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X36)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__cube)). 6.97/7.21 fof(fact_diff__Suc, axiom, ![X32, X34]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X34),hAPP(c_Nat_OSuc,X32))=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),X34),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__Suc)). 6.97/7.21 fof(fact_Union__def, axiom, ![X44, X5]:c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X44)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X44),c_COMBI(tc_fun(X5,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__def)). 6.97/7.21 fof(fact_Inter__def, axiom, ![X44, X5]:c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X44)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X44),c_COMBI(tc_fun(X5,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__def)). 6.97/7.21 fof(fact_rel__comp__empty1, axiom, ![X67, X12, X62, X5]:hAPP(hAPP(c_Relation_Orel__comp(X5,X62,X12),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X62),tc_HOL_Obool))),X67)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__comp__empty1)). 6.97/7.21 fof(fact_converse__pred__comp, axiom, ![X66, X3, X62, X5, X12]:c_Predicate_Oconversep(X12,X5,c_Predicate_Opred__comp(X12,X62,X5,X3,X66))=c_Predicate_Opred__comp(X5,X62,X12,c_Predicate_Oconversep(X62,X5,X66),c_Predicate_Oconversep(X12,X62,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__pred__comp)). 6.97/7.21 fof(fact_list__update__code_I2_J, axiom, ![X7, X41, X6, X8]:hAPP(hAPP(c_List_Olist__update(X8,hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7)=hAPP(hAPP(c_List_Olist_OCons(X8),X7),X41), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__code_I2_J)). 6.97/7.21 fof(fact_rel__comp__empty2, axiom, ![X67, X12, X62, X5]:c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X12),tc_HOL_Obool))=hAPP(hAPP(c_Relation_Orel__comp(X5,X62,X12),X67),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X62,X12),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__comp__empty2)). 6.97/7.21 fof(fact_remdups__map__remdups, axiom, ![X23, X18, X12, X5]:c_List_Oremdups(X5,hAPP(hAPP(c_List_Omap(X12,X5),X18),X23))=c_List_Oremdups(X5,hAPP(hAPP(c_List_Omap(X12,X5),X18),c_List_Oremdups(X12,X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remdups__map__remdups)). 6.97/7.21 fof(fact_div__mod__code__numeral__def, axiom, ![X36, X25]: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),X25),X36)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X25,X36))=c_Code__Numeral_Odiv__mod__code__numeral(X25,X36), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mod__code__numeral__def)). 6.97/7.21 fof(fact_nth__Cons__Suc, axiom, ![X25, X41, X6, X8]:hAPP(hAPP(c_List_Onth(X8),X41),X25)=hAPP(hAPP(c_List_Onth(X8),hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41)),hAPP(c_Nat_OSuc,X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__Cons__Suc)). 6.97/7.21 fof(fact_take__tl, axiom, ![X41, X25, X8]:hAPP(hAPP(c_List_Otake(X8),X25),hAPP(c_List_Otl(X8),X41))=hAPP(c_List_Otl(X8),hAPP(hAPP(c_List_Otake(X8),hAPP(c_Nat_OSuc,X25)),X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__tl)). 6.97/7.21 fof(fact_drop__Suc__Cons, axiom, ![X41, X6, X25, X8]:hAPP(hAPP(c_List_Odrop(X8),hAPP(c_Nat_OSuc,X25)),hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41))=hAPP(hAPP(c_List_Odrop(X8),X25),X41), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__Suc__Cons)). 6.97/7.21 fof(fact_mod__mult__self3, axiom, ![X36, X25, X19]: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),X19),X25)),X36),X25)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X36,X25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__self3)). 6.97/7.21 fof(fact_append__take__drop__id, axiom, ![X41, X25, X8]:X41=hAPP(hAPP(c_List_Oappend(X8),hAPP(hAPP(c_List_Otake(X8),X25),X41)),hAPP(hAPP(c_List_Odrop(X8),X25),X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__take__drop__id)). 6.97/7.21 fof(fact_take__1__Cons, axiom, ![X41, X6, X8]:hAPP(hAPP(c_List_Otake(X8),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41))=hAPP(hAPP(c_List_Olist_OCons(X8),X6),c_List_Olist_ONil(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__1__Cons)). 6.97/7.21 fof(fact_Diff__subset, axiom, ![X11, X4, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X11)),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__subset)). 6.97/7.21 fof(fact_Int__lower1, axiom, ![X11, 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),X11)),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__lower1)). 6.97/7.21 fof(fact_Int__lower2, axiom, ![X11, 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),X11)),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__lower2)). 6.97/7.21 fof(fact_sym__Int__converse, axiom, ![X3, X5]:c_Relation_Osym(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),hAPP(c_Relation_Oconverse(X5,X5),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sym__Int__converse)). 6.97/7.21 fof(fact_sym__Un__converse, axiom, ![X3, X5]:c_Relation_Osym(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X3),hAPP(c_Relation_Oconverse(X5,X5),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sym__Un__converse)). 6.97/7.21 fof(fact_Un__upper1, axiom, ![X11, X4, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__upper1)). 6.97/7.21 fof(fact_Un__upper2, axiom, ![X4, X11, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__upper2)). 6.97/7.21 fof(fact_negative__zless__0, axiom, ![X25]: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,X25)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negative__zless__0)). 6.97/7.21 fof(fact_negative__zle, axiom, ![X36, X25]: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),X25))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X36))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negative__zle)). 6.97/7.21 fof(fact_zero__le__zpower__abs, axiom, ![X25, X6]: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),X6)),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__zpower__abs)). 6.97/7.21 fof(fact_takeWhile__eq__take, axiom, ![X23, X17, X5]:hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X17,X23))),X23)=c_List_OtakeWhile(X5,X17,X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__eq__take)). 6.97/7.21 fof(fact_length__n__lists, axiom, ![X41, X25, X8]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X8))),c_Enum_On__lists(X8,X25,X41))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)),X25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__n__lists)). 6.97/7.21 fof(fact_surjective__pairing, axiom, ![X5, X8, X146]:hAPP(hAPP(c_Product__Type_OPair(X8,X5),hAPP(c_Product__Type_Ofst(X8,X5),X146)),hAPP(c_Product__Type_Osnd(X8,X5),X146))=X146, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_surjective__pairing)). 6.97/7.21 fof(fact_Compl__partition, axiom, ![X4, X5]:c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__partition)). 6.97/7.21 fof(fact_prod_Orecs, axiom, ![X1, X2, X85, X5, X62, X12]:c_Product__Type_Oprod_Oprod__rec(X12,X62,X5,X85,hAPP(hAPP(c_Product__Type_OPair(X12,X62),X2),X1))=hAPP(hAPP(X85,X2),X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_prod_Orecs)). 6.97/7.21 fof(fact_list_Osimps_I5_J, axiom, ![X253, X2, X120, X85, X12, X5]:hAPP(c_List_Olist_Olist__case(X5,X12,X85,X120),hAPP(hAPP(c_List_Olist_OCons(X12),X2),X253))=hAPP(hAPP(X120,X2),X253), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list_Osimps_I5_J)). 6.97/7.21 fof(fact_length__tl, axiom, ![X41, X8]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),hAPP(c_List_Otl(X8),X41))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)),c_Groups_Oone__class_Oone(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__tl)). 6.97/7.21 fof(fact_Pow__bottom, axiom, ![X11, X5]:hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),hAPP(c_Set_OPow(X5),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__bottom)). 6.97/7.21 fof(fact_Pair__scomp, axiom, ![X18, X35, X12, X62, X5]:hAPP(hAPP(c_Product__Type_Oscomp(X5,X62,X5,X12),hAPP(c_Product__Type_OPair(X62,X5),X35)),X18)=hAPP(X18,X35), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pair__scomp)). 6.97/7.21 fof(fact_UNIV__Plus__UNIV, axiom, ![X12, X5]:c_Sum__Type_OPlus(X5,X12,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X5,X12),tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UNIV__Plus__UNIV)). 6.97/7.21 fof(fact_Compl__eq__Diff__UNIV, axiom, ![X4, X5]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X4)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__eq__Diff__UNIV)). 6.97/7.21 fof(fact_drop__replicate, axiom, ![X6, X19, X28, X8]:hAPP(hAPP(c_List_Odrop(X8),X28),c_List_Oreplicate(X8,X19,X6))=c_List_Oreplicate(X8,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X28),X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__replicate)). 6.97/7.21 fof(fact_nth_Osimps, axiom, ![X32, X23, X35, X5]:hAPP(hAPP(c_List_Onth(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X35),X23)),X32)=c_Nat_Onat_Onat__case(X5,X35,hAPP(c_List_Onth(X5),X23),X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth_Osimps)). 6.97/7.21 fof(fact_set__replicate__Suc, axiom, ![X35, X32, X5]:hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))=hAPP(c_List_Oset(X5),c_List_Oreplicate(X5,hAPP(c_Nat_OSuc,X32),X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__replicate__Suc)). 6.97/7.21 fof(fact_int__power, axiom, ![X25, X36]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X36)),X25)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X36),X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__power)). 6.97/7.21 fof(fact_zmult__zminus, axiom, ![X39, X26]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),X39))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26)),X39), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult__zminus)). 6.97/7.21 fof(fact_insert__absorb2, axiom, ![X4, X35, X5]:hAPP(hAPP(c_Set_Oinsert(X5),X35),hAPP(hAPP(c_Set_Oinsert(X5),X35),X4))=hAPP(hAPP(c_Set_Oinsert(X5),X35),X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__absorb2)). 6.97/7.21 fof(fact_zdiv__zminus2, axiom, ![X29, X30]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X29))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X30)),X29), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__zminus2)). 6.97/7.21 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J, axiom, ![X7, X6]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6),X7))=c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J)). 6.97/7.21 fof(fact_curry__def, axiom, ![X38, X35, X10, X5, X62, X12]:hAPP(hAPP(c_Product__Type_Ocurry(X12,X62,X5,X10),X35),X38)=hAPP(X10,hAPP(hAPP(c_Product__Type_OPair(X12,X62),X35),X38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_curry__def)). 6.97/7.21 fof(fact_zminus__zmod, axiom, ![X36, X6]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6),X36)=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,X6,X36)),X36), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zminus__zmod)). 6.97/7.21 fof(fact_INT__empty, axiom, ![X11, X5, X12]:c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12,tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool))),X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__empty)). 6.97/7.21 fof(fact_zmod__zminus2, axiom, ![X29, X30]: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),X30),X29))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zminus2)). 6.97/7.21 fof(fact_card__eq__setsum, axiom, ![X4, X5]:hAPP(c_Finite__Set_Ocard(X5),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X5),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__eq__setsum)). 6.97/7.21 fof(fact_zmod__int, axiom, ![X29, X30]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X30,X29))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X30),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__int)). 6.97/7.21 fof(fact_zmod__zminus__zminus, axiom, ![X29, X30]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X29))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X30),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zminus__zminus)). 6.97/7.21 fof(fact_fun__upd__upd, axiom, ![X14, X38, X35, X18, X12, X5]:c_Fun_Ofun__upd(X5,X12,c_Fun_Ofun__upd(X5,X12,X18,X35,X38),X35,X14)=c_Fun_Ofun__upd(X5,X12,X18,X35,X14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upd__upd)). 6.97/7.21 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)). 6.97/7.21 fof(fact_diff__less__Suc, axiom, ![X25, X36]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),X25)),hAPP(c_Nat_OSuc,X36))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__less__Suc)). 6.97/7.21 fof(fact_less__add__Suc2, axiom, ![X36, X28]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X28)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__add__Suc2)). 6.97/7.21 fof(fact_subset__insertI, axiom, ![X2, X11, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X11),hAPP(hAPP(c_Set_Oinsert(X5),X2),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__insertI)). 6.97/7.21 fof(fact_negative__zle__0, axiom, ![X25]: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),X25))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negative__zle__0)). 6.97/7.21 fof(fact_image__Suc__atLeastAtMost, axiom, ![X46, X47]:hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X47,X46))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X47),hAPP(c_Nat_OSuc,X46)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__Suc__atLeastAtMost)). 6.97/7.21 fof(fact_length__list__update, axiom, ![X6, X28, X41, X8]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),hAPP(hAPP(c_List_Olist__update(X8,X41),X28),X6))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__list__update)). 6.97/7.21 fof(fact_length__butlast, axiom, ![X41, X8]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),c_List_Obutlast(X8,X41))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)),c_Groups_Oone__class_Oone(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__butlast)). 6.97/7.21 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)). 6.97/7.21 fof(fact_rtrancl__idemp__self__comp, axiom, ![X67, X5]:hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),c_Transitive__Closure_Ortrancl(X5,X67)),c_Transitive__Closure_Ortrancl(X5,X67))=c_Transitive__Closure_Ortrancl(X5,X67), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__idemp__self__comp)). 6.97/7.21 fof(fact_map__replicate, axiom, ![X35, X32, X18, X5, X12]:hAPP(hAPP(c_List_Omap(X12,X5),X18),c_List_Oreplicate(X12,X32,X35))=c_List_Oreplicate(X5,X32,hAPP(X18,X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__replicate)). 6.97/7.21 fof(fact_Sigma__empty1, axiom, ![X11, X12, X5]:hAPP(hAPP(c_Product__Type_OSigma(X5,X12),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X11)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X12),tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__empty1)). 6.97/7.21 fof(fact_scomp__Pair, axiom, ![X35, X62, X12, X5]:hAPP(hAPP(c_Product__Type_Oscomp(X5,X12,X62,tc_prod(X12,X62)),X35),c_Product__Type_OPair(X12,X62))=X35, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_scomp__Pair)). 6.97/7.21 fof(fact_fold__image__empty, axiom, ![X14, X50, X18, X12, X5]:X14=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X12,X18),X50),X14),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__empty)). 6.97/7.21 fof(fact_Un__UNIV__left, axiom, ![X11, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X11)=c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__UNIV__left)). 6.97/7.21 fof(fact_empty__Diff, axiom, ![X4, X5]:c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__Diff)). 6.97/7.21 fof(fact_Int__empty__left, axiom, ![X11, X5]:c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__empty__left)). 6.97/7.21 fof(fact_fold1__singleton, axiom, ![X2, X18, X5]:X2=hAPP(c_Finite__Set_Ofold1(X5,X18),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__singleton)). 6.97/7.21 fof(fact_Diff__UNIV, axiom, ![X4, X5]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__UNIV)). 6.97/7.21 fof(fact_Int__empty__right, axiom, ![X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__empty__right)). 6.97/7.21 fof(fact_Un__UNIV__right, axiom, ![X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__UNIV__right)). 6.97/7.21 fof(fact_int__Suc, axiom, ![X36]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X36))=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),X36)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__Suc)). 6.97/7.21 fof(fact_listrel1__converse, axiom, ![X3, X5]:c_List_Olistrel1(X5,hAPP(c_Relation_Oconverse(X5,X5),X3))=hAPP(c_Relation_Oconverse(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel1(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1__converse)). 6.97/7.21 fof(fact_inj__on__add__nat, axiom, ![X20, X33]: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)),X33),X20), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__add__nat)). 6.97/7.21 fof(fact_Rep__Integ, axiom, ![X35]:hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X35)),c_Int_OInteg)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Rep__Integ)). 6.97/7.21 fof(help_c__COMBC__1, axiom, ![X67, X104, X17, X5, X62, X12]:hAPP(hAPP(hAPP(c_COMBC(X12,X62,X5),X17),X104),X67)=hAPP(hAPP(X17,X67),X104), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__COMBC__1)). 6.97/7.21 fof(help_c__COMBB__1, axiom, ![X67, X104, X17, X62, X5, X12]:hAPP(hAPP(hAPP(c_COMBB(X12,X5,X62),X17),X104),X67)=hAPP(X17,hAPP(X104,X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__COMBB__1)). 6.97/7.21 fof(fact_fst__def, axiom, ![X24, X12, X5]:hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X12,X5),c_COMBK(X5,X12)),X24)=hAPP(c_Product__Type_Ofst(X5,X12),X24), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fst__def)). 6.97/7.21 fof(fact_Image__Id__on, axiom, ![X11, X4, X5]:hAPP(c_Relation_OImage(X5,X5,c_Relation_OId__on(X5,X4)),X11)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__Id__on)). 6.97/7.21 fof(fact_pair__box_Orecs, axiom, ![X1, X2, X85, X5, X62, X12]:c_Nitpick_Opair__box_Opair__box__rec(X12,X62,X5,X85,c_Nitpick_Opair__box_OPairBox(X12,X62,X2,X1))=hAPP(hAPP(X85,X2),X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__box_Orecs)). 6.97/7.21 fof(fact_pair__box_Osimps_I2_J, axiom, ![X1, X2, X85, X5, X62, X12]:hAPP(hAPP(X85,X2),X1)=c_Nitpick_Opair__box_Opair__box__case(X12,X62,X5,X85,c_Nitpick_Opair__box_OPairBox(X12,X62,X2,X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__box_Osimps_I2_J)). 6.97/7.21 fof(fact_partition__filter1, axiom, ![X23, X17, X5]:hAPP(c_Product__Type_Ofst(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Opartition(X5,X17,X23))=hAPP(c_List_Ofilter(X5,X17),X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_partition__filter1)). 6.97/7.21 fof(fact_drop__butlast, axiom, ![X41, X25, X8]:c_List_Obutlast(X8,hAPP(hAPP(c_List_Odrop(X8),X25),X41))=hAPP(hAPP(c_List_Odrop(X8),X25),c_List_Obutlast(X8,X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__butlast)). 6.97/7.21 fof(fact_mod__Suc__eq__Suc__mod, axiom, ![X25, X36]:c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X36),X25)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X36,X25)),X25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__Suc__eq__Suc__mod)). 6.97/7.21 fof(fact_replicate__Suc, axiom, ![X6, X25, X8]:hAPP(hAPP(c_List_Olist_OCons(X8),X6),c_List_Oreplicate(X8,X25,X6))=c_List_Oreplicate(X8,hAPP(c_Nat_OSuc,X25),X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_replicate__Suc)). 6.97/7.21 fof(fact_List_Oset__insert, axiom, ![X23, X35, X5]:hAPP(c_List_Oset(X5),c_List_Oinsert(X5,X35,X23))=hAPP(hAPP(c_Set_Oinsert(X5),X35),hAPP(c_List_Oset(X5),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_List_Oset__insert)). 6.97/7.21 fof(fact_fold__def, axiom, ![X4, X14, X18, X5, X12]:hAPP(hAPP(c_Finite__Set_Ofold(X12,X5,X18),X14),X4)=c_HOL_OThe(X5,c_Finite__Set_Ofold__graph(X12,X5,X18,X14,X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__def)). 6.97/7.21 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J, axiom, ![X4]: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)),X4))=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J)). 6.97/7.21 fof(fact_nth__Cons__0, axiom, ![X41, X6, X8]:X6=hAPP(hAPP(c_List_Onth(X8),hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__Cons__0)). 6.97/7.21 fof(fact_Union__empty, axiom, ![X5]:c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__empty)). 6.97/7.21 fof(fact_Inter__UNIV, axiom, ![X5]:c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__UNIV)). 6.97/7.21 fof(fact_Union__UNIV, axiom, ![X5]:c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__UNIV)). 6.97/7.21 fof(fact_Inter__empty, axiom, ![X5]:c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__empty)). 6.97/7.21 fof(fact_list__update__id, axiom, ![X28, X41, X8]:hAPP(hAPP(c_List_Olist__update(X8,X41),X28),hAPP(hAPP(c_List_Onth(X8),X41),X28))=X41, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__id)). 6.97/7.21 fof(fact_listset_Osimps_I2_J, axiom, ![X272, X4, X5]:c_List_Oset__Cons(X5,X4,c_List_Olistset(X5,X272))=c_List_Olistset(X5,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X5,tc_HOL_Obool)),X4),X272)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listset_Osimps_I2_J)). 6.97/7.21 fof(fact_drop__1__Cons, axiom, ![X41, X6, X8]:X41=hAPP(hAPP(c_List_Odrop(X8),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__1__Cons)). 6.97/7.21 fof(fact_fold__graph_Oequations_I1_J, axiom, ![X14, X18, X12, X5]:hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X12,X18,X14,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__graph_Oequations_I1_J)). 6.97/7.21 fof(fact_Abs__Integ__cases, axiom, ![X35]:~(![X72]:(~(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X72),c_Int_OInteg)))<=X35=hAPP(c_Int_OAbs__Integ,X72))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Abs__Integ__cases)). 6.97/7.21 fof(fact_empty__subsetI, axiom, ![X4, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__subsetI)). 6.97/7.21 fof(fact_div__le__dividend, axiom, ![X25, X36]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X36),X25)),X36)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__le__dividend)). 6.97/7.21 fof(fact_diff__le__self, axiom, ![X25, X36]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),X25)),X36)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__le__self)). 6.97/7.21 fof(fact_neg__zminus__int, axiom, ![X25]: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,X25))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__zminus__int)). 6.97/7.21 fof(fact_subset__UNIV, axiom, ![X4, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__UNIV)). 6.97/7.21 fof(fact_Pow__top, axiom, ![X4, X5]:hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Set_OPow(X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__top)). 6.97/7.21 fof(fact_insertI1, axiom, ![X11, X2, X5]:hBOOL(hAPP(hAPP(c_member(X5),X2),hAPP(hAPP(c_Set_Oinsert(X5),X2),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insertI1)). 6.97/7.21 fof(fact_le__add2, axiom, ![X36, X25]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__add2)). 6.97/7.21 fof(fact_le__square, axiom, ![X36]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X36))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__square)). 6.97/7.21 fof(fact_refl__on__empty, axiom, ![X5]:c_Relation_Orefl__on(X5,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__on__empty)). 6.97/7.21 fof(fact_Range__converse, axiom, ![X3, X5, X12]:hAPP(c_Relation_ORange(X12,X5),hAPP(c_Relation_Oconverse(X5,X12),X3))=hAPP(c_Relation_ODomain(X5,X12),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__converse)). 6.97/7.21 fof(fact_Range__def, axiom, ![X3, X5, X12]:hAPP(c_Relation_ORange(X12,X5),X3)=hAPP(c_Relation_ODomain(X5,X12),hAPP(c_Relation_Oconverse(X12,X5),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__def)). 6.97/7.21 fof(fact_diff__add__0, axiom, ![X36, X25]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X36))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__add__0)). 6.97/7.21 fof(fact_pos__single__def, axiom, ![X57, X58, X59, X35, X5]:hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X5),X35),X59),X58),X57)=c_New__DSequence_Opos__single(X5,X35), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__single__def)). 6.97/7.21 fof(fact_neg__single__def, axiom, ![X57, X58, X59, X35, X5]:hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(X5),X35),X59),X58),X57)=c_New__DSequence_Oneg__single(X5,X35), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__single__def)). 6.97/7.21 fof(fact_transpose_Osimps_I2_J, axiom, ![X219, X8]:c_List_Otranspose(X8,X219)=c_List_Otranspose(X8,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X8)),c_List_Olist_ONil(X8)),X219)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose_Osimps_I2_J)). 6.97/7.21 fof(fact__05, axiom, ![X18, X64, X5, X12]:c_Lazy__Sequence_Oflat(X5,c_Lazy__Sequence_Omap(X12,tc_Lazy__Sequence_Olazy__sequence(X5),X18,X64))=hAPP(c_Lazy__Sequence_Obind(X12,X5,X64),X18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact__05)). 6.97/7.21 fof(fact_card__atLeastLessThan, axiom, ![X51, X52]:hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X52),X51))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X51),X52), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__atLeastLessThan)). 6.97/7.21 fof(fact_map__pair_Oidentity, axiom, ![X12, X5]:c_Fun_Oid(tc_prod(X5,X12))=c_Product__Type_Omap__pair(X5,X5,X12,X12,c_COMBI(X5),c_COMBI(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair_Oidentity)). 6.97/7.21 fof(fact_map__pair_Oid, axiom, ![X12, X5]:c_Fun_Oid(tc_prod(X5,X12))=c_Product__Type_Omap__pair(X5,X5,X12,X12,c_Fun_Oid(X5),c_Fun_Oid(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair_Oid)). 6.97/7.21 fof(fact_eq__comp__r, axiom, ![X67, X5]:X67=c_Predicate_Opred__comp(X5,X5,X5,c_fequal,c_Predicate_Opred__comp(X5,X5,X5,X67,c_fequal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__comp__r)). 6.97/7.21 fof(fact_fold__empty, axiom, ![X14, X18, X5, X12]:hAPP(hAPP(c_Finite__Set_Ofold(X12,X5,X18),X14),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool)))=X14, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__empty)). 6.97/7.21 fof(fact_Int__UNIV__left, axiom, ![X11, X5]:X11=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__UNIV__left)). 6.97/7.21 fof(fact_diff__add__inverse2, axiom, ![X25, X36]:X36=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X25)),X25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__add__inverse2)). 6.97/7.21 fof(fact_diff__add__inverse, axiom, ![X36, X25]:X36=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X36)),X25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__add__inverse)). 6.97/7.21 fof(fact_the__elem__eq, axiom, ![X35, X5]:c_Set_Othe__elem(X5,hAPP(hAPP(c_Set_Oinsert(X5),X35),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))=X35, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__elem__eq)). 6.97/7.21 fof(fact_Field__empty, axiom, ![X5]:hAPP(c_Relation_OField(X5),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Field__empty)). 6.97/7.21 fof(fact_Image__empty, axiom, ![X67, X5, X12]:c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(c_Relation_OImage(X12,X5,X67),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__empty)). 6.97/7.21 fof(fact_Int__UNIV__right, axiom, ![X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))=X4, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__UNIV__right)). 6.97/7.21 fof(fact_double__complement, axiom, ![X4, X5]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X4))=X4, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_double__complement)). 6.97/7.21 fof(fact_Diff__empty, axiom, ![X4, X5]:X4=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__empty)). 6.97/7.21 fof(fact_rtrancl__converse, axiom, ![X3, X5]:hAPP(c_Relation_Oconverse(X5,X5),c_Transitive__Closure_Ortrancl(X5,X3))=c_Transitive__Closure_Ortrancl(X5,hAPP(c_Relation_Oconverse(X5,X5),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__converse)). 6.97/7.21 fof(fact__01, axiom, ![X126, X127, X6, X8]:c_Lazy__Sequence_Olazy__sequence_OInsert(X8,X6,c_Lazy__Sequence_Oappend(X8,X127,X126))=c_Lazy__Sequence_Oappend(X8,c_Lazy__Sequence_Olazy__sequence_OInsert(X8,X6,X127),X126), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact__01)). 6.97/7.21 fof(fact_remdups__filter, axiom, ![X23, X17, X5]:hAPP(c_List_Ofilter(X5,X17),c_List_Oremdups(X5,X23))=c_List_Oremdups(X5,hAPP(c_List_Ofilter(X5,X17),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remdups__filter)). 6.97/7.21 fof(fact_Compl__UNIV__eq, axiom, ![X5]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__UNIV__eq)). 6.97/7.21 fof(fact_Compl__empty__eq, axiom, ![X5]:c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__empty__eq)). 6.97/7.21 fof(fact_pair__box_Osize_I2_J, axiom, ![X29, X30, X5, X8]:hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X8,X5)),c_Nitpick_Opair__box_OPairBox(X8,X5,X30,X29))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__box_Osize_I2_J)). 6.97/7.21 fof(fact_lists_ONil, axiom, ![X4, X5]:hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),c_List_Olists(X5,X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists_ONil)). 6.97/7.21 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J, axiom, ![X26]: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),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J)). 6.97/7.21 fof(fact_length__rotate1, axiom, ![X41, X8]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),hAPP(c_List_Orotate1(X8),X41))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__rotate1)). 6.97/7.21 fof(fact_length__rev, axiom, ![X41, X8]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X41)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),hAPP(c_List_Orev(X8),X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__rev)). 6.97/7.21 fof(fact__03, axiom, ![X175, X127, X8]:c_Lazy__Sequence_Oappend(X8,X127,c_Lazy__Sequence_Oflat(X8,X175))=c_Lazy__Sequence_Oflat(X8,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(X8),X127,X175)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact__03)). 6.97/7.21 fof(fact_Pow__UNIV, axiom, ![X5]:c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))=hAPP(c_Set_OPow(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__UNIV)). 6.97/7.21 fof(fact_div__int__def, axiom, ![X29, X30]:hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X30,X29))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),X29), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__int__def)). 6.97/7.21 fof(fact_split__curry, axiom, ![X18, X62, X12, X5]:X18=hAPP(c_Product__Type_Oprod_Oprod__case(X5,X12,X62),c_Product__Type_Ocurry(X5,X12,X62,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__curry)). 6.97/7.21 fof(fact_curry__split, axiom, ![X18, X62, X12, X5]:c_Product__Type_Ocurry(X5,X12,X62,hAPP(c_Product__Type_Oprod_Oprod__case(X5,X12,X62),X18))=X18, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_curry__split)). 6.97/7.21 fof(fact_less__than__def, axiom, c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)=c_Wellfounded_Oless__than, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__than__def)). 6.97/7.21 fof(fact_rel__pow__1, axiom, ![X67, X5]:hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X67)=X67, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__1)). 6.97/7.21 fof(fact_Diff__cancel, axiom, ![X4, X5]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X4),X4)=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__cancel)). 6.97/7.21 fof(fact_zip__Nil, axiom, ![X45, X5, X8]:hAPP(hAPP(c_List_Ozip(X8,X5),c_List_Olist_ONil(X8)),X45)=c_List_Olist_ONil(tc_prod(X8,X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__Nil)). 6.97/7.21 fof(fact_zip_Osimps_I1_J, axiom, ![X41, X5, X8]:hAPP(hAPP(c_List_Ozip(X8,X5),X41),c_List_Olist_ONil(X5))=c_List_Olist_ONil(tc_prod(X8,X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip_Osimps_I1_J)). 6.97/7.21 fof(fact_Field__converse, axiom, ![X3, X5]:hAPP(c_Relation_OField(X5),hAPP(c_Relation_Oconverse(X5,X5),X3))=hAPP(c_Relation_OField(X5),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Field__converse)). 6.97/7.21 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)). 6.97/7.21 fof(fact_fold__graph_H_Ointros_I1_J, axiom, ![X14, X18, X12, X5]:c_Nitpick_Ofold__graph_H(X5,X12,X18,X14,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),X14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__graph_H_Ointros_I1_J)). 6.97/7.21 fof(fact_mod__less__eq__dividend, axiom, ![X25, X36]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X36,X25)),X36)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__less__eq__dividend)). 6.97/7.21 fof(fact_inv__id, axiom, ![X5]:c_Fun_Oid(X5)=c_Hilbert__Choice_Oinv__into(X5,X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Fun_Oid(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inv__id)). 6.97/7.21 fof(fact_zmod__zdiv__trivial, axiom, ![X29, X30]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X29)),X29)=c_Groups_Ozero__class_Ozero(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zdiv__trivial)). 6.97/7.21 fof(fact_zero__less__Suc, axiom, ![X25]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__Suc)). 6.97/7.21 fof(fact_insert__remdups, axiom, ![X41, X6, X8]:c_List_Oremdups(X8,c_List_Oinsert(X8,X6,X41))=c_List_Oinsert(X8,X6,c_List_Oremdups(X8,X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__remdups)). 6.97/7.21 fof(fact_Id__on__empty, axiom, ![X5]:c_Relation_OId__on(X5,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Id__on__empty)). 6.97/7.21 fof(fact_posDivAlg__0, axiom, ![X29]:c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X29)=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_posDivAlg__0)). 6.97/7.21 fof(fact_negateSnd__def, axiom, c_Divides_OnegateSnd=c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negateSnd__def)). 6.97/7.21 fof(fact_override__on__emptyset, axiom, ![X50, X18, X12, X5]:c_Fun_Ooverride__on(X5,X12,X18,X50,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))=X18, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_override__on__emptyset)). 6.97/7.21 fof(fact_power_Opower_Opower__0, axiom, ![X2, X156, X157, X5]:hAPP(hAPP(c_Power_Opower_Opower(X5,X157,X156),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X157, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power_Opower_Opower__0)). 6.97/7.21 fof(fact_rev__replicate, axiom, ![X6, X25, X8]:hAPP(c_List_Orev(X8),c_List_Oreplicate(X8,X25,X6))=c_List_Oreplicate(X8,X25,X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__replicate)). 6.97/7.21 fof(fact_hd_Osimps, axiom, ![X41, X6, X8]:hAPP(c_List_Ohd(X8),hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41))=X6, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd_Osimps)). 6.97/7.21 fof(fact_tl_Osimps_I2_J, axiom, ![X41, X6, X8]:X41=hAPP(c_List_Otl(X8),hAPP(hAPP(c_List_Olist_OCons(X8),X6),X41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tl_Osimps_I2_J)). 6.97/7.21 fof(fact_insert__Nil, axiom, ![X6, X8]:hAPP(hAPP(c_List_Olist_OCons(X8),X6),c_List_Olist_ONil(X8))=c_List_Oinsert(X8,X6,c_List_Olist_ONil(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__Nil)). 6.97/7.21 fof(fact_converse__converse, axiom, ![X3, X5, X12]:hAPP(c_Relation_Oconverse(X12,X5),hAPP(c_Relation_Oconverse(X5,X12),X3))=X3, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__converse)). 6.97/7.21 fof(fact_mod__int__def, axiom, ![X29, X30]:c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X29)=hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X30,X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__int__def)). 6.97/7.21 fof(fact_diff__Suc__1, axiom, ![X25]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X25, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__Suc__1)). 6.97/7.21 fof(fact_Domain__rtrancl, axiom, ![X67, X5]:hAPP(c_Relation_ODomain(X5,X5),c_Transitive__Closure_Ortrancl(X5,X67))=c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__rtrancl)). 6.97/7.21 fof(fact_Range__rtrancl, axiom, ![X67, X5]:hAPP(c_Relation_ORange(X5,X5),c_Transitive__Closure_Ortrancl(X5,X67))=c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__rtrancl)). 6.97/7.21 fof(fact_set__rotate1, axiom, ![X23, X5]:hAPP(c_List_Oset(X5),hAPP(c_List_Orotate1(X5),X23))=hAPP(c_List_Oset(X5),X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__rotate1)). 6.97/7.21 fof(fact_set__rev, axiom, ![X23, X5]:hAPP(c_List_Oset(X5),hAPP(c_List_Orev(X5),X23))=hAPP(c_List_Oset(X5),X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__rev)). 6.97/7.21 fof(fact_abs__int__eq, axiom, ![X36]:hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X36))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X36), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__int__eq)). 6.97/7.21 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)). 6.97/7.21 fof(fact_subset__refl, axiom, ![X4, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__refl)). 6.97/7.21 fof(fact_finite__atLeastLessThan__int, axiom, ![X51, X52]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X52),X51))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__atLeastLessThan__int)). 6.97/7.21 fof(fact_finite__atLeastLessThan, axiom, ![X51, X52]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X52),X51))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__atLeastLessThan)). 6.97/7.21 fof(fact_fold1__def, axiom, ![X4, X18, X5]:hAPP(c_Finite__Set_Ofold1(X5,X18),X4)=c_HOL_OThe(X5,c_Finite__Set_Ofold1Set(X5,X18,X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__def)). 6.97/7.21 fof(fact_lessI, axiom, ![X25]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_OSuc,X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lessI)). 6.97/7.21 fof(fact_refl__rtrancl, axiom, ![X3, X5]:c_Relation_Orefl__on(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__rtrancl)). 6.97/7.21 fof(fact_list__update__code_I1_J, axiom, ![X7, X28, X8]:hAPP(hAPP(c_List_Olist__update(X8,c_List_Olist_ONil(X8)),X28),X7)=c_List_Olist_ONil(X8), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__code_I1_J)). 6.97/7.21 fof(fact_lists__UNIV, axiom, ![X5]:c_List_Olists(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists__UNIV)). 6.97/7.21 fof(fact_funpow_Osimps_I1_J, axiom, ![X18, X5]:hAPP(hAPP(c_Nat_Ocompow(X5,X5),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18)=c_Fun_Oid(X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_funpow_Osimps_I1_J)). 6.97/7.21 fof(fact_nat__case__Suc, axiom, ![X128, X120, X85, X5]:c_Nat_Onat_Onat__case(X5,X85,X120,hAPP(c_Nat_OSuc,X128))=hAPP(X120,X128), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__case__Suc)). 6.97/7.21 fof(fact_Nitpick_Ofrac__def, axiom, ![X29, X30, X8]:c_Nitpick_OAbs__Frac(X8,c_Nitpick_Onorm__frac(X30,X29))=hAPP(hAPP(c_Nitpick_Ofrac(X8),X30),X29), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Ofrac__def)). 6.97/7.21 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1, axiom, ![X3, X5]:c_List_Olistrel(X5,c_Transitive__Closure_Ortrancl(X5,X3))=c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__rtrancl__eq__rtrancl__listrel1)). 6.97/7.21 fof(fact_converse__Id__on, axiom, ![X4, X5]:hAPP(c_Relation_Oconverse(X5,X5),c_Relation_OId__on(X5,X4))=c_Relation_OId__on(X5,X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__Id__on)). 6.97/7.21 fof(fact_fun__upd__same, axiom, ![X38, X35, X18, X5, X12]:hAPP(c_Fun_Ofun__upd(X12,X5,X18,X35,X38),X35)=X38, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upd__same)). 6.97/7.21 fof(fact_id__o, axiom, ![X50, X5, X12]:X50=hAPP(c_Fun_Ocomp(X12,X12,X5,c_Fun_Oid(X12)),X50), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_id__o)). 6.97/7.21 fof(fact_o__id, axiom, ![X18, X12, X5]:hAPP(c_Fun_Ocomp(X5,X12,X5,X18),c_Fun_Oid(X5))=X18, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_o__id)). 6.97/7.21 fof(fact_list_Osimps_I4_J, axiom, ![X120, X85, X12, X5]:X85=hAPP(c_List_Olist_Olist__case(X5,X12,X85,X120),c_List_Olist_ONil(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list_Osimps_I4_J)). 6.97/7.21 fof(fact_foldl__Nil, axiom, ![X2, X18, X12, X5]:X2=hAPP(c_List_Ofoldl(X5,X12,X18,X2),c_List_Olist_ONil(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__Nil)). 6.97/7.21 fof(fact_product_Osimps_I1_J, axiom, ![X184, X5, X8]:c_Enum_Oproduct(X8,X5,c_List_Olist_ONil(X8),X184)=c_List_Olist_ONil(tc_prod(X8,X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_product_Osimps_I1_J)). 6.97/7.21 fof(fact_Int__absorb, axiom, ![X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X4)=X4, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__absorb)). 6.97/7.21 fof(fact_Un__absorb, axiom, ![X4, X5]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X4)=X4, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__absorb)). 6.97/7.21 fof(fact_length__replicate, axiom, ![X6, X25, X8]:X25=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),c_List_Oreplicate(X8,X25,X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__replicate)). 6.97/7.21 fof(fact_atLeastSucLessThan__greaterThanLessThan, axiom, ![X51, X52]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X52)),X51)=c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X52,X51), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastSucLessThan__greaterThanLessThan)). 6.97/7.21 fof(fact_Union__Pow__eq, axiom, ![X4, X5]:c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_OPow(X5),X4))=X4, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__Pow__eq)). 6.97/7.21 fof(fact_set__remdups, axiom, ![X23, X5]:hAPP(c_List_Oset(X5),X23)=hAPP(c_List_Oset(X5),c_List_Oremdups(X5,X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__remdups)). 6.97/7.21 fof(fact_nat__of__number, axiom, ![X19]:hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19)=hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__of__number)). 6.97/7.21 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)). 6.97/7.21 fof(fact_inj__on__empty, axiom, ![X18, X12, X5]:c_Fun_Oinj__on(X5,X12,X18,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__empty)). 6.97/7.21 fof(fact_inj__on__rev, axiom, ![X4, X5]:c_Fun_Oinj__on(tc_List_Olist(X5),tc_List_Olist(X5),c_List_Orev(X5),X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__rev)). 6.97/7.21 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J, axiom, ![X65]: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)),X65)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J)). 6.97/7.21 fof(fact_finite__atLeastAtMost__int, axiom, ![X51, X52]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X52,X51))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__atLeastAtMost__int)). 6.97/7.21 fof(fact_finite__atLeastAtMost, axiom, ![X51, X52]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X52,X51))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__atLeastAtMost)). 6.97/7.21 fof(fact_sublist__empty, axiom, ![X23, X5]:c_List_Olist_ONil(X5)=c_List_Osublist(X5,X23,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublist__empty)). 6.97/7.21 fof(fact_antisym__empty, axiom, ![X5]:c_Relation_Oantisym(X5,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_antisym__empty)). 6.97/7.21 fof(fact_wf__empty, axiom, ![X5]:c_Wellfounded_Owf(X5,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__empty)). 6.97/7.21 fof(fact_finite_Oequations_I1_J, axiom, ![X5]:hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite_Oequations_I1_J)). 6.97/7.21 fof(fact_take__0, axiom, ![X41, X8]:c_List_Olist_ONil(X8)=hAPP(hAPP(c_List_Otake(X8),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X41), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__0)). 6.97/7.21 fof(fact_drop__Nil, axiom, ![X25, X8]:c_List_Olist_ONil(X8)=hAPP(hAPP(c_List_Odrop(X8),X25),c_List_Olist_ONil(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__Nil)). 6.97/7.21 fof(fact_take__Nil, axiom, ![X25, X8]:c_List_Olist_ONil(X8)=hAPP(hAPP(c_List_Otake(X8),X25),c_List_Olist_ONil(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__Nil)). 6.97/7.21 fof(fact_zdiv__zero, axiom, ![X29]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X29)=c_Groups_Ozero__class_Ozero(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__zero)). 6.97/7.21 fof(fact_diff__0__eq__0, axiom, ![X25]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__0__eq__0)). 6.97/7.21 fof(fact_DIVISION__BY__ZERO, axiom, ![X30]:(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),c_Groups_Ozero__class_Ozero(tc_Int_Oint))&X30=c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,c_Groups_Ozero__class_Ozero(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_DIVISION__BY__ZERO)). 6.97/7.21 fof(fact_small__lazy__int__def, axiom, ![X74]:c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,X74)=c_Lazy__Sequence_Osmall__lazy_H(X74,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X74)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_small__lazy__int__def)). 6.97/7.21 fof(fact_List_Omap_Oid, axiom, ![X5]:hAPP(c_List_Omap(X5,X5),c_Fun_Oid(X5))=c_Fun_Oid(tc_List_Olist(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_List_Omap_Oid)). 6.97/7.21 fof(fact_List_Omap_Oidentity, axiom, ![X5]:c_Fun_Oid(tc_List_Olist(X5))=hAPP(c_List_Omap(X5,X5),c_COMBI(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_List_Omap_Oidentity)). 6.97/7.21 fof(fact_lazy__sequence_Orecs_I1_J, axiom, ![X120, X85, X12, X5]:X85=c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X5,X12,X85,X120,c_Lazy__Sequence_Olazy__sequence_OEmpty(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lazy__sequence_Orecs_I1_J)). 6.97/7.21 fof(fact_conversep__conversep, axiom, ![X3, X5, X12]:c_Predicate_Oconversep(X12,X5,c_Predicate_Oconversep(X5,X12,X3))=X3, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_conversep__conversep)). 6.97/7.21 fof(fact_image__id, axiom, ![X95, X5]:hAPP(c_Set_Oimage(X5,X5,c_Fun_Oid(X5)),X95)=X95, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__id)). 6.97/7.21 fof(fact_image__ident, axiom, ![X95, X5]:X95=hAPP(c_Set_Oimage(X5,X5,c_COMBI(X5)),X95), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__ident)). 6.97/7.21 fof(fact_nat__rec__0, axiom, ![X120, X85, X5]:hAPP(c_Nat_Onat_Onat__rec(X5,X85,X120),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X85, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__rec__0)). 6.97/7.21 fof(help_c__COMBK__1, axiom, ![X161, X162, X5, X8]:X162=hAPP(hAPP(c_COMBK(X8,X5),X162),X161), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__COMBK__1)). 6.97/7.21 fof(fact_Domain__Id__on, axiom, ![X4, X5]:hAPP(c_Relation_ODomain(X5,X5),c_Relation_OId__on(X5,X4))=X4, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__Id__on)). 6.97/7.21 fof(fact_Range__Id__on, axiom, ![X4, X5]:X4=hAPP(c_Relation_ORange(X5,X5),c_Relation_OId__on(X5,X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__Id__on)). 6.97/7.21 fof(fact_append__Nil, axiom, ![X45, X8]:hAPP(hAPP(c_List_Oappend(X8),c_List_Olist_ONil(X8)),X45)=X45, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__Nil)). 6.97/7.21 fof(fact_New__DSequence_Opos__single__def, axiom, ![X195, X6, X8]:hAPP(c_New__DSequence_Opos__single(X8,X6),X195)=hAPP(c_Lazy__Sequence_Osingle(X8),X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Opos__single__def)). 6.97/7.21 fof(fact_drop__0, axiom, ![X41, X8]:X41=hAPP(hAPP(c_List_Odrop(X8),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X41), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__0)). 6.97/7.21 fof(fact_append__Nil2, axiom, ![X41, X8]:hAPP(hAPP(c_List_Oappend(X8),X41),c_List_Olist_ONil(X8))=X41, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__Nil2)). 6.97/7.21 fof(fact_List_Oset_Osimps_I1_J, axiom, ![X5]:c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=hAPP(c_List_Oset(X5),c_List_Olist_ONil(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_List_Oset_Osimps_I1_J)). 6.97/7.21 fof(fact_zmult__1, axiom, ![X26]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X26)=X26, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult__1)). 6.97/7.21 fof(fact_plus__nat_Oadd__0, axiom, ![X25]:X25=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_plus__nat_Oadd__0)). 6.97/7.21 fof(fact_nat__mult__1, axiom, ![X25]:X25=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__1)). 6.97/7.21 fof(fact_zmult__1__right, axiom, ![X26]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),c_Groups_Oone__class_Oone(tc_Int_Oint))=X26, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult__1__right)). 6.97/7.21 fof(fact_nat__mult__1__right, axiom, ![X25]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X25, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__1__right)). 6.97/7.21 fof(fact_minus__nat_Odiff__0, axiom, ![X36]:X36=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__nat_Odiff__0)). 6.97/7.21 fof(fact_zminus__zminus, axiom, ![X26]:X26=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zminus__zminus)). 6.97/7.21 fof(fact_empty, axiom, ![X117, X5]:c_Hoare__Mirabelle_Ohoare__derivs(X5,X117,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty)). 6.97/7.21 fof(fact_listrelp_Oequations_I1_J, axiom, ![X3, X5]:c_List_Olistrelp(X5,X3,c_List_Olist_ONil(X5),c_List_Olist_ONil(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrelp_Oequations_I1_J)). 6.97/7.21 fof(fact__07, axiom, ![X18, X5, X12]:c_Lazy__Sequence_Olazy__sequence_OEmpty(X5)=c_Lazy__Sequence_Omap(X12,X5,X18,c_Lazy__Sequence_Olazy__sequence_OEmpty(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact__07)). 6.97/7.21 fof(fact_maps__simps_I2_J, axiom, ![X18, X5, X12]:c_List_Olist_ONil(X5)=c_List_Omaps(X12,X5,X18,c_List_Olist_ONil(X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_maps__simps_I2_J)). 6.97/7.21 fof(fact_top1I, axiom, ![X35, X5]:hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_top1I)). 6.97/7.21 fof(fact_total__on__empty, axiom, ![X3, X5]:c_Relation_Ototal__on(X5,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_total__on__empty)). 6.97/7.21 fof(fact_dvd_Oorder__refl, axiom, ![X6]:hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dvd_Oorder__refl)). 6.97/7.21 fof(fact_zle__refl, axiom, ![X39]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X39),X39)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zle__refl)). 6.97/7.21 fof(fact_le__refl, axiom, ![X25]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__refl)). 6.97/7.21 fof(fact_bij__betw__id, axiom, ![X4, X5]:c_Fun_Obij__betw(X5,X5,c_Fun_Oid(X5),X4,X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bij__betw__id)). 6.97/7.21 fof(fact_listsp_Oequations_I1_J, axiom, ![X4, X5]:hBOOL(hAPP(c_List_Olistsp(X5,X4),c_List_Olist_ONil(X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsp_Oequations_I1_J)). 6.97/7.21 fof(fact_distinct__remdups, axiom, ![X41, X8]:hBOOL(hAPP(c_List_Odistinct(X8),c_List_Oremdups(X8,X41))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__remdups)). 6.97/7.21 fof(fact_distinct__upto, axiom, ![X27, X28]:hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X28,X27))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__upto)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 fof(fact_fun__left__comm__idem__insert, axiom, ![X5]:c_Finite__Set_Ofun__left__comm__idem(X5,tc_fun(X5,tc_HOL_Obool),c_Set_Oinsert(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem__insert)). 6.97/7.21 fof(fact_filter_Osimps_I1_J, axiom, ![X17, X5]:hAPP(c_List_Ofilter(X5,X17),c_List_Olist_ONil(X5))=c_List_Olist_ONil(X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter_Osimps_I1_J)). 6.97/7.21 fof(fact_diff__self__eq__0, axiom, ![X36]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),X36)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__self__eq__0)). 6.97/7.21 fof(fact_lazy__sequence_Osize_I1_J, axiom, ![X131, X5]:hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X5,X131),c_Lazy__Sequence_Olazy__sequence_OEmpty(X5))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lazy__sequence_Osize_I1_J)). 6.97/7.21 fof(fact_list_Osize_I3_J, axiom, ![X8]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),c_List_Olist_ONil(X8))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list_Osize_I3_J)). 6.97/7.21 fof(fact_lazy__sequence_Osize_I3_J, axiom, ![X8]:hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X8)),c_Lazy__Sequence_Olazy__sequence_OEmpty(X8))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lazy__sequence_Osize_I3_J)). 6.97/7.21 fof(fact_New__DSequence_Oneg__single__def, axiom, ![X195, X6, X8]:hAPP(c_New__DSequence_Oneg__single(X8,X6),X195)=c_Lazy__Sequence_Ohb__single(X8,X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Oneg__single__def)). 6.97/7.21 fof(fact_rtrancl__idemp, axiom, ![X3, X5]:c_Transitive__Closure_Ortrancl(X5,c_Transitive__Closure_Ortrancl(X5,X3))=c_Transitive__Closure_Ortrancl(X5,X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__idemp)). 6.97/7.21 fof(fact_remdups__remdups, axiom, ![X41, X8]:c_List_Oremdups(X8,c_List_Oremdups(X8,X41))=c_List_Oremdups(X8,X41), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remdups__remdups)). 6.97/7.21 fof(fact_transpose_Osimps_I1_J, axiom, ![X8]:c_List_Otranspose(X8,c_List_Olist_ONil(tc_List_Olist(X8)))=c_List_Olist_ONil(tc_List_Olist(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose_Osimps_I1_J)). 6.97/7.21 fof(fact_code__numeral_Osimps_I4_J, axiom, ![X120, X85, X5]:c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X5,X85,X120,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=X85, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral_Osimps_I4_J)). 6.97/7.21 fof(fact_nat__case__0, axiom, ![X120, X85, X5]:c_Nat_Onat_Onat__case(X5,X85,X120,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X85, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__case__0)). 6.97/7.21 fof(fact_code__numeral_Orecs_I1_J, axiom, ![X120, X85, X5]:X85=c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X5,X85,X120,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral_Orecs_I1_J)). 6.97/7.21 fof(fact_takeWhile_Osimps_I1_J, axiom, ![X17, X5]:c_List_OtakeWhile(X5,X17,c_List_Olist_ONil(X5))=c_List_Olist_ONil(X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile_Osimps_I1_J)). 6.97/7.21 fof(fact_sublist__nil, axiom, ![X4, X5]:c_List_Olist_ONil(X5)=c_List_Osublist(X5,c_List_Olist_ONil(X5),X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublist__nil)). 6.97/7.21 fof(fact_remove1_Osimps_I1_J, axiom, ![X6, X8]:c_List_Olist_ONil(X8)=c_List_Oremove1(X8,X6,c_List_Olist_ONil(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remove1_Osimps_I1_J)). 6.97/7.21 fof(fact_list_Osize_I1_J, axiom, ![X131, X5]:c_List_Olist_Olist__size(X5,X131,c_List_Olist_ONil(X5))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list_Osize_I1_J)). 6.97/7.21 fof(fact_inj__on__id2, axiom, ![X4, X5]:c_Fun_Oinj__on(X5,X5,c_COMBI(X5),X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__id2)). 6.97/7.21 fof(fact_inj__on__id, axiom, ![X4, X5]:c_Fun_Oinj__on(X5,X5,c_Fun_Oid(X5),X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__id)). 6.97/7.21 fof(fact_single__valued__Id__on, axiom, ![X4, X5]:c_Relation_Osingle__valued(X5,X5,c_Relation_OId__on(X5,X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_single__valued__Id__on)). 6.97/7.21 fof(fact_replicate__0, axiom, ![X6, X8]:c_List_Oreplicate(X8,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)=c_List_Olist_ONil(X8), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_replicate__0)). 6.97/7.21 fof(fact_zmod__zero, axiom, ![X29]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X29), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zero)). 6.97/7.21 fof(fact_refl__on__Id__on, axiom, ![X4, X5]:c_Relation_Orefl__on(X5,X4,c_Relation_OId__on(X5,X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__on__Id__on)). 6.97/7.21 fof(fact_distinct_Osimps_I1_J, axiom, ![X8]:hBOOL(hAPP(c_List_Odistinct(X8),c_List_Olist_ONil(X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct_Osimps_I1_J)). 6.97/7.21 fof(fact_trans__finite__psubset, axiom, ![X5]:c_Relation_Otrans(tc_fun(X5,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trans__finite__psubset)). 6.97/7.21 fof(fact_wf__finite__psubset, axiom, ![X5]:c_Wellfounded_Owf(tc_fun(X5,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__finite__psubset)). 6.97/7.21 fof(fact__04, axiom, ![X8]:c_Lazy__Sequence_Olazy__sequence_OEmpty(X8)=c_Lazy__Sequence_Oflat(X8,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact__04)). 6.97/7.21 fof(fact_tl_Osimps_I1_J, axiom, ![X8]:hAPP(c_List_Otl(X8),c_List_Olist_ONil(X8))=c_List_Olist_ONil(X8), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tl_Osimps_I1_J)). 6.97/7.21 fof(fact_rev_Osimps_I1_J, axiom, ![X8]:c_List_Olist_ONil(X8)=hAPP(c_List_Orev(X8),c_List_Olist_ONil(X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev_Osimps_I1_J)). 6.97/7.21 fof(fact__02, axiom, ![X126, X8]:c_Lazy__Sequence_Oappend(X8,c_Lazy__Sequence_Olazy__sequence_OEmpty(X8),X126)=X126, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact__02)). 6.97/7.21 fof(fact_splice__Nil2, axiom, ![X41, X8]:c_List_Osplice(X8,X41,c_List_Olist_ONil(X8))=X41, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_splice__Nil2)). 6.97/7.21 fof(fact_splice_Osimps_I1_J, axiom, ![X45, X8]:X45=c_List_Osplice(X8,c_List_Olist_ONil(X8),X45), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_splice_Osimps_I1_J)). 6.97/7.21 fof(fact_the__sym__eq__trivial, axiom, ![X35, X5]:c_HOL_OThe(X5,hAPP(c_fequal,X35))=X35, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__sym__eq__trivial)). 6.97/7.21 fof(fact_some__sym__eq__trivial, axiom, ![X35, X5]:X35=c_Hilbert__Choice_OEps(X5,hAPP(c_fequal,X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_some__sym__eq__trivial)). 6.97/7.21 fof(fact_Rep__Integ__inverse, axiom, ![X35]:X35=hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Rep__Integ__inverse)). 6.97/7.21 fof(fact_zmod__self, axiom, ![X30]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X30), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__self)). 6.97/7.21 fof(fact_inj__Suc, axiom, ![X20]:c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X20), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__Suc)). 6.97/7.21 fof(fact_list__all__simps_I2_J, axiom, ![X17, X5]:c_List_Olist__all(X5,X17,c_List_Olist_ONil(X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all__simps_I2_J)). 6.97/7.21 fof(fact_antisym__Id__on, axiom, ![X4, X5]:c_Relation_Oantisym(X5,c_Relation_OId__on(X5,X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_antisym__Id__on)). 6.97/7.21 fof(fact_trans__rtrancl, axiom, ![X3, X5]:c_Relation_Otrans(X5,c_Transitive__Closure_Ortrancl(X5,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trans__rtrancl)). 6.97/7.21 fof(fact_trans__Id__on, axiom, ![X4, X5]:c_Relation_Otrans(X5,c_Relation_OId__on(X5,X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trans__Id__on)). 6.97/7.21 fof(fact_sym__Id__on, axiom, ![X4, X5]:c_Relation_Osym(X5,c_Relation_OId__on(X5,X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sym__Id__on)). 6.97/7.21 fof(fact_wf__measures, axiom, ![X121, X5]:c_Wellfounded_Owf(X5,c_List_Omeasures(X5,X121)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__measures)). 6.97/7.21 fof(fact_sorted__upto, axiom, ![X27, X28]:c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X28,X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__upto)). 6.97/7.21 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J, axiom, ![X26]:c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J)). 6.97/7.21 fof(fact_butlast_Osimps_I1_J, axiom, ![X8]:c_List_Obutlast(X8,c_List_Olist_ONil(X8))=c_List_Olist_ONil(X8), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_butlast_Osimps_I1_J)). 6.97/7.21 fof(fact_remdups_Osimps_I1_J, axiom, ![X8]:c_List_Oremdups(X8,c_List_Olist_ONil(X8))=c_List_Olist_ONil(X8), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remdups_Osimps_I1_J)). 6.97/7.21 fof(fact_New__DSequence_Opos__empty__def, axiom, ![X195, X8]:c_Lazy__Sequence_Oempty(X8)=hAPP(c_New__DSequence_Opos__empty(X8),X195), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Opos__empty__def)). 6.97/7.21 fof(fact_beyond__zero, axiom, ![X19]:c_Quickcheck_Obeyond(X19,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_beyond__zero)). 6.97/7.21 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)). 6.97/7.21 fof(fact_one__code__numeral__def, axiom, c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)=hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__code__numeral__def)). 6.97/7.21 fof(fact_conversep__eq, axiom, ![X5]:c_Predicate_Oconversep(X5,X5,c_fequal)=c_fequal, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_conversep__eq)). 6.97/7.21 fof(help_c__COMBI__1, axiom, ![X162, X8]:X162=hAPP(c_COMBI(X8),X162), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__COMBI__1)). 6.97/7.21 fof(fact_id__apply, axiom, ![X6, X8]:X6=hAPP(c_Fun_Oid(X8),X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_id__apply)). 6.97/7.21 fof(fact_nat__size, axiom, ![X25]:hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X25)=X25, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__size)). 6.97/7.21 fof(arity_Nitpick__Opair____box__Nat_Osize, axiom, ![X16, X98]:class_Nat_Osize(tc_Nitpick_Opair__box(X98,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nitpick__Opair____box__Nat_Osize)). 6.97/7.21 fof(arity_sum__Nat_Osize, axiom, ![X16, X98]:class_Nat_Osize(tc_sum(X98,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_sum__Nat_Osize)). 6.97/7.21 fof(arity_prod__Nat_Osize, axiom, ![X16, X98]:class_Nat_Osize(tc_prod(X98,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_prod__Nat_Osize)). 6.97/7.21 fof(fact_wf__int__ge__less__than2, axiom, ![X97]:c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X97)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__int__ge__less__than2)). 6.97/7.21 fof(fact_wf__int__ge__less__than, axiom, ![X97]:c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X97)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__int__ge__less__than)). 6.97/7.21 fof(fact_identity__equivp, axiom, ![X5]:c_Equiv__Relations_Oequivp(X5,c_fequal), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_identity__equivp)). 6.97/7.21 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize, axiom, ![X16]:class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Hoare____Mirabelle__Otriple__Nat_Osize)). 6.97/7.21 fof(arity_List__Olist__Nat_Osize, axiom, ![X16]:class_Nat_Osize(tc_List_Olist(X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_List__Olist__Nat_Osize)). 6.97/7.21 fof(arity_Option__Ooption__Nat_Osize, axiom, ![X16]:class_Nat_Osize(tc_Option_Ooption(X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Option__Ooption__Nat_Osize)). 6.97/7.21 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize, axiom, ![X16]:class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Lazy____Sequence__Olazy____sequence__Nat_Osize)). 6.97/7.21 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)). 6.97/7.21 fof(fact_Nitpick_OFrac__def, axiom, c_Nitpick_OFrac=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)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_OFrac__def)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 fof(fact_INT__greaterThan__UNIV, axiom, 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)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__greaterThan__UNIV)). 6.97/7.21 fof(fact_UN__atLeast__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_OatLeast(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__atLeast__UNIV)). 6.97/7.21 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)). 6.97/7.21 fof(fact_UN__atMost__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_OatMost(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__atMost__UNIV)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 fof(fact_int__of__def, axiom, c_Code__Numeral_Oint__of=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), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__of__def)). 6.97/7.21 fof(fact_code__numeral__zero__minus__one, axiom, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=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)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral__zero__minus__one)). 6.97/7.21 fof(conj_0, hypothesis, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_G)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', conj_0)). 6.97/7.21 fof(conj_1, hypothesis, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),v_Ga)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', conj_1)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 fof(fact_pair__less__def, axiom, c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than)=c_FunDef_Opair__less, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__less__def)). 6.97/7.21 fof(fact_transfer__int__nat__numerals_I2_J, 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_transfer__int__nat__numerals_I2_J)). 6.97/7.21 fof(fact_transfer__int__nat__numerals_I1_J, 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_transfer__int__nat__numerals_I1_J)). 6.97/7.21 fof(fact_min__strict__def, axiom, c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)=c_FunDef_Omin__strict, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__strict__def)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 fof(fact_mono__Suc, axiom, c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mono__Suc)). 6.97/7.21 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)). 6.97/7.21 fof(fact_trans__less__than, axiom, c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trans__less__than)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 fof(fact_bool_Osize_I2_J, axiom, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_HOL_Obool_Obool__size(c_fFalse), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bool_Osize_I2_J)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 fof(fact_bot__nat__def, axiom, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Orderings_Obot__class_Obot(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bot__nat__def)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 fof(arity_Int__Oint__Rings_Ozero__neq__one, axiom, class_Rings_Ozero__neq__one(tc_Int_Oint), 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file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__ring__strict)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Nat_Osemiring__char__0)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Ocomm__semiring__1)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 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)). 6.97/7.21 fof(help_c__fTrue__1, axiom, hBOOL(c_fTrue), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fTrue__1)). 6.97/7.21 fof(c_0_4401, plain, ![X13865]:c_Int_OBit1(X13865)=c_Int_Osucc(c_Int_OBit0(X13865)), inference(variable_rename,[status(thm)],[fact_succ__Bit0])). 6.97/7.21 fof(c_0_4402, plain, ![X319]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X319),X319)=c_Int_OBit0(X319), inference(variable_rename,[status(thm)],[fact_Bit0__def])). 6.97/7.21 fof(c_0_4403, plain, ![X11698]:c_Int_Osucc(X11698)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X11698),c_Int_OMin), inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I2_J])). 6.97/7.21 fof(c_0_4404, plain, ![X5425]:X5425=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X5425), inference(variable_rename,[status(thm)],[fact_add__Pls])). 6.97/7.21 fof(c_0_4405, plain, ![X15056, X15057]:(((X15057!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)!=X15056|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15057),X15056)=c_Groups_Oone__class_Oone(tc_Int_Oint))&(c_Groups_Oone__class_Oone(tc_Int_Oint)!=X15056|c_Groups_Oone__class_Oone(tc_Int_Oint)!=X15057|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15057),X15056)=c_Groups_Oone__class_Oone(tc_Int_Oint)))&(((c_Groups_Oone__class_Oone(tc_Int_Oint)=X15056|X15057=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15057),X15056)!=c_Groups_Oone__class_Oone(tc_Int_Oint))&(c_Groups_Oone__class_Oone(tc_Int_Oint)=X15057|X15057=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15057),X15056)!=c_Groups_Oone__class_Oone(tc_Int_Oint)))&((c_Groups_Oone__class_Oone(tc_Int_Oint)=X15056|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=X15056|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15057),X15056)!=c_Groups_Oone__class_Oone(tc_Int_Oint))&(c_Groups_Oone__class_Oone(tc_Int_Oint)=X15057|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=X15056|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15057),X15056)!=c_Groups_Oone__class_Oone(tc_Int_Oint))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__eq__1__iff])])])). 6.97/7.21 fof(c_0_4406, plain, ![X947]:hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X947)=X947, inference(variable_rename,[status(thm)],[fact_number__of__is__id])). 6.97/7.21 fof(c_0_4407, plain, ![X12137]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X12137)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12137), inference(variable_rename,[status(thm)],[fact_mult__Min])). 6.97/7.21 cnf(c_0_4408, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)=c_Int_OBit1(c_Int_OPls)), inference(split_conjunct,[status(thm)],[fact_minus__Min])). 6.97/7.21 cnf(c_0_4409, plain, (c_Int_OBit1(X1)=c_Int_Osucc(c_Int_OBit0(X1))), inference(split_conjunct,[status(thm)],[c_0_4401])). 6.97/7.21 cnf(c_0_4410, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)=c_Int_OBit0(X1)), inference(split_conjunct,[status(thm)],[c_0_4402])). 6.97/7.21 cnf(c_0_4411, 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_4403])). 6.97/7.21 cnf(c_0_4412, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X1)), inference(split_conjunct,[status(thm)],[c_0_4404])). 6.97/7.21 cnf(c_0_4413, plain, (c_Int_OPls=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[fact_Pls__def]), ['final']). 6.97/7.21 cnf(c_0_4414, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)=c_Groups_Oone__class_Oone(tc_Int_Oint)|X1!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)!=X2), inference(split_conjunct,[status(thm)],[c_0_4405])). 6.97/7.21 cnf(c_0_4415, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)=X1), inference(split_conjunct,[status(thm)],[c_0_4406]), ['final']). 6.97/7.21 cnf(c_0_4416, 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_4407]), ['final']). 6.97/7.21 fof(c_0_4417, plain, ![X8288]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X8288),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Int_Osucc(X8288), inference(variable_rename,[status(thm)],[fact_succ__def])). 6.97/7.21 fof(c_0_4418, plain, ![X2797, X2798, X2799, X2800]:hAPP(c_Set_OCollect(X2800),hAPP(hAPP(c_COMBB(X2799,tc_HOL_Obool,X2800),X2797),X2798))=hAPP(c_Set_Ovimage(X2800,X2799,X2798),hAPP(c_Set_OCollect(X2799),X2797)), inference(variable_rename,[status(thm)],[fact_vimage__Collect__eq])). 6.97/7.21 fof(c_0_4419, plain, ![X14123, X14124]:X14123=hAPP(c_Set_OCollect(X14124),X14123), inference(variable_rename,[status(thm)],[fact_Collect__def])). 6.97/7.21 fof(c_0_4420, plain, ![X13117]:c_List_Oupt(X13117,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_List_Olist_ONil(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_upt__0])). 6.97/7.21 fof(c_0_4421, plain, ![X6212, X6213]:c_List_Oupt(X6213,X6212)=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X6213),X6212)), inference(variable_rename,[status(thm)],[fact_sorted__list__of__set__range])). 6.97/7.21 fof(c_0_4422, plain, ![X760, X761]:hAPP(c_Set_OCollect(X761),hAPP(hAPP(c_COMBC(X761,tc_fun(X761,tc_HOL_Obool),tc_HOL_Obool),c_member(X761)),X760))=X760, inference(variable_rename,[status(thm)],[fact_Collect__mem__eq])). 6.97/7.21 fof(c_0_4423, plain, ![X9898, X9899, X9900, X9901]:hAPP(c_Set_OCollect(tc_prod(X9901,X9900)),hAPP(c_Product__Type_Oprod_Oprod__case(X9901,X9900,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X9901,tc_fun(X9900,tc_HOL_Obool),tc_fun(X9900,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X9900,tc_HOL_Obool),tc_fun(X9900,tc_HOL_Obool)),X9901),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X9900)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X9901),c_fconj),X9899))),X9898)))=hAPP(hAPP(c_Product__Type_OSigma(X9901,X9900),hAPP(c_Set_OCollect(X9901),X9899)),hAPP(c_COMBK(tc_fun(X9900,tc_HOL_Obool),X9901),hAPP(c_Set_OCollect(X9900),X9898))), inference(variable_rename,[status(thm)],[fact_Collect__split])). 6.97/7.21 fof(c_0_4424, plain, ![X2156, X2157, X2158]:hAPP(c_Set_OCollect(X2158),hAPP(hAPP(c_COMBS(X2158,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2158),c_fconj),X2157)),X2156))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2158,tc_HOL_Obool)),hAPP(c_Set_OCollect(X2158),X2157)),hAPP(c_Set_OCollect(X2158),X2156)), inference(variable_rename,[status(thm)],[fact_Collect__conj__eq])). 6.97/7.21 fof(c_0_4425, plain, ![X5265]:hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X5265)=hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X5265)), inference(variable_rename,[status(thm)],[fact_nat__number__of])). 6.97/7.21 fof(c_0_4426, plain, ![X10129, X10130]:((hAPP(hAPP(c_Power_Opower__class_Opower(X10130),X10129),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))!=c_Groups_Oone__class_Oone(X10130)|(X10129=c_Groups_Oone__class_Oone(X10130)|hAPP(c_Groups_Ouminus__class_Ouminus(X10130),c_Groups_Oone__class_Oone(X10130))=X10129)|~class_Rings_Oring__1__no__zero__divisors(X10130))&((X10129!=c_Groups_Oone__class_Oone(X10130)|hAPP(hAPP(c_Power_Opower__class_Opower(X10130),X10129),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Oone__class_Oone(X10130)|~class_Rings_Oring__1__no__zero__divisors(X10130))&(hAPP(c_Groups_Ouminus__class_Ouminus(X10130),c_Groups_Oone__class_Oone(X10130))!=X10129|hAPP(hAPP(c_Power_Opower__class_Opower(X10130),X10129),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Oone__class_Oone(X10130)|~class_Rings_Oring__1__no__zero__divisors(X10130)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power2__eq__1__iff])])])])). 6.97/7.21 fof(c_0_4427, plain, ![X1616]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1616),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))|(X1616=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1616)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__2__cases])])). 6.97/7.21 fof(c_0_4428, plain, ![X13385, X13386]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13386),c_Groups_Ozero__class_Ozero(X13386)),hAPP(hAPP(c_Power_Opower__class_Opower(X13386),X13385),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|c_Groups_Ozero__class_Ozero(X13386)!=X13385|~class_Rings_Olinordered__idom(X13386))&(c_Groups_Ozero__class_Ozero(X13386)=X13385|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13386),c_Groups_Ozero__class_Ozero(X13386)),hAPP(hAPP(c_Power_Opower__class_Opower(X13386),X13385),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|~class_Rings_Olinordered__idom(X13386))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__less__power2])])])])). 6.97/7.21 fof(c_0_4429, plain, ![X7067, X7068]:(~class_Rings_Olinordered__idom(X7068)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7068),hAPP(hAPP(c_Power_Opower__class_Opower(X7068),X7067),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X7068)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power2__less__0])])])). 6.97/7.21 fof(c_0_4430, plain, ![X1468]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1468),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Int_Opred(X1468), inference(variable_rename,[status(thm)],[fact_pred__def])). 6.97/7.21 fof(c_0_4431, plain, ![X8489]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X8489),c_Int_OMin)=c_Int_Opred(X8489), inference(variable_rename,[status(thm)],[fact_add__Min__right])). 6.97/7.21 fof(c_0_4432, plain, ![X16212, X16213, X16214, X16215]:(hBOOL(hAPP(X16215,X16214))|hAPP(c_List_Ofilter(X16213,X16215),X16212)=hAPP(c_List_OremoveAll(X16213,X16214),hAPP(c_List_Ofilter(X16213,X16215),X16212))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_removeAll__filter__not])])])). 6.97/7.21 fof(c_0_4433, plain, ![X12345, X12346]:c_List_Ofilter(X12346,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X12346),c_fNot),hAPP(c_fequal,X12345)))=c_List_OremoveAll(X12346,X12345), inference(variable_rename,[status(thm)],[fact_removeAll__filter__not__eq])). 6.97/7.21 fof(c_0_4434, plain, ![X11843, X11844]:hAPP(c_Set_OCollect(X11844),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X11844),c_fNot),X11843))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11844,tc_HOL_Obool)),hAPP(c_Set_OCollect(X11844),X11843)), inference(variable_rename,[status(thm)],[fact_Collect__neg__eq])). 6.97/7.21 fof(c_0_4435, plain, ![X1289]:(~class_Int_Onumber__ring(X1289)|~c_Int_Oiszero(X1289,hAPP(c_Int_Onumber__class_Onumber__of(X1289),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])])])). 6.97/7.21 fof(c_0_4436, plain, ![X3890, X3891]:c_List_Ofoldr(tc_List_Olist(X3891),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3891)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X3891))),X3890,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X3891))),c_List_Otranspose(X3891,X3890)), inference(variable_rename,[status(thm)],[fact_length__transpose])). 6.97/7.21 fof(c_0_4437, plain, ![X12416, X12417, X12418, X12419, X12420]:hAPP(c_List_Ofoldl(X12419,X12420,hAPP(c_COMBC(X12420,X12419,X12419),X12418),X12416),hAPP(c_List_Orev(X12420),X12417))=c_List_Ofoldr(X12420,X12419,X12418,X12417,X12416), inference(variable_rename,[status(thm)],[fact_foldr__foldl])). 6.97/7.21 fof(c_0_4438, plain, ![X15278, X15279]:hAPP(hAPP(c_List_Omap(tc_List_Olist(X15279),X15279),c_List_Ohd(X15279)),hAPP(c_List_Ofilter(tc_List_Olist(X15279),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X15279)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X15279),tc_List_Olist(X15279),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X15279)))),X15278))=c_List_Oconcat(X15279,hAPP(hAPP(c_List_Omap(tc_List_Olist(X15279),tc_List_Olist(X15279)),c_List_Olist_Olist__case(tc_List_Olist(X15279),X15279,c_List_Olist_ONil(X15279),hAPP(hAPP(c_COMBB(tc_List_Olist(X15279),tc_fun(tc_List_Olist(X15279),tc_List_Olist(X15279)),X15279),c_COMBK(tc_List_Olist(X15279),tc_List_Olist(X15279))),hAPP(hAPP(c_COMBC(X15279,tc_List_Olist(X15279),tc_List_Olist(X15279)),c_List_Olist_OCons(X15279)),c_List_Olist_ONil(X15279))))),X15278)), inference(variable_rename,[status(thm)],[fact_transpose__aux__filter__head])). 6.97/7.21 fof(c_0_4439, plain, ![X3119, X3120]:c_List_Oconcat(X3120,X3119)=hAPP(c_List_Ofoldl(tc_List_Olist(X3120),tc_List_Olist(X3120),c_List_Oappend(X3120),c_List_Olist_ONil(X3120)),X3119), inference(variable_rename,[status(thm)],[fact_concat__conv__foldl])). 6.97/7.21 fof(c_0_4440, plain, ![X6021, X6022, X6023, X6024]:c_List_Oconcat(X6023,hAPP(hAPP(c_List_Omap(X6024,tc_List_Olist(X6023)),X6022),X6021))=c_List_Omaps(X6024,X6023,X6022,X6021), inference(variable_rename,[status(thm)],[fact_maps__def])). 6.97/7.21 fof(c_0_4441, plain, ![X3376, X3377]:hAPP(hAPP(c_Set_Oinsert(X3377),X3376),c_Orderings_Obot__class_Obot(tc_fun(X3377,tc_HOL_Obool)))=hAPP(c_Set_OCollect(X3377),hAPP(hAPP(c_COMBC(X3377,X3377,tc_HOL_Obool),c_fequal),X3376)), inference(variable_rename,[status(thm)],[fact_singleton__conv])). 6.97/7.21 fof(c_0_4442, plain, ![X2174, X2175]:hAPP(hAPP(c_Set_Oinsert(X2175),X2174),c_Orderings_Obot__class_Obot(tc_fun(X2175,tc_HOL_Obool)))=hAPP(c_Set_OCollect(X2175),hAPP(c_fequal,X2174)), inference(variable_rename,[status(thm)],[fact_singleton__conv2])). 6.97/7.21 fof(c_0_4443, plain, ![X16809, X16810]:hAPP(hAPP(c_List_Omap(tc_List_Olist(X16810),tc_List_Olist(X16810)),c_List_Otl(X16810)),hAPP(c_List_Ofilter(tc_List_Olist(X16810),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X16810)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X16810),tc_List_Olist(X16810),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X16810)))),X16809))=c_List_Oconcat(tc_List_Olist(X16810),hAPP(hAPP(c_List_Omap(tc_List_Olist(X16810),tc_List_Olist(tc_List_Olist(X16810))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X16810)),X16810,c_List_Olist_ONil(tc_List_Olist(X16810)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X16810),tc_List_Olist(tc_List_Olist(X16810))),X16810),hAPP(hAPP(c_COMBC(tc_List_Olist(X16810),tc_List_Olist(tc_List_Olist(X16810)),tc_List_Olist(tc_List_Olist(X16810))),c_List_Olist_OCons(tc_List_Olist(X16810))),c_List_Olist_ONil(tc_List_Olist(X16810)))))),X16809)), inference(variable_rename,[status(thm)],[fact_transpose__aux__filter__tail])). 6.97/7.21 fof(c_0_4444, plain, ![X16410, X16411]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X16411)),c_Int_OBit1(X16410))=c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16411),X16410)), inference(variable_rename,[status(thm)],[fact_add__Bit0__Bit1])). 6.97/7.21 fof(c_0_4445, plain, ![X9073]:c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X9073))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X9073)), inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I5_J])). 6.97/7.21 fof(c_0_4446, plain, ![X4482, X4483]:c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4483),X4482))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X4483)),c_Int_OBit0(X4482)), inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I7_J])). 6.97/7.21 fof(c_0_4447, plain, ![X7817, X7818, X7819, X7820]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7820,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7820,tc_HOL_Obool)),X7819),X7818)),X7817)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7820,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7820,tc_HOL_Obool)),X7819),X7817)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7820,tc_HOL_Obool)),X7818),X7817)), inference(variable_rename,[status(thm)],[fact_Diff__Int__distrib2])). 6.97/7.21 fof(c_0_4448, plain, ![X7287, X7288, X7289, X7290]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7290,tc_HOL_Obool)),X7289),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7290,tc_HOL_Obool)),X7288),X7287))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7290,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7290,tc_HOL_Obool)),X7289),X7288)),X7287), inference(variable_rename,[status(thm)],[fact_Int__Diff])). 6.97/7.21 fof(c_0_4449, plain, ![X2578, X2579]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X2579|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(X2579,X2578))&((X2578!=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)),X2579)=c_Divides_Odivmod__int(X2579,X2578)|X2579=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(X2578=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,X2578))),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)),X2578)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2579))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2578),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2579),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(X2579,X2578)),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),X2578))))),c_Divides_Opdivmod(X2579,X2578))))=c_Divides_Odivmod__int(X2579,X2578)|X2579=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__pdivmod])])])])). 6.97/7.21 fof(c_0_4450, plain, ![X5401, X5402, X5403, X5404]:c_Product__Type_Oapsnd(X5404,X5403,X5402,X5401)=c_Product__Type_Omap__pair(X5402,X5402,X5404,X5403,c_Fun_Oid(X5402),X5401), inference(variable_rename,[status(thm)],[fact_apsnd__def])). 6.97/7.21 fof(c_0_4451, plain, ![X3800, X3801]:(((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X3800|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,X3800))),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,X3801)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X3800))),c_Divides_Opdivmod(X3801,X3800)),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),X3800))))),c_Divides_Opdivmod(X3801,X3800))))=c_Divides_Odivmod__int(X3801,X3800)|X3801=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(X3800!=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)),X3801)=c_Divides_Odivmod__int(X3801,X3800)|X3801=c_Groups_Ozero__class_Ozero(tc_Int_Oint)))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X3801|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(X3801,X3800))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__int__code])])])])). 6.97/7.21 fof(c_0_4452, plain, ![X3698, X3699]:((X3698!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(c_Int_Oring__1__class_Oof__int(X3699),X3698)=c_Groups_Ozero__class_Ozero(X3699)|~class_Rings_Oring__1(X3699))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3698),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Oring__1__class_Oof__int(X3699),X3698)=hAPP(c_Groups_Ouminus__class_Ouminus(X3699),hAPP(c_Int_Oring__1__class_Oof__int(X3699),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3698)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X3698|~class_Rings_Oring__1(X3699))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3698),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Oring__1__class_Oof__int(X3699),X3698)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X3699),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X3699,X3699)),tc_fun(tc_Int_Oint,X3699)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3699,X3699),X3699),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X3699,X3699)),tc_fun(tc_Int_Oint,X3699)),tc_Int_Oint),c_COMBB(tc_fun(X3699,X3699),X3699,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X3699,tc_fun(tc_fun(X3699,X3699),X3699),tc_Int_Oint),c_HOL_OLet(X3699,X3699)),c_Int_Oring__1__class_Oof__int(X3699)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X3699,X3699),tc_fun(X3699,X3699)),hAPP(hAPP(c_COMBB(tc_fun(X3699,tc_fun(X3699,X3699)),tc_fun(tc_fun(X3699,X3699),tc_fun(X3699,X3699)),tc_Int_Oint),c_COMBS(X3699,X3699,X3699)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X3699,X3699),tc_fun(X3699,tc_fun(X3699,X3699))),hAPP(hAPP(c_COMBB(tc_fun(X3699,tc_fun(X3699,X3699)),tc_fun(tc_fun(X3699,X3699),tc_fun(X3699,tc_fun(X3699,X3699))),tc_Int_Oint),c_COMBB(X3699,tc_fun(X3699,X3699),X3699)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X3699,tc_fun(X3699,X3699)),tc_Int_Oint),c_If(X3699)),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(X3699,X3699,X3699),c_Groups_Oplus__class_Oplus(X3699)),c_COMBI(X3699))))),hAPP(hAPP(c_COMBC(X3699,X3699,X3699),hAPP(hAPP(c_COMBB(X3699,tc_fun(X3699,X3699),X3699),c_Groups_Oplus__class_Oplus(X3699)),hAPP(hAPP(c_COMBS(X3699,X3699,X3699),c_Groups_Oplus__class_Oplus(X3699)),c_COMBI(X3699)))),c_Groups_Oone__class_Oone(X3699))))),c_Divides_Odivmod__int(X3698,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)=X3698|~class_Rings_Oring__1(X3699)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__num])])])])). 6.97/7.21 fof(c_0_4453, plain, ![X16055, X16056, X16057]:(~class_Int_Onumber__ring(X16057)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X16057),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16057),hAPP(hAPP(c_Power_Opower__class_Opower(X16057),X16056),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(X16057),X16055),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(X16057),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16057),hAPP(c_Int_Onumber__class_Onumber__of(X16057),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X16056)),X16055))=hAPP(hAPP(c_Power_Opower__class_Opower(X16057),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X16057),X16056),X16055)),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])])])). 6.97/7.21 cnf(c_0_4454, 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])). 6.97/7.21 cnf(c_0_4455, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(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),c_Int_OPls),c_Int_OPls)),c_Int_OMin)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4408, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.21 cnf(c_0_4456, 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_4412, c_0_4413]), ['final']). 6.97/7.21 cnf(c_0_4457, 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_4414, c_0_4415]), c_0_4415])])]), c_0_4416]), ['final']). 6.97/7.21 cnf(c_0_4458, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Int_Osucc(X1)), inference(split_conjunct,[status(thm)],[c_0_4417])). 6.97/7.21 fof(c_0_4459, plain, ![X11722, X11723, X11724]:(~class_Int_Onumber__ring(X11724)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11724),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11724),hAPP(hAPP(c_Power_Opower__class_Opower(X11724),X11723),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(X11724),X11722),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(X11724),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11724),hAPP(c_Int_Onumber__class_Onumber__of(X11724),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X11723)),X11722))=hAPP(hAPP(c_Power_Opower__class_Opower(X11724),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11724),X11723),X11722)),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__sum])])). 6.97/7.21 fof(c_0_4460, plain, ![X10432, X10433]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10433),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),X10432),c_Groups_Oone__class_Oone(tc_Int_Oint)),X10433))),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)))),X10432)),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)))),X10433))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__zmod__mult__2])])). 6.97/7.21 fof(c_0_4461, plain, ![X6231, X6232]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6232))|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)))),X6231)),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)))),X6232))=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,X6231,X6232)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmod__mult__2])])). 6.97/7.21 fof(c_0_4462, plain, ![X15798]:(((c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X15798,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,X15798)=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),X15798),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))|X15798=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))&(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X15798,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),X15798),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,X15798)|X15798=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))&(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X15798|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(c_Code__Numeral_Oint__of,X15798))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_int__of__code])])])])). 6.97/7.21 fof(c_0_4463, plain, ![X12501, X12502]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12502),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),X12501),c_Groups_Oone__class_Oone(tc_Int_Oint))),X12502)=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)))),X12501))),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)))),X12502))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__zdiv__mult__2])])])). 6.97/7.21 fof(c_0_4464, plain, ![X15815, X15816]:((~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),X15816)))|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),X15815),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15816)))),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(X15815)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X15816))))&(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),X15816)))|c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X15815)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X15816)))=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),X15815)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15816)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmod__number__of__Bit1])])])). 6.97/7.21 fof(c_0_4465, plain, ![X9780, X9781, X9782, X9783]:hAPP(c_Set_Ovimage(X9783,X9782,X9781),X9780)=hAPP(c_Set_OCollect(X9783),hAPP(hAPP(c_COMBC(X9783,tc_fun(X9782,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(X9782,tc_fun(tc_fun(X9782,tc_HOL_Obool),tc_HOL_Obool),X9783),c_member(X9782)),X9781)),X9780)), inference(variable_rename,[status(thm)],[fact_vimage__def])). 6.97/7.21 cnf(c_0_4466, 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_4418])). 6.97/7.21 cnf(c_0_4467, plain, (X1=hAPP(c_Set_OCollect(X2),X1)), inference(split_conjunct,[status(thm)],[c_0_4419]), ['final']). 6.97/7.21 fof(c_0_4468, plain, ![X15282, X15283]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15283))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X15282),X15283)=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)))),X15282))),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)))),X15283))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pos__zdiv__mult__2])])])). 6.97/7.21 fof(c_0_4469, plain, ![X5280, X5281, X5282]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk171_3(X5280,X5281,X5282)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5281))),X5282)))|c_List_Otranspose(X5281,X5282)=hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X5281)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X5281)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X5281),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X5281)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X5281)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X5281),hAPP(hAPP(c_COMBB(tc_List_Olist(X5281),tc_fun(tc_Nat_Onat,X5281),tc_Nat_Onat),c_List_Onth(X5281)),hAPP(c_List_Onth(tc_List_Olist(X5281)),X5282))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5281))),X5282)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5280))|c_List_Olist_ONil(tc_List_Olist(X5281))=X5282)&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5281)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X5281)),X5282),esk171_3(X5280,X5281,X5282)))!=X5280|c_List_Otranspose(X5281,X5282)=hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X5281)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X5281)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X5281),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X5281)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X5281)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X5281),hAPP(hAPP(c_COMBB(tc_List_Olist(X5281),tc_fun(tc_Nat_Onat,X5281),tc_Nat_Onat),c_List_Onth(X5281)),hAPP(c_List_Onth(tc_List_Olist(X5281)),X5282))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5281))),X5282)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5280))|c_List_Olist_ONil(tc_List_Olist(X5281))=X5282))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk171_3(X5280,X5281,X5282)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5281))),X5282)))|c_List_Otranspose(X5281,X5282)=hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X5281)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X5281)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X5281),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X5281)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X5281)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X5281),hAPP(hAPP(c_COMBB(tc_List_Olist(X5281),tc_fun(tc_Nat_Onat,X5281),tc_Nat_Onat),c_List_Onth(X5281)),hAPP(c_List_Onth(tc_List_Olist(X5281)),X5282))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5281))),X5282)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5280))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X5280)&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5281)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X5281)),X5282),esk171_3(X5280,X5281,X5282)))!=X5280|c_List_Otranspose(X5281,X5282)=hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X5281)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X5281)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X5281),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X5281)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X5281)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X5281),hAPP(hAPP(c_COMBB(tc_List_Olist(X5281),tc_fun(tc_Nat_Onat,X5281),tc_Nat_Onat),c_List_Onth(X5281)),hAPP(c_List_Onth(tc_List_Olist(X5281)),X5282))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5281))),X5282)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5280))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X5280))), 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])])])])])). 6.97/7.21 cnf(c_0_4470, plain, (c_List_Oupt(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_List_Olist_ONil(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_4420])). 6.97/7.21 cnf(c_0_4471, plain, (c_List_Oupt(X1,X2)=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4421])). 6.97/7.21 fof(c_0_4472, plain, ![X10829]:c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X10829),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_atLeastLessThan0])). 6.97/7.21 fof(c_0_4473, plain, ![X6384, X6385, X6386]:((X6384!=c_Groups_Ozero__class_Ozero(X6386)|X6385!=c_Groups_Ozero__class_Ozero(X6386)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6386),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6386),hAPP(hAPP(c_Power_Opower__class_Opower(X6386),X6385),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(X6386),X6384),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X6386)))|~class_Rings_Olinordered__idom(X6386))&((X6384=c_Groups_Ozero__class_Ozero(X6386)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6386),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6386),hAPP(hAPP(c_Power_Opower__class_Opower(X6386),X6385),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(X6386),X6384),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X6386)))|~class_Rings_Olinordered__idom(X6386))&(X6385=c_Groups_Ozero__class_Ozero(X6386)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6386),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6386),hAPP(hAPP(c_Power_Opower__class_Opower(X6386),X6385),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(X6386),X6384),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X6386)))|~class_Rings_Olinordered__idom(X6386)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__le__zero__iff])])])). 6.97/7.21 fof(c_0_4474, plain, ![X5860, X5861, X5862]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5862),c_Groups_Ozero__class_Ozero(X5862)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5862),hAPP(hAPP(c_Power_Opower__class_Opower(X5862),X5861),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(X5862),X5860),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))|(c_Groups_Ozero__class_Ozero(X5862)!=X5860|c_Groups_Ozero__class_Ozero(X5862)!=X5861)|~class_Rings_Olinordered__idom(X5862))&((c_Groups_Ozero__class_Ozero(X5862)=X5860|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5862),c_Groups_Ozero__class_Ozero(X5862)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5862),hAPP(hAPP(c_Power_Opower__class_Opower(X5862),X5861),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(X5862),X5860),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))|~class_Rings_Olinordered__idom(X5862))&(c_Groups_Ozero__class_Ozero(X5862)=X5861|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5862),c_Groups_Ozero__class_Ozero(X5862)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5862),hAPP(hAPP(c_Power_Opower__class_Opower(X5862),X5861),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(X5862),X5860),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))|~class_Rings_Olinordered__idom(X5862)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__gt__zero__iff])])])). 6.97/7.21 fof(c_0_4475, plain, ![X9121, X9122]:((hAPP(c_Nat_OSuc,X9122)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X9121)|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(X9121))),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)),X9122))))))&(~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(X9121))),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)),X9122)))))|hAPP(c_Nat_OSuc,X9122)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X9121))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__eq__number__of])])). 6.97/7.21 fof(c_0_4476, plain, ![X5812, X5813, X5814]:hAPP(c_Set_OCollect(X5814),hAPP(hAPP(c_COMBS(X5814,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5814),c_fimplies),X5813)),X5812))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5814,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5814,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5814),X5813))),hAPP(c_Set_OCollect(X5814),X5812)), inference(variable_rename,[status(thm)],[fact_Collect__imp__eq])). 6.97/7.21 fof(c_0_4477, plain, ![X12818, X12819, X12820]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12820,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X12820,tc_HOL_Obool)),X12819)),X12818)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X12820,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12820,tc_HOL_Obool)),X12819),X12818)), inference(variable_rename,[status(thm)],[fact_Compl__Diff__eq])). 6.97/7.21 fof(c_0_4478, plain, ![X15072, X15073, X15074]:(~class_Rings_Olinordered__idom(X15074)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15074),c_Groups_Ozero__class_Ozero(X15074)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15074),hAPP(hAPP(c_Power_Opower__class_Opower(X15074),X15073),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(X15074),X15072),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])])). 6.97/7.21 fof(c_0_4479, plain, ![X1116, X1117]:hAPP(c_Set_OCollect(tc_List_Olist(X1117)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1117),tc_fun(X1117,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1117,tc_HOL_Obool),tc_fun(tc_fun(X1117,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1117)),c_Orderings_Oord__class_Oless__eq(tc_fun(X1117,tc_HOL_Obool))),c_List_Oset(X1117))),X1116))=c_List_Olists(X1117,X1116), inference(variable_rename,[status(thm)],[fact_lists__eq__set])). 6.97/7.21 fof(c_0_4480, plain, ![X8366, X8367]:((~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(X8366))),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),X8367)),c_Int_Onat)))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X8367)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8366))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X8367)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8366)))|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(X8366))),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),X8367)),c_Int_Onat))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__number__of])])). 6.97/7.21 fof(c_0_4481, plain, ![X15942, X15943]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X15943)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15942)))|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(X15942))),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),X15943)),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(X15942))),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),X15943)),c_Int_Onat)))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X15943)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15942))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__number__of])])). 6.97/7.21 fof(c_0_4482, plain, ![X13331, X13332, X13333]:((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),esk438_3(X13331,X13332,X13333)),esk439_3(X13331,X13332,X13333))))|hBOOL(hAPP(hAPP(X13331,X13333),X13332))|~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),X13333),X13332))))&((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),esk438_3(X13331,X13332,X13333)),esk439_3(X13331,X13332,X13333))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk439_3(X13331,X13332,X13333)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(X13331,esk438_3(X13331,X13332,X13333)),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)))),esk439_3(X13331,X13332,X13333))))|hBOOL(hAPP(hAPP(X13331,X13333),X13332))|~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),X13333),X13332))))&(~hBOOL(hAPP(hAPP(X13331,esk438_3(X13331,X13332,X13333)),esk439_3(X13331,X13332,X13333)))|hBOOL(hAPP(hAPP(X13331,X13333),X13332))|~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),X13333),X13332)))))), 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])])])])])). 6.97/7.21 fof(c_0_4483, plain, ![X14773, X14774, X14775]:(((c_Groups_Ozero__class_Ozero(X14775)=X14774|c_Groups_Ozero__class_Ozero(X14775)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14775),hAPP(hAPP(c_Power_Opower__class_Opower(X14775),X14774),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(X14775),X14773),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))|~class_Rings_Olinordered__idom(X14775))&(c_Groups_Ozero__class_Ozero(X14775)=X14773|c_Groups_Ozero__class_Ozero(X14775)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14775),hAPP(hAPP(c_Power_Opower__class_Opower(X14775),X14774),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(X14775),X14773),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))|~class_Rings_Olinordered__idom(X14775)))&(c_Groups_Ozero__class_Ozero(X14775)!=X14774|c_Groups_Ozero__class_Ozero(X14775)!=X14773|c_Groups_Ozero__class_Ozero(X14775)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14775),hAPP(hAPP(c_Power_Opower__class_Opower(X14775),X14774),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(X14775),X14773),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))|~class_Rings_Olinordered__idom(X14775))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__eq__zero__iff])])])). 6.97/7.21 fof(c_0_4484, plain, ![X16712, X16713]:(~class_Complete__Lattice_Ocomplete__lattice(X16713)|c_Complete__Lattice_OInf__class_OInf(X16713,hAPP(c_Set_OCollect(X16713),hAPP(hAPP(c_COMBB(tc_fun(X16713,tc_HOL_Obool),tc_HOL_Obool,X16713),c_HOL_OAll(X16713)),hAPP(hAPP(c_COMBB(tc_fun(X16713,tc_HOL_Obool),tc_fun(X16713,tc_HOL_Obool),X16713),hAPP(c_COMBS(X16713,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X16713),c_fimplies),hAPP(hAPP(c_COMBC(X16713,tc_fun(X16713,tc_HOL_Obool),tc_HOL_Obool),c_member(X16713)),X16712)))),hAPP(c_COMBC(X16713,X16713,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X16713))))))=c_Complete__Lattice_OSup__class_OSup(X16713,X16712)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__Inf])])])). 6.97/7.21 cnf(c_0_4485, 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_4422])). 6.97/7.21 fof(c_0_4486, plain, ![X12594, X12595, X12596, X12597]:hAPP(c_Set_OCollect(X12597),hAPP(hAPP(c_COMBB(tc_fun(X12596,tc_HOL_Obool),tc_HOL_Obool,X12597),c_HOL_OAll(X12596)),hAPP(hAPP(c_COMBB(tc_fun(X12596,tc_HOL_Obool),tc_fun(X12596,tc_HOL_Obool),X12597),hAPP(c_COMBS(X12596,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X12596),c_fimplies),hAPP(hAPP(c_COMBC(X12596,tc_fun(X12596,tc_HOL_Obool),tc_HOL_Obool),c_member(X12596)),X12595)))),X12594)))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12596,tc_fun(X12597,tc_HOL_Obool)),X12595),hAPP(hAPP(c_COMBB(tc_fun(X12597,tc_HOL_Obool),tc_fun(X12597,tc_HOL_Obool),X12596),c_Set_OCollect(X12597)),hAPP(c_COMBC(X12597,X12596,tc_HOL_Obool),X12594))), inference(variable_rename,[status(thm)],[fact_Collect__ball__eq])). 6.97/7.21 fof(c_0_4487, plain, ![X11985, X11986]:(~class_Complete__Lattice_Ocomplete__lattice(X11986)|c_Complete__Lattice_OInf__class_OInf(X11986,X11985)=c_Complete__Lattice_OSup__class_OSup(X11986,hAPP(c_Set_OCollect(X11986),hAPP(hAPP(c_COMBB(tc_fun(X11986,tc_HOL_Obool),tc_HOL_Obool,X11986),c_HOL_OAll(X11986)),hAPP(hAPP(c_COMBB(tc_fun(X11986,tc_HOL_Obool),tc_fun(X11986,tc_HOL_Obool),X11986),hAPP(c_COMBS(X11986,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X11986),c_fimplies),hAPP(hAPP(c_COMBC(X11986,tc_fun(X11986,tc_HOL_Obool),tc_HOL_Obool),c_member(X11986)),X11985)))),c_Orderings_Oord__class_Oless__eq(X11986)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__Sup])])])). 6.97/7.21 fof(c_0_4488, plain, ![X8944, X8945, X8946]:((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),esk290_3(X8944,X8945,X8946)),esk291_3(X8944,X8945,X8946))))|hBOOL(hAPP(hAPP(X8944,X8946),X8945))|~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),X8946),X8945))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk290_3(X8944,X8945,X8946)),esk291_3(X8944,X8945,X8946)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk291_3(X8944,X8945,X8946)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(X8944,esk290_3(X8944,X8945,X8946)),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)))),esk291_3(X8944,X8945,X8946))))|hBOOL(hAPP(hAPP(X8944,X8946),X8945))|~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),X8946),X8945))))&(~hBOOL(hAPP(hAPP(X8944,esk290_3(X8944,X8945,X8946)),esk291_3(X8944,X8945,X8946)))|hBOOL(hAPP(hAPP(X8944,X8946),X8945))|~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),X8946),X8945)))))), 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])])])])])). 6.97/7.21 fof(c_0_4489, plain, ![X13872, X13873, X13874, X13875]:hAPP(c_Set_OCollect(tc_prod(X13875,X13874)),hAPP(c_Product__Type_Oprod_Oprod__case(X13875,X13874,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X13875,tc_fun(X13874,tc_HOL_Obool),tc_fun(X13874,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X13874,tc_HOL_Obool),tc_fun(X13874,tc_HOL_Obool)),X13875),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X13874)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X13875),c_fconj),hAPP(hAPP(c_COMBC(X13875,tc_fun(X13875,tc_HOL_Obool),tc_HOL_Obool),c_member(X13875)),X13873)))),hAPP(hAPP(c_COMBC(X13874,tc_fun(X13874,tc_HOL_Obool),tc_HOL_Obool),c_member(X13874)),X13872))))=c_Nitpick_Oprod(X13875,X13874,X13873,X13872), inference(variable_rename,[status(thm)],[fact_Nitpick_Oprod__def])). 6.97/7.21 cnf(c_0_4490, 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_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(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Set_OCollect(X2),X4)))), inference(split_conjunct,[status(thm)],[c_0_4423])). 6.97/7.21 fof(c_0_4491, plain, ![X3398, X3399, X3400]:(~class_Groups_Omonoid__mult(X3400)|hAPP(hAPP(c_Power_Opower__class_Opower(X3400),X3399),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)))),X3398)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3400),X3399),hAPP(hAPP(c_Power_Opower__class_Opower(X3400),hAPP(hAPP(c_Power_Opower__class_Opower(X3400),X3399),X3398)),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])])). 6.97/7.21 fof(c_0_4492, plain, ![X11555, X11556, X11557]:(~class_Rings_Oring__1(X11557)|hAPP(hAPP(c_Power_Opower__class_Opower(X11557),hAPP(c_Groups_Ouminus__class_Ouminus(X11557),X11556)),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)))),X11555))=hAPP(hAPP(c_Power_Opower__class_Opower(X11557),X11556),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)))),X11555))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus__even])])). 6.97/7.21 fof(c_0_4493, plain, ![X5161, X5162, X5163]:(~class_Groups_Omonoid__mult(X5163)|hAPP(hAPP(c_Power_Opower__class_Opower(X5163),hAPP(hAPP(c_Power_Opower__class_Opower(X5163),X5162),X5161)),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(X5163),X5162),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)))),X5161))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__even__eq])])])). 6.97/7.21 fof(c_0_4494, plain, ![X7162, X7163, X7164]:(~hBOOL(hAPP(c_List_Odistinct(X7164),X7163))|(~hBOOL(hAPP(hAPP(c_member(X7164),X7162),hAPP(c_List_Oset(X7164),X7163)))|hAPP(hAPP(c_List_Olist_OCons(X7164),X7162),hAPP(c_List_Orev(X7164),c_List_OtakeWhile(X7164,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7164),c_fNot),hAPP(hAPP(c_COMBC(X7164,X7164,tc_HOL_Obool),c_fequal),X7162)),X7163)))=c_List_OdropWhile(X7164,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7164),c_fNot),hAPP(hAPP(c_COMBC(X7164,X7164,tc_HOL_Obool),c_fequal),X7162)),hAPP(c_List_Orev(X7164),X7163)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dropWhile__neq__rev])])])). 6.97/7.21 fof(c_0_4495, plain, ![X12504, X12505, X12506]:c_List_OdropWhile(X12506,X12505,X12504)=hAPP(hAPP(c_List_Odrop(X12506),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12506)),c_List_OtakeWhile(X12506,X12505,X12504))),X12504), inference(variable_rename,[status(thm)],[fact_dropWhile__eq__drop])). 6.97/7.21 fof(c_0_4496, plain, ![X1197, X1198, X1199, X1200, X1201]:hAPP(c_Hilbert__Choice_Oinv__into(X1201,X1200,X1199,X1198),X1197)=c_Hilbert__Choice_OEps(X1201,hAPP(hAPP(c_COMBS(X1201,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1201),c_fconj),hAPP(hAPP(c_COMBC(X1201,tc_fun(X1201,tc_HOL_Obool),tc_HOL_Obool),c_member(X1201)),X1199))),hAPP(hAPP(c_COMBC(X1201,X1200,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X1200,tc_fun(X1200,tc_HOL_Obool),X1201),c_fequal),X1198)),X1197))), inference(variable_rename,[status(thm)],[fact_inv__into__def])). 6.97/7.21 cnf(c_0_4497, 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_4424])). 6.97/7.21 fof(c_0_4498, plain, ![X7228, X7229, X7230]:(~class_Rings_Ocomm__semiring__1(X7230)|hAPP(hAPP(c_Power_Opower__class_Opower(X7230),X7229),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)))),X7228)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7230),X7229),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7230),hAPP(hAPP(c_Power_Opower__class_Opower(X7230),X7229),X7228)),hAPP(hAPP(c_Power_Opower__class_Opower(X7230),X7229),X7228)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J])])). 6.97/7.21 fof(c_0_4499, plain, ![X10313, X10314]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X10314),X10313))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X10314)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X10313)), inference(variable_rename,[status(thm)],[fact_zminus__zadd__distrib])). 6.97/7.21 fof(c_0_4500, plain, ![X11457, X11458]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X11458),X11457)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11458),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11457)), inference(variable_rename,[status(thm)],[fact_diff__int__def__symmetric])). 6.97/7.21 fof(c_0_4501, plain, ![X8137, X8138]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8138)),hAPP(c_Nat_OSuc,X8137)))|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(X8138))),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)),X8137)))))&(~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(X8138))),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)),X8137))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8138)),hAPP(c_Nat_OSuc,X8137))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of__Suc])])). 6.97/7.21 fof(c_0_4502, plain, ![X16199, X16200]:((~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(X16200))),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)),X16199))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X16200)),hAPP(c_Nat_OSuc,X16199))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X16200)),hAPP(c_Nat_OSuc,X16199)))|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(X16200))),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)),X16199)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__number__of__Suc])])). 6.97/7.21 fof(c_0_4503, plain, ![X6591, X6592, X6593, X6596, X6597, X6598, X6599, X6600]:((((hBOOL(hAPP(hAPP(c_member(X6593),esk217_3(X6591,X6592,X6593)),X6592))|hBOOL(hAPP(hAPP(c_member(tc_prod(X6593,X6593)),esk216_3(X6591,X6592,X6593)),X6591))|c_Relation_Orefl__on(X6593,X6592,X6591))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X6593,X6593)),hAPP(hAPP(c_Product__Type_OPair(X6593,X6593),esk217_3(X6591,X6592,X6593)),esk217_3(X6591,X6592,X6593))),X6591))|hBOOL(hAPP(hAPP(c_member(tc_prod(X6593,X6593)),esk216_3(X6591,X6592,X6593)),X6591))|c_Relation_Orefl__on(X6593,X6592,X6591)))&((hBOOL(hAPP(hAPP(c_member(X6593),esk217_3(X6591,X6592,X6593)),X6592))|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6593,X6593,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X6593,tc_fun(X6593,tc_HOL_Obool),tc_fun(X6593,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X6593,tc_HOL_Obool),tc_fun(X6593,tc_HOL_Obool)),X6593),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X6593)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X6593),c_fconj),hAPP(hAPP(c_COMBC(X6593,tc_fun(X6593,tc_HOL_Obool),tc_HOL_Obool),c_member(X6593)),X6592)))),hAPP(hAPP(c_COMBC(X6593,tc_fun(X6593,tc_HOL_Obool),tc_HOL_Obool),c_member(X6593)),X6592))),esk216_3(X6591,X6592,X6593)))|c_Relation_Orefl__on(X6593,X6592,X6591))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X6593,X6593)),hAPP(hAPP(c_Product__Type_OPair(X6593,X6593),esk217_3(X6591,X6592,X6593)),esk217_3(X6591,X6592,X6593))),X6591))|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6593,X6593,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X6593,tc_fun(X6593,tc_HOL_Obool),tc_fun(X6593,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X6593,tc_HOL_Obool),tc_fun(X6593,tc_HOL_Obool)),X6593),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X6593)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X6593),c_fconj),hAPP(hAPP(c_COMBC(X6593,tc_fun(X6593,tc_HOL_Obool),tc_HOL_Obool),c_member(X6593)),X6592)))),hAPP(hAPP(c_COMBC(X6593,tc_fun(X6593,tc_HOL_Obool),tc_HOL_Obool),c_member(X6593)),X6592))),esk216_3(X6591,X6592,X6593)))|c_Relation_Orefl__on(X6593,X6592,X6591))))&((~hBOOL(hAPP(hAPP(c_member(tc_prod(X6598,X6598)),X6599),X6596))|hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6598,X6598,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X6598,tc_fun(X6598,tc_HOL_Obool),tc_fun(X6598,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X6598,tc_HOL_Obool),tc_fun(X6598,tc_HOL_Obool)),X6598),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X6598)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X6598),c_fconj),hAPP(hAPP(c_COMBC(X6598,tc_fun(X6598,tc_HOL_Obool),tc_HOL_Obool),c_member(X6598)),X6597)))),hAPP(hAPP(c_COMBC(X6598,tc_fun(X6598,tc_HOL_Obool),tc_HOL_Obool),c_member(X6598)),X6597))),X6599))|~c_Relation_Orefl__on(X6598,X6597,X6596))&(~hBOOL(hAPP(hAPP(c_member(X6598),X6600),X6597))|hBOOL(hAPP(hAPP(c_member(tc_prod(X6598,X6598)),hAPP(hAPP(c_Product__Type_OPair(X6598,X6598),X6600),X6600)),X6596))|~c_Relation_Orefl__on(X6598,X6597,X6596)))), 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])])])])])])])). 6.97/7.21 fof(c_0_4504, plain, ![X2895, X2896]:(~class_Rings_Olinordered__idom(X2896)|hAPP(c_Groups_Oabs__class_Oabs(X2896),hAPP(hAPP(c_Power_Opower__class_Opower(X2896),X2895),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(X2896),X2895),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_abs__power2])])). 6.97/7.21 fof(c_0_4505, plain, ![X10057, X10058]:(~class_Rings_Olinordered__idom(X10058)|hAPP(hAPP(c_Power_Opower__class_Opower(X10058),hAPP(c_Groups_Oabs__class_Oabs(X10058),X10057)),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(X10058),X10057),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__abs])])). 6.97/7.21 fof(c_0_4506, plain, ![X15557, X15558]:(~class_Rings_Oring__1(X15558)|hAPP(hAPP(c_Power_Opower__class_Opower(X15558),X15557),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(X15558),hAPP(c_Groups_Ouminus__class_Ouminus(X15558),X15557)),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])])). 6.97/7.21 fof(c_0_4507, plain, ![X7710, X7711]:(~class_Rings_Osemiring__1(X7711)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7710))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7711),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)))),X7710)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7711),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7711),hAPP(c_Int_Onat,X7710))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7711),hAPP(c_Int_Onat,X7710))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__double])])])). 6.97/7.21 fof(c_0_4508, plain, ![X6775, X6776, X6777]:(~class_Rings_Ocomm__semiring__1(X6777)|hAPP(hAPP(c_Power_Opower__class_Opower(X6777),X6776),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)))),X6775))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6777),hAPP(hAPP(c_Power_Opower__class_Opower(X6777),X6776),X6775)),hAPP(hAPP(c_Power_Opower__class_Opower(X6777),X6776),X6775))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J])])). 6.97/7.21 fof(c_0_4509, plain, ![X10714, X10715]:(((~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),X10715),X10714)))|c_Divides_OnegDivAlg(X10715,X10714)=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),X10715),X10714)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10714),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Divides_OnegDivAlg(X10715,X10714)=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),X10715),X10714))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10714),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),X10715),X10714)))|c_Divides_OnegDivAlg(X10715,X10714)=hAPP(c_Divides_Oadjust(X10714),c_Divides_OnegDivAlg(X10715,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)))),X10714))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg_Osimps])])])). 6.97/7.21 fof(c_0_4510, plain, ![X3086]:((~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,X3086,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,X3086,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,X3086,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,X3086,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])])). 6.97/7.21 fof(c_0_4511, plain, ![X9597, X9598, X9599]:(~hBOOL(hAPP(c_List_Odistinct(X9599),X9598))|(~hBOOL(hAPP(hAPP(c_member(X9599),X9597),hAPP(c_List_Oset(X9599),X9598)))|hAPP(c_List_Orev(X9599),hAPP(c_List_Otl(X9599),c_List_OdropWhile(X9599,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X9599),c_fNot),hAPP(hAPP(c_COMBC(X9599,X9599,tc_HOL_Obool),c_fequal),X9597)),X9598)))=c_List_OtakeWhile(X9599,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X9599),c_fNot),hAPP(hAPP(c_COMBC(X9599,X9599,tc_HOL_Obool),c_fequal),X9597)),hAPP(c_List_Orev(X9599),X9598)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_takeWhile__neq__rev])])])). 6.97/7.21 fof(c_0_4512, plain, ![X2529, X2530, X2531]:hAPP(hAPP(c_List_Odrop(X2531),X2530),hAPP(c_List_Otl(X2531),X2529))=hAPP(c_List_Otl(X2531),hAPP(hAPP(c_List_Odrop(X2531),X2530),X2529)), inference(variable_rename,[status(thm)],[fact_drop__tl])). 6.97/7.21 fof(c_0_4513, plain, ![X13858, X13859, X13860]:hAPP(hAPP(c_List_Odrop(X13860),hAPP(c_Nat_OSuc,X13859)),X13858)=hAPP(hAPP(c_List_Odrop(X13860),X13859),hAPP(c_List_Otl(X13860),X13858)), inference(variable_rename,[status(thm)],[fact_drop__Suc])). 6.97/7.21 fof(c_0_4514, plain, ![X12407, X12408]:((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),X12407),X12408)))|c_Divides_OnegDivAlg(X12407,X12408)=hAPP(c_Divides_Oadjust(X12408),c_Divides_OnegDivAlg(X12407,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)))),X12408)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12408)))&(~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),X12407),X12408)))|c_Divides_OnegDivAlg(X12407,X12408)=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),X12407),X12408))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12408)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_negDivAlg__eqn])])])])). 6.97/7.21 fof(c_0_4515, plain, ![X3155, X3156, X3157]:(~class_Rings_Olinordered__idom(X3157)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3157),X3156),c_Groups_Ozero__class_Ozero(X3157)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3157),hAPP(hAPP(c_Power_Opower__class_Opower(X3157),X3156),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)))),X3155)))),c_Groups_Ozero__class_Ozero(X3157))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_odd__power__less__zero])])). 6.97/7.21 fof(c_0_4516, plain, ![X14914, X14915, X14916]:((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),X14915)))|c_Groups_Oone__class_Oone(X14916)=hAPP(hAPP(c_Power_Opower__class_Opower(X14916),X14914),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X14915)))|~class_Int_Onumber__ring(X14916))&(~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),X14915)))|hAPP(hAPP(c_HOL_OLet(X14916,X14916),hAPP(hAPP(c_Power_Opower__class_Opower(X14916),X14914),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X14915))),hAPP(hAPP(c_COMBS(X14916,X14916,X14916),hAPP(hAPP(c_COMBB(X14916,tc_fun(X14916,X14916),X14916),c_Groups_Otimes__class_Otimes(X14916)),hAPP(c_Groups_Otimes__class_Otimes(X14916),X14914))),c_COMBI(X14916)))=hAPP(hAPP(c_Power_Opower__class_Opower(X14916),X14914),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X14915)))|~class_Int_Onumber__ring(X14916))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__number__of__odd])])])])). 6.97/7.21 fof(c_0_4517, plain, ![X7890, X7891]:((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),X7891)))|c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X7890),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X7891))))&(~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),X7891)))|hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X7890),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7891))),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),X7890))),c_COMBI(tc_Int_Oint)))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X7890),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X7891))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zpower__number__of__odd])])])). 6.97/7.21 fof(c_0_4518, plain, ![X4469, X4470]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4470),X4469))|c_Divides_OposDivAlg(X4470,X4469)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4470))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4469),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Divides_OposDivAlg(X4470,X4469)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4470)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4470),X4469))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4469),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Divides_OposDivAlg(X4470,X4469)=hAPP(c_Divides_Oadjust(X4469),c_Divides_OposDivAlg(X4470,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)))),X4469))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_posDivAlg_Osimps])])])])). 6.97/7.21 fof(c_0_4519, plain, ![X17022, X17023]:(~class_Groups_Omonoid__mult(X17023)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17023),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17023),X17022),X17022)),X17022)=hAPP(hAPP(c_Power_Opower__class_Opower(X17023),X17022),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power3__eq__cube])])])). 6.97/7.21 cnf(c_0_4520, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))=hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), inference(split_conjunct,[status(thm)],[fact_numeral__3__eq__3])). 6.97/7.21 fof(c_0_4521, plain, ![X6558]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6558))|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),X6558),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)],[inference(fof_simplification,[status(thm)],[fact_Suc__n__div__2__gt__zero])])])). 6.97/7.21 fof(c_0_4522, plain, ![X7689, X7690, X7691]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7691)),hAPP(hAPP(c_List_Otake(X7691),X7690),X7689))=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7691)),X7689)),X7690), inference(variable_rename,[status(thm)],[fact_length__take])). 6.97/7.21 fof(c_0_4523, plain, ![X13689, X13690]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13689),X13690))|c_Divides_OposDivAlg(X13689,X13690)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13689)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13690)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13689),X13690))|hAPP(c_Divides_Oadjust(X13690),c_Divides_OposDivAlg(X13689,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)))),X13690)))=c_Divides_OposDivAlg(X13689,X13690)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13690)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_posDivAlg__eqn])])])])). 6.97/7.21 fof(c_0_4524, plain, ![X11892, X11893]:(~class_Rings_Oring__1(X11893)|hAPP(hAPP(c_Power_Opower__class_Opower(X11893),hAPP(c_Groups_Ouminus__class_Ouminus(X11893),c_Groups_Oone__class_Oone(X11893))),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)))),X11892)))=hAPP(c_Groups_Ouminus__class_Ouminus(X11893),c_Groups_Oone__class_Oone(X11893))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__minus1__odd])])])). 6.97/7.21 fof(c_0_4525, plain, ![X15956, X15957, X15958]:(~class_Rings_Olinordered__idom(X15958)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15958),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15958),hAPP(hAPP(c_Power_Opower__class_Opower(X15958),X15957),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(X15958),X15956),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X15958)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__sum__power2__lt__zero])])])). 6.97/7.21 fof(c_0_4526, plain, ![X7423, X7424, X7425, X7426, X7427]:(~c_Fun_Oinj__on(X7427,X7426,X7425,hAPP(hAPP(c_Set_Oinsert(X7427),X7424),hAPP(c_List_Oset(X7427),X7423)))|hAPP(hAPP(c_List_Omap(X7427,X7426),X7425),hAPP(c_List_OremoveAll(X7427,X7424),X7423))=hAPP(c_List_OremoveAll(X7426,hAPP(X7425,X7424)),hAPP(hAPP(c_List_Omap(X7427,X7426),X7425),X7423))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__removeAll__inj__on])])). 6.97/7.21 fof(c_0_4527, plain, ![X12056, X12057]:(~class_Int_Onumber__ring(X12057)|hAPP(hAPP(c_Power_Opower__class_Opower(X12057),hAPP(c_Int_Onumber__class_Onumber__of(X12057),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)))),X12056)))=hAPP(c_Int_Onumber__class_Onumber__of(X12057),c_Int_OMin)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__m1__odd])])). 6.97/7.21 fof(c_0_4528, plain, ![X7616, X7617, X7618]:(~class_Rings_Olinordered__idom(X7618)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7618),c_Groups_Ozero__class_Ozero(X7618)),hAPP(hAPP(c_Power_Opower__class_Opower(X7618),X7617),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)))),X7616))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__le__even__power_H])])])). 6.97/7.21 fof(c_0_4529, plain, ![X592, X593]:(~class_Int_Onumber__ring(X593)|~class_Fields_Olinordered__field__inverse__zero(X593)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X593),c_Groups_Ozero__class_Ozero(X593)),X592))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X593),c_Groups_Ozero__class_Ozero(X593)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X593),X592),hAPP(c_Int_Onumber__class_Onumber__of(X593),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_half__gt__zero])])])). 6.97/7.21 fof(c_0_4530, plain, ![X740, X741]:((~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),X741)))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X740))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X741)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X740)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X741)))&(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),X741)))|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),X740)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X741))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X740))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X741))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__number__of__Bit1])])])). 6.97/7.21 fof(c_0_4531, plain, ![X10667, X10668, X10669, X10670, X10671]:(~c_Fun_Oinj__on(X10671,X10670,X10669,c_Orderings_Otop__class_Otop(tc_fun(X10671,tc_HOL_Obool)))|hAPP(hAPP(c_List_Omap(X10671,X10670),X10669),hAPP(c_List_OremoveAll(X10671,X10668),X10667))=hAPP(c_List_OremoveAll(X10670,hAPP(X10669,X10668)),hAPP(hAPP(c_List_Omap(X10671,X10670),X10669),X10667))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__removeAll__inj])])). 6.97/7.21 fof(c_0_4532, plain, ![X4606, X4607]:(~class_Rings_Oring__1(X4607)|c_Groups_Oone__class_Oone(X4607)=hAPP(hAPP(c_Power_Opower__class_Opower(X4607),hAPP(c_Groups_Ouminus__class_Ouminus(X4607),c_Groups_Oone__class_Oone(X4607))),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)))),X4606))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus1__even])])). 6.97/7.21 fof(c_0_4533, plain, ![X7907]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X7907))|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),X7907),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_div__2__gt__zero])])). 6.97/7.21 fof(c_0_4534, plain, ![X17264, X17265]:(~class_Int_Onumber__ring(X17265)|hAPP(hAPP(c_Power_Opower__class_Opower(X17265),hAPP(c_Int_Onumber__class_Onumber__of(X17265),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)))),X17264))=c_Groups_Oone__class_Oone(X17265)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__m1__even])])])). 6.97/7.21 fof(c_0_4535, plain, ![X8760]:((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8760)))|hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8760)),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(X8760)))&(~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8760)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X8760))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__number__of__Bit1])])])). 6.97/7.21 fof(c_0_4536, plain, ![X3850, X3851, X3852]:(~class_Rings_Oring__1(X3852)|~class_Rings_Oinverse(X3852)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3852),hAPP(c_Int_Oring__1__class_Oof__int(X3852),hAPP(c_Nitpick_Onum(X3851),X3850))),hAPP(c_Int_Oring__1__class_Oof__int(X3852),hAPP(c_Nitpick_Odenom(X3851),X3850)))=c_Nitpick_Oof__frac(X3851,X3852,X3850)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Oof__frac__def])])). 6.97/7.21 fof(c_0_4537, plain, ![X10849]:c_Nitpick_Odenom(X10849)=hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X10849,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X10849)), inference(variable_rename,[status(thm)],[fact_Nitpick_Odenom__def])). 6.97/7.21 fof(c_0_4538, plain, ![X2106]:hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X2106,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X2106))=c_Nitpick_Onum(X2106), inference(variable_rename,[status(thm)],[fact_Nitpick_Onum__def])). 6.97/7.21 fof(c_0_4539, plain, ![X4439, X4440]:(~class_Rings_Olinordered__idom(X4440)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4440),c_Groups_Ozero__class_Ozero(X4440)),hAPP(hAPP(c_Power_Opower__class_Opower(X4440),X4439),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])])])). 6.97/7.21 fof(c_0_4540, plain, ![X2761, X2762]:(~class_Int_Onumber__ring(X2762)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2762),X2761),X2761)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2762),hAPP(c_Int_Onumber__class_Onumber__of(X2762),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2761)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__2])])])). 6.97/7.21 fof(c_0_4541, plain, ![X14952, X14953]:(~class_Int_Onumber__ring(X14953)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14953),X14952),hAPP(c_Int_Onumber__class_Onumber__of(X14953),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14953),X14952),X14952)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2__right])])). 6.97/7.21 fof(c_0_4542, plain, ![X17599, X17600]:(~class_Groups_Omonoid__mult(X17600)|hAPP(hAPP(c_Power_Opower__class_Opower(X17600),X17599),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(X17600),X17599),X17599)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power2__eq__square])])])). 6.97/7.21 fof(c_0_4543, plain, ![X2927, X2928]:(~class_Rings_Ocomm__semiring__1(X2928)|hAPP(hAPP(c_Power_Opower__class_Opower(X2928),X2927),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(X2928),X2927),X2927)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J])])). 6.97/7.21 fof(c_0_4544, plain, ![X14253, X14254, X14255, X14256]:((X14255=X14256|hAPP(c_List_OremoveAll(X14254,X14256),hAPP(hAPP(c_List_Olist_OCons(X14254),X14255),X14253))=hAPP(hAPP(c_List_Olist_OCons(X14254),X14255),hAPP(c_List_OremoveAll(X14254,X14256),X14253)))&(X14255!=X14256|hAPP(c_List_OremoveAll(X14254,X14256),hAPP(hAPP(c_List_Olist_OCons(X14254),X14255),X14253))=hAPP(c_List_OremoveAll(X14254,X14256),X14253))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_removeAll_Osimps_I2_J])])])). 6.97/7.21 fof(c_0_4545, plain, ![X16060]:(~class_Int_Onumber__ring(X16060)|hAPP(c_Int_Onumber__class_Onumber__of(X16060),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16060),c_Groups_Oone__class_Oone(X16060)),c_Groups_Oone__class_Oone(X16060))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__add__one__is__two])])). 6.97/7.21 fof(c_0_4546, plain, ![X7019, X7020]:((c_Groups_Ozero__class_Ozero(X7020)!=hAPP(hAPP(c_Power_Opower__class_Opower(X7020),X7019),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|X7019=c_Groups_Ozero__class_Ozero(X7020)|~class_Rings_Oring__1__no__zero__divisors(X7020))&(X7019!=c_Groups_Ozero__class_Ozero(X7020)|c_Groups_Ozero__class_Ozero(X7020)=hAPP(hAPP(c_Power_Opower__class_Opower(X7020),X7019),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(X7020))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__eq__power2])])])])). 6.97/7.21 fof(c_0_4547, plain, ![X11737]:(~class_Rings_Osemiring__1(X11737)|c_Groups_Oone__class_Oone(X11737)=hAPP(hAPP(c_Power_Opower__class_Opower(X11737),c_Groups_Oone__class_Oone(X11737)),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_one__power2])])). 6.97/7.21 fof(c_0_4548, plain, ![X15398]:(~class_Rings_Osemiring__1(X15398)|c_Groups_Ozero__class_Ozero(X15398)=hAPP(hAPP(c_Power_Opower__class_Opower(X15398),c_Groups_Ozero__class_Ozero(X15398)),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_zero__power2])])). 6.97/7.21 fof(c_0_4549, plain, ![X11132, X11133]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11133),X11132)),X11132)=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X11133),X11132), inference(variable_rename,[status(thm)],[fact_nat__minus__add__max])). 6.97/7.21 fof(c_0_4550, plain, ![X14067, X14068]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14068),X14067)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14067),X14068), inference(variable_rename,[status(thm)],[fact_nat__add__commute])). 6.97/7.21 fof(c_0_4551, plain, ![X8742, X8743, X8744]:(~class_Rings_Olinordered__idom(X8744)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8744),c_Groups_Ozero__class_Ozero(X8744)),hAPP(hAPP(c_Power_Opower__class_Opower(X8744),X8743),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)))),X8742)))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8744),c_Groups_Ozero__class_Ozero(X8744)),X8743)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_odd__0__le__power__imp__0__le])])])). 6.97/7.21 fof(c_0_4552, plain, ![X8082, X8083, X8084]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8084,tc_HOL_Obool)),hAPP(c_Set_OCollect(X8084),X8083)),hAPP(c_Set_OCollect(X8084),X8082))=hAPP(c_Set_OCollect(X8084),hAPP(hAPP(c_COMBS(X8084,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X8084),c_fdisj),X8083)),X8082)), inference(variable_rename,[status(thm)],[fact_Collect__disj__eq])). 6.97/7.21 fof(c_0_4553, plain, ![X1643, X1644]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),X1644))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1643)),X1644)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1643),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1644),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Suc__diff__eq__diff__pred])])])). 6.97/7.21 cnf(c_0_4554, 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_4425])). 6.97/7.21 fof(c_0_4555, plain, ![X12856, X12857, X12858, X12859]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12859),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12858)),c_List_OdropWhile(X12858,X12857,X12856))))|hAPP(hAPP(c_List_Onth(X12858),c_List_OdropWhile(X12858,X12857,X12856)),X12859)=hAPP(hAPP(c_List_Onth(X12858),X12856),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12859),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12858)),c_List_OtakeWhile(X12858,X12857,X12856))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dropWhile__nth])])). 6.97/7.21 fof(c_0_4556, plain, ![X11883, X11884]:(~class_Int_Onumber__ring(X11884)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X11884),hAPP(c_Int_Onumber__class_Onumber__of(X11884),X11883)),c_Groups_Oone__class_Oone(X11884))=hAPP(c_Int_Onumber__class_Onumber__of(X11884),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11883),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)],[inference(fof_simplification,[status(thm)],[fact_diff__special_I2_J])])])). 6.97/7.21 fof(c_0_4557, plain, ![X15591, X15592]:(~class_Int_Onumber__ring(X15592)|hAPP(c_Int_Onumber__class_Onumber__of(X15592),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),X15591)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15592),c_Groups_Oone__class_Oone(X15592)),hAPP(c_Int_Onumber__class_Onumber__of(X15592),X15591))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__special_I1_J])])). 6.97/7.21 cnf(c_0_4558, plain, (X2=c_Groups_Oone__class_Oone(X1)|hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))=X2|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_Oone__class_Oone(X1)|~class_Rings_Oring__1__no__zero__divisors(X1)), inference(split_conjunct,[status(thm)],[c_0_4426])). 6.97/7.21 cnf(c_0_4559, plain, (X1=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|~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_4427])). 6.97/7.21 cnf(c_0_4560, 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_4428])). 6.97/7.21 cnf(c_0_4561, 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_4429])). 6.97/7.21 fof(c_0_4562, plain, ![X1236, X1237]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1237),c_Groups_Ozero__class_Ozero(X1237)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1237),X1236),hAPP(c_Int_Onumber__class_Onumber__of(X1237),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1237),c_Groups_Ozero__class_Ozero(X1237)),X1236))|(~class_Int_Onumber__ring(X1237)|~class_Fields_Olinordered__field__inverse__zero(X1237)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1237),c_Groups_Ozero__class_Ozero(X1237)),X1236))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1237),c_Groups_Ozero__class_Ozero(X1237)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1237),X1236),hAPP(c_Int_Onumber__class_Onumber__of(X1237),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|(~class_Int_Onumber__ring(X1237)|~class_Fields_Olinordered__field__inverse__zero(X1237)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_half__gt__zero__iff])])])). 6.97/7.21 fof(c_0_4563, plain, ![X10194]:c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X10194)=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),X10194),c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(variable_rename,[status(thm)],[fact_negDivAlg__minus1])). 6.97/7.21 cnf(c_0_4564, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Int_Opred(X1)), inference(split_conjunct,[status(thm)],[c_0_4430])). 6.97/7.21 cnf(c_0_4565, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)=c_Int_Opred(X1)), inference(split_conjunct,[status(thm)],[c_0_4431])). 6.97/7.21 fof(c_0_4566, plain, ![X16472, X16473, X16474, X16475, X16476]:(hAPP(c_Product__Type_Ofst(X16476,X16475),hAPP(hAPP(c_Product__Type_OPair(X16476,X16475),X16474),X16473))!=X16472|X16472=X16474), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fst__eqD])])). 6.97/7.21 fof(c_0_4567, plain, ![X9013, X9014]:(~class_Int_Onumber__ring(X9014)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9014),c_Groups_Oone__class_Oone(X9014)),hAPP(c_Int_Onumber__class_Onumber__of(X9014),X9013))=hAPP(c_Int_Onumber__class_Onumber__of(X9014),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X9013))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__special_I2_J])])])). 6.97/7.21 fof(c_0_4568, plain, ![X2318, X2319]:(~class_Int_Onumber__ring(X2319)|hAPP(c_Int_Onumber__class_Onumber__of(X2319),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2318),c_Int_OBit1(c_Int_OPls)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2319),hAPP(c_Int_Onumber__class_Onumber__of(X2319),X2318)),c_Groups_Oone__class_Oone(X2319))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__special_I3_J])])). 6.97/7.21 fof(c_0_4569, plain, ![X1980, X1981, X1982, X1983]:((((~hBOOL(hAPP(hAPP(c_member(X1983),X1981),X1982))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1983,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1983,tc_HOL_Obool)),X1982),hAPP(hAPP(c_Set_Oinsert(X1983),X1981),c_Orderings_Obot__class_Obot(tc_fun(X1983,tc_HOL_Obool))))),X1980))|hBOOL(hAPP(hAPP(c_member(X1983),X1981),X1980))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1983,tc_HOL_Obool)),X1982),hAPP(hAPP(c_Set_Oinsert(X1983),X1981),X1980))))&(hBOOL(hAPP(hAPP(c_member(X1983),X1981),X1982))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1983,tc_HOL_Obool)),X1982),X1980))|hBOOL(hAPP(hAPP(c_member(X1983),X1981),X1980))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1983,tc_HOL_Obool)),X1982),hAPP(hAPP(c_Set_Oinsert(X1983),X1981),X1980)))))&(~hBOOL(hAPP(hAPP(c_member(X1983),X1981),X1980))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1983,tc_HOL_Obool)),X1982),X1980))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1983,tc_HOL_Obool)),X1982),hAPP(hAPP(c_Set_Oinsert(X1983),X1981),X1980)))))&(((hBOOL(hAPP(hAPP(c_member(X1983),X1981),X1980))|~hBOOL(hAPP(hAPP(c_member(X1983),X1981),X1980))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1983,tc_HOL_Obool)),X1982),hAPP(hAPP(c_Set_Oinsert(X1983),X1981),X1980))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1983,tc_HOL_Obool)),X1982),X1980))|~hBOOL(hAPP(hAPP(c_member(X1983),X1981),X1980))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1983,tc_HOL_Obool)),X1982),hAPP(hAPP(c_Set_Oinsert(X1983),X1981),X1980)))))&((((hBOOL(hAPP(hAPP(c_member(X1983),X1981),X1980))|(~hBOOL(hAPP(hAPP(c_member(X1983),X1981),X1982))|hBOOL(hAPP(hAPP(c_member(X1983),X1981),X1982)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1983,tc_HOL_Obool)),X1982),hAPP(hAPP(c_Set_Oinsert(X1983),X1981),X1980))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1983,tc_HOL_Obool)),X1982),X1980))|(~hBOOL(hAPP(hAPP(c_member(X1983),X1981),X1982))|hBOOL(hAPP(hAPP(c_member(X1983),X1981),X1982)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1983,tc_HOL_Obool)),X1982),hAPP(hAPP(c_Set_Oinsert(X1983),X1981),X1980)))))&((hBOOL(hAPP(hAPP(c_member(X1983),X1981),X1980))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1983,tc_HOL_Obool)),X1982),X1980))|hBOOL(hAPP(hAPP(c_member(X1983),X1981),X1982)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1983,tc_HOL_Obool)),X1982),hAPP(hAPP(c_Set_Oinsert(X1983),X1981),X1980))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1983,tc_HOL_Obool)),X1982),X1980))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1983,tc_HOL_Obool)),X1982),X1980))|hBOOL(hAPP(hAPP(c_member(X1983),X1981),X1982)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1983,tc_HOL_Obool)),X1982),hAPP(hAPP(c_Set_Oinsert(X1983),X1981),X1980))))))&(((hBOOL(hAPP(hAPP(c_member(X1983),X1981),X1980))|(~hBOOL(hAPP(hAPP(c_member(X1983),X1981),X1982))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1983,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1983,tc_HOL_Obool)),X1982),hAPP(hAPP(c_Set_Oinsert(X1983),X1981),c_Orderings_Obot__class_Obot(tc_fun(X1983,tc_HOL_Obool))))),X1980)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1983,tc_HOL_Obool)),X1982),hAPP(hAPP(c_Set_Oinsert(X1983),X1981),X1980))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1983,tc_HOL_Obool)),X1982),X1980))|(~hBOOL(hAPP(hAPP(c_member(X1983),X1981),X1982))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1983,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1983,tc_HOL_Obool)),X1982),hAPP(hAPP(c_Set_Oinsert(X1983),X1981),c_Orderings_Obot__class_Obot(tc_fun(X1983,tc_HOL_Obool))))),X1980)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1983,tc_HOL_Obool)),X1982),hAPP(hAPP(c_Set_Oinsert(X1983),X1981),X1980)))))&((hBOOL(hAPP(hAPP(c_member(X1983),X1981),X1980))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1983,tc_HOL_Obool)),X1982),X1980))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1983,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1983,tc_HOL_Obool)),X1982),hAPP(hAPP(c_Set_Oinsert(X1983),X1981),c_Orderings_Obot__class_Obot(tc_fun(X1983,tc_HOL_Obool))))),X1980)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1983,tc_HOL_Obool)),X1982),hAPP(hAPP(c_Set_Oinsert(X1983),X1981),X1980))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1983,tc_HOL_Obool)),X1982),X1980))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1983,tc_HOL_Obool)),X1982),X1980))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1983,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1983,tc_HOL_Obool)),X1982),hAPP(hAPP(c_Set_Oinsert(X1983),X1981),c_Orderings_Obot__class_Obot(tc_fun(X1983,tc_HOL_Obool))))),X1980)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1983,tc_HOL_Obool)),X1982),hAPP(hAPP(c_Set_Oinsert(X1983),X1981),X1980))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_psubset__insert__iff])])])])). 6.97/7.21 fof(c_0_4570, plain, ![X6523, X6524, X6525]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6525,tc_HOL_Obool)),X6524),X6523))|X6523=X6524|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X6525,tc_HOL_Obool)),X6524),X6523)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6525,tc_HOL_Obool)),X6524),X6523))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X6525,tc_HOL_Obool)),X6524),X6523)))&(X6523!=X6524|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X6525,tc_HOL_Obool)),X6524),X6523))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__eq])])])). 6.97/7.21 fof(c_0_4571, plain, ![X11681, X11682, X11683, X11684, X11685]:(X11681!=hAPP(c_Product__Type_Osnd(X11685,X11684),hAPP(hAPP(c_Product__Type_OPair(X11685,X11684),X11683),X11682))|X11682=X11681), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_snd__eqD])])])). 6.97/7.21 cnf(c_0_4572, 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_4432])). 6.97/7.21 cnf(c_0_4573, 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_4433])). 6.97/7.21 cnf(c_0_4574, plain, (hAPP(c_Set_OCollect(X1),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)),hAPP(c_Set_OCollect(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4434])). 6.97/7.21 fof(c_0_4575, plain, ![X9485, X9486, X9487, X9488]:hAPP(c_List_Ofilter(X9488,X9487),hAPP(c_List_Ofilter(X9488,X9486),X9485))=hAPP(c_List_Ofilter(X9488,hAPP(hAPP(c_COMBS(X9488,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X9488),c_fconj),X9486)),X9487)),X9485), inference(variable_rename,[status(thm)],[fact_filter__filter])). 6.97/7.21 fof(c_0_4576, plain, ![X3030, X3031, X3032]:((~hBOOL(hAPP(X3032,X3031))|hAPP(hAPP(c_Set_Oinsert(X3030),X3031),c_Orderings_Obot__class_Obot(tc_fun(X3030,tc_HOL_Obool)))=hAPP(c_Set_OCollect(X3030),hAPP(hAPP(c_COMBS(X3030,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3030),c_fconj),hAPP(c_fequal,X3031))),X3032)))&(hBOOL(hAPP(X3032,X3031))|c_Orderings_Obot__class_Obot(tc_fun(X3030,tc_HOL_Obool))=hAPP(c_Set_OCollect(X3030),hAPP(hAPP(c_COMBS(X3030,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3030),c_fconj),hAPP(c_fequal,X3031))),X3032)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Collect__conv__if2])])])). 6.97/7.21 fof(c_0_4577, plain, ![X5171, X5172, X5173, X5174]:(((hBOOL(hAPP(X5173,X5172))|c_List_Olist__ex1(X5174,X5173,X5171)|~c_List_Olist__ex1(X5174,X5173,hAPP(hAPP(c_List_Olist_OCons(X5174),X5172),X5171)))&(~hBOOL(hAPP(X5173,X5172))|c_List_Olist__all(X5174,hAPP(hAPP(c_COMBS(X5174,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5174),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5174),c_fNot),X5173))),hAPP(c_fequal,X5172)),X5171)|~c_List_Olist__ex1(X5174,X5173,hAPP(hAPP(c_List_Olist_OCons(X5174),X5172),X5171))))&(((hBOOL(hAPP(X5173,X5172))|~hBOOL(hAPP(X5173,X5172))|c_List_Olist__ex1(X5174,X5173,hAPP(hAPP(c_List_Olist_OCons(X5174),X5172),X5171)))&(~c_List_Olist__all(X5174,hAPP(hAPP(c_COMBS(X5174,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5174),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5174),c_fNot),X5173))),hAPP(c_fequal,X5172)),X5171)|~hBOOL(hAPP(X5173,X5172))|c_List_Olist__ex1(X5174,X5173,hAPP(hAPP(c_List_Olist_OCons(X5174),X5172),X5171))))&((hBOOL(hAPP(X5173,X5172))|~c_List_Olist__ex1(X5174,X5173,X5171)|c_List_Olist__ex1(X5174,X5173,hAPP(hAPP(c_List_Olist_OCons(X5174),X5172),X5171)))&(~c_List_Olist__all(X5174,hAPP(hAPP(c_COMBS(X5174,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5174),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5174),c_fNot),X5173))),hAPP(c_fequal,X5172)),X5171)|~c_List_Olist__ex1(X5174,X5173,X5171)|c_List_Olist__ex1(X5174,X5173,hAPP(hAPP(c_List_Olist_OCons(X5174),X5172),X5171)))))), 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])])])])). 6.97/7.21 fof(c_0_4578, plain, ![X7985, X7986]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X7986)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X7985)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7986)),X7985)))&(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X7986)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X7986))),X7985)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7986)),X7985)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Suc__nat__number__of__add])])])). 6.97/7.21 fof(c_0_4579, plain, ![X3925, X3926, X3927]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X3927),c_Nitpick_Oplus__frac(X3927,X3926,c_Nitpick_Ouminus__frac(X3927,X3925)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Nitpick_Oless__frac(X3927,X3926,X3925))&(~c_Nitpick_Oless__frac(X3927,X3926,X3925)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X3927),c_Nitpick_Oplus__frac(X3927,X3926,c_Nitpick_Ouminus__frac(X3927,X3925)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Oless__frac__def])])). 6.97/7.21 fof(c_0_4580, plain, ![X11304, X11305, X11306]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X11306),c_Nitpick_Oplus__frac(X11306,X11305,c_Nitpick_Ouminus__frac(X11306,X11304)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Nitpick_Oless__eq__frac(X11306,X11305,X11304))&(~c_Nitpick_Oless__eq__frac(X11306,X11305,X11304)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X11306),c_Nitpick_Oplus__frac(X11306,X11305,c_Nitpick_Ouminus__frac(X11306,X11304)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Oless__eq__frac__def])])). 6.97/7.21 fof(c_0_4581, plain, ![X6476, X6477]:((c_Groups_Oone__class_Oone(X6477)!=hAPP(c_Int_Onumber__class_Onumber__of(X6477),X6476)|c_Int_Oiszero(X6477,hAPP(c_Int_Onumber__class_Onumber__of(X6477),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),X6476))))|~class_Int_Onumber__ring(X6477))&(~c_Int_Oiszero(X6477,hAPP(c_Int_Onumber__class_Onumber__of(X6477),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),X6476))))|c_Groups_Oone__class_Oone(X6477)=hAPP(c_Int_Onumber__class_Onumber__of(X6477),X6476)|~class_Int_Onumber__ring(X6477))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I2_J])])])). 6.97/7.21 fof(c_0_4582, plain, ![X4298, X4299]:((~c_Int_Oiszero(X4299,hAPP(c_Int_Onumber__class_Onumber__of(X4299),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4298),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))|hAPP(c_Int_Onumber__class_Onumber__of(X4299),X4298)=c_Groups_Oone__class_Oone(X4299)|~class_Int_Onumber__ring(X4299))&(hAPP(c_Int_Onumber__class_Onumber__of(X4299),X4298)!=c_Groups_Oone__class_Oone(X4299)|c_Int_Oiszero(X4299,hAPP(c_Int_Onumber__class_Onumber__of(X4299),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4298),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))|~class_Int_Onumber__ring(X4299))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I4_J])])])). 6.97/7.21 fof(c_0_4583, plain, ![X11408, X11409, X11410, X11411]:(~class_Groups_Ocomm__monoid__add(X11411)|hAPP(c_List_Omonoid__add__class_Olistsum(X11411),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X11411),X11410),c_List_Oupt(X11409,X11408)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X11411),X11410),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X11409,X11408)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_interv__listsum__conv__setsum__set__nat])])])). 6.97/7.21 fof(c_0_4584, plain, ![X8929, X8930]:hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X8930,X8929))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X8930),X8929), inference(variable_rename,[status(thm)],[fact_set__upt])). 6.97/7.21 fof(c_0_4585, plain, ![X8794, X8795]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8795),X8794))|c_List_Oupt(X8795,hAPP(c_Nat_OSuc,X8794))=hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X8795,X8794)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X8794),c_List_Olist_ONil(tc_Nat_Onat)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_upt__Suc__append])])])). 6.97/7.21 fof(c_0_4586, plain, ![X1104, X1105]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X1104))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1105),c_Groups_Oone__class_Oone(X1105)),hAPP(c_Int_Onumber__class_Onumber__of(X1105),X1104)))|(~class_Rings_Olinordered__idom(X1105)|~class_Int_Onumber__ring(X1105)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1105),c_Groups_Oone__class_Oone(X1105)),hAPP(c_Int_Onumber__class_Onumber__of(X1105),X1104)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X1104))|(~class_Rings_Olinordered__idom(X1105)|~class_Int_Onumber__ring(X1105)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__special_I2_J])])])])). 6.97/7.21 fof(c_0_4587, plain, ![X3438, X3439]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X3438))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3439),c_Groups_Oone__class_Oone(X3439)),hAPP(c_Int_Onumber__class_Onumber__of(X3439),X3438)))|(~class_Int_Onumber__ring(X3439)|~class_Rings_Olinordered__idom(X3439)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3439),c_Groups_Oone__class_Oone(X3439)),hAPP(c_Int_Onumber__class_Onumber__of(X3439),X3438)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X3438))|(~class_Int_Onumber__ring(X3439)|~class_Rings_Olinordered__idom(X3439)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__special_I2_J])])])])). 6.97/7.21 fof(c_0_4588, plain, ![X3327, X3328]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3327),c_Int_OBit1(c_Int_OPls)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3328),hAPP(c_Int_Onumber__class_Onumber__of(X3328),X3327)),c_Groups_Oone__class_Oone(X3328)))|(~class_Int_Onumber__ring(X3328)|~class_Rings_Olinordered__idom(X3328)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3328),hAPP(c_Int_Onumber__class_Onumber__of(X3328),X3327)),c_Groups_Oone__class_Oone(X3328)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3327),c_Int_OBit1(c_Int_OPls)))|(~class_Int_Onumber__ring(X3328)|~class_Rings_Olinordered__idom(X3328)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I4_J])])])). 6.97/7.21 fof(c_0_4589, plain, ![X14917, X14918]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14918),hAPP(c_Int_Onumber__class_Onumber__of(X14918),X14917)),c_Groups_Oone__class_Oone(X14918)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X14917),c_Int_OBit1(c_Int_OPls)))|(~class_Rings_Olinordered__idom(X14918)|~class_Int_Onumber__ring(X14918)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X14917),c_Int_OBit1(c_Int_OPls)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14918),hAPP(c_Int_Onumber__class_Onumber__of(X14918),X14917)),c_Groups_Oone__class_Oone(X14918)))|(~class_Rings_Olinordered__idom(X14918)|~class_Int_Onumber__ring(X14918)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__special_I4_J])])])])). 6.97/7.21 fof(c_0_4590, plain, ![X7825, X7826]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X7826))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X7825)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7826))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X7825),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X7826)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__number__of])])). 6.97/7.21 fof(c_0_4591, plain, ![X10709, X10710, X10711]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10711,X10711),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X10711,X10711),X10710)),c_Transitive__Closure_Ortrancl(X10711,X10710))!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10711,X10711),tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X10711,X10711)),hAPP(hAPP(c_Product__Type_OPair(X10711,X10711),X10709),X10709)),c_Transitive__Closure_Otrancl(X10711,X10710)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_irrefl__tranclI])])])). 6.97/7.21 fof(c_0_4592, plain, ![X4598, X4599]:c_Transitive__Closure_Otrancl(X4599,X4598)=hAPP(hAPP(c_Relation_Orel__comp(X4599,X4599,X4599),X4598),c_Transitive__Closure_Ortrancl(X4599,X4598)), inference(variable_rename,[status(thm)],[fact_trancl__unfold__left])). 6.97/7.21 fof(c_0_4593, plain, ![X3050, X3051, X3052, X3053]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3053),X3052))|hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X3051),X3050)!=c_List_Oupt(X3053,X3052))&(X3051=X3053|hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X3051),X3050)!=c_List_Oupt(X3053,X3052)))&(X3050=c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3053),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3052)|hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X3051),X3050)!=c_List_Oupt(X3053,X3052)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3053),X3052))|X3051!=X3053|X3050!=c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3053),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3052)|hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X3051),X3050)=c_List_Oupt(X3053,X3052))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__eq__Cons__conv])])])). 6.97/7.21 fof(c_0_4594, plain, ![X3658, X3659]:((c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X3659|c_Code__Numeral_Onat__of__aux(X3659,X3658)=c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X3659),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,X3658)))&(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X3659|X3658=c_Code__Numeral_Onat__of__aux(X3659,X3658))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__of__aux__code])])])). 6.97/7.21 fof(c_0_4595, plain, ![X7194, X7195]:c_Code__Numeral_Onat__of__aux(X7195,X7194)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X7195)),X7194), inference(variable_rename,[status(thm)],[fact_nat__of__aux__def])). 6.97/7.21 fof(c_0_4596, plain, ![X1909, X1910]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1910)),X1909)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1910),X1909)), inference(variable_rename,[status(thm)],[fact_add__Suc])). 6.97/7.21 fof(c_0_4597, plain, ![X13007, X13008]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X13008)),X13007)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13008),hAPP(c_Nat_OSuc,X13007)), inference(variable_rename,[status(thm)],[fact_add__Suc__shift])). 6.97/7.21 fof(c_0_4598, plain, ![X13403, X13404]:(~class_Fields_Ofield(X13404)|~class_Int_Onumber__ring(X13404)|X13403=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13404),X13403),hAPP(c_Int_Onumber__class_Onumber__of(X13404),c_Int_OBit1(c_Int_OPls)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__Numeral1])])])). 6.97/7.21 fof(c_0_4599, plain, ![X12532, X12533, X12534]:(hBOOL(hAPP(hAPP(c_member(X12534),X12533),hAPP(c_List_Oset(X12534),X12532)))|hAPP(c_List_OremoveAll(X12534,X12533),X12532)=X12532), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_removeAll__id])])])). 6.97/7.21 fof(c_0_4600, plain, ![X479, X480]:(~class_Int_Onumber__ring(X480)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X480),hAPP(c_Int_Onumber__class_Onumber__of(X480),c_Int_OBit1(c_Int_OPls))),X479)=X479), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__numeral__1])])). 6.97/7.21 fof(c_0_4601, plain, ![X10891, X10892]:(~class_Int_Onumber__ring(X10892)|X10891=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10892),X10891),hAPP(c_Int_Onumber__class_Onumber__of(X10892),c_Int_OBit1(c_Int_OPls)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__numeral__1__right])])])). 6.97/7.21 fof(c_0_4602, plain, ![X5266]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X5266)),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5266),c_Int_OPls)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5266),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X5266)),c_Int_OPls)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I12_J])])). 6.97/7.21 fof(c_0_4603, plain, ![X13032]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X13032)),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13032),c_Int_OPls)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13032),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X13032)),c_Int_OPls)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I29_J])])). 6.97/7.21 fof(c_0_4604, plain, ![X10008]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X10008)))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X10008)))))&(~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X10008))))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X10008))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__Bit1])])). 6.97/7.21 fof(c_0_4605, plain, ![X8804]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X8804))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X8804))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X8804)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X8804)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I5_J])])). 6.97/7.21 fof(c_0_4606, plain, ![X11668]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X11668)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X11668)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X11668))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X11668))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I22_J])])). 6.97/7.21 fof(c_0_4607, plain, ![X12831]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12831),c_Int_OPls))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X12831)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X12831)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12831),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),X12831)),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__number__of__diff__1])])])). 6.97/7.21 fof(c_0_4608, plain, ![X8073]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8073),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),X8073))=c_Groups_Oone__class_Oone(tc_Nat_Onat))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8073),c_Int_OPls))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X8073))=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),X8073)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__1__add__number__of])])])). 6.97/7.21 fof(c_0_4609, plain, ![X7388, X7389, X7390]:(~hBOOL(hAPP(c_List_Odistinct(X7390),X7389))|c_List_Oremove1(X7390,X7388,X7389)=hAPP(c_List_OremoveAll(X7390,X7388),X7389)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__remove1__removeAll])])). 6.97/7.21 fof(c_0_4610, plain, ![X12685]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X12685),c_Int_OPls)=X12685, inference(variable_rename,[status(thm)],[fact_add__Pls__right])). 6.97/7.21 fof(c_0_4611, plain, ![X1795]:(~class_Int_Onumber__ring(X1795)|c_Groups_Oone__class_Oone(X1795)=hAPP(c_Int_Onumber__class_Onumber__of(X1795),c_Int_OBit1(c_Int_OPls))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I110_J])])). 6.97/7.21 fof(c_0_4612, plain, ![X11446]:((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X11446)))|hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X11446))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X11446)))&(~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X11446)))|hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X11446))=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__nat__number__of])])])). 6.97/7.21 fof(c_0_4613, plain, ![X16174]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X16174)),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16174),c_Int_OPls)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16174),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X16174)),c_Int_OPls)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I10_J])])). 6.97/7.21 fof(c_0_4614, plain, ![X10373]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X10373)),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10373),c_Int_OPls)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10373),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X10373)),c_Int_OPls)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I27_J])])). 6.97/7.21 fof(c_0_4615, plain, ![X10981]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X10981))))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X10981))))&(~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X10981)))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X10981)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__Bit0])])). 6.97/7.21 fof(c_0_4616, plain, ![X1750]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1750))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X1750))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X1750)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1750)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I4_J])])). 6.97/7.21 fof(c_0_4617, plain, ![X8777]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X8777)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X8777)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X8777))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X8777))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I21_J])])). 6.97/7.21 fof(c_0_4618, plain, ![X15669, X15670]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15670),X15669))|c_List_Olist_ONil(tc_Nat_Onat)=c_List_Oupt(X15670,hAPP(c_Nat_OSuc,X15669)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15670),X15669))|c_List_Oupt(X15670,hAPP(c_Nat_OSuc,X15669))=hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X15670,X15669)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X15669),c_List_Olist_ONil(tc_Nat_Onat))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_upt__Suc])])])). 6.97/7.21 fof(c_0_4619, plain, ![X12703]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X12703))))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X12703))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X12703)|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X12703)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__pred__iff__0])])). 6.97/7.21 cnf(c_0_4620, 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_4435])). 6.97/7.21 fof(c_0_4621, plain, ![X14763, X14764]:((c_Code__Numeral_OSuc__code__numeral(X14763)!=c_Code__Numeral_OSuc__code__numeral(X14764)|X14763=X14764)&(X14763!=X14764|c_Code__Numeral_OSuc__code__numeral(X14763)=c_Code__Numeral_OSuc__code__numeral(X14764))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral_Oinject])])). 6.97/7.21 fof(c_0_4622, plain, ![X12239]:hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X12239)))=c_Code__Numeral_OSuc__code__numeral(X12239), inference(variable_rename,[status(thm)],[fact_Suc__code__numeral__def])). 6.97/7.21 fof(c_0_4623, plain, ![X12209]:((c_Int_OPls!=X12209|c_Int_OPls=c_Int_OBit0(X12209))&(c_Int_OPls!=c_Int_OBit0(X12209)|c_Int_OPls=X12209)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I38_J])])). 6.97/7.21 fof(c_0_4624, plain, ![X2169]:c_Int_OPls!=c_Int_OBit1(X2169), inference(variable_rename,[status(thm)],[fact_rel__simps_I39_J])). 6.97/7.21 fof(c_0_4625, plain, ![X3975]:c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=c_Code__Numeral_OSuc__code__numeral(X3975), inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I3_J])). 6.97/7.21 fof(c_0_4626, plain, ![X11540, X11541, X11542, X11543]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X11543,X11543),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X11543,X11540)),hAPP(c_Set_OCollect(tc_prod(X11543,X11543)),hAPP(c_Product__Type_Oprod_Oprod__case(X11543,X11543,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X11543,tc_fun(X11543,tc_HOL_Obool),tc_fun(X11543,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X11543,tc_HOL_Obool),tc_fun(X11543,tc_HOL_Obool)),X11543),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X11543)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X11543),c_fconj),hAPP(hAPP(c_COMBC(X11543,tc_fun(tc_prod(X11543,X11543),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X11543,X11543),tc_fun(tc_fun(tc_prod(X11543,X11543),tc_HOL_Obool),tc_HOL_Obool),X11543),c_member(tc_prod(X11543,X11543))),hAPP(hAPP(c_COMBC(X11543,X11543,tc_prod(X11543,X11543)),c_Product__Type_OPair(X11543,X11543)),X11542))),c_Transitive__Closure_Ortrancl(X11543,X11540))))),hAPP(hAPP(c_COMBC(X11543,tc_fun(tc_prod(X11543,X11543),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X11543,X11543),tc_fun(tc_fun(tc_prod(X11543,X11543),tc_HOL_Obool),tc_HOL_Obool),X11543),c_member(tc_prod(X11543,X11543))),hAPP(c_Product__Type_OPair(X11543,X11543),X11541))),c_Transitive__Closure_Ortrancl(X11543,X11540))))))=c_Transitive__Closure_Otrancl(X11543,hAPP(hAPP(c_Set_Oinsert(tc_prod(X11543,X11543)),hAPP(hAPP(c_Product__Type_OPair(X11543,X11543),X11542),X11541)),X11540)), inference(variable_rename,[status(thm)],[fact_trancl__insert])). 6.97/7.21 fof(c_0_4627, plain, ![X13866, X13867, X13868, X13869]:hAPP(hAPP(c_List_Omap(tc_prod(X13869,tc_Nat_Onat),X13869),c_Product__Type_Ofst(X13869,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X13869,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X13869,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(X13869,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X13869,tc_Nat_Onat))),X13868)),hAPP(hAPP(c_List_Ozip(X13869,tc_Nat_Onat),X13867),c_List_Oupt(X13866,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13866),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13869)),X13867))))))=hAPP(hAPP(c_List_Omap(tc_prod(X13869,tc_Nat_Onat),X13869),c_Product__Type_Ofst(X13869,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X13869,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X13869,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(X13869,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X13869,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(X13869,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(X13869,tc_Nat_Onat))),X13866))),X13868)),hAPP(hAPP(c_List_Ozip(X13869,tc_Nat_Onat),X13867),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13869)),X13867))))), inference(variable_rename,[status(thm)],[fact_sublist__shift__lemma])). 6.97/7.21 fof(c_0_4628, plain, ![X9186, X9187, X9188]: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),X9188)),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))),X9187))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X9186)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X9186)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X9188),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X9188),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),X9186),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X9187)))), inference(variable_rename,[status(thm)],[fact_arith__series__int])). 6.97/7.21 fof(c_0_4629, plain, ![X400, X401]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X401)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X400)))=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),X401),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X400))), inference(variable_rename,[status(thm)],[fact_zmod__number__of__Bit0])). 6.97/7.21 fof(c_0_4630, plain, ![X8594, X8595]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X8595))),hAPP(c_List_Ofilter(tc_List_Olist(X8595),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X8595)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X8595),tc_List_Olist(X8595),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X8595)))),X8594))=c_List_Ofoldr(tc_List_Olist(X8595),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X8595)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X8595))),c_List_Otranspose(X8595,X8594),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_transpose__max__length])). 6.97/7.21 cnf(c_0_4631, 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_4436])). 6.97/7.21 cnf(c_0_4632, plain, (hAPP(c_List_Ofoldl(X1,X2,hAPP(c_COMBC(X2,X1,X1),X3),X4),hAPP(c_List_Orev(X2),X5))=c_List_Ofoldr(X2,X1,X3,X5,X4)), inference(split_conjunct,[status(thm)],[c_0_4437])). 6.97/7.21 fof(c_0_4633, plain, ![X11251]: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)))),X11251)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11251),X11251), inference(variable_rename,[status(thm)],[fact_nat__mult__2])). 6.97/7.21 fof(c_0_4634, plain, ![X6221]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6221),X6221)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6221),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])). 6.97/7.21 fof(c_0_4635, plain, ![X6222, X6223, X6224, X6225]:c_List_Oconcat(X6224,hAPP(hAPP(c_List_Omap(tc_List_Olist(X6225),tc_List_Olist(X6224)),hAPP(c_List_Omap(X6225,X6224),X6223)),X6222))=hAPP(hAPP(c_List_Omap(X6225,X6224),X6223),c_List_Oconcat(X6225,X6222)), inference(variable_rename,[status(thm)],[fact_map__concat])). 6.97/7.21 fof(c_0_4636, plain, ![X9092, X9093]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X9093),X9092))),X9092)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(X9093)),X9092), inference(variable_rename,[status(thm)],[fact_mult__Bit1])). 6.97/7.21 fof(c_0_4637, plain, ![X11294, X11295]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X11295)),c_Int_OBit0(X11294))=c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X11295),X11294)), inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I9_J])). 6.97/7.21 fof(c_0_4638, plain, ![X1557, X1558]:c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1558),X1557))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(X1558)),X1557), inference(variable_rename,[status(thm)],[fact_mult__Bit0])). 6.97/7.21 fof(c_0_4639, plain, ![X16602, X16603, X16604, X16605]:c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X16605,X16604,X16603,c_Code__Numeral_OSuc__code__numeral(X16602))=hAPP(hAPP(X16603,X16602),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X16605,X16604,X16603,X16602)), inference(variable_rename,[status(thm)],[fact_code__numeral_Orecs_I2_J])). 6.97/7.21 fof(c_0_4640, plain, ![X17378]: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)),X17378))))),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)),X17378))))),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(X17378), inference(variable_rename,[status(thm)],[fact_adjust__def])). 6.97/7.21 fof(c_0_4641, plain, ![X13347, X13348, X13349]:c_Nitpick_Oplus__frac(X13349,X13348,X13347)=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X13349),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(X13349),X13348),hAPP(c_Nitpick_Odenom(X13349),X13347))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,X13349),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,X13349),tc_Int_Oint),c_Nitpick_Ofrac(X13349)),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(X13349),X13348))),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(X13349),X13348))))),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(X13349),X13347))),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(X13349),X13347)))))),c_COMBI(tc_Int_Oint))), inference(variable_rename,[status(thm)],[fact_Nitpick_Oplus__frac__def])). 6.97/7.21 fof(c_0_4642, plain, ![X17240, X17241, X17242]: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),X17240),X17242)),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)))),X17241)),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)))),X17241)),X17240)))=hAPP(c_Divides_Oadjust(X17242),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X17241),X17240)), inference(variable_rename,[status(thm)],[fact_adjust__eq])). 6.97/7.21 fof(c_0_4643, plain, ![X4630, X4631, X4632, X4633]:hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X4633)),hAPP(hAPP(c_List_Olist_OCons(X4633),X4632),c_List_Oconcat(X4633,hAPP(hAPP(c_List_Omap(tc_List_Olist(X4633),tc_List_Olist(X4633)),c_List_Olist_Olist__case(tc_List_Olist(X4633),X4633,c_List_Olist_ONil(X4633),hAPP(hAPP(c_COMBB(tc_List_Olist(X4633),tc_fun(tc_List_Olist(X4633),tc_List_Olist(X4633)),X4633),c_COMBK(tc_List_Olist(X4633),tc_List_Olist(X4633))),hAPP(hAPP(c_COMBC(X4633,tc_List_Olist(X4633),tc_List_Olist(X4633)),c_List_Olist_OCons(X4633)),c_List_Olist_ONil(X4633))))),X4630)))),c_List_Otranspose(X4633,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X4633)),X4631),c_List_Oconcat(tc_List_Olist(X4633),hAPP(hAPP(c_List_Omap(tc_List_Olist(X4633),tc_List_Olist(tc_List_Olist(X4633))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X4633)),X4633,c_List_Olist_ONil(tc_List_Olist(X4633)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X4633),tc_List_Olist(tc_List_Olist(X4633))),X4633),hAPP(hAPP(c_COMBC(tc_List_Olist(X4633),tc_List_Olist(tc_List_Olist(X4633)),tc_List_Olist(tc_List_Olist(X4633))),c_List_Olist_OCons(tc_List_Olist(X4633))),c_List_Olist_ONil(tc_List_Olist(X4633)))))),X4630)))))=c_List_Otranspose(X4633,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X4633)),hAPP(hAPP(c_List_Olist_OCons(X4633),X4632),X4631)),X4630)), inference(variable_rename,[status(thm)],[fact_transpose_Osimps_I3_J])). 6.97/7.21 cnf(c_0_4644, plain, (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))=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))), inference(split_conjunct,[status(thm)],[c_0_4438])). 6.97/7.21 cnf(c_0_4645, 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_4439])). 6.97/7.21 cnf(c_0_4646, plain, (c_List_Oconcat(X1,hAPP(hAPP(c_List_Omap(X2,tc_List_Olist(X1)),X3),X4))=c_List_Omaps(X2,X1,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_4440])). 6.97/7.21 cnf(c_0_4647, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))), inference(split_conjunct,[status(thm)],[c_0_4441])). 6.97/7.21 cnf(c_0_4648, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=hAPP(c_Set_OCollect(X1),hAPP(c_fequal,X2))), inference(split_conjunct,[status(thm)],[c_0_4442])). 6.97/7.21 cnf(c_0_4649, 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_4443])). 6.97/7.21 fof(c_0_4650, plain, ![X2258, X2259, X2260, X2261, X2262]:hAPP(c_Nat_Onat_Onat__rec(X2262,X2261,X2260),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2259)),X2258))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X2262),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X2259))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X2262,X2262),hAPP(hAPP(c_COMBC(tc_Int_Oint,X2262,tc_fun(X2262,X2262)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2262,tc_fun(X2262,X2262)),tc_Int_Oint),c_If(X2262)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(X2262,X2261,X2260),X2258))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X2262,X2262),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X2262,X2262),tc_Int_Oint),X2260),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)),X2258))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X2262,tc_Int_Oint),c_Nat_Onat_Onat__rec(X2262,X2261,X2260)),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)),X2258))))), inference(variable_rename,[status(thm)],[fact_nat__rec__add__eq__if])). 6.97/7.21 fof(c_0_4651, plain, ![X10938, X10939, X10940, X10941]:hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10941)),X10940)),c_List_Ofoldr(tc_List_Olist(X10939),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X10939)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X10939),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X10939)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X10939)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(X10939),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X10939)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X10939),tc_List_Olist(X10939),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X10939)))),X10938),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10941)),X10940))),c_List_Ofoldr(tc_List_Olist(X10939),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X10939)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X10939))),X10938,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_transpose__aux__max])). 6.97/7.21 fof(c_0_4652, plain, ![X6566, X6567, X6568, X6569, X6570]:hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X6570),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X6567))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X6570,X6570),hAPP(hAPP(c_COMBC(tc_Int_Oint,X6570,tc_fun(X6570,X6570)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X6570,tc_fun(X6570,X6570)),tc_Int_Oint),c_If(X6570)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(X6570,X6569,X6568,X6566))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X6570,tc_Int_Oint),X6568),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)),X6566))))=c_Nat_Onat_Onat__case(X6570,X6569,X6568,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X6567)),X6566)), inference(variable_rename,[status(thm)],[fact_nat__case__add__eq__if])). 6.97/7.21 fof(c_0_4653, plain, ![X1697, X1698]:hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1698)),hAPP(c_Nat_OSuc,X1697))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1698))),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,X1697))),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)),X1697)))), inference(variable_rename,[status(thm)],[fact_max__Suc__number__of])). 6.97/7.21 fof(c_0_4654, plain, ![X6923, X6924]:hAPP(c_Set_OCollect(X6924),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X6924,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X6924),c_HOL_OAll(tc_fun(X6924,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X6924,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X6924,tc_HOL_Obool),tc_HOL_Obool),X6924),hAPP(c_COMBS(tc_fun(X6924,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(X6924,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(X6924,tc_HOL_Obool),tc_fun(tc_fun(X6924,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X6924,tc_HOL_Obool))),X6923)))),c_member(X6924))))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X6924,tc_HOL_Obool),X6923), inference(variable_rename,[status(thm)],[fact_Inter__eq])). 6.97/7.21 fof(c_0_4655, plain, ![X8750, X8751]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8751)),hAPP(c_Nat_OSuc,X8750))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X8751))),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)),X8750)))), inference(variable_rename,[status(thm)],[fact_min__Suc__number__of])). 6.97/7.21 fof(c_0_4656, plain, ![X3080]:c_Relation_OId(X3080)=hAPP(c_Set_OCollect(tc_prod(X3080,X3080)),hAPP(hAPP(c_COMBB(tc_fun(X3080,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X3080,X3080)),c_HOL_OEx(X3080)),hAPP(hAPP(c_COMBC(tc_prod(X3080,X3080),tc_fun(X3080,tc_prod(X3080,X3080)),tc_fun(X3080,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X3080,X3080),tc_HOL_Obool),tc_fun(tc_fun(X3080,tc_prod(X3080,X3080)),tc_fun(X3080,tc_HOL_Obool)),tc_prod(X3080,X3080)),c_COMBB(tc_prod(X3080,X3080),tc_HOL_Obool,X3080)),c_fequal)),hAPP(hAPP(c_COMBS(X3080,X3080,tc_prod(X3080,X3080)),c_Product__Type_OPair(X3080,X3080)),c_COMBI(X3080))))), inference(variable_rename,[status(thm)],[fact_Id__def])). 6.97/7.21 fof(c_0_4657, plain, ![X9854]:c_Transitive__Closure_Ortrancl(X9854,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X9854,X9854),tc_HOL_Obool)))=c_Relation_OId(X9854), inference(variable_rename,[status(thm)],[fact_rtrancl__empty])). 6.97/7.21 fof(c_0_4658, plain, ![X4358, X4359, X4360, X4361]:hAPP(c_Nat_Onat_Onat__rec(X4361,X4360,X4359),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4358))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X4361),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X4358))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X4361,X4361),hAPP(hAPP(c_COMBC(tc_Int_Oint,X4361,tc_fun(X4361,X4361)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4361,tc_fun(X4361,X4361)),tc_Int_Oint),c_If(X4361)),c_Nat__Numeral_Oneg)),X4360)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X4361,X4361),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X4361,X4361),tc_Int_Oint),X4359),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4361,tc_Int_Oint),c_Nat_Onat_Onat__rec(X4361,X4360,X4359)),c_Int_Onat)))), inference(variable_rename,[status(thm)],[fact_nat__rec__number__of])). 6.97/7.21 fof(c_0_4659, plain, ![X9436, X9437, X9438]:c_Nitpick_Otimes__frac(X9438,X9437,X9436)=hAPP(hAPP(c_Nitpick_Ofrac(X9438),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X9438),X9437)),hAPP(c_Nitpick_Onum(X9438),X9436))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(X9438),X9437)),hAPP(c_Nitpick_Odenom(X9438),X9436))), inference(variable_rename,[status(thm)],[fact_Nitpick_Otimes__frac__def])). 6.97/7.21 fof(c_0_4660, plain, ![X4785, X4786]:hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X4785))),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,X4786))),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),X4786)),c_Int_Onat))))=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X4786)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4785)), inference(variable_rename,[status(thm)],[fact_max__number__of__Suc])). 6.97/7.21 fof(c_0_4661, plain, ![X3861, X3862, X3863]:c_Enum_On__lists(X3863,hAPP(c_Nat_OSuc,X3862),X3861)=c_List_Oconcat(tc_List_Olist(X3863),hAPP(hAPP(c_List_Omap(tc_List_Olist(X3863),tc_List_Olist(tc_List_Olist(X3863))),hAPP(hAPP(c_COMBC(tc_List_Olist(X3863),tc_List_Olist(X3863),tc_List_Olist(tc_List_Olist(X3863))),hAPP(hAPP(c_COMBB(tc_fun(X3863,tc_List_Olist(X3863)),tc_fun(tc_List_Olist(X3863),tc_List_Olist(tc_List_Olist(X3863))),tc_List_Olist(X3863)),c_List_Omap(X3863,tc_List_Olist(X3863))),hAPP(c_COMBC(X3863,tc_List_Olist(X3863),tc_List_Olist(X3863)),c_List_Olist_OCons(X3863)))),X3861)),c_Enum_On__lists(X3863,X3862,X3861))), inference(variable_rename,[status(thm)],[fact_n__lists_Osimps_I2_J])). 6.97/7.21 fof(c_0_4662, plain, ![X6044, X6045]:hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X6044))),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),X6045)),c_Int_Onat))))=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X6045)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X6044)), inference(variable_rename,[status(thm)],[fact_min__number__of__Suc])). 6.97/7.21 fof(c_0_4663, plain, ![X1362]:c_Int_Oint__ge__less__than(X1362)=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),X1362)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))), inference(variable_rename,[status(thm)],[fact_int__ge__less__than__def])). 6.97/7.21 fof(c_0_4664, plain, ![X7149, X7150, X7151, X7152]:hAPP(c_Set_OCollect(tc_prod(X7152,X7151)),hAPP(c_Product__Type_Oprod_Oprod__case(X7152,X7151,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X7152,tc_fun(X7151,tc_HOL_Obool),tc_fun(X7151,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X7151,tc_HOL_Obool),tc_fun(X7151,tc_HOL_Obool)),X7152),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7151)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7152),c_fconj),X7150))),X7149)))=hAPP(hAPP(c_Product__Type_OSigma(X7152,X7151),hAPP(c_Set_OCollect(X7152),X7150)),hAPP(hAPP(c_COMBB(tc_fun(X7151,tc_HOL_Obool),tc_fun(X7151,tc_HOL_Obool),X7152),c_Set_OCollect(X7151)),X7149)), inference(variable_rename,[status(thm)],[fact_SetCompr__Sigma__eq])). 6.97/7.21 fof(c_0_4665, plain, ![X10526, X10527, X10528]:hAPP(hAPP(c_List_Omap(tc_prod(X10528,tc_Nat_Onat),X10528),c_Product__Type_Ofst(X10528,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X10528,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X10528,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(X10528,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X10528,tc_Nat_Onat))),X10526)),hAPP(hAPP(c_List_Ozip(X10528,tc_Nat_Onat),X10527),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10528)),X10527)))))=c_List_Osublist(X10528,X10527,X10526), inference(variable_rename,[status(thm)],[fact_sublist__def])). 6.97/7.21 fof(c_0_4666, plain, ![X8225]:hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X8225),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X8225))),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])). 6.97/7.21 fof(c_0_4667, plain, ![X13293]:c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X13293)),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,X13293,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])). 6.97/7.21 fof(c_0_4668, plain, ![X2556, X2557, X2558, X2559]:c_Nat_Onat_Onat__case(X2559,X2558,X2557,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2556))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X2559),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X2556))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X2559,X2559),hAPP(hAPP(c_COMBC(tc_Int_Oint,X2559,tc_fun(X2559,X2559)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2559,tc_fun(X2559,X2559)),tc_Int_Oint),c_If(X2559)),c_Nat__Numeral_Oneg)),X2558)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X2559,tc_Int_Oint),X2557),c_Int_Onat))), inference(variable_rename,[status(thm)],[fact_nat__case__number__of])). 6.97/7.21 fof(c_0_4669, plain, ![X4725, X4726]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X4726)),c_Int_OBit1(X4725))=c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4726),c_Int_Osucc(X4725))), inference(variable_rename,[status(thm)],[fact_add__Bit1__Bit1])). 6.97/7.21 fof(c_0_4670, plain, ![X7589, X7590]:c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(X7590)),X7589))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X7590)),c_Int_OBit1(X7589)), inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I8_J])). 6.97/7.21 fof(c_0_4671, plain, ![X7243, X7244]:hAPP(c_New__DSequence_Opos__not__seq(X7244),X7243)=c_Lazy__Sequence_Ohb__not__seq(hAPP(X7244,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)))),X7243))), inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__not__seq__def])). 6.97/7.21 fof(c_0_4672, plain, ![X17313, X17314, X17315, X17316]:c_List_Oconcat(X17316,hAPP(hAPP(c_List_Omap(X17315,tc_List_Olist(X17316)),hAPP(hAPP(c_COMBC(X17315,tc_List_Olist(X17316),tc_List_Olist(X17316)),hAPP(hAPP(c_COMBB(X17316,tc_fun(tc_List_Olist(X17316),tc_List_Olist(X17316)),X17315),c_List_Olist_OCons(X17316)),X17314)),c_List_Olist_ONil(X17316))),X17313))=hAPP(hAPP(c_List_Omap(X17315,X17316),X17314),X17313), inference(variable_rename,[status(thm)],[fact_concat__map__singleton])). 6.97/7.21 fof(c_0_4673, plain, ![X12893, X12894]:c_Transitive__Closure_Ortrancl(X12894,X12893)=c_Transitive__Closure_Otrancl(X12894,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X12894,X12894),tc_HOL_Obool)),X12893),c_Relation_OId(X12894))), inference(variable_rename,[status(thm)],[fact_trancl__reflcl])). 6.97/7.21 fof(c_0_4674, plain, ![X7761, X7762]:c_Transitive__Closure_Ortrancl(X7762,X7761)=c_Transitive__Closure_Ortrancl(X7762,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7762,X7762),tc_HOL_Obool)),X7761),c_Relation_OId(X7762))), inference(variable_rename,[status(thm)],[fact_rtrancl__reflcl])). 6.97/7.21 fof(c_0_4675, plain, ![X3071, X3072]:c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3072),X3071))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X3072)),c_Int_OBit0(X3071)), inference(variable_rename,[status(thm)],[fact_add__Bit1__Bit0])). 6.97/7.21 cnf(c_0_4676, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2))=c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4444])). 6.97/7.21 fof(c_0_4677, plain, ![X16292, X16293, X16294]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16294),X16293)),X16292)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16294),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16293),X16292)), inference(variable_rename,[status(thm)],[fact_zadd__assoc])). 6.97/7.21 fof(c_0_4678, plain, ![X689, X690]:c_Nitpick_OAbs__Frac(X690,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(X690),X689))),hAPP(c_Nitpick_Odenom(X690),X689)))=c_Nitpick_Ouminus__frac(X690,X689), inference(variable_rename,[status(thm)],[fact_Nitpick_Ouminus__frac__def])). 6.97/7.21 fof(c_0_4679, plain, ![X9739]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9739),X9739)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=X9739, inference(variable_rename,[status(thm)],[fact_add__self__div__2])). 6.97/7.21 fof(c_0_4680, plain, ![X13666, X13667]:c_Nitpick_Oint__lcm(X13667,X13666)=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),X13667)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X13666)))), inference(variable_rename,[status(thm)],[fact_Nitpick_Oint__lcm__def])). 6.97/7.21 fof(c_0_4681, plain, ![X12050, X12051]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12051),X12050)),c_Nitpick_Onat__gcd(X12051,X12050))=c_Nitpick_Onat__lcm(X12051,X12050), inference(variable_rename,[status(thm)],[fact_Nitpick_Onat__lcm__def])). 6.97/7.21 fof(c_0_4682, plain, ![X633, X634]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X634))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X633)))=hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X634),X633))), inference(variable_rename,[status(thm)],[fact_nat__abs__mult__distrib])). 6.97/7.21 fof(c_0_4683, plain, ![X16793]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16793),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,X16793)), inference(variable_rename,[status(thm)],[fact_add__2__eq__Suc_H])). 6.97/7.21 fof(c_0_4684, plain, ![X6686, X6687]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X6687)),c_Int_OBit1(X6686))=c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X6687),X6686)), inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I10_J])). 6.97/7.21 fof(c_0_4685, plain, ![X9496]:c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X9496)))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(X9496)), inference(variable_rename,[status(thm)],[fact_minus__Bit1])). 6.97/7.21 cnf(c_0_4686, 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_4445])). 6.97/7.21 cnf(c_0_4687, 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_4446])). 6.97/7.21 fof(c_0_4688, plain, ![X4039, X4040]:c_List_Oconcat(X4040,hAPP(hAPP(c_List_Omap(tc_List_Olist(X4040),tc_List_Olist(X4040)),c_List_Orev(X4040)),hAPP(c_List_Orev(tc_List_Olist(X4040)),X4039)))=hAPP(c_List_Orev(X4040),c_List_Oconcat(X4040,X4039)), inference(variable_rename,[status(thm)],[fact_rev__concat])). 6.97/7.21 fof(c_0_4689, plain, ![X2955, X2956]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2956,X2956),tc_HOL_Obool)),X2955),hAPP(hAPP(c_Relation_Orel__comp(X2956,X2956,X2956),c_Transitive__Closure_Otrancl(X2956,X2955)),X2955))=c_Transitive__Closure_Otrancl(X2956,X2955), inference(variable_rename,[status(thm)],[fact_trancl__unfold])). 6.97/7.21 fof(c_0_4690, plain, ![X16073, X16074, X16075, X16076]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16076,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16076,tc_HOL_Obool)),X16075),X16074)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16076,tc_HOL_Obool)),X16073),X16074))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16076,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16076,tc_HOL_Obool)),X16075),X16074)),X16073), inference(variable_rename,[status(thm)],[fact_Diff__Int2])). 6.97/7.21 cnf(c_0_4691, 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_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),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_4447])). 6.97/7.21 cnf(c_0_4692, 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_4448]), ['final']). 6.97/7.21 fof(c_0_4693, plain, ![X4449]:c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X4449))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X4449)), inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I4_J])). 6.97/7.21 fof(c_0_4694, plain, ![X326, X327, X328]:c_List_Oconcat(X328,hAPP(hAPP(c_List_Omap(tc_List_Olist(X328),tc_List_Olist(X328)),c_List_Ofilter(X328,X327)),X326))=hAPP(c_List_Ofilter(X328,X327),c_List_Oconcat(X328,X326)), inference(variable_rename,[status(thm)],[fact_filter__concat])). 6.97/7.21 fof(c_0_4695, plain, ![X14469, X14470]:hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),X14470),X14469)=c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(X14470)),c_List_Oembed__list(X14469))), inference(variable_rename,[status(thm)],[fact_transfer__nat__int__list__functions_I1_J])). 6.97/7.21 fof(c_0_4696, plain, ![X12471]:c_List_Oreturn__list(X12471)=hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X12471), inference(variable_rename,[status(thm)],[fact_return__list__def])). 6.97/7.21 fof(c_0_4697, plain, ![X13861]:hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X13861)=c_List_Oembed__list(X13861), inference(variable_rename,[status(thm)],[fact_embed__list__def])). 6.97/7.21 fof(c_0_4698, plain, ![X4369, X4370]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X4370)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X4369))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X4370))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X4369))), inference(variable_rename,[status(thm)],[fact_zdiv__number__of__Bit0])). 6.97/7.21 fof(c_0_4699, plain, ![X13146]: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)))),X13146))), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J])). 6.97/7.21 fof(c_0_4700, plain, ![X7908, X7909]:c_Transitive__Closure_Ortrancl(X7909,X7908)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7909,X7909),tc_HOL_Obool)),c_Relation_OId(X7909)),hAPP(hAPP(c_Relation_Orel__comp(X7909,X7909,X7909),c_Transitive__Closure_Ortrancl(X7909,X7908)),X7908)), inference(variable_rename,[status(thm)],[fact_rtrancl__unfold])). 6.97/7.21 fof(c_0_4701, plain, ![X12433, X12434, X12435, X12436, X12437]:c_List_Ofoldr(X12436,X12437,hAPP(c_COMBC(X12437,X12436,X12437),X12435),hAPP(c_List_Orev(X12436),X12433),X12434)=hAPP(c_List_Ofoldl(X12437,X12436,X12435,X12434),X12433), inference(variable_rename,[status(thm)],[fact_foldl__foldr])). 6.97/7.21 fof(c_0_4702, plain, ![X4594]:c_Int_Osucc(c_Int_OBit1(X4594))=c_Int_OBit0(c_Int_Osucc(X4594)), inference(variable_rename,[status(thm)],[fact_succ__Bit1])). 6.97/7.21 fof(c_0_4703, plain, ![X15229]:c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X15229))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X15229)), inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I6_J])). 6.97/7.21 fof(c_0_4704, plain, ![X7638, X7639]:(((c_Orderings_Obot__class_Obot(tc_fun(X7639,tc_HOL_Obool))!=X7638|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(X7639),X7638))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X7639),X7638))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(X7639),X7638)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Finite__Set_Ocard(X7639),X7638)|(c_Orderings_Obot__class_Obot(tc_fun(X7639,tc_HOL_Obool))=X7638|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7639),X7638))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__eq__0__iff])])])])). 6.97/7.21 fof(c_0_4705, plain, ![X5100, X5101]:hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(X5101,X5100))=c_List_Oupt(hAPP(c_Nat_OSuc,X5101),hAPP(c_Nat_OSuc,X5100)), inference(variable_rename,[status(thm)],[fact_map__Suc__upt])). 6.97/7.21 fof(c_0_4706, plain, ![X14066]:c_Int_Opred(c_Int_OBit1(X14066))=c_Int_OBit0(X14066), inference(variable_rename,[status(thm)],[fact_pred__Bit1])). 6.97/7.21 fof(c_0_4707, plain, ![X13440]:c_Int_OBit1(X13440)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X13440)),X13440), inference(variable_rename,[status(thm)],[fact_Bit1__def])). 6.97/7.21 fof(c_0_4708, plain, ![X6290, X6291]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X6291)),hAPP(c_Nat_OSuc,X6290))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X6291),X6290)), inference(variable_rename,[status(thm)],[fact_image__Suc__atLeastLessThan])). 6.97/7.21 fof(c_0_4709, plain, ![X8686, X8687]:c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X8687,X8686)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X8687),hAPP(c_Nat_OSuc,X8686)), inference(variable_rename,[status(thm)],[fact_atLeastLessThanSuc__atLeastAtMost])). 6.97/7.21 fof(c_0_4710, plain, ![X13996]:hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X13996))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),X13996)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_code__numeral_Osize_I4_J])). 6.97/7.21 fof(c_0_4711, plain, ![X5952, X5953]:hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X5953,X5952))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X5952),X5953)), inference(variable_rename,[status(thm)],[fact_card__greaterThanAtMost__int])). 6.97/7.21 fof(c_0_4712, plain, ![X15826, X15827]:c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X15827,X15826)=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15827),c_Groups_Oone__class_Oone(tc_Int_Oint)),X15826), inference(variable_rename,[status(thm)],[fact_atLeastPlusOneAtMost__greaterThanAtMost__int])). 6.97/7.21 fof(c_0_4713, plain, ![X12653, X12654]:hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X12653),X12654)),c_Groups_Oone__class_Oone(tc_Int_Oint)))=hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X12654,X12653)), inference(variable_rename,[status(thm)],[fact_card__atLeastAtMost__int])). 6.97/7.21 fof(c_0_4714, 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])). 6.97/7.21 fof(c_0_4715, plain, ![X12480, X12481, X12482]:((hAPP(c_List_Orotate(X12482,X12481),X12480)!=c_List_Olist_ONil(X12482)|c_List_Olist_ONil(X12482)=X12480)&(c_List_Olist_ONil(X12482)!=X12480|hAPP(c_List_Orotate(X12482,X12481),X12480)=c_List_Olist_ONil(X12482))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate__is__Nil__conv])])). 6.97/7.21 fof(c_0_4716, plain, ![X14639, X14640]:hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X14640),tc_List_Olist(X14640)),X14639),c_List_Orotate1(X14640))=c_List_Orotate(X14640,X14639), inference(variable_rename,[status(thm)],[fact_rotate__def])). 6.97/7.21 fof(c_0_4717, plain, ![X1965, X1966]:hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X1966,hAPP(c_Nat_OSuc,X1965)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1966,X1965), inference(variable_rename,[status(thm)],[fact_atLeastAtMost__upt])). 6.97/7.21 fof(c_0_4718, plain, ![X13491]:c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(X13491))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X13491)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_code__numeral_Osize_I2_J])). 6.97/7.21 fof(c_0_4719, plain, ![X11748]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X11748),hAPP(c_Nat_OSuc,X11748))=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X11748),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_atLeastLessThan__singleton])). 6.97/7.21 fof(c_0_4720, plain, ![X13941]:X13941=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X13941)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), inference(variable_rename,[status(thm)],[fact_Suc__code__numeral__minus__one])). 6.97/7.21 fof(c_0_4721, plain, ![X11725]:hAPP(c_Set_OCollect(X11725),hAPP(c_COMBK(tc_HOL_Obool,X11725),c_fFalse))=c_Orderings_Obot__class_Obot(tc_fun(X11725,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_empty__def])). 6.97/7.21 fof(c_0_4722, plain, ![X9622, X9623, X9624, X9625]:c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X9625,X9624,X9623,c_Code__Numeral_OSuc__code__numeral(X9622))=hAPP(X9623,X9622), inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I5_J])). 6.97/7.21 fof(c_0_4723, plain, ![X16676]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X16676)),X16676)=c_Groups_Ozero__class_Ozero(tc_Int_Oint), inference(variable_rename,[status(thm)],[fact_zadd__zminus__inverse2])). 6.97/7.21 fof(c_0_4724, plain, ![X10856, X10857]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X10856),X10857)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X10857),X10856), inference(variable_rename,[status(thm)],[fact_zadd__commute])). 6.97/7.21 fof(c_0_4725, plain, ![X9680, X9681]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X9680),X9681)=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X9681,X9680)), inference(variable_rename,[status(thm)],[fact_card__greaterThanAtMost])). 6.97/7.21 fof(c_0_4726, plain, ![X5778, X5779]:c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X5779),X5778)=c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X5779,X5778), inference(variable_rename,[status(thm)],[fact_atLeastSucAtMost__greaterThanAtMost])). 6.97/7.21 fof(c_0_4727, plain, ![X10045]:c_Orderings_Otop__class_Otop(tc_fun(X10045,tc_HOL_Obool))=hAPP(c_Set_OCollect(X10045),hAPP(c_COMBK(tc_HOL_Obool,X10045),c_fTrue)), inference(variable_rename,[status(thm)],[fact_UNIV__def])). 6.97/7.21 fof(c_0_4728, plain, ![X5224, X5225, X5226, X5227, X5228, X5229, X5230]:(~class_Rings_Osemiring__0(X5230)|(~c_Fun_Oinj__on(tc_prod(X5229,X5228),X5230,hAPP(c_Product__Type_Oprod_Oprod__case(X5229,X5228,X5230),hAPP(hAPP(c_COMBC(X5229,tc_fun(X5228,X5230),tc_fun(X5228,X5230)),hAPP(hAPP(c_COMBB(tc_fun(X5230,X5230),tc_fun(tc_fun(X5228,X5230),tc_fun(X5228,X5230)),X5229),c_COMBB(X5230,X5230,X5228)),hAPP(hAPP(c_COMBB(X5230,tc_fun(X5230,X5230),X5229),c_Groups_Otimes__class_Otimes(X5230)),X5227))),X5226)),hAPP(hAPP(c_Product__Type_OSigma(X5229,X5228),X5225),hAPP(c_COMBK(tc_fun(X5228,tc_HOL_Obool),X5229),X5224)))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5230),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5229,X5230),X5227),X5225)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5228,X5230),X5226),X5224))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5230,X5230),c_Fun_Oid(X5230)),hAPP(c_Set_OCollect(X5230),hAPP(hAPP(c_COMBB(tc_fun(X5229,tc_HOL_Obool),tc_HOL_Obool,X5230),c_HOL_OEx(X5229)),hAPP(hAPP(c_COMBB(tc_fun(X5229,tc_fun(X5228,tc_HOL_Obool)),tc_fun(X5229,tc_HOL_Obool),X5230),hAPP(c_COMBB(tc_fun(X5228,tc_HOL_Obool),tc_HOL_Obool,X5229),c_HOL_OEx(X5228))),hAPP(hAPP(c_COMBC(X5230,tc_fun(X5229,tc_fun(X5228,tc_HOL_Obool)),tc_fun(X5229,tc_fun(X5228,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5229,tc_fun(tc_fun(X5228,tc_HOL_Obool),tc_fun(X5228,tc_HOL_Obool))),tc_fun(tc_fun(X5229,tc_fun(X5228,tc_HOL_Obool)),tc_fun(X5229,tc_fun(X5228,tc_HOL_Obool))),X5230),c_COMBS(X5229,tc_fun(X5228,tc_HOL_Obool),tc_fun(X5228,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5229,tc_fun(X5228,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X5229,tc_fun(tc_fun(X5228,tc_HOL_Obool),tc_fun(X5228,tc_HOL_Obool))),X5230),hAPP(c_COMBB(tc_fun(X5228,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5228,tc_HOL_Obool),tc_fun(X5228,tc_HOL_Obool)),X5229),c_COMBS(X5228,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5229,tc_fun(X5228,tc_HOL_Obool)),tc_fun(X5229,tc_fun(X5228,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X5230),hAPP(c_COMBB(tc_fun(X5228,tc_HOL_Obool),tc_fun(X5228,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5229),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5228),c_fconj))),hAPP(hAPP(c_COMBC(X5230,tc_fun(X5229,tc_fun(X5228,X5230)),tc_fun(X5229,tc_fun(X5228,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5228,X5230),tc_fun(X5228,tc_HOL_Obool)),tc_fun(tc_fun(X5229,tc_fun(X5228,X5230)),tc_fun(X5229,tc_fun(X5228,tc_HOL_Obool))),X5230),c_COMBB(tc_fun(X5228,X5230),tc_fun(X5228,tc_HOL_Obool),X5229)),hAPP(hAPP(c_COMBB(tc_fun(X5230,tc_HOL_Obool),tc_fun(tc_fun(X5228,X5230),tc_fun(X5228,tc_HOL_Obool)),X5230),c_COMBB(X5230,tc_HOL_Obool,X5228)),c_fequal))),hAPP(hAPP(c_COMBC(X5229,tc_fun(X5228,X5230),tc_fun(X5228,X5230)),hAPP(hAPP(c_COMBB(tc_fun(X5230,X5230),tc_fun(tc_fun(X5228,X5230),tc_fun(X5228,X5230)),X5229),c_COMBB(X5230,X5230,X5228)),hAPP(hAPP(c_COMBB(X5230,tc_fun(X5230,X5230),X5229),c_Groups_Otimes__class_Otimes(X5230)),X5227))),X5226)))))),hAPP(hAPP(c_COMBC(X5229,tc_fun(X5228,tc_HOL_Obool),tc_fun(X5228,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X5228,tc_HOL_Obool),tc_fun(X5228,tc_HOL_Obool)),X5229),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5228)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5229),c_fconj),hAPP(hAPP(c_COMBC(X5229,tc_fun(X5229,tc_HOL_Obool),tc_HOL_Obool),c_member(X5229)),X5225)))),hAPP(hAPP(c_COMBC(X5228,tc_fun(X5228,tc_HOL_Obool),tc_HOL_Obool),c_member(X5228)),X5224))))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__mult__setsum__if__inj])])])). 6.97/7.21 fof(c_0_4729, plain, ![X7271, X7272, X7273]:(~class_Orderings_Olinorder(X7273)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7273),X7272))|(c_Orderings_Obot__class_Obot(tc_fun(X7273,tc_HOL_Obool))=X7272|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7273),X7271))|(X7271=c_Orderings_Obot__class_Obot(tc_fun(X7273,tc_HOL_Obool))|c_Big__Operators_Olattice_OSup__fin(X7273,c_Orderings_Oord__class_Omax(X7273),hAPP(c_Set_OCollect(X7273),hAPP(hAPP(c_COMBB(tc_fun(X7273,tc_HOL_Obool),tc_HOL_Obool,X7273),c_HOL_OEx(X7273)),hAPP(hAPP(c_COMBB(tc_fun(X7273,tc_fun(X7273,tc_HOL_Obool)),tc_fun(X7273,tc_HOL_Obool),X7273),hAPP(c_COMBB(tc_fun(X7273,tc_HOL_Obool),tc_HOL_Obool,X7273),c_HOL_OEx(X7273))),hAPP(hAPP(c_COMBC(X7273,tc_fun(X7273,tc_fun(X7273,tc_HOL_Obool)),tc_fun(X7273,tc_fun(X7273,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7273,tc_fun(tc_fun(X7273,tc_HOL_Obool),tc_fun(X7273,tc_HOL_Obool))),tc_fun(tc_fun(X7273,tc_fun(X7273,tc_HOL_Obool)),tc_fun(X7273,tc_fun(X7273,tc_HOL_Obool))),X7273),c_COMBS(X7273,tc_fun(X7273,tc_HOL_Obool),tc_fun(X7273,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7273,tc_fun(X7273,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X7273,tc_fun(tc_fun(X7273,tc_HOL_Obool),tc_fun(X7273,tc_HOL_Obool))),X7273),hAPP(c_COMBB(tc_fun(X7273,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X7273,tc_HOL_Obool),tc_fun(X7273,tc_HOL_Obool)),X7273),c_COMBS(X7273,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7273,tc_fun(X7273,tc_HOL_Obool)),tc_fun(X7273,tc_fun(X7273,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X7273),hAPP(c_COMBB(tc_fun(X7273,tc_HOL_Obool),tc_fun(X7273,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X7273),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7273),c_fconj))),hAPP(hAPP(c_COMBC(X7273,tc_fun(X7273,tc_fun(X7273,X7273)),tc_fun(X7273,tc_fun(X7273,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7273,X7273),tc_fun(X7273,tc_HOL_Obool)),tc_fun(tc_fun(X7273,tc_fun(X7273,X7273)),tc_fun(X7273,tc_fun(X7273,tc_HOL_Obool))),X7273),c_COMBB(tc_fun(X7273,X7273),tc_fun(X7273,tc_HOL_Obool),X7273)),hAPP(hAPP(c_COMBB(tc_fun(X7273,tc_HOL_Obool),tc_fun(tc_fun(X7273,X7273),tc_fun(X7273,tc_HOL_Obool)),X7273),c_COMBB(X7273,tc_HOL_Obool,X7273)),c_fequal))),c_Orderings_Oord__class_Omin(X7273)))))),hAPP(hAPP(c_COMBC(X7273,tc_fun(X7273,tc_HOL_Obool),tc_fun(X7273,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X7273,tc_HOL_Obool),tc_fun(X7273,tc_HOL_Obool)),X7273),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7273)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7273),c_fconj),hAPP(hAPP(c_COMBC(X7273,tc_fun(X7273,tc_HOL_Obool),tc_HOL_Obool),c_member(X7273)),X7272)))),hAPP(hAPP(c_COMBC(X7273,tc_fun(X7273,tc_HOL_Obool),tc_HOL_Obool),c_member(X7273)),X7271)))))))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X7273),c_Big__Operators_Olattice_OSup__fin(X7273,c_Orderings_Oord__class_Omax(X7273),X7272)),c_Big__Operators_Olattice_OSup__fin(X7273,c_Orderings_Oord__class_Omax(X7273),X7271))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oinf__Sup2__distrib])])])). 6.97/7.21 fof(c_0_4730, plain, ![X15483, X15484, X15485]:(~class_Orderings_Olinorder(X15485)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15485),X15484))|(c_Orderings_Obot__class_Obot(tc_fun(X15485,tc_HOL_Obool))=X15484|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15485),X15483))|(X15483=c_Orderings_Obot__class_Obot(tc_fun(X15485,tc_HOL_Obool))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X15485),c_Big__Operators_Olattice_OInf__fin(X15485,c_Orderings_Oord__class_Omin(X15485),X15484)),c_Big__Operators_Olattice_OInf__fin(X15485,c_Orderings_Oord__class_Omin(X15485),X15483))=c_Big__Operators_Olattice_OInf__fin(X15485,c_Orderings_Oord__class_Omin(X15485),hAPP(c_Set_OCollect(X15485),hAPP(hAPP(c_COMBB(tc_fun(X15485,tc_HOL_Obool),tc_HOL_Obool,X15485),c_HOL_OEx(X15485)),hAPP(hAPP(c_COMBB(tc_fun(X15485,tc_fun(X15485,tc_HOL_Obool)),tc_fun(X15485,tc_HOL_Obool),X15485),hAPP(c_COMBB(tc_fun(X15485,tc_HOL_Obool),tc_HOL_Obool,X15485),c_HOL_OEx(X15485))),hAPP(hAPP(c_COMBC(X15485,tc_fun(X15485,tc_fun(X15485,tc_HOL_Obool)),tc_fun(X15485,tc_fun(X15485,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X15485,tc_fun(tc_fun(X15485,tc_HOL_Obool),tc_fun(X15485,tc_HOL_Obool))),tc_fun(tc_fun(X15485,tc_fun(X15485,tc_HOL_Obool)),tc_fun(X15485,tc_fun(X15485,tc_HOL_Obool))),X15485),c_COMBS(X15485,tc_fun(X15485,tc_HOL_Obool),tc_fun(X15485,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X15485,tc_fun(X15485,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X15485,tc_fun(tc_fun(X15485,tc_HOL_Obool),tc_fun(X15485,tc_HOL_Obool))),X15485),hAPP(c_COMBB(tc_fun(X15485,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X15485,tc_HOL_Obool),tc_fun(X15485,tc_HOL_Obool)),X15485),c_COMBS(X15485,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X15485,tc_fun(X15485,tc_HOL_Obool)),tc_fun(X15485,tc_fun(X15485,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X15485),hAPP(c_COMBB(tc_fun(X15485,tc_HOL_Obool),tc_fun(X15485,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X15485),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X15485),c_fconj))),hAPP(hAPP(c_COMBC(X15485,tc_fun(X15485,tc_fun(X15485,X15485)),tc_fun(X15485,tc_fun(X15485,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X15485,X15485),tc_fun(X15485,tc_HOL_Obool)),tc_fun(tc_fun(X15485,tc_fun(X15485,X15485)),tc_fun(X15485,tc_fun(X15485,tc_HOL_Obool))),X15485),c_COMBB(tc_fun(X15485,X15485),tc_fun(X15485,tc_HOL_Obool),X15485)),hAPP(hAPP(c_COMBB(tc_fun(X15485,tc_HOL_Obool),tc_fun(tc_fun(X15485,X15485),tc_fun(X15485,tc_HOL_Obool)),X15485),c_COMBB(X15485,tc_HOL_Obool,X15485)),c_fequal))),c_Orderings_Oord__class_Omax(X15485)))))),hAPP(hAPP(c_COMBC(X15485,tc_fun(X15485,tc_HOL_Obool),tc_fun(X15485,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X15485,tc_HOL_Obool),tc_fun(X15485,tc_HOL_Obool)),X15485),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X15485)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X15485),c_fconj),hAPP(hAPP(c_COMBC(X15485,tc_fun(X15485,tc_HOL_Obool),tc_HOL_Obool),c_member(X15485)),X15484)))),hAPP(hAPP(c_COMBC(X15485,tc_fun(X15485,tc_HOL_Obool),tc_HOL_Obool),c_member(X15485)),X15483)))))))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf2__distrib])])). 6.97/7.21 fof(c_0_4731, plain, ![X12193, X12194, X12195]:(~class_Lattices_Odistrib__lattice(X12195)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12195),X12194))|(c_Orderings_Obot__class_Obot(tc_fun(X12195,tc_HOL_Obool))=X12194|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12195),X12193))|(c_Orderings_Obot__class_Obot(tc_fun(X12195,tc_HOL_Obool))=X12193|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X12195),c_Big__Operators_Olattice__class_OInf__fin(X12195,X12194)),c_Big__Operators_Olattice__class_OInf__fin(X12195,X12193))=c_Big__Operators_Olattice__class_OInf__fin(X12195,hAPP(c_Set_OCollect(X12195),hAPP(hAPP(c_COMBB(tc_fun(X12195,tc_HOL_Obool),tc_HOL_Obool,X12195),c_HOL_OEx(X12195)),hAPP(hAPP(c_COMBB(tc_fun(X12195,tc_fun(X12195,tc_HOL_Obool)),tc_fun(X12195,tc_HOL_Obool),X12195),hAPP(c_COMBB(tc_fun(X12195,tc_HOL_Obool),tc_HOL_Obool,X12195),c_HOL_OEx(X12195))),hAPP(hAPP(c_COMBC(X12195,tc_fun(X12195,tc_fun(X12195,tc_HOL_Obool)),tc_fun(X12195,tc_fun(X12195,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X12195,tc_fun(tc_fun(X12195,tc_HOL_Obool),tc_fun(X12195,tc_HOL_Obool))),tc_fun(tc_fun(X12195,tc_fun(X12195,tc_HOL_Obool)),tc_fun(X12195,tc_fun(X12195,tc_HOL_Obool))),X12195),c_COMBS(X12195,tc_fun(X12195,tc_HOL_Obool),tc_fun(X12195,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X12195,tc_fun(X12195,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X12195,tc_fun(tc_fun(X12195,tc_HOL_Obool),tc_fun(X12195,tc_HOL_Obool))),X12195),hAPP(c_COMBB(tc_fun(X12195,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X12195,tc_HOL_Obool),tc_fun(X12195,tc_HOL_Obool)),X12195),c_COMBS(X12195,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X12195,tc_fun(X12195,tc_HOL_Obool)),tc_fun(X12195,tc_fun(X12195,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X12195),hAPP(c_COMBB(tc_fun(X12195,tc_HOL_Obool),tc_fun(X12195,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X12195),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X12195),c_fconj))),hAPP(hAPP(c_COMBC(X12195,tc_fun(X12195,tc_fun(X12195,X12195)),tc_fun(X12195,tc_fun(X12195,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X12195,X12195),tc_fun(X12195,tc_HOL_Obool)),tc_fun(tc_fun(X12195,tc_fun(X12195,X12195)),tc_fun(X12195,tc_fun(X12195,tc_HOL_Obool))),X12195),c_COMBB(tc_fun(X12195,X12195),tc_fun(X12195,tc_HOL_Obool),X12195)),hAPP(hAPP(c_COMBB(tc_fun(X12195,tc_HOL_Obool),tc_fun(tc_fun(X12195,X12195),tc_fun(X12195,tc_HOL_Obool)),X12195),c_COMBB(X12195,tc_HOL_Obool,X12195)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(X12195)))))),hAPP(hAPP(c_COMBC(X12195,tc_fun(X12195,tc_HOL_Obool),tc_fun(X12195,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X12195,tc_HOL_Obool),tc_fun(X12195,tc_HOL_Obool)),X12195),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X12195)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X12195),c_fconj),hAPP(hAPP(c_COMBC(X12195,tc_fun(X12195,tc_HOL_Obool),tc_HOL_Obool),c_member(X12195)),X12194)))),hAPP(hAPP(c_COMBC(X12195,tc_fun(X12195,tc_HOL_Obool),tc_HOL_Obool),c_member(X12195)),X12193)))))))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__Inf2__distrib])])])). 6.97/7.21 fof(c_0_4732, plain, ![X15771, X15772, X15773]:(~class_Lattices_Odistrib__lattice(X15773)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15773),X15772))|(c_Orderings_Obot__class_Obot(tc_fun(X15773,tc_HOL_Obool))=X15772|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15773),X15771))|(X15771=c_Orderings_Obot__class_Obot(tc_fun(X15773,tc_HOL_Obool))|c_Big__Operators_Olattice__class_OSup__fin(X15773,hAPP(c_Set_OCollect(X15773),hAPP(hAPP(c_COMBB(tc_fun(X15773,tc_HOL_Obool),tc_HOL_Obool,X15773),c_HOL_OEx(X15773)),hAPP(hAPP(c_COMBB(tc_fun(X15773,tc_fun(X15773,tc_HOL_Obool)),tc_fun(X15773,tc_HOL_Obool),X15773),hAPP(c_COMBB(tc_fun(X15773,tc_HOL_Obool),tc_HOL_Obool,X15773),c_HOL_OEx(X15773))),hAPP(hAPP(c_COMBC(X15773,tc_fun(X15773,tc_fun(X15773,tc_HOL_Obool)),tc_fun(X15773,tc_fun(X15773,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X15773,tc_fun(tc_fun(X15773,tc_HOL_Obool),tc_fun(X15773,tc_HOL_Obool))),tc_fun(tc_fun(X15773,tc_fun(X15773,tc_HOL_Obool)),tc_fun(X15773,tc_fun(X15773,tc_HOL_Obool))),X15773),c_COMBS(X15773,tc_fun(X15773,tc_HOL_Obool),tc_fun(X15773,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X15773,tc_fun(X15773,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X15773,tc_fun(tc_fun(X15773,tc_HOL_Obool),tc_fun(X15773,tc_HOL_Obool))),X15773),hAPP(c_COMBB(tc_fun(X15773,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X15773,tc_HOL_Obool),tc_fun(X15773,tc_HOL_Obool)),X15773),c_COMBS(X15773,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X15773,tc_fun(X15773,tc_HOL_Obool)),tc_fun(X15773,tc_fun(X15773,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X15773),hAPP(c_COMBB(tc_fun(X15773,tc_HOL_Obool),tc_fun(X15773,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X15773),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X15773),c_fconj))),hAPP(hAPP(c_COMBC(X15773,tc_fun(X15773,tc_fun(X15773,X15773)),tc_fun(X15773,tc_fun(X15773,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X15773,X15773),tc_fun(X15773,tc_HOL_Obool)),tc_fun(tc_fun(X15773,tc_fun(X15773,X15773)),tc_fun(X15773,tc_fun(X15773,tc_HOL_Obool))),X15773),c_COMBB(tc_fun(X15773,X15773),tc_fun(X15773,tc_HOL_Obool),X15773)),hAPP(hAPP(c_COMBB(tc_fun(X15773,tc_HOL_Obool),tc_fun(tc_fun(X15773,X15773),tc_fun(X15773,tc_HOL_Obool)),X15773),c_COMBB(X15773,tc_HOL_Obool,X15773)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(X15773)))))),hAPP(hAPP(c_COMBC(X15773,tc_fun(X15773,tc_HOL_Obool),tc_fun(X15773,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X15773,tc_HOL_Obool),tc_fun(X15773,tc_HOL_Obool)),X15773),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X15773)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X15773),c_fconj),hAPP(hAPP(c_COMBC(X15773,tc_fun(X15773,tc_HOL_Obool),tc_HOL_Obool),c_member(X15773)),X15772)))),hAPP(hAPP(c_COMBC(X15773,tc_fun(X15773,tc_HOL_Obool),tc_HOL_Obool),c_member(X15773)),X15771)))))))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15773),c_Big__Operators_Olattice__class_OSup__fin(X15773,X15772)),c_Big__Operators_Olattice__class_OSup__fin(X15773,X15771))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__Sup2__distrib])])])). 6.97/7.21 cnf(c_0_4733, 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_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)|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_4449])). 6.97/7.21 cnf(c_0_4734, 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_4450])). 6.97/7.21 cnf(c_0_4735, 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_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_4451])). 6.97/7.21 cnf(c_0_4736, 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_4452])). 6.97/7.21 fof(c_0_4737, plain, ![X13775, X13776, X13777, X13778, X13779, X13780, X13781]:(~class_Groups_Ocomm__monoid__add(X13781)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13780),X13779))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13778),X13777))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13780,X13781),hAPP(hAPP(c_COMBS(X13780,tc_fun(X13778,tc_HOL_Obool),X13781),hAPP(hAPP(c_COMBB(tc_fun(X13778,X13781),tc_fun(tc_fun(X13778,tc_HOL_Obool),X13781),X13780),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13778,X13781)),X13776)),hAPP(hAPP(c_COMBB(tc_fun(X13778,tc_HOL_Obool),tc_fun(X13778,tc_HOL_Obool),X13780),c_Set_OCollect(X13778)),hAPP(hAPP(c_COMBB(tc_fun(X13778,tc_HOL_Obool),tc_fun(X13778,tc_HOL_Obool),X13780),hAPP(c_COMBS(X13778,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X13778),c_fconj),hAPP(hAPP(c_COMBC(X13778,tc_fun(X13778,tc_HOL_Obool),tc_HOL_Obool),c_member(X13778)),X13777)))),X13775)))),X13779)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13778,X13781),hAPP(hAPP(c_COMBS(X13778,tc_fun(X13780,tc_HOL_Obool),X13781),hAPP(hAPP(c_COMBB(tc_fun(X13780,X13781),tc_fun(tc_fun(X13780,tc_HOL_Obool),X13781),X13778),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13780,X13781)),hAPP(c_COMBC(X13780,X13778,X13781),X13776))),hAPP(hAPP(c_COMBB(tc_fun(X13780,tc_HOL_Obool),tc_fun(X13780,tc_HOL_Obool),X13778),c_Set_OCollect(X13780)),hAPP(hAPP(c_COMBB(tc_fun(X13780,tc_HOL_Obool),tc_fun(X13780,tc_HOL_Obool),X13778),hAPP(c_COMBS(X13780,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X13780),c_fconj),hAPP(hAPP(c_COMBC(X13780,tc_fun(X13780,tc_HOL_Obool),tc_HOL_Obool),c_member(X13780)),X13779)))),hAPP(c_COMBC(X13780,X13778,tc_HOL_Obool),X13775))))),X13777)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__setsum__restrict])])])). 6.97/7.21 cnf(c_0_4738, 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_4453])). 6.97/7.21 cnf(c_0_4739, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[c_0_4454, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.21 cnf(c_0_4740, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),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)],[c_0_4455, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4457]), ['final']). 6.97/7.21 cnf(c_0_4741, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin)), inference(rw,[status(thm)],[c_0_4458, c_0_4411]), ['final']). 6.97/7.21 cnf(c_0_4742, plain, (hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[fact_One__nat__def]), ['final']). 6.97/7.21 cnf(c_0_4743, 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_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_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))))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4459])). 6.97/7.21 fof(c_0_4744, plain, ![X10446, X10447, X10448, X10449]:(~class_Complete__Lattice_Ocomplete__lattice(X10449)|hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X10448,X10449),X10447),X10446)=c_Complete__Lattice_OSup__class_OSup(X10449,hAPP(c_Set_OCollect(X10449),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10448,X10449),tc_HOL_Obool),tc_HOL_Obool,X10449),c_HOL_OEx(tc_fun(X10448,X10449))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10448,X10449),tc_HOL_Obool),tc_fun(tc_fun(X10448,X10449),tc_HOL_Obool),X10449),hAPP(c_COMBS(tc_fun(X10448,X10449),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X10448,X10449)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X10448,X10449),tc_fun(tc_fun(X10448,X10449),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X10448,X10449))),X10447)))),hAPP(hAPP(c_COMBC(X10449,tc_fun(tc_fun(X10448,X10449),X10449),tc_fun(tc_fun(X10448,X10449),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10449,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X10448,X10449),X10449),tc_fun(tc_fun(X10448,X10449),tc_HOL_Obool)),X10449),c_COMBB(X10449,tc_HOL_Obool,tc_fun(X10448,X10449))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X10448,X10449),X10448,X10449),c_COMBI(tc_fun(X10448,X10449))),X10446))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__apply])])). 6.97/7.21 fof(c_0_4745, plain, ![X2891, X2892, X2893, X2894]:(~class_Complete__Lattice_Ocomplete__lattice(X2894)|hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X2893,X2894),X2892),X2891)=c_Complete__Lattice_OInf__class_OInf(X2894,hAPP(c_Set_OCollect(X2894),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2893,X2894),tc_HOL_Obool),tc_HOL_Obool,X2894),c_HOL_OEx(tc_fun(X2893,X2894))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2893,X2894),tc_HOL_Obool),tc_fun(tc_fun(X2893,X2894),tc_HOL_Obool),X2894),hAPP(c_COMBS(tc_fun(X2893,X2894),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X2893,X2894)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X2893,X2894),tc_fun(tc_fun(X2893,X2894),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X2893,X2894))),X2892)))),hAPP(hAPP(c_COMBC(X2894,tc_fun(tc_fun(X2893,X2894),X2894),tc_fun(tc_fun(X2893,X2894),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2894,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X2893,X2894),X2894),tc_fun(tc_fun(X2893,X2894),tc_HOL_Obool)),X2894),c_COMBB(X2894,tc_HOL_Obool,tc_fun(X2893,X2894))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X2893,X2894),X2893,X2894),c_COMBI(tc_fun(X2893,X2894))),X2891))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__apply])])])). 6.97/7.21 fof(c_0_4746, plain, ![X14572, X14573, X14574]:(~class_Orderings_Olinorder(X14574)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14574),X14573))|(c_Orderings_Obot__class_Obot(tc_fun(X14574,tc_HOL_Obool))=X14573|c_Big__Operators_Olattice_OInf__fin(X14574,c_Orderings_Oord__class_Omin(X14574),hAPP(c_Set_OCollect(X14574),hAPP(hAPP(c_COMBB(tc_fun(X14574,tc_HOL_Obool),tc_HOL_Obool,X14574),c_HOL_OEx(X14574)),hAPP(hAPP(c_COMBC(X14574,tc_fun(X14574,tc_HOL_Obool),tc_fun(X14574,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14574,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X14574,tc_HOL_Obool),tc_fun(X14574,tc_HOL_Obool)),X14574),c_COMBS(X14574,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14574,tc_HOL_Obool),tc_fun(X14574,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X14574),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X14574),c_fconj)),hAPP(hAPP(c_COMBC(X14574,tc_fun(X14574,X14574),tc_fun(X14574,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14574,tc_HOL_Obool),tc_fun(tc_fun(X14574,X14574),tc_fun(X14574,tc_HOL_Obool)),X14574),c_COMBB(X14574,tc_HOL_Obool,X14574)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(X14574),X14572))))),hAPP(hAPP(c_COMBC(X14574,tc_fun(X14574,tc_HOL_Obool),tc_HOL_Obool),c_member(X14574)),X14573)))))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X14574),X14572),c_Big__Operators_Olattice_OInf__fin(X14574,c_Orderings_Oord__class_Omin(X14574),X14573))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf1__distrib])])). 6.97/7.21 fof(c_0_4747, plain, ![X13801, X13802, X13803]:(~class_Orderings_Olinorder(X13803)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13803),X13802))|(X13802=c_Orderings_Obot__class_Obot(tc_fun(X13803,tc_HOL_Obool))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X13803),X13801),c_Big__Operators_Olattice_OSup__fin(X13803,c_Orderings_Oord__class_Omax(X13803),X13802))=c_Big__Operators_Olattice_OSup__fin(X13803,c_Orderings_Oord__class_Omax(X13803),hAPP(c_Set_OCollect(X13803),hAPP(hAPP(c_COMBB(tc_fun(X13803,tc_HOL_Obool),tc_HOL_Obool,X13803),c_HOL_OEx(X13803)),hAPP(hAPP(c_COMBC(X13803,tc_fun(X13803,tc_HOL_Obool),tc_fun(X13803,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13803,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X13803,tc_HOL_Obool),tc_fun(X13803,tc_HOL_Obool)),X13803),c_COMBS(X13803,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13803,tc_HOL_Obool),tc_fun(X13803,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X13803),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X13803),c_fconj)),hAPP(hAPP(c_COMBC(X13803,tc_fun(X13803,X13803),tc_fun(X13803,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13803,tc_HOL_Obool),tc_fun(tc_fun(X13803,X13803),tc_fun(X13803,tc_HOL_Obool)),X13803),c_COMBB(X13803,tc_HOL_Obool,X13803)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(X13803),X13801))))),hAPP(hAPP(c_COMBC(X13803,tc_fun(X13803,tc_HOL_Obool),tc_HOL_Obool),c_member(X13803)),X13802)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oinf__Sup1__distrib])])])). 6.97/7.21 fof(c_0_4748, plain, ![X9576, X9577, X9578]:(~class_Groups_Olinordered__ab__semigroup__add(X9578)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9578),X9577))|(c_Orderings_Obot__class_Obot(tc_fun(X9578,tc_HOL_Obool))=X9577|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9578),X9576),c_Big__Operators_Olinorder__class_OMin(X9578,X9577))=c_Big__Operators_Olinorder__class_OMin(X9578,hAPP(c_Set_OCollect(X9578),hAPP(hAPP(c_COMBB(tc_fun(X9578,tc_HOL_Obool),tc_HOL_Obool,X9578),c_HOL_OEx(X9578)),hAPP(hAPP(c_COMBC(X9578,tc_fun(X9578,tc_HOL_Obool),tc_fun(X9578,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9578,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X9578,tc_HOL_Obool),tc_fun(X9578,tc_HOL_Obool)),X9578),c_COMBS(X9578,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9578,tc_HOL_Obool),tc_fun(X9578,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X9578),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X9578),c_fconj)),hAPP(hAPP(c_COMBC(X9578,tc_fun(X9578,X9578),tc_fun(X9578,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9578,tc_HOL_Obool),tc_fun(tc_fun(X9578,X9578),tc_fun(X9578,tc_HOL_Obool)),X9578),c_COMBB(X9578,tc_HOL_Obool,X9578)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X9578),X9576))))),hAPP(hAPP(c_COMBC(X9578,tc_fun(X9578,tc_HOL_Obool),tc_HOL_Obool),c_member(X9578)),X9577)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__Min__commute])])])). 6.97/7.21 fof(c_0_4749, plain, ![X6698, X6699, X6700]:(~class_Lattices_Odistrib__lattice(X6700)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6700),X6699))|(c_Orderings_Obot__class_Obot(tc_fun(X6700,tc_HOL_Obool))=X6699|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6700),X6698),c_Big__Operators_Olattice__class_OInf__fin(X6700,X6699))=c_Big__Operators_Olattice__class_OInf__fin(X6700,hAPP(c_Set_OCollect(X6700),hAPP(hAPP(c_COMBB(tc_fun(X6700,tc_HOL_Obool),tc_HOL_Obool,X6700),c_HOL_OEx(X6700)),hAPP(hAPP(c_COMBC(X6700,tc_fun(X6700,tc_HOL_Obool),tc_fun(X6700,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6700,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X6700,tc_HOL_Obool),tc_fun(X6700,tc_HOL_Obool)),X6700),c_COMBS(X6700,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6700,tc_HOL_Obool),tc_fun(X6700,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X6700),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X6700),c_fconj)),hAPP(hAPP(c_COMBC(X6700,tc_fun(X6700,X6700),tc_fun(X6700,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6700,tc_HOL_Obool),tc_fun(tc_fun(X6700,X6700),tc_fun(X6700,tc_HOL_Obool)),X6700),c_COMBB(X6700,tc_HOL_Obool,X6700)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6700),X6698))))),hAPP(hAPP(c_COMBC(X6700,tc_fun(X6700,tc_HOL_Obool),tc_HOL_Obool),c_member(X6700)),X6699)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__Inf1__distrib])])])). 6.97/7.21 fof(c_0_4750, plain, ![X14284, X14285, X14286]:(~class_Groups_Olinordered__ab__semigroup__add(X14286)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14286),X14285))|(X14285=c_Orderings_Obot__class_Obot(tc_fun(X14286,tc_HOL_Obool))|c_Big__Operators_Olinorder__class_OMax(X14286,hAPP(c_Set_OCollect(X14286),hAPP(hAPP(c_COMBB(tc_fun(X14286,tc_HOL_Obool),tc_HOL_Obool,X14286),c_HOL_OEx(X14286)),hAPP(hAPP(c_COMBC(X14286,tc_fun(X14286,tc_HOL_Obool),tc_fun(X14286,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14286,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X14286,tc_HOL_Obool),tc_fun(X14286,tc_HOL_Obool)),X14286),c_COMBS(X14286,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14286,tc_HOL_Obool),tc_fun(X14286,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X14286),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X14286),c_fconj)),hAPP(hAPP(c_COMBC(X14286,tc_fun(X14286,X14286),tc_fun(X14286,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14286,tc_HOL_Obool),tc_fun(tc_fun(X14286,X14286),tc_fun(X14286,tc_HOL_Obool)),X14286),c_COMBB(X14286,tc_HOL_Obool,X14286)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X14286),X14284))))),hAPP(hAPP(c_COMBC(X14286,tc_fun(X14286,tc_HOL_Obool),tc_HOL_Obool),c_member(X14286)),X14285)))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14286),X14284),c_Big__Operators_Olinorder__class_OMax(X14286,X14285))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__Max__commute])])])). 6.97/7.21 fof(c_0_4751, plain, ![X14906, X14907, X14908]:(~class_Lattices_Odistrib__lattice(X14908)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14908),X14907))|(X14907=c_Orderings_Obot__class_Obot(tc_fun(X14908,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X14908),X14906),c_Big__Operators_Olattice__class_OSup__fin(X14908,X14907))=c_Big__Operators_Olattice__class_OSup__fin(X14908,hAPP(c_Set_OCollect(X14908),hAPP(hAPP(c_COMBB(tc_fun(X14908,tc_HOL_Obool),tc_HOL_Obool,X14908),c_HOL_OEx(X14908)),hAPP(hAPP(c_COMBC(X14908,tc_fun(X14908,tc_HOL_Obool),tc_fun(X14908,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14908,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X14908,tc_HOL_Obool),tc_fun(X14908,tc_HOL_Obool)),X14908),c_COMBS(X14908,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14908,tc_HOL_Obool),tc_fun(X14908,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X14908),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X14908),c_fconj)),hAPP(hAPP(c_COMBC(X14908,tc_fun(X14908,X14908),tc_fun(X14908,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14908,tc_HOL_Obool),tc_fun(tc_fun(X14908,X14908),tc_fun(X14908,tc_HOL_Obool)),X14908),c_COMBB(X14908,tc_HOL_Obool,X14908)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X14908),X14906))))),hAPP(hAPP(c_COMBC(X14908,tc_fun(X14908,tc_HOL_Obool),tc_HOL_Obool),c_member(X14908)),X14907)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__Sup1__distrib])])])). 6.97/7.21 cnf(c_0_4752, 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_4460])). 6.97/7.21 fof(c_0_4753, plain, ![X9394, X9395, X9396, X9397]:((~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9397,tc_fun(X9397,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X9397,tc_fun(tc_prod(X9397,X9397),tc_HOL_Obool),tc_fun(X9397,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9397,tc_fun(tc_fun(tc_prod(X9397,X9397),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X9397,X9397),tc_HOL_Obool),tc_fun(X9397,tc_HOL_Obool)),X9397),c_COMBC(X9397,tc_fun(tc_prod(X9397,X9397),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9397,tc_prod(X9397,X9397)),tc_fun(X9397,tc_fun(tc_fun(tc_prod(X9397,X9397),tc_HOL_Obool),tc_HOL_Obool)),X9397),hAPP(c_COMBB(tc_prod(X9397,X9397),tc_fun(tc_fun(tc_prod(X9397,X9397),tc_HOL_Obool),tc_HOL_Obool),X9397),c_member(tc_prod(X9397,X9397)))),c_Product__Type_OPair(X9397,X9397)))),X9396)),c_fequal),X9395),X9394))|hBOOL(hAPP(hAPP(c_member(tc_prod(X9397,X9397)),hAPP(hAPP(c_Product__Type_OPair(X9397,X9397),X9395),X9394)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X9397,X9397),tc_HOL_Obool)),X9396),c_Relation_OId(X9397)))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X9397,X9397)),hAPP(hAPP(c_Product__Type_OPair(X9397,X9397),X9395),X9394)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X9397,X9397),tc_HOL_Obool)),X9396),c_Relation_OId(X9397))))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9397,tc_fun(X9397,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X9397,tc_fun(tc_prod(X9397,X9397),tc_HOL_Obool),tc_fun(X9397,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9397,tc_fun(tc_fun(tc_prod(X9397,X9397),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X9397,X9397),tc_HOL_Obool),tc_fun(X9397,tc_HOL_Obool)),X9397),c_COMBC(X9397,tc_fun(tc_prod(X9397,X9397),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9397,tc_prod(X9397,X9397)),tc_fun(X9397,tc_fun(tc_fun(tc_prod(X9397,X9397),tc_HOL_Obool),tc_HOL_Obool)),X9397),hAPP(c_COMBB(tc_prod(X9397,X9397),tc_fun(tc_fun(tc_prod(X9397,X9397),tc_HOL_Obool),tc_HOL_Obool),X9397),c_member(tc_prod(X9397,X9397)))),c_Product__Type_OPair(X9397,X9397)))),X9396)),c_fequal),X9395),X9394)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reflcl__set__eq])])). 6.97/7.21 fof(c_0_4754, plain, ![X872, X873, X874, X875, X876, X877]:((hBOOL(hAPP(hAPP(c_member(X875),esk25_6(X872,X873,X874,X875,X876,X877)),X874))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X877,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X875,tc_HOL_Obool),tc_Nat_Onat,X877),c_Finite__Set_Ocard(X875)),hAPP(hAPP(c_COMBB(tc_fun(X875,tc_HOL_Obool),tc_fun(X875,tc_HOL_Obool),X877),c_Set_OCollect(X875)),hAPP(hAPP(c_COMBB(tc_fun(X875,tc_HOL_Obool),tc_fun(X875,tc_HOL_Obool),X877),hAPP(c_COMBS(X875,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X875),c_fconj),hAPP(hAPP(c_COMBC(X875,tc_fun(X875,tc_HOL_Obool),tc_HOL_Obool),c_member(X875)),X874)))),X873)))),X876)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X875,tc_Nat_Onat),X872),X874)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X875),X874))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X877),X876)))&(hAPP(c_Finite__Set_Ocard(X877),hAPP(c_Set_OCollect(X877),hAPP(hAPP(c_COMBS(X877,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X877),c_fconj),hAPP(hAPP(c_COMBC(X877,tc_fun(X877,tc_HOL_Obool),tc_HOL_Obool),c_member(X877)),X876))),hAPP(hAPP(c_COMBC(X877,X875,tc_HOL_Obool),X873),esk25_6(X872,X873,X874,X875,X876,X877)))))!=hAPP(X872,esk25_6(X872,X873,X874,X875,X876,X877))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X877,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X875,tc_HOL_Obool),tc_Nat_Onat,X877),c_Finite__Set_Ocard(X875)),hAPP(hAPP(c_COMBB(tc_fun(X875,tc_HOL_Obool),tc_fun(X875,tc_HOL_Obool),X877),c_Set_OCollect(X875)),hAPP(hAPP(c_COMBB(tc_fun(X875,tc_HOL_Obool),tc_fun(X875,tc_HOL_Obool),X877),hAPP(c_COMBS(X875,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X875),c_fconj),hAPP(hAPP(c_COMBC(X875,tc_fun(X875,tc_HOL_Obool),tc_HOL_Obool),c_member(X875)),X874)))),X873)))),X876)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X875,tc_Nat_Onat),X872),X874)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X875),X874))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X877),X876)))), 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])])])])])). 6.97/7.21 cnf(c_0_4755, 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_4461])). 6.97/7.21 fof(c_0_4756, plain, ![X4608, X4609, X4610, X4611]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4611),hAPP(c_Set_OCollect(X4611),X4610)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X4609),hAPP(c_Set_OCollect(X4609),hAPP(hAPP(c_COMBB(tc_fun(X4611,tc_HOL_Obool),tc_HOL_Obool,X4609),c_HOL_OEx(X4611)),hAPP(hAPP(c_COMBC(X4609,tc_fun(X4611,tc_HOL_Obool),tc_fun(X4611,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4611,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X4611,tc_HOL_Obool),tc_fun(X4611,tc_HOL_Obool)),X4609),c_COMBS(X4611,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4611,tc_HOL_Obool),tc_fun(X4611,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4609),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4611),c_fconj)),hAPP(hAPP(c_COMBC(X4609,tc_fun(X4611,X4609),tc_fun(X4611,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4609,tc_HOL_Obool),tc_fun(tc_fun(X4611,X4609),tc_fun(X4611,tc_HOL_Obool)),X4609),c_COMBB(X4609,tc_HOL_Obool,X4611)),c_fequal)),X4608)))),X4610)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__image__set])])])). 6.97/7.21 fof(c_0_4757, plain, ![X1674, X1675, X1676, X1677, X1678, X1679]:((hBOOL(hAPP(hAPP(c_member(X1677),esk47_6(X1674,X1675,X1676,X1677,X1678,X1679)),X1676))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1679,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X1677,tc_HOL_Obool),tc_Nat_Onat,X1679),c_Finite__Set_Ocard(X1677)),hAPP(hAPP(c_COMBB(tc_fun(X1677,tc_HOL_Obool),tc_fun(X1677,tc_HOL_Obool),X1679),c_Set_OCollect(X1677)),hAPP(hAPP(c_COMBB(tc_fun(X1677,tc_HOL_Obool),tc_fun(X1677,tc_HOL_Obool),X1679),hAPP(c_COMBS(X1677,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1677),c_fconj),hAPP(hAPP(c_COMBC(X1677,tc_fun(X1677,tc_HOL_Obool),tc_HOL_Obool),c_member(X1677)),X1676)))),X1675)))),X1678)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1674),hAPP(c_Finite__Set_Ocard(X1677),X1676))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1677),X1676))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1679),X1678)))&(X1674!=hAPP(c_Finite__Set_Ocard(X1679),hAPP(c_Set_OCollect(X1679),hAPP(hAPP(c_COMBS(X1679,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1679),c_fconj),hAPP(hAPP(c_COMBC(X1679,tc_fun(X1679,tc_HOL_Obool),tc_HOL_Obool),c_member(X1679)),X1678))),hAPP(hAPP(c_COMBC(X1679,X1677,tc_HOL_Obool),X1675),esk47_6(X1674,X1675,X1676,X1677,X1678,X1679)))))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1679,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X1677,tc_HOL_Obool),tc_Nat_Onat,X1679),c_Finite__Set_Ocard(X1677)),hAPP(hAPP(c_COMBB(tc_fun(X1677,tc_HOL_Obool),tc_fun(X1677,tc_HOL_Obool),X1679),c_Set_OCollect(X1677)),hAPP(hAPP(c_COMBB(tc_fun(X1677,tc_HOL_Obool),tc_fun(X1677,tc_HOL_Obool),X1679),hAPP(c_COMBS(X1677,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1677),c_fconj),hAPP(hAPP(c_COMBC(X1677,tc_fun(X1677,tc_HOL_Obool),tc_HOL_Obool),c_member(X1677)),X1676)))),X1675)))),X1678)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1674),hAPP(c_Finite__Set_Ocard(X1677),X1676))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1677),X1676))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1679),X1678)))), 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])])])])])). 6.97/7.21 cnf(c_0_4758, 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))|X1=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[c_0_4462])). 6.97/7.21 fof(c_0_4759, plain, ![X13214, X13215]:(~class_Lazy__Sequence_Osmall__lazy(X13215)|c_Lazy__Sequence_Oappend(tc_List_Olist(X13215),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(X13215)),c_List_Olist_ONil(X13215)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X13215))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13214)),hAPP(c_Lazy__Sequence_Obind(tc_prod(X13215,tc_List_Olist(X13215)),tc_List_Olist(X13215),c_Lazy__Sequence_Oproduct(X13215,tc_List_Olist(X13215),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X13215,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X13214),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X13215),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X13214),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(X13215,tc_List_Olist(X13215),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X13215))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X13215),tc_List_Olist(X13215)),tc_fun(tc_List_Olist(X13215),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X13215))),X13215),hAPP(c_COMBB(tc_List_Olist(X13215),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X13215)),tc_List_Olist(X13215)),c_Lazy__Sequence_Osingle(tc_List_Olist(X13215)))),c_List_Olist_OCons(X13215))))),c_Lazy__Sequence_Oempty(tc_List_Olist(X13215))))=c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X13215),X13214)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_small__lazy__list_Osimps])])])). 6.97/7.21 fof(c_0_4760, plain, ![X6790, X6791, X6792, X6793, X6794, X6795]:(~class_Groups_Ocomm__monoid__add(X6795)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6794),X6793))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6791,X6795),hAPP(hAPP(c_COMBB(tc_fun(X6794,tc_HOL_Obool),X6795,X6791),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6794,X6795),X6792)),hAPP(hAPP(c_COMBB(tc_fun(X6794,tc_HOL_Obool),tc_fun(X6794,tc_HOL_Obool),X6791),c_Set_OCollect(X6794)),hAPP(hAPP(c_COMBB(tc_fun(X6794,tc_HOL_Obool),tc_fun(X6794,tc_HOL_Obool),X6791),hAPP(c_COMBS(X6794,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X6794),c_fconj),hAPP(hAPP(c_COMBC(X6794,tc_fun(X6794,tc_HOL_Obool),tc_HOL_Obool),c_member(X6794)),X6793)))),hAPP(c_COMBC(X6794,X6791,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X6791,tc_fun(X6791,tc_HOL_Obool),X6794),c_fequal),X6790)))))),hAPP(c_Set_Oimage(X6794,X6791,X6790),X6793))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6794,X6795),X6792),X6793))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__image__gen])])])). 6.97/7.21 fof(c_0_4761, plain, ![X2553, X2554, X2555]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2555,X2555),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X2555,X2555,X2555),X2554),X2553)),X2554))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X2555,tc_HOL_Obool),tc_fun(X2555,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X2555,tc_HOL_Obool),tc_fun(X2555,tc_HOL_Obool),tc_fun(X2555,tc_HOL_Obool)),c_Wellfounded_Omin__ext(X2555,X2554)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X2555,tc_HOL_Obool),tc_fun(X2555,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(X2555,X2553)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X2555,tc_HOL_Obool),tc_fun(X2555,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2555,tc_HOL_Obool),tc_fun(X2555,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X2555,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X2555,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X2555,tc_HOL_Obool),tc_fun(X2555,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(X2555,X2554)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__ext__compat])])])). 6.97/7.21 fof(c_0_4762, plain, ![X14921, X14922, X14923]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X14923,X14923),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X14923,X14923,X14923),X14922),X14921)),X14922))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X14923,tc_HOL_Obool),tc_fun(X14923,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X14923,tc_HOL_Obool),tc_fun(X14923,tc_HOL_Obool),tc_fun(X14923,tc_HOL_Obool)),c_Wellfounded_Omax__ext(X14923,X14922)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X14923,tc_HOL_Obool),tc_fun(X14923,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(X14923,X14921)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X14923,tc_HOL_Obool),tc_fun(X14923,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X14923,tc_HOL_Obool),tc_fun(X14923,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X14923,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X14923,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X14923,tc_HOL_Obool),tc_fun(X14923,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(X14923,X14922)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ext__compat])])). 6.97/7.21 cnf(c_0_4763, 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)|X1=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|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_4462])). 6.97/7.21 cnf(c_0_4764, plain, (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)=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),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_4463])). 6.97/7.21 cnf(c_0_4765, 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)))|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)))=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))), inference(split_conjunct,[status(thm)],[c_0_4464])). 6.97/7.21 fof(c_0_4766, plain, ![X7160, X7161]:(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7161))|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)),X7161))),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,X7160)))))=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)),X7161))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X7160))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__less__Suc2])])])). 6.97/7.21 cnf(c_0_4767, plain, (hAPP(c_Set_Ovimage(X1,X2,X3),X4)=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))), inference(split_conjunct,[status(thm)],[c_0_4465])). 6.97/7.21 cnf(c_0_4768, 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_4466, c_0_4467]), c_0_4467]), ['final']). 6.97/7.21 fof(c_0_4769, plain, ![X5328, X5329]:(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5329))|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)),X5329))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X5328)))))=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)),X5329))),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,X5328)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__less__Suc])])). 6.97/7.21 cnf(c_0_4770, 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_4468])). 6.97/7.21 cnf(c_0_4771, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk171_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3)))|c_List_Otranspose(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_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1), inference(split_conjunct,[status(thm)],[c_0_4469])). 6.97/7.21 cnf(c_0_4772, plain, (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)))=c_List_Olist_ONil(tc_Nat_Onat)), inference(rw,[status(thm)],[c_0_4470, c_0_4471])). 6.97/7.21 cnf(c_0_4773, 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_4472]), ['final']). 6.97/7.21 fof(c_0_4774, plain, ![X6544, X6545, X6546]:hAPP(hAPP(c_List_Omap(X6546,X6545),X6544),c_List_Olist_ONil(X6546))=c_List_Olist_ONil(X6545), inference(variable_rename,[status(thm)],[fact_map_Osimps_I1_J])). 6.97/7.21 cnf(c_0_4775, 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),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)))|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_4473])). 6.97/7.21 fof(c_0_4776, plain, ![X5491, X5492, X5493, X5494]:(~class_Rings_Ocomm__semiring__1(X5494)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5494),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5494),X5491)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5494),X5493),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5494),X5493),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5494),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5494),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5491),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X5492))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5494),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5494),c_Groups_Oone__class_Oone(X5494)),c_Groups_Oone__class_Oone(X5494))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5494),hAPP(hAPP(c_COMBB(X5494,X5494,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(X5494),X5493)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X5494,X5494),hAPP(hAPP(c_COMBB(X5494,tc_fun(X5494,X5494),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(X5494)),c_Nat_Osemiring__1__class_Oof__nat(X5494))),X5492))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X5491)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_arith__series__general])])])). 6.97/7.21 fof(c_0_4777, plain, ![X485]:hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X485)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X485), inference(variable_rename,[status(thm)],[fact_atLeast0LessThan])). 6.97/7.21 cnf(c_0_4778, 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),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_4474])). 6.97/7.21 cnf(c_0_4779, 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_4475])). 6.97/7.21 cnf(c_0_4780, 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),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)),hAPP(c_Set_OCollect(X1),X2))),hAPP(c_Set_OCollect(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_4476])). 6.97/7.21 cnf(c_0_4781, 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))), inference(split_conjunct,[status(thm)],[c_0_4477]), ['final']). 6.97/7.21 fof(c_0_4782, plain, ![X14196, X14197, X14198]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14198,tc_HOL_Obool)),X14197),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X14198,tc_HOL_Obool)),X14196))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X14198,tc_HOL_Obool)),X14197),X14196), inference(variable_rename,[status(thm)],[fact_Diff__eq])). 6.97/7.21 cnf(c_0_4783, plain, (c_List_Otranspose(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_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))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),esk171_3(X3,X1,X2)))!=X3|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X3), inference(split_conjunct,[status(thm)],[c_0_4469])). 6.97/7.21 cnf(c_0_4784, 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_4474])). 6.97/7.21 cnf(c_0_4785, 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_4478])). 6.97/7.21 fof(c_0_4786, plain, ![X8279, X8280, X8281]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8281),X8280))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X8281)),hAPP(c_Set_OCollect(tc_List_Olist(X8281)),hAPP(hAPP(c_COMBS(tc_List_Olist(X8281),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X8281)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X8281),tc_fun(X8281,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X8281,tc_HOL_Obool),tc_fun(tc_fun(X8281,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X8281)),c_Orderings_Oord__class_Oless__eq(tc_fun(X8281,tc_HOL_Obool))),c_List_Oset(X8281))),X8280))),hAPP(hAPP(c_COMBC(tc_List_Olist(X8281),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X8281)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X8281)))),X8279)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__lists__length__le])])). 6.97/7.21 cnf(c_0_4787, 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_4479])). 6.97/7.21 cnf(c_0_4788, 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_4464])). 6.97/7.21 fof(c_0_4789, plain, ![X10054, X10055, X10056]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10056),X10055))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X10056)),hAPP(c_Set_OCollect(tc_List_Olist(X10056)),hAPP(hAPP(c_COMBS(tc_List_Olist(X10056),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X10056)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X10056),tc_fun(X10056,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X10056,tc_HOL_Obool),tc_fun(tc_fun(X10056,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X10056)),c_Orderings_Oord__class_Oless__eq(tc_fun(X10056,tc_HOL_Obool))),c_List_Oset(X10056))),X10055))),hAPP(hAPP(c_COMBC(tc_List_Olist(X10056),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X10056)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X10056)))),X10054)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__lists__length__eq])])). 6.97/7.21 fof(c_0_4790, plain, ![X14693, X14694, X14695, X14696, X14697, X14698]:(~class_Groups_Ocomm__monoid__add(X14698)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14697),X14696))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14698),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14697,X14698),X14694),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14697,tc_HOL_Obool)),X14696),hAPP(c_Set_OCollect(X14697),X14695)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14697,X14698),X14693),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14697,tc_HOL_Obool)),X14696),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X14697,tc_HOL_Obool)),hAPP(c_Set_OCollect(X14697),X14695)))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14697,X14698),hAPP(hAPP(c_COMBS(X14697,X14698,X14698),hAPP(hAPP(c_COMBS(X14697,X14698,tc_fun(X14698,X14698)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X14698,tc_fun(X14698,X14698)),X14697),c_If(X14698)),X14695)),X14694)),X14693)),X14696))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__cases])])])). 6.97/7.21 fof(c_0_4791, plain, ![X16811, X16812, X16813, X16814]:((hBOOL(hAPP(X16814,esk565_4(X16811,X16812,X16813,X16814)))|c_Wellfounded_Owf(X16811,hAPP(c_Set_OCollect(tc_prod(X16811,X16811)),hAPP(c_Product__Type_Oprod_Oprod__case(X16811,X16811,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X16811,tc_HOL_Obool),tc_fun(X16811,tc_HOL_Obool),X16811),hAPP(c_COMBS(X16811,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X16811),c_fconj),X16814))),hAPP(hAPP(c_COMBC(X16811,tc_fun(X16811,X16811),tc_fun(X16811,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16811,tc_HOL_Obool),tc_fun(tc_fun(X16811,X16811),tc_fun(X16811,tc_HOL_Obool)),X16811),c_COMBB(X16811,tc_HOL_Obool,X16811)),c_fequal)),X16812))))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X16813,hAPP(X16812,esk565_4(X16811,X16812,X16813,X16814)))),hAPP(X16813,esk565_4(X16811,X16812,X16813,X16814))))|c_Wellfounded_Owf(X16811,hAPP(c_Set_OCollect(tc_prod(X16811,X16811)),hAPP(c_Product__Type_Oprod_Oprod__case(X16811,X16811,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X16811,tc_HOL_Obool),tc_fun(X16811,tc_HOL_Obool),X16811),hAPP(c_COMBS(X16811,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X16811),c_fconj),X16814))),hAPP(hAPP(c_COMBC(X16811,tc_fun(X16811,X16811),tc_fun(X16811,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16811,tc_HOL_Obool),tc_fun(tc_fun(X16811,X16811),tc_fun(X16811,tc_HOL_Obool)),X16811),c_COMBB(X16811,tc_HOL_Obool,X16811)),c_fequal)),X16812))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__if__measure])])])])). 6.97/7.21 cnf(c_0_4792, 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_4480])). 6.97/7.21 cnf(c_0_4793, 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_4481])). 6.97/7.21 fof(c_0_4794, plain, ![X14073]:hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X14073))=hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14073), inference(variable_rename,[status(thm)],[fact_less__eq__Suc__le__raw])). 6.97/7.21 cnf(c_0_4795, 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),esk438_3(X1,X2,X3)),esk439_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk439_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(X1,esk438_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)))),esk439_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_4482])). 6.97/7.21 cnf(c_0_4796, plain, (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)!=X2|c_Groups_Ozero__class_Ozero(X1)!=X3|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_4483])). 6.97/7.21 cnf(c_0_4797, 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_4484])). 6.97/7.21 cnf(c_0_4798, 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_4485, c_0_4467]), ['final']). 6.97/7.21 cnf(c_0_4799, 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)))),X4)))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(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_Set_OCollect(X1)),hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X4)))), inference(split_conjunct,[status(thm)],[c_0_4486])). 6.97/7.21 cnf(c_0_4800, plain, (c_Complete__Lattice_OInf__class_OInf(X1,X2)=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)))))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_4487])). 6.97/7.21 fof(c_0_4801, plain, ![X4765, X4766, X4767, X4768]:((~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),X4768),X4767)),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),X4766),X4765)),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),X4768),X4765)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4766),X4767))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4768),X4765)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4766),X4767)))|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),X4768),X4767)),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),X4766),X4765)),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_less])])). 6.97/7.21 fof(c_0_4802, plain, ![X4267, X4268, X4269, X4270]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4270),X4267)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4268),X4269)))|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),X4270),X4269)),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),X4268),X4267)),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),X4270),X4269)),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),X4268),X4267)),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),X4270),X4267)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4268),X4269))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le])])). 6.97/7.21 cnf(c_0_4803, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk290_3(X1,X2,X3)),esk291_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk291_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(X1,esk290_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)))),esk291_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_4488])). 6.97/7.21 fof(c_0_4804, plain, ![X15136, X15137, X15138]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X15138,X15138),tc_HOL_Obool)),X15137),hAPP(hAPP(c_Product__Type_OSigma(X15138,X15138),X15136),hAPP(c_COMBK(tc_fun(X15138,tc_HOL_Obool),X15138),X15136))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X15138),tc_List_Olist(X15138)),tc_HOL_Obool)),c_List_Olistrel(X15138,X15137)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(X15138),tc_List_Olist(X15138)),c_List_Olists(X15138,X15136)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X15138),tc_HOL_Obool),tc_List_Olist(X15138)),c_List_Olists(X15138,X15136)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__subset])])). 6.97/7.21 cnf(c_0_4805, 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_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))))=c_Nitpick_Oprod(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_4489])). 6.97/7.21 cnf(c_0_4806, 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_4490, c_0_4467]), c_0_4467]), c_0_4467]), ['final']). 6.97/7.21 cnf(c_0_4807, 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_4491])). 6.97/7.21 cnf(c_0_4808, 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_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),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_4492])). 6.97/7.21 fof(c_0_4809, plain, ![X10272, X10273, X10274, X10275, X10276, X10277]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X10277,X10276)),hAPP(hAPP(c_Product__Type_OPair(X10277,X10276),esk336_6(X10272,X10273,X10274,X10275,X10276,X10277)),esk337_6(X10272,X10273,X10274,X10275,X10276,X10277))),hAPP(X10273,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10277,X10276),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(X10277,X10276),tc_HOL_Obool),X10273)),hAPP(c_Set_OCollect(tc_prod(X10277,X10276)),hAPP(c_Product__Type_Oprod_Oprod__case(X10277,X10276,tc_HOL_Obool),X10272))))))|hBOOL(hAPP(hAPP(X10272,X10275),X10274))|~c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(X10277,X10276),tc_HOL_Obool),tc_fun(tc_prod(X10277,X10276),tc_HOL_Obool),X10273)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X10277,X10276)),hAPP(hAPP(c_Product__Type_OPair(X10277,X10276),X10275),X10274)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(X10277,X10276),tc_HOL_Obool),X10273))))&(~hBOOL(hAPP(hAPP(X10272,esk336_6(X10272,X10273,X10274,X10275,X10276,X10277)),esk337_6(X10272,X10273,X10274,X10275,X10276,X10277)))|hBOOL(hAPP(hAPP(X10272,X10275),X10274))|~c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(X10277,X10276),tc_HOL_Obool),tc_fun(tc_prod(X10277,X10276),tc_HOL_Obool),X10273)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X10277,X10276)),hAPP(hAPP(c_Product__Type_OPair(X10277,X10276),X10275),X10274)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(X10277,X10276),tc_HOL_Obool),X10273))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lfp__induct2])])])])])). 6.97/7.21 fof(c_0_4810, plain, ![X1892, X1893, X1894, X1895, X1897]:(((hBOOL(hAPP(hAPP(c_member(X1895),esk62_4(X1892,X1893,X1894,X1895)),X1894))|hBOOL(hAPP(c_Finite__Set_Ofinite(X1893),hAPP(c_Set_OCollect(X1893),hAPP(hAPP(c_COMBB(tc_fun(X1895,tc_HOL_Obool),tc_HOL_Obool,X1893),c_HOL_OEx(X1895)),hAPP(hAPP(c_COMBB(tc_fun(X1895,tc_HOL_Obool),tc_fun(X1895,tc_HOL_Obool),X1893),hAPP(c_COMBS(X1895,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1895),c_fconj),hAPP(hAPP(c_COMBC(X1895,tc_fun(X1895,tc_HOL_Obool),tc_HOL_Obool),c_member(X1895)),X1894)))),X1892)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1895),X1894)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1893),hAPP(c_Set_OCollect(X1893),hAPP(hAPP(c_COMBC(X1893,X1895,tc_HOL_Obool),X1892),esk62_4(X1892,X1893,X1894,X1895)))))|hBOOL(hAPP(c_Finite__Set_Ofinite(X1893),hAPP(c_Set_OCollect(X1893),hAPP(hAPP(c_COMBB(tc_fun(X1895,tc_HOL_Obool),tc_HOL_Obool,X1893),c_HOL_OEx(X1895)),hAPP(hAPP(c_COMBB(tc_fun(X1895,tc_HOL_Obool),tc_fun(X1895,tc_HOL_Obool),X1893),hAPP(c_COMBS(X1895,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1895),c_fconj),hAPP(hAPP(c_COMBC(X1895,tc_fun(X1895,tc_HOL_Obool),tc_HOL_Obool),c_member(X1895)),X1894)))),X1892)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1895),X1894))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1893),hAPP(c_Set_OCollect(X1893),hAPP(hAPP(c_COMBB(tc_fun(X1895,tc_HOL_Obool),tc_HOL_Obool,X1893),c_HOL_OEx(X1895)),hAPP(hAPP(c_COMBB(tc_fun(X1895,tc_HOL_Obool),tc_fun(X1895,tc_HOL_Obool),X1893),hAPP(c_COMBS(X1895,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1895),c_fconj),hAPP(hAPP(c_COMBC(X1895,tc_fun(X1895,tc_HOL_Obool),tc_HOL_Obool),c_member(X1895)),X1894)))),X1892)))))|(~hBOOL(hAPP(hAPP(c_member(X1895),X1897),X1894))|hBOOL(hAPP(c_Finite__Set_Ofinite(X1893),hAPP(c_Set_OCollect(X1893),hAPP(hAPP(c_COMBC(X1893,X1895,tc_HOL_Obool),X1892),X1897)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1895),X1894)))), 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__Collect__bex])])])])])). 6.97/7.21 cnf(c_0_4811, 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_4493])). 6.97/7.21 cnf(c_0_4812, 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_4494])). 6.97/7.21 cnf(c_0_4813, plain, (c_List_OdropWhile(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)), inference(split_conjunct,[status(thm)],[c_0_4495])). 6.97/7.21 fof(c_0_4814, plain, ![X5515, X5516, X5517, X5518]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X5517),X5516))|c_Nitpick_Osetsum_H(X5517,X5518,X5515,X5516)=c_Groups_Ozero__class_Ozero(X5518)|~class_Groups_Ocomm__monoid__add(X5518))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5517),X5516))|c_Nitpick_Osetsum_H(X5517,X5518,X5515,X5516)=hAPP(c_List_Omonoid__add__class_Olistsum(X5518),hAPP(hAPP(c_List_Omap(X5517,X5518),X5515),c_Hilbert__Choice_OEps(tc_List_Olist(X5517),hAPP(hAPP(c_COMBS(tc_List_Olist(X5517),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5517)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X5517),tc_fun(X5517,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5517,tc_HOL_Obool),tc_fun(tc_fun(X5517,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X5517)),c_fequal),c_List_Oset(X5517))),X5516))),c_List_Odistinct(X5517)))))|~class_Groups_Ocomm__monoid__add(X5518))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nitpick_Osetsum_H__def])])])])). 6.97/7.21 fof(c_0_4815, plain, ![X3047, X3048, X3049]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3049,tc_HOL_Obool)),X3047),X3048)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3049,tc_HOL_Obool)),X3048),X3047), inference(variable_rename,[status(thm)],[fact_Int__commute])). 6.97/7.21 cnf(c_0_4816, plain, (hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X5)=c_Hilbert__Choice_OEps(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_4496])). 6.97/7.21 cnf(c_0_4817, 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_4497, c_0_4467]), c_0_4467]), c_0_4467]), ['final']). 6.97/7.21 cnf(c_0_4818, 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_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_4498])). 6.97/7.21 fof(c_0_4819, plain, ![X11386, X11387, X11388, X11389]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X11389,X11388),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X11387),X11386)))|hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11389),X11388),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X11386),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11387)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11387)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X11386),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),X11388),X11386)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zminus1__lemma])])])). 6.97/7.21 cnf(c_0_4820, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(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),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_4499])). 6.97/7.21 cnf(c_0_4821, 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_4500]), ['final']). 6.97/7.21 fof(c_0_4822, plain, ![X6153, X6154, X6155]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6155),X6154))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6155,tc_HOL_Obool)),X6153),X6154)=hAPP(hAPP(c_Finite__Set_Ofold(X6155,tc_fun(X6155,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X6155,tc_HOL_Obool),tc_fun(tc_fun(X6155,tc_HOL_Obool),tc_fun(X6155,tc_HOL_Obool)),X6155),hAPP(c_COMBC(tc_fun(X6155,tc_HOL_Obool),tc_fun(X6155,tc_HOL_Obool),tc_fun(X6155,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X6155,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X6155,tc_fun(X6155,tc_HOL_Obool),tc_fun(X6155,tc_HOL_Obool)),c_Set_Oinsert(X6155)),c_Orderings_Obot__class_Obot(tc_fun(X6155,tc_HOL_Obool))))),X6153),X6154)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__fold__remove])])). 6.97/7.21 fof(c_0_4823, plain, ![X8949, X8950, X8951, X8952]:c_Finite__Set_Ofold(X8951,X8952,hAPP(hAPP(c_COMBB(X8952,tc_fun(X8952,X8952),X8951),X8950),X8949))=hAPP(c_Finite__Set_Ofold__image(X8952,X8951,X8950),X8949), inference(variable_rename,[status(thm)],[fact_fold__image__def])). 6.97/7.21 cnf(c_0_4824, 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_4501])). 6.97/7.21 cnf(c_0_4825, 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_4502])). 6.97/7.21 cnf(c_0_4826, 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),esk217_3(X2,X3,X1)),esk217_3(X2,X3,X1))),X2))|~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)),X3)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3))),esk216_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_4503])). 6.97/7.21 cnf(c_0_4827, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk217_3(X2,X3,X1)),X3))|c_Relation_Orefl__on(X1,X3,X2)|~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)),X3)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3))),esk216_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_4503])). 6.97/7.21 fof(c_0_4828, plain, ![X16559, X16560, X16561, X16562, X16563]:(c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X16562,tc_HOL_Obool),X16561)!=X16563|(~c_Orderings_Oorder__class_Omono(tc_fun(X16562,tc_HOL_Obool),tc_fun(X16562,tc_HOL_Obool),X16561)|(~hBOOL(hAPP(hAPP(c_member(X16562),X16560),X16559))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16562,tc_HOL_Obool)),X16559),hAPP(X16561,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X16562,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X16562,tc_HOL_Obool),tc_fun(X16562,tc_HOL_Obool),tc_fun(X16562,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16562,tc_HOL_Obool),tc_fun(tc_fun(X16562,tc_HOL_Obool),tc_fun(X16562,tc_HOL_Obool)),tc_fun(X16562,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16562,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X16562,tc_HOL_Obool),tc_fun(X16562,tc_HOL_Obool),tc_fun(X16562,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16562,tc_HOL_Obool),tc_fun(tc_fun(X16562,tc_HOL_Obool),tc_fun(X16562,tc_HOL_Obool)),tc_fun(X16562,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16562,tc_HOL_Obool))),X16561)),X16559))),X16563)))))|hBOOL(hAPP(hAPP(c_member(X16562),X16560),X16563)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_def__coinduct3])])])). 6.97/7.21 cnf(c_0_4829, 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_4504])). 6.97/7.21 cnf(c_0_4830, plain, (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))))=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_4505])). 6.97/7.21 cnf(c_0_4831, 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_4506])). 6.97/7.21 cnf(c_0_4832, plain, (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)))=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)))|~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_4507])). 6.97/7.21 fof(c_0_4833, plain, ![X11978, X11979, X11980, X11981, X11982, X11983, X11984]:(~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X11984,X11983),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X11982),X11981)))|(~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X11980,X11983),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X11979),X11978)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X11983))|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11984),X11980),X11983),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),X11982),X11979)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11981),X11978)),X11983))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11981),X11978),X11983))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__add1__eq])])). 6.97/7.21 fof(c_0_4834, plain, ![X2124, X2125, X2126]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2126),X2125)),X2124)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2126),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2125),X2124)), inference(variable_rename,[status(thm)],[fact_nat__add__assoc])). 6.97/7.21 fof(c_0_4835, plain, ![X531, X532]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X532),c_Int_OPls))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X531)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X531)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X532)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X532),c_Int_OPls))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X531)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X532))=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),X531),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X532)))),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)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__nat__number__of])])])). 6.97/7.21 fof(c_0_4836, plain, ![X7628, X7629, X7630, X7631, X7632, X7633]:((hBOOL(hAPP(hAPP(c_member(X7632),X7630),X7631))|hAPP(hAPP(c_Power_Opower__class_Opower(X7633),X7628),hAPP(c_Finite__Set_Ocard(X7632),X7631))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7632,X7633),hAPP(hAPP(c_COMBC(X7632,X7633,X7633),hAPP(hAPP(c_COMBS(X7632,X7633,tc_fun(X7633,X7633)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7633,tc_fun(X7633,X7633)),X7632),c_If(X7633)),hAPP(hAPP(c_COMBC(X7632,X7632,tc_HOL_Obool),c_fequal),X7630))),X7629)),X7628)),X7631)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7632),X7631))|~class_Groups_Ocomm__monoid__mult(X7633))&(~hBOOL(hAPP(hAPP(c_member(X7632),X7630),X7631))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7633),hAPP(X7629,X7630)),hAPP(hAPP(c_Power_Opower__class_Opower(X7633),X7628),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7632),X7631)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7632,X7633),hAPP(hAPP(c_COMBC(X7632,X7633,X7633),hAPP(hAPP(c_COMBS(X7632,X7633,tc_fun(X7633,X7633)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7633,tc_fun(X7633,X7633)),X7632),c_If(X7633)),hAPP(hAPP(c_COMBC(X7632,X7632,tc_HOL_Obool),c_fequal),X7630))),X7629)),X7628)),X7631)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7632),X7631))|~class_Groups_Ocomm__monoid__mult(X7633))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__gen__delta])])])])). 6.97/7.21 fof(c_0_4837, plain, ![X3450, X3451, X3452, X3453, X3455]:(((hBOOL(hAPP(X3452,esk110_4(X3450,X3451,X3452,X3453)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X3451),hAPP(c_Set_OCollect(X3451),hAPP(hAPP(c_COMBB(tc_fun(X3453,tc_HOL_Obool),tc_HOL_Obool,X3451),c_HOL_OEx(X3453)),hAPP(hAPP(c_COMBB(tc_fun(X3453,tc_HOL_Obool),tc_fun(X3453,tc_HOL_Obool),X3451),hAPP(c_COMBS(X3453,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3453),c_fconj),X3452))),X3450)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3453),hAPP(c_Set_OCollect(X3453),X3452))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3451),hAPP(c_Set_OCollect(X3451),hAPP(hAPP(c_COMBC(X3451,X3453,tc_HOL_Obool),X3450),esk110_4(X3450,X3451,X3452,X3453)))))|hBOOL(hAPP(c_Finite__Set_Ofinite(X3451),hAPP(c_Set_OCollect(X3451),hAPP(hAPP(c_COMBB(tc_fun(X3453,tc_HOL_Obool),tc_HOL_Obool,X3451),c_HOL_OEx(X3453)),hAPP(hAPP(c_COMBB(tc_fun(X3453,tc_HOL_Obool),tc_fun(X3453,tc_HOL_Obool),X3451),hAPP(c_COMBS(X3453,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3453),c_fconj),X3452))),X3450)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3453),hAPP(c_Set_OCollect(X3453),X3452)))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3451),hAPP(c_Set_OCollect(X3451),hAPP(hAPP(c_COMBB(tc_fun(X3453,tc_HOL_Obool),tc_HOL_Obool,X3451),c_HOL_OEx(X3453)),hAPP(hAPP(c_COMBB(tc_fun(X3453,tc_HOL_Obool),tc_fun(X3453,tc_HOL_Obool),X3451),hAPP(c_COMBS(X3453,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3453),c_fconj),X3452))),X3450)))))|(~hBOOL(hAPP(X3452,X3455))|hBOOL(hAPP(c_Finite__Set_Ofinite(X3451),hAPP(c_Set_OCollect(X3451),hAPP(hAPP(c_COMBC(X3451,X3453,tc_HOL_Obool),X3450),X3455)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3453),hAPP(c_Set_OCollect(X3453),X3452))))), 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])])])])])])). 6.97/7.21 fof(c_0_4838, plain, ![X9549, X9550]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk311_2(X9549,X9550)))|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)))),X9550))=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)))),X9549)))&((~hBOOL(hAPP(X9550,esk311_2(X9549,X9550)))|~hBOOL(hAPP(X9549,esk311_2(X9549,X9550)))|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)))),X9550))=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)))),X9549)))&(hBOOL(hAPP(X9550,esk311_2(X9549,X9550)))|hBOOL(hAPP(X9549,esk311_2(X9549,X9550)))|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)))),X9550))=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)))),X9549))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__cong])])])])). 6.97/7.21 fof(c_0_4839, plain, ![X9943, X9944, X9945, X9946, X9947, X9948, X9949]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X9949,X9948),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X9947),X9946)))|(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X9945,X9948),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X9944),X9943)))|(X9948=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X9949),X9945),X9948),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),X9947),X9944)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X9946),X9943)),X9948))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X9946),X9943),X9948))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zadd1__lemma])])])). 6.97/7.21 fof(c_0_4840, plain, ![X15430, X15431, X15432, X15433]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15432),X15431))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15433),hAPP(X15430,X15432)),hAPP(X15430,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15431),c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X15433),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X15433,X15433),hAPP(hAPP(c_COMBB(X15433,tc_fun(X15433,X15433),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X15433)),X15430)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X15433,tc_Nat_Onat),X15430),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,X15432,X15431))|~class_Groups_Oab__group__add(X15433))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15432),X15431))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X15433),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X15433,X15433),hAPP(hAPP(c_COMBB(X15433,tc_fun(X15433,X15433),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X15433)),X15430)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X15433,tc_Nat_Onat),X15430),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,X15432,X15431))=c_Groups_Ozero__class_Ozero(X15433)|~class_Groups_Oab__group__add(X15433))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__natinterval__difff])])])])). 6.97/7.21 fof(c_0_4841, plain, ![X14044]:hAPP(c_Nat_OSuc,X14044)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14044),c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1])). 6.97/7.21 fof(c_0_4842, plain, ![X14814, X14815]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X14815),X14814))|c_Nitpick_Ocard_H(X14815,X14814)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14815)),c_Hilbert__Choice_OEps(tc_List_Olist(X14815),hAPP(hAPP(c_COMBS(tc_List_Olist(X14815),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X14815)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X14815),tc_fun(X14815,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X14815,tc_HOL_Obool),tc_fun(tc_fun(X14815,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X14815)),c_fequal),c_List_Oset(X14815))),X14814))),c_List_Odistinct(X14815)))))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X14815),X14814))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Nitpick_Ocard_H(X14815,X14814))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nitpick_Ocard_H__def])])])). 6.97/7.21 cnf(c_0_4843, 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_4508])). 6.97/7.21 fof(c_0_4844, plain, ![X5480, X5481, X5482, X5483, X5484]:(~class_Groups_Ocomm__monoid__add(X5484)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5483),X5482))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5483,X5484),X5481),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5483,tc_HOL_Obool)),X5482),X5480))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5483,X5484),hAPP(hAPP(c_COMBC(X5483,X5484,X5484),hAPP(hAPP(c_COMBS(X5483,X5484,tc_fun(X5484,X5484)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5484,tc_fun(X5484,X5484)),X5483),c_If(X5484)),hAPP(hAPP(c_COMBC(X5483,tc_fun(X5483,tc_HOL_Obool),tc_HOL_Obool),c_member(X5483)),X5480))),X5481)),c_Groups_Ozero__class_Ozero(X5484))),X5482))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__restrict__set])])])). 6.97/7.21 fof(c_0_4845, plain, ![X8551, X8552, X8553, X8554, X8555, X8556]:(((~hBOOL(hAPP(hAPP(c_member(X8556),X8553),X8554))|hAPP(c_Set_Ovimage(X8552,X8556,hAPP(hAPP(c_COMBC(X8552,X8556,X8556),hAPP(hAPP(c_COMBC(X8552,X8556,tc_fun(X8556,X8556)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X8556,tc_fun(X8556,X8556)),X8552),c_If(X8556)),hAPP(hAPP(c_COMBC(X8552,tc_fun(X8552,tc_HOL_Obool),tc_HOL_Obool),c_member(X8552)),X8551))),X8555)),X8553)),X8554)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8552,tc_HOL_Obool)),X8551)|hBOOL(hAPP(hAPP(c_member(X8556),X8555),X8554)))&(hBOOL(hAPP(hAPP(c_member(X8556),X8553),X8554))|c_Orderings_Obot__class_Obot(tc_fun(X8552,tc_HOL_Obool))=hAPP(c_Set_Ovimage(X8552,X8556,hAPP(hAPP(c_COMBC(X8552,X8556,X8556),hAPP(hAPP(c_COMBC(X8552,X8556,tc_fun(X8556,X8556)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X8556,tc_fun(X8556,X8556)),X8552),c_If(X8556)),hAPP(hAPP(c_COMBC(X8552,tc_fun(X8552,tc_HOL_Obool),tc_HOL_Obool),c_member(X8552)),X8551))),X8555)),X8553)),X8554)|hBOOL(hAPP(hAPP(c_member(X8556),X8555),X8554))))&((~hBOOL(hAPP(hAPP(c_member(X8556),X8553),X8554))|c_Orderings_Otop__class_Otop(tc_fun(X8552,tc_HOL_Obool))=hAPP(c_Set_Ovimage(X8552,X8556,hAPP(hAPP(c_COMBC(X8552,X8556,X8556),hAPP(hAPP(c_COMBC(X8552,X8556,tc_fun(X8556,X8556)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X8556,tc_fun(X8556,X8556)),X8552),c_If(X8556)),hAPP(hAPP(c_COMBC(X8552,tc_fun(X8552,tc_HOL_Obool),tc_HOL_Obool),c_member(X8552)),X8551))),X8555)),X8553)),X8554)|~hBOOL(hAPP(hAPP(c_member(X8556),X8555),X8554)))&(hBOOL(hAPP(hAPP(c_member(X8556),X8553),X8554))|hAPP(c_Set_Ovimage(X8552,X8556,hAPP(hAPP(c_COMBC(X8552,X8556,X8556),hAPP(hAPP(c_COMBC(X8552,X8556,tc_fun(X8556,X8556)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X8556,tc_fun(X8556,X8556)),X8552),c_If(X8556)),hAPP(hAPP(c_COMBC(X8552,tc_fun(X8552,tc_HOL_Obool),tc_HOL_Obool),c_member(X8552)),X8551))),X8555)),X8553)),X8554)=X8551|~hBOOL(hAPP(hAPP(c_member(X8556),X8555),X8554))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_vimage__if])])])])). 6.97/7.21 cnf(c_0_4846, 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)))|c_Divides_OnegDivAlg(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)))), inference(split_conjunct,[status(thm)],[c_0_4509])). 6.97/7.21 fof(c_0_4847, plain, ![X570, X571]:((~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)),X571),X570)),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)),X571),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)),X570),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)),X571),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)),X570),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)),X571),X570)),c_Int_Ointrel)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__intrel__iff])])). 6.97/7.21 cnf(c_0_4848, 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_4510])). 6.97/7.21 cnf(c_0_4849, plain, (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)))=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))|~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_4511])). 6.97/7.21 cnf(c_0_4850, 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_4512])). 6.97/7.21 cnf(c_0_4851, 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_4513]), ['final']). 6.97/7.21 fof(c_0_4852, plain, ![X3680, X3681, X3682]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X3682,esk124_3(X3680,X3681,X3682))),hAPP(X3681,esk124_3(X3680,X3681,X3682))))|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)),X3681)),X3682)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X3680))=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),X3681),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X3680))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X3682),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X3680)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sum__diff__distrib])])])])). 6.97/7.21 cnf(c_0_4853, 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_4475])). 6.97/7.21 cnf(c_0_4854, 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_4480])). 6.97/7.21 cnf(c_0_4855, 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_4514])). 6.97/7.21 cnf(c_0_4856, 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_4481])). 6.97/7.21 cnf(c_0_4857, 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_4515])). 6.97/7.21 fof(c_0_4858, plain, ![X6561, X6562, X6563, X6564, X6565]:((~hBOOL(hAPP(hAPP(c_member(X6564),X6562),X6563))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X6564,X6565),hAPP(hAPP(c_COMBC(X6564,X6565,X6565),hAPP(hAPP(c_COMBS(X6564,X6565,tc_fun(X6565,X6565)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X6565,tc_fun(X6565,X6565)),X6564),c_If(X6565)),hAPP(hAPP(c_COMBC(X6564,X6564,tc_HOL_Obool),c_fequal),X6562))),X6561)),c_Groups_Oone__class_Oone(X6565))),X6563)=hAPP(X6561,X6562)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6564),X6563))|~class_Groups_Ocomm__monoid__mult(X6565))&(hBOOL(hAPP(hAPP(c_member(X6564),X6562),X6563))|c_Groups_Oone__class_Oone(X6565)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X6564,X6565),hAPP(hAPP(c_COMBC(X6564,X6565,X6565),hAPP(hAPP(c_COMBS(X6564,X6565,tc_fun(X6565,X6565)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X6565,tc_fun(X6565,X6565)),X6564),c_If(X6565)),hAPP(hAPP(c_COMBC(X6564,X6564,tc_HOL_Obool),c_fequal),X6562))),X6561)),c_Groups_Oone__class_Oone(X6565))),X6563)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6564),X6563))|~class_Groups_Ocomm__monoid__mult(X6565))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__delta])])])])). 6.97/7.21 fof(c_0_4859, plain, ![X473, X474, X475, X476]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X475),X474))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X476,X475,c_Groups_Otimes__class_Otimes(X476)),X473),c_Groups_Oone__class_Oone(X476)),X474)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X475,X476),X473),X474)|~class_Groups_Ocomm__monoid__mult(X476))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X475),X474))|c_Groups_Oone__class_Oone(X476)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X475,X476),X473),X474)|~class_Groups_Ocomm__monoid__mult(X476))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod_OF__eq])])])])). 6.97/7.21 fof(c_0_4860, plain, ![X3646, X3647, X3648, X3649, X3650]:((hBOOL(hAPP(hAPP(c_member(X3649),X3647),X3648))|c_Groups_Ozero__class_Ozero(X3650)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3649,X3650),hAPP(hAPP(c_COMBC(X3649,X3650,X3650),hAPP(hAPP(c_COMBS(X3649,X3650,tc_fun(X3650,X3650)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X3650,tc_fun(X3650,X3650)),X3649),c_If(X3650)),hAPP(hAPP(c_COMBC(X3649,X3649,tc_HOL_Obool),c_fequal),X3647))),X3646)),c_Groups_Ozero__class_Ozero(X3650))),X3648)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3649),X3648))|~class_Groups_Ocomm__monoid__add(X3650))&(~hBOOL(hAPP(hAPP(c_member(X3649),X3647),X3648))|hAPP(X3646,X3647)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3649,X3650),hAPP(hAPP(c_COMBC(X3649,X3650,X3650),hAPP(hAPP(c_COMBS(X3649,X3650,tc_fun(X3650,X3650)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X3650,tc_fun(X3650,X3650)),X3649),c_If(X3650)),hAPP(hAPP(c_COMBC(X3649,X3649,tc_HOL_Obool),c_fequal),X3647))),X3646)),c_Groups_Ozero__class_Ozero(X3650))),X3648)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3649),X3648))|~class_Groups_Ocomm__monoid__add(X3650))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__delta])])])])). 6.97/7.21 fof(c_0_4861, plain, ![X17639, X17640, X17641, X17642]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X17641),X17640))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17642,X17641,c_Groups_Oplus__class_Oplus(X17642)),X17639),c_Groups_Ozero__class_Ozero(X17642)),X17640)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17641,X17642),X17639),X17640)|~class_Groups_Ocomm__monoid__add(X17642))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X17641),X17640))|c_Groups_Ozero__class_Ozero(X17642)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17641,X17642),X17639),X17640)|~class_Groups_Ocomm__monoid__add(X17642))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum_OF__eq])])])])). 6.97/7.21 cnf(c_0_4862, 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_4516])). 6.97/7.21 fof(c_0_4863, plain, ![X16656, X16657, X16658, X16659, X16660]:((hBOOL(hAPP(hAPP(c_member(X16658),esk554_5(X16656,X16657,X16658,X16659,X16660)),X16656))|~hBOOL(hAPP(hAPP(c_member(X16658),X16660),X16656))|c_Orderings_Oord__class_OLeast(X16659,hAPP(hAPP(c_COMBC(X16659,tc_fun(X16659,tc_HOL_Obool),tc_HOL_Obool),c_member(X16659)),hAPP(c_Set_Oimage(X16658,X16659,X16657),X16656)))=hAPP(X16657,c_Orderings_Oord__class_OLeast(X16658,hAPP(hAPP(c_COMBC(X16658,tc_fun(X16658,tc_HOL_Obool),tc_HOL_Obool),c_member(X16658)),X16656)))|~c_Orderings_Oorder__class_Omono(X16658,X16659,X16657)|(~class_Orderings_Oorder(X16658)|~class_Orderings_Oorder(X16659)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16658),X16660),esk554_5(X16656,X16657,X16658,X16659,X16660)))|~hBOOL(hAPP(hAPP(c_member(X16658),X16660),X16656))|c_Orderings_Oord__class_OLeast(X16659,hAPP(hAPP(c_COMBC(X16659,tc_fun(X16659,tc_HOL_Obool),tc_HOL_Obool),c_member(X16659)),hAPP(c_Set_Oimage(X16658,X16659,X16657),X16656)))=hAPP(X16657,c_Orderings_Oord__class_OLeast(X16658,hAPP(hAPP(c_COMBC(X16658,tc_fun(X16658,tc_HOL_Obool),tc_HOL_Obool),c_member(X16658)),X16656)))|~c_Orderings_Oorder__class_Omono(X16658,X16659,X16657)|(~class_Orderings_Oorder(X16658)|~class_Orderings_Oorder(X16659)))), 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_Least__mono])])])])])])). 6.97/7.21 fof(c_0_4864, plain, ![X15967, X15968, X15969, X15970]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15970,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X15970,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk539_4(X15967,X15968,X15969,X15970))),X15969)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X15970,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),esk539_4(X15967,X15968,X15969,X15970)),X15968))),X15967)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15970,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X15970,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X15969)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X15970,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X15967)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__finite2__subset])])])). 6.97/7.21 fof(c_0_4865, plain, ![X6194, X6195, X6196, X6197]:(~c_Fun_Oinj__on(X6197,X6196,X6195,c_Orderings_Otop__class_Otop(tc_fun(X6197,tc_HOL_Obool)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6197,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X6197,X6196,X6195),hAPP(hAPP(c_Set_Oinsert(X6196),X6194),c_Orderings_Obot__class_Obot(tc_fun(X6196,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X6197),c_HOL_OThe(X6197,hAPP(hAPP(c_COMBC(X6197,X6196,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X6196,tc_fun(X6196,tc_HOL_Obool),X6197),c_fequal),X6195)),X6194))),c_Orderings_Obot__class_Obot(tc_fun(X6197,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__vimage__singleton])])). 6.97/7.21 fof(c_0_4866, plain, ![X14433, X14434, X14435, X14436]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14436),X14435))|(~hBOOL(hAPP(hAPP(c_member(X14436),X14434),X14435))|(~hBOOL(hAPP(hAPP(c_member(X14436),X14433),X14435))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X14436),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X14436,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X14436,tc_HOL_Obool)),X14435),hAPP(hAPP(c_Set_Oinsert(X14436),X14434),c_Orderings_Obot__class_Obot(tc_fun(X14436,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X14436),X14433),c_Orderings_Obot__class_Obot(tc_fun(X14436,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X14436),X14435)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Diff2__less])])])). 6.97/7.21 fof(c_0_4867, plain, ![X9341, X9342, X9343, X9344]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9344,tc_HOL_Obool)),X9343),hAPP(hAPP(c_Set_Oinsert(X9344),X9342),X9341))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9344,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9344,tc_HOL_Obool)),X9343),hAPP(hAPP(c_Set_Oinsert(X9344),X9342),c_Orderings_Obot__class_Obot(tc_fun(X9344,tc_HOL_Obool))))),X9341), inference(variable_rename,[status(thm)],[fact_Diff__insert2])). 6.97/7.21 fof(c_0_4868, plain, ![X17643, X17644, X17645]:(((X17644!=X17643|c_List_Oconcat(X17645,X17643)=c_List_Oconcat(X17645,X17644)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X17645))),X17644)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X17645))),X17643)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17645),tc_List_Olist(X17645))),esk599_3(X17643,X17644,X17645)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X17645),tc_List_Olist(X17645))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X17645),tc_List_Olist(X17645)),X17644),X17643)))))&(c_List_Oconcat(X17645,X17643)!=c_List_Oconcat(X17645,X17644)|X17644=X17643|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X17645))),X17644)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X17645))),X17643)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17645),tc_List_Olist(X17645))),esk599_3(X17643,X17644,X17645)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X17645),tc_List_Olist(X17645))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X17645),tc_List_Olist(X17645)),X17644),X17643))))))&((X17644!=X17643|c_List_Oconcat(X17645,X17643)=c_List_Oconcat(X17645,X17644)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X17645))),X17644)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X17645))),X17643)|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X17645),tc_List_Olist(X17645),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X17645),tc_fun(tc_List_Olist(X17645),tc_Nat_Onat),tc_fun(tc_List_Olist(X17645),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X17645),tc_Nat_Onat),tc_fun(tc_List_Olist(X17645),tc_HOL_Obool)),tc_List_Olist(X17645)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X17645))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X17645)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X17645))))),c_Nat_Osize__class_Osize(tc_List_Olist(X17645)))),esk599_3(X17643,X17644,X17645))))&(c_List_Oconcat(X17645,X17643)!=c_List_Oconcat(X17645,X17644)|X17644=X17643|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X17645))),X17644)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X17645))),X17643)|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X17645),tc_List_Olist(X17645),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X17645),tc_fun(tc_List_Olist(X17645),tc_Nat_Onat),tc_fun(tc_List_Olist(X17645),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X17645),tc_Nat_Onat),tc_fun(tc_List_Olist(X17645),tc_HOL_Obool)),tc_List_Olist(X17645)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X17645))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X17645)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X17645))))),c_Nat_Osize__class_Osize(tc_List_Olist(X17645)))),esk599_3(X17643,X17644,X17645)))))), 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])])])])])). 6.97/7.21 fof(c_0_4869, plain, ![X17615, X17616, X17617]:((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17617),tc_List_Olist(X17617))),esk598_3(X17615,X17616,X17617)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X17617),tc_List_Olist(X17617))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X17617),tc_List_Olist(X17617)),X17616),X17615))))|X17616=X17615|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X17617))),X17615)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X17617))),X17616)|c_List_Oconcat(X17617,X17615)!=c_List_Oconcat(X17617,X17616))&(~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X17617),tc_List_Olist(X17617),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X17617),tc_fun(tc_List_Olist(X17617),tc_Nat_Onat),tc_fun(tc_List_Olist(X17617),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X17617),tc_Nat_Onat),tc_fun(tc_List_Olist(X17617),tc_HOL_Obool)),tc_List_Olist(X17617)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X17617))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X17617)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X17617))))),c_Nat_Osize__class_Osize(tc_List_Olist(X17617)))),esk598_3(X17615,X17616,X17617)))|X17616=X17615|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X17617))),X17615)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X17617))),X17616)|c_List_Oconcat(X17617,X17615)!=c_List_Oconcat(X17617,X17616))), 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])])])])])). 6.97/7.21 cnf(c_0_4870, plain, (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)))=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)))|~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_4517])). 6.97/7.21 cnf(c_0_4871, 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)))|c_Divides_OposDivAlg(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)))), inference(split_conjunct,[status(thm)],[c_0_4518])). 6.97/7.21 cnf(c_0_4872, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),X2)=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))))|~class_Groups_Omonoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_4519])). 6.97/7.21 cnf(c_0_4873, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin))=hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(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)],[c_0_4520, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.21 cnf(c_0_4874, 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_4473])). 6.97/7.21 cnf(c_0_4875, 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_4473])). 6.97/7.21 cnf(c_0_4876, 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|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_4474])). 6.97/7.21 cnf(c_0_4877, 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_4521])). 6.97/7.21 fof(c_0_4878, plain, ![X2645, X2646]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,X2646))|hAPP(c_Int_Onat,X2645)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X2645)),hAPP(c_Int_Onat,X2646)))&(hBOOL(hAPP(c_Nat__Numeral_Oneg,X2646))|hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2645),X2646)),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,X2645)),hAPP(c_Int_Onat,X2646)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__nat__eq__if])])])). 6.97/7.21 fof(c_0_4879, plain, ![X13039, X13040, X13041, X13042, X13043]:((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13043)),hAPP(hAPP(c_List_Otake(X13043),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13043)),X13042)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13041)),X13040))),X13042))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13041)),hAPP(hAPP(c_List_Otake(X13041),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13043)),X13042)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13041)),X13040))),X13040))|hBOOL(hAPP(X13039,hAPP(hAPP(c_List_Ozip(X13043,X13041),X13042),X13040))))&(~hBOOL(hAPP(X13039,hAPP(hAPP(c_List_Ozip(X13043,X13041),hAPP(hAPP(c_List_Otake(X13043),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13043)),X13042)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13041)),X13040))),X13042)),hAPP(hAPP(c_List_Otake(X13041),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13043)),X13042)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13041)),X13040))),X13040))))|hBOOL(hAPP(X13039,hAPP(hAPP(c_List_Ozip(X13043,X13041),X13042),X13040))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__obtain__same__length])])])). 6.97/7.21 cnf(c_0_4880, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Otake(X1),X2),X3))=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2)), inference(split_conjunct,[status(thm)],[c_0_4522])). 6.97/7.21 cnf(c_0_4881, 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']). 6.97/7.21 fof(c_0_4882, plain, ![X4799, X4800, X4801, X4802, X4803]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X4803,X4803)),hAPP(hAPP(c_Product__Type_OPair(X4803,X4803),X4802),X4801)),c_Transitive__Closure_Otrancl(X4803,X4800)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X4803,X4803)),hAPP(hAPP(c_Product__Type_OPair(X4803,X4803),X4801),X4799)),c_Transitive__Closure_Otrancl(X4803,X4800)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X4803,X4803)),hAPP(hAPP(c_Product__Type_OPair(X4803,X4803),X4802),X4799)),c_Transitive__Closure_Otrancl(X4803,X4800))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_trancl__trans])])])). 6.97/7.21 cnf(c_0_4883, 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_4523])). 6.97/7.21 fof(c_0_4884, plain, ![X2675, X2676, X2677, X2678, X2679]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X2679,X2679)),hAPP(hAPP(c_Product__Type_OPair(X2679,X2679),X2676),X2675)),X2677))|hAPP(hAPP(c_Equiv__Relations_Oquotient(X2679),hAPP(hAPP(c_Set_Oinsert(X2679),X2676),c_Orderings_Obot__class_Obot(tc_fun(X2679,tc_HOL_Obool)))),X2677)=hAPP(hAPP(c_Equiv__Relations_Oquotient(X2679),hAPP(hAPP(c_Set_Oinsert(X2679),X2675),c_Orderings_Obot__class_Obot(tc_fun(X2679,tc_HOL_Obool)))),X2677)|~hBOOL(hAPP(hAPP(c_member(X2679),X2675),X2678))|~hBOOL(hAPP(hAPP(c_member(X2679),X2676),X2678))|~c_Equiv__Relations_Oequiv(X2679,X2678,X2677))&(hAPP(hAPP(c_Equiv__Relations_Oquotient(X2679),hAPP(hAPP(c_Set_Oinsert(X2679),X2676),c_Orderings_Obot__class_Obot(tc_fun(X2679,tc_HOL_Obool)))),X2677)!=hAPP(hAPP(c_Equiv__Relations_Oquotient(X2679),hAPP(hAPP(c_Set_Oinsert(X2679),X2675),c_Orderings_Obot__class_Obot(tc_fun(X2679,tc_HOL_Obool)))),X2677)|hBOOL(hAPP(hAPP(c_member(tc_prod(X2679,X2679)),hAPP(hAPP(c_Product__Type_OPair(X2679,X2679),X2676),X2675)),X2677))|~hBOOL(hAPP(hAPP(c_member(X2679),X2675),X2678))|~hBOOL(hAPP(hAPP(c_member(X2679),X2676),X2678))|~c_Equiv__Relations_Oequiv(X2679,X2678,X2677))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__equiv__class__iff2])])])). 6.97/7.21 fof(c_0_4885, plain, ![X4061, X4062, X4063, X4064, X4065]:((((hAPP(c_Relation_OImage(X4065,X4065,X4063),hAPP(hAPP(c_Set_Oinsert(X4065),X4062),c_Orderings_Obot__class_Obot(tc_fun(X4065,tc_HOL_Obool))))=hAPP(c_Relation_OImage(X4065,X4065,X4063),hAPP(hAPP(c_Set_Oinsert(X4065),X4061),c_Orderings_Obot__class_Obot(tc_fun(X4065,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4065,X4065)),hAPP(hAPP(c_Product__Type_OPair(X4065,X4065),X4062),X4061)),X4063))|~c_Equiv__Relations_Oequiv(X4065,X4064,X4063))&(hBOOL(hAPP(hAPP(c_member(X4065),X4062),X4064))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4065,X4065)),hAPP(hAPP(c_Product__Type_OPair(X4065,X4065),X4062),X4061)),X4063))|~c_Equiv__Relations_Oequiv(X4065,X4064,X4063)))&(hBOOL(hAPP(hAPP(c_member(X4065),X4061),X4064))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4065,X4065)),hAPP(hAPP(c_Product__Type_OPair(X4065,X4065),X4062),X4061)),X4063))|~c_Equiv__Relations_Oequiv(X4065,X4064,X4063)))&(hAPP(c_Relation_OImage(X4065,X4065,X4063),hAPP(hAPP(c_Set_Oinsert(X4065),X4062),c_Orderings_Obot__class_Obot(tc_fun(X4065,tc_HOL_Obool))))!=hAPP(c_Relation_OImage(X4065,X4065,X4063),hAPP(hAPP(c_Set_Oinsert(X4065),X4061),c_Orderings_Obot__class_Obot(tc_fun(X4065,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_member(X4065),X4062),X4064))|~hBOOL(hAPP(hAPP(c_member(X4065),X4061),X4064))|hBOOL(hAPP(hAPP(c_member(tc_prod(X4065,X4065)),hAPP(hAPP(c_Product__Type_OPair(X4065,X4065),X4062),X4061)),X4063))|~c_Equiv__Relations_Oequiv(X4065,X4064,X4063))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__eq__iff])])])). 6.97/7.21 cnf(c_0_4886, 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_4524])). 6.97/7.21 cnf(c_0_4887, 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_4525])). 6.97/7.21 cnf(c_0_4888, 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_4510])). 6.97/7.21 fof(c_0_4889, plain, ![X5998, X5999, X6000, X6001, X6003, X6004, X6005, X6006, X6007]:(((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6001)),X6000)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6001)),X5999)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk202_4(X5998,X5999,X6000,X6001)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6001)),X6000)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6001)),X5999))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6001),tc_List_Olist(X6001))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6001),tc_List_Olist(X6001)),X6000),X5999)),c_List_Olexord(X6001,X5998))))&(X6000=hAPP(hAPP(c_List_Otake(X6001),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6001)),X6000)),X5999)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk202_4(X5998,X5999,X6000,X6001)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6001)),X6000)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6001)),X5999))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6001),tc_List_Olist(X6001))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6001),tc_List_Olist(X6001)),X6000),X5999)),c_List_Olexord(X6001,X5998)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6001)),X6000)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6001)),X5999)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X6001,X6001)),hAPP(hAPP(c_Product__Type_OPair(X6001,X6001),hAPP(hAPP(c_List_Onth(X6001),X6000),esk202_4(X5998,X5999,X6000,X6001))),hAPP(hAPP(c_List_Onth(X6001),X5999),esk202_4(X5998,X5999,X6000,X6001)))),X5998))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6001),tc_List_Olist(X6001))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6001),tc_List_Olist(X6001)),X6000),X5999)),c_List_Olexord(X6001,X5998))))&(X6000=hAPP(hAPP(c_List_Otake(X6001),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6001)),X6000)),X5999)|hBOOL(hAPP(hAPP(c_member(tc_prod(X6001,X6001)),hAPP(hAPP(c_Product__Type_OPair(X6001,X6001),hAPP(hAPP(c_List_Onth(X6001),X6000),esk202_4(X5998,X5999,X6000,X6001))),hAPP(hAPP(c_List_Onth(X6001),X5999),esk202_4(X5998,X5999,X6000,X6001)))),X5998))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6001),tc_List_Olist(X6001))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6001),tc_List_Olist(X6001)),X6000),X5999)),c_List_Olexord(X6001,X5998))))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6001)),X6000)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6001)),X5999)))|hAPP(hAPP(c_List_Otake(X6001),esk202_4(X5998,X5999,X6000,X6001)),X6000)=hAPP(hAPP(c_List_Otake(X6001),esk202_4(X5998,X5999,X6000,X6001)),X5999)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6001),tc_List_Olist(X6001))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6001),tc_List_Olist(X6001)),X6000),X5999)),c_List_Olexord(X6001,X5998))))&(X6000=hAPP(hAPP(c_List_Otake(X6001),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6001)),X6000)),X5999)|hAPP(hAPP(c_List_Otake(X6001),esk202_4(X5998,X5999,X6000,X6001)),X6000)=hAPP(hAPP(c_List_Otake(X6001),esk202_4(X5998,X5999,X6000,X6001)),X5999)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6001),tc_List_Olist(X6001))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6001),tc_List_Olist(X6001)),X6000),X5999)),c_List_Olexord(X6001,X5998))))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6007),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6006)),X6005)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6006)),X6004))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X6006,X6006)),hAPP(hAPP(c_Product__Type_OPair(X6006,X6006),hAPP(hAPP(c_List_Onth(X6006),X6005),X6007)),hAPP(hAPP(c_List_Onth(X6006),X6004),X6007))),X6003))|hAPP(hAPP(c_List_Otake(X6006),X6007),X6005)!=hAPP(hAPP(c_List_Otake(X6006),X6007),X6004)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6006),tc_List_Olist(X6006))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6006),tc_List_Olist(X6006)),X6005),X6004)),c_List_Olexord(X6006,X6003))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6006)),X6005)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6006)),X6004)))|X6005!=hAPP(hAPP(c_List_Otake(X6006),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6006)),X6005)),X6004)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6006),tc_List_Olist(X6006))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6006),tc_List_Olist(X6006)),X6005),X6004)),c_List_Olexord(X6006,X6003)))))), 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])])])])])])). 6.97/7.21 cnf(c_0_4890, 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_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_4483])). 6.97/7.21 cnf(c_0_4891, 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_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_4483])). 6.97/7.21 fof(c_0_4892, plain, ![X4883, X4884, X4885, X4886, X4887]:(~class_Groups_Ocomm__monoid__add(X4887)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4886),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4885),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4887),X4884),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X4886,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4885),X4883)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4887),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4887),X4884),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X4886,X4885))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4887),X4884),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4885),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4885),X4883)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__ub__add__nat])])). 6.97/7.21 cnf(c_0_4893, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_OremoveAll(X1,X4),X5))=hAPP(c_List_OremoveAll(X2,hAPP(X3,X4)),hAPP(hAPP(c_List_Omap(X1,X2),X3),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_4526])). 6.97/7.21 cnf(c_0_4894, 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_4527])). 6.97/7.21 fof(c_0_4895, plain, ![X9659, X9660, X9661, X9662, X9663]:((hBOOL(hAPP(hAPP(c_member(X9662),X9660),X9661))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X9662,X9663),hAPP(hAPP(c_COMBC(X9662,X9663,X9663),hAPP(hAPP(c_COMBS(X9662,X9663,tc_fun(X9663,X9663)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X9663,tc_fun(X9663,X9663)),X9662),c_If(X9663)),hAPP(c_fequal,X9660))),X9659)),c_Groups_Oone__class_Oone(X9663))),X9661)=c_Groups_Oone__class_Oone(X9663)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9662),X9661))|~class_Groups_Ocomm__monoid__mult(X9663))&(~hBOOL(hAPP(hAPP(c_member(X9662),X9660),X9661))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X9662,X9663),hAPP(hAPP(c_COMBC(X9662,X9663,X9663),hAPP(hAPP(c_COMBS(X9662,X9663,tc_fun(X9663,X9663)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X9663,tc_fun(X9663,X9663)),X9662),c_If(X9663)),hAPP(c_fequal,X9660))),X9659)),c_Groups_Oone__class_Oone(X9663))),X9661)=hAPP(X9659,X9660)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9662),X9661))|~class_Groups_Ocomm__monoid__mult(X9663))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__delta_H])])])])). 6.97/7.21 fof(c_0_4896, plain, ![X2737, X2738, X2739, X2740, X2741]:((hBOOL(hAPP(hAPP(c_member(X2740),X2738),X2739))|c_Groups_Ozero__class_Ozero(X2741)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2740,X2741),hAPP(hAPP(c_COMBC(X2740,X2741,X2741),hAPP(hAPP(c_COMBS(X2740,X2741,tc_fun(X2741,X2741)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2741,tc_fun(X2741,X2741)),X2740),c_If(X2741)),hAPP(c_fequal,X2738))),X2737)),c_Groups_Ozero__class_Ozero(X2741))),X2739)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2740),X2739))|~class_Groups_Ocomm__monoid__add(X2741))&(~hBOOL(hAPP(hAPP(c_member(X2740),X2738),X2739))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2740,X2741),hAPP(hAPP(c_COMBC(X2740,X2741,X2741),hAPP(hAPP(c_COMBS(X2740,X2741,tc_fun(X2741,X2741)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2741,tc_fun(X2741,X2741)),X2740),c_If(X2741)),hAPP(c_fequal,X2738))),X2737)),c_Groups_Ozero__class_Ozero(X2741))),X2739)=hAPP(X2737,X2738)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2740),X2739))|~class_Groups_Ocomm__monoid__add(X2741))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__delta_H])])])])). 6.97/7.21 cnf(c_0_4897, 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_4528])). 6.97/7.21 cnf(c_0_4898, 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))))))|~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(split_conjunct,[status(thm)],[c_0_4529])). 6.97/7.21 cnf(c_0_4899, 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(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))=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)))), inference(split_conjunct,[status(thm)],[c_0_4530])). 6.97/7.21 fof(c_0_4900, plain, ![X16960, X16961, X16962, X16963, X16964, X16965, X16966, X16967]:(((~hBOOL(hAPP(hAPP(c_member(tc_prod(X16966,X16966)),hAPP(hAPP(c_Product__Type_OPair(X16966,X16966),X16964),X16962)),X16960))|X16963!=X16965|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X16967,X16966),tc_prod(X16967,X16966))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X16967,X16966),tc_prod(X16967,X16966)),hAPP(hAPP(c_Product__Type_OPair(X16967,X16966),X16965),X16964)),hAPP(hAPP(c_Product__Type_OPair(X16967,X16966),X16963),X16962))),c_Wellfounded_Olex__prod(X16967,X16966,X16961,X16960))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X16967,X16967)),hAPP(hAPP(c_Product__Type_OPair(X16967,X16967),X16965),X16963)),X16961))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X16967,X16966),tc_prod(X16967,X16966))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X16967,X16966),tc_prod(X16967,X16966)),hAPP(hAPP(c_Product__Type_OPair(X16967,X16966),X16965),X16964)),hAPP(hAPP(c_Product__Type_OPair(X16967,X16966),X16963),X16962))),c_Wellfounded_Olex__prod(X16967,X16966,X16961,X16960)))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X16966,X16966)),hAPP(hAPP(c_Product__Type_OPair(X16966,X16966),X16964),X16962)),X16960))|hBOOL(hAPP(hAPP(c_member(tc_prod(X16967,X16967)),hAPP(hAPP(c_Product__Type_OPair(X16967,X16967),X16965),X16963)),X16961))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X16967,X16966),tc_prod(X16967,X16966))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X16967,X16966),tc_prod(X16967,X16966)),hAPP(hAPP(c_Product__Type_OPair(X16967,X16966),X16965),X16964)),hAPP(hAPP(c_Product__Type_OPair(X16967,X16966),X16963),X16962))),c_Wellfounded_Olex__prod(X16967,X16966,X16961,X16960))))&(X16963=X16965|hBOOL(hAPP(hAPP(c_member(tc_prod(X16967,X16967)),hAPP(hAPP(c_Product__Type_OPair(X16967,X16967),X16965),X16963)),X16961))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X16967,X16966),tc_prod(X16967,X16966))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X16967,X16966),tc_prod(X16967,X16966)),hAPP(hAPP(c_Product__Type_OPair(X16967,X16966),X16965),X16964)),hAPP(hAPP(c_Product__Type_OPair(X16967,X16966),X16963),X16962))),c_Wellfounded_Olex__prod(X16967,X16966,X16961,X16960)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__lex__prod])])])). 6.97/7.21 fof(c_0_4901, plain, ![X14927, X14928, X14929]:(~class_Rings_Oring__1(X14929)|hAPP(c_Int_Oring__1__class_Oof__int(X14929),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),X14928),X14927)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X14929),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X14929),X14928)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X14929),X14927))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int])])). 6.97/7.21 cnf(c_0_4902, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_OremoveAll(X1,X4),X5))=hAPP(c_List_OremoveAll(X2,hAPP(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_4531])). 6.97/7.21 fof(c_0_4903, plain, ![X13044, X13045, X13046, X13047, X13048]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X13048,X13048)),hAPP(hAPP(c_Product__Type_OPair(X13048,X13048),X13047),X13046)),c_Transitive__Closure_Ortrancl(X13048,X13045)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X13048,X13048)),hAPP(hAPP(c_Product__Type_OPair(X13048,X13048),X13046),X13044)),c_Transitive__Closure_Otrancl(X13048,X13045)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X13048,X13048)),hAPP(hAPP(c_Product__Type_OPair(X13048,X13048),X13047),X13044)),c_Transitive__Closure_Otrancl(X13048,X13045))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__trancl__trancl])])). 6.97/7.21 fof(c_0_4904, plain, ![X13435, X13436, X13437, X13438, X13439]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X13439,X13439)),hAPP(hAPP(c_Product__Type_OPair(X13439,X13439),X13438),X13437)),c_Transitive__Closure_Otrancl(X13439,X13436)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X13439,X13439)),hAPP(hAPP(c_Product__Type_OPair(X13439,X13439),X13437),X13435)),c_Transitive__Closure_Ortrancl(X13439,X13436)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X13439,X13439)),hAPP(hAPP(c_Product__Type_OPair(X13439,X13439),X13438),X13435)),c_Transitive__Closure_Otrancl(X13439,X13436))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__rtrancl__trancl])])). 6.97/7.21 cnf(c_0_4905, 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_4532])). 6.97/7.21 fof(c_0_4906, plain, ![X2668, X2669]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2669|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2668),X2669))|c_Divides_Odivmod__nat(X2668,X2669)=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),X2668),X2669),X2669)))&((X2669!=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)),X2668)=c_Divides_Odivmod__nat(X2668,X2669))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2668),X2669))|hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2668)=c_Divides_Odivmod__nat(X2668,X2669)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__if])])])). 6.97/7.21 fof(c_0_4907, plain, ![X8194, X8195]:c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X8195,X8194))=c_Divides_Odivmod__nat(X8195,X8194), inference(variable_rename,[status(thm)],[fact_divmod__nat__def])). 6.97/7.21 fof(c_0_4908, plain, ![X3378, X3379, X3380, X3381, X3382]:((hBOOL(hAPP(hAPP(c_member(X3382),esk108_5(X3378,X3379,X3380,X3381,X3382)),X3381))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3382,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3382,tc_HOL_Obool)),X3381),hAPP(c_Set_OCollect(X3382),X3379))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3382,tc_HOL_Obool)),X3380),hAPP(c_Set_OCollect(X3382),X3378))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3382,tc_HOL_Obool)),X3381),X3380)))&((hBOOL(hAPP(X3379,esk108_5(X3378,X3379,X3380,X3381,X3382)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3382,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3382,tc_HOL_Obool)),X3381),hAPP(c_Set_OCollect(X3382),X3379))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3382,tc_HOL_Obool)),X3380),hAPP(c_Set_OCollect(X3382),X3378))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3382,tc_HOL_Obool)),X3381),X3380)))&(~hBOOL(hAPP(X3378,esk108_5(X3378,X3379,X3380,X3381,X3382)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3382,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3382,tc_HOL_Obool)),X3381),hAPP(c_Set_OCollect(X3382),X3379))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3382,tc_HOL_Obool)),X3380),hAPP(c_Set_OCollect(X3382),X3378))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3382,tc_HOL_Obool)),X3381),X3380))))), 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])])])])])). 6.97/7.21 fof(c_0_4909, plain, ![X7623, X7624, X7625, X7626, X7627]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X7627,X7627)),hAPP(hAPP(c_Product__Type_OPair(X7627,X7627),X7626),X7625)),X7624))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X7627,X7627)),hAPP(hAPP(c_Product__Type_OPair(X7627,X7627),X7625),X7623)),c_Transitive__Closure_Otrancl(X7627,X7624)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X7627,X7627)),hAPP(hAPP(c_Product__Type_OPair(X7627,X7627),X7626),X7623)),c_Transitive__Closure_Otrancl(X7627,X7624))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__into__trancl2])])). 6.97/7.21 cnf(c_0_4910, 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_4533])). 6.97/7.21 cnf(c_0_4911, 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_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2))=c_Groups_Oone__class_Oone(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4534])). 6.97/7.21 fof(c_0_4912, plain, ![X5501, X5502, X5503, X5504, X5505]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X5505,X5505)),hAPP(hAPP(c_Product__Type_OPair(X5505,X5505),X5504),X5503)),c_Transitive__Closure_Otrancl(X5505,X5502)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X5505,X5505)),hAPP(hAPP(c_Product__Type_OPair(X5505,X5505),X5503),X5501)),X5502))|hBOOL(hAPP(hAPP(c_member(tc_prod(X5505,X5505)),hAPP(hAPP(c_Product__Type_OPair(X5505,X5505),X5504),X5501)),c_Transitive__Closure_Otrancl(X5505,X5502))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Transitive__Closure_Otrancl__into__trancl])])). 6.97/7.21 cnf(c_0_4913, 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_4535])). 6.97/7.21 cnf(c_0_4914, 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_4428])). 6.97/7.21 fof(c_0_4915, plain, ![X4683, X4684, X4685, X4686, X4687]:(~hBOOL(hAPP(hAPP(c_member(X4687),X4686),hAPP(c_List_Oset(X4687),X4685)))|(hBOOL(hAPP(X4684,X4686))|hAPP(hAPP(c_List_Oappend(X4687),c_List_OdropWhile(X4687,X4684,X4685)),X4683)=c_List_OdropWhile(X4687,X4684,hAPP(hAPP(c_List_Oappend(X4687),X4685),X4683)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dropWhile__append1])])])). 6.97/7.21 cnf(c_0_4916, 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_4501])). 6.97/7.21 cnf(c_0_4917, 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_4502])). 6.97/7.21 fof(c_0_4918, plain, ![X9065, X9066, X9067, X9068, X9069, X9070, X9071, X9072]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X9072,X9072)),hAPP(hAPP(c_Product__Type_OPair(X9072,X9072),X9071),X9070)),X9069))|(hAPP(hAPP(c_List_Oappend(X9072),X9067),hAPP(hAPP(c_List_Olist_OCons(X9072),X9071),X9066))!=X9068|(X9065!=hAPP(hAPP(c_List_Oappend(X9072),X9067),hAPP(hAPP(c_List_Olist_OCons(X9072),X9070),X9066))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X9072),tc_List_Olist(X9072))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X9072),tc_List_Olist(X9072)),X9068),X9065)),c_List_Olistrel1(X9072,X9069)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel1I])])])). 6.97/7.21 fof(c_0_4919, plain, ![X11549, X11550, X11551, X11552, X11553]:((hBOOL(hAPP(hAPP(c_member(X11552),esk385_5(X11549,X11550,X11551,X11552,X11553)),X11549))|hBOOL(hAPP(hAPP(c_member(X11552),X11550),X11553))|~hBOOL(hAPP(hAPP(c_member(X11552),X11550),X11549))|~c_Orderings_Oorder__class_Omono(tc_fun(X11552,tc_HOL_Obool),tc_fun(X11552,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X11552,tc_HOL_Obool),tc_fun(X11552,tc_HOL_Obool),tc_fun(X11552,tc_HOL_Obool)),c_Set_OCollect(X11552)),X11551))|c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X11552,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X11552,tc_HOL_Obool),tc_fun(X11552,tc_HOL_Obool),tc_fun(X11552,tc_HOL_Obool)),c_Set_OCollect(X11552)),X11551))!=X11553)&(~hBOOL(hAPP(hAPP(X11551,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11552,tc_HOL_Obool)),X11549),X11553)),esk385_5(X11549,X11550,X11551,X11552,X11553)))|hBOOL(hAPP(hAPP(c_member(X11552),X11550),X11553))|~hBOOL(hAPP(hAPP(c_member(X11552),X11550),X11549))|~c_Orderings_Oorder__class_Omono(tc_fun(X11552,tc_HOL_Obool),tc_fun(X11552,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X11552,tc_HOL_Obool),tc_fun(X11552,tc_HOL_Obool),tc_fun(X11552,tc_HOL_Obool)),c_Set_OCollect(X11552)),X11551))|c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X11552,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X11552,tc_HOL_Obool),tc_fun(X11552,tc_HOL_Obool),tc_fun(X11552,tc_HOL_Obool)),c_Set_OCollect(X11552)),X11551))!=X11553)), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_def__Collect__coinduct])])])])])). 6.97/7.21 cnf(c_0_4920, plain, (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)))=c_Nitpick_Oof__frac(X2,X1,X3)|~class_Rings_Oring__1(X1)|~class_Rings_Oinverse(X1)), inference(split_conjunct,[status(thm)],[c_0_4536])). 6.97/7.21 cnf(c_0_4921, plain, (c_Nitpick_Odenom(X1)=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))), inference(split_conjunct,[status(thm)],[c_0_4537])). 6.97/7.21 cnf(c_0_4922, plain, (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_Onum(X1)), inference(split_conjunct,[status(thm)],[c_0_4538])). 6.97/7.21 fof(c_0_4923, plain, ![X16596, X16597, X16598, X16599, X16600, X16601]:hAPP(X16598,hAPP(X16597,X16596))=hAPP(hAPP(c_Fun_Ocomp(X16601,X16600,X16599,X16598),X16597),X16596), inference(variable_rename,[status(thm)],[fact_o__def])). 6.97/7.21 fof(c_0_4924, plain, ![X1158, X1159, X1160, X1161]:(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1161)),X1160),c_List_Olists(X1161,X1159)))|(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1161)),X1160),c_List_Olists(X1161,X1158)))|hBOOL(hAPP(c_List_Olistsp(X1161,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1161,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1161,tc_fun(X1161,tc_HOL_Obool),tc_HOL_Obool),c_member(X1161)),X1159)),hAPP(hAPP(c_COMBC(X1161,tc_fun(X1161,tc_HOL_Obool),tc_HOL_Obool),c_member(X1161)),X1158))),X1160)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lists__IntI])])])). 6.97/7.21 fof(c_0_4925, plain, ![X14054, X14055, X14056, X14057]:(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X14057,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk478_4(X14054,X14055,X14056,X14057))),X14056)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X14057,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),esk478_4(X14054,X14055,X14056,X14057)),X14055))),X14054)|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X14057,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X14056)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X14057,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X14054)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__finite2__eq])])])])). 6.97/7.21 cnf(c_0_4926, 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_4539])). 6.97/7.21 fof(c_0_4927, plain, ![X2153, X2154, X2155]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2155,tc_HOL_Obool)),X2154),hAPP(hAPP(c_Set_Oinsert(X2155),X2153),c_Orderings_Obot__class_Obot(tc_fun(X2155,tc_HOL_Obool)))))|c_Partial__Function_Oflat__lub(X2155,X2153,X2154)=X2153)&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2155,tc_HOL_Obool)),X2154),hAPP(hAPP(c_Set_Oinsert(X2155),X2153),c_Orderings_Obot__class_Obot(tc_fun(X2155,tc_HOL_Obool)))))|c_HOL_OThe(X2155,hAPP(hAPP(c_COMBC(X2155,tc_fun(X2155,tc_HOL_Obool),tc_HOL_Obool),c_member(X2155)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2155,tc_HOL_Obool)),X2154),hAPP(hAPP(c_Set_Oinsert(X2155),X2153),c_Orderings_Obot__class_Obot(tc_fun(X2155,tc_HOL_Obool))))))=c_Partial__Function_Oflat__lub(X2155,X2153,X2154))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_flat__lub__def])])])). 6.97/7.21 fof(c_0_4928, plain, ![X10834, X10835, X10836]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10836,X10836),tc_HOL_Obool)),X10835),hAPP(hAPP(c_Product__Type_OSigma(X10836,X10836),X10834),hAPP(c_COMBK(tc_fun(X10836,tc_HOL_Obool),X10836),X10834))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10836,X10836),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X10836,X10835)),hAPP(hAPP(c_Product__Type_OSigma(X10836,X10836),X10834),hAPP(c_COMBK(tc_fun(X10836,tc_HOL_Obool),X10836),X10834))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_trancl__subset__Sigma])])])). 6.97/7.21 fof(c_0_4929, plain, ![X17270, X17271, X17272, X17273, X17274, X17275]:((X17273!=X17274|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17275),tc_List_Olist(X17275))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17275),tc_List_Olist(X17275)),X17271),X17270)),c_List_Olistrel1(X17275,X17272)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17275),tc_List_Olist(X17275))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17275),tc_List_Olist(X17275)),hAPP(hAPP(c_List_Oappend(X17275),X17274),X17271)),hAPP(hAPP(c_List_Oappend(X17275),X17273),X17270))),c_List_Olistrel1(X17275,X17272))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17275),tc_List_Olist(X17275))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17275),tc_List_Olist(X17275)),X17274),X17273)),c_List_Olistrel1(X17275,X17272)))|X17270!=X17271|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17275),tc_List_Olist(X17275))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17275),tc_List_Olist(X17275)),hAPP(hAPP(c_List_Oappend(X17275),X17274),X17271)),hAPP(hAPP(c_List_Oappend(X17275),X17273),X17270))),c_List_Olistrel1(X17275,X17272))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__listrel1I])])])). 6.97/7.21 fof(c_0_4930, plain, ![X4085, X4086, X4087, X4088, X4089, X4090]:(((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4090),tc_List_Olist(X4090))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4090),tc_List_Olist(X4090)),X4088),X4086)),c_List_Olexord(X4090,X4085)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X4090,X4090)),hAPP(hAPP(c_Product__Type_OPair(X4090,X4090),X4089),X4087)),X4085))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4090),tc_List_Olist(X4090))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4090),tc_List_Olist(X4090)),hAPP(hAPP(c_List_Olist_OCons(X4090),X4089),X4088)),hAPP(hAPP(c_List_Olist_OCons(X4090),X4087),X4086))),c_List_Olexord(X4090,X4085))))&(X4087=X4089|hBOOL(hAPP(hAPP(c_member(tc_prod(X4090,X4090)),hAPP(hAPP(c_Product__Type_OPair(X4090,X4090),X4089),X4087)),X4085))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4090),tc_List_Olist(X4090))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4090),tc_List_Olist(X4090)),hAPP(hAPP(c_List_Olist_OCons(X4090),X4089),X4088)),hAPP(hAPP(c_List_Olist_OCons(X4090),X4087),X4086))),c_List_Olexord(X4090,X4085)))))&((~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4090),tc_List_Olist(X4090))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4090),tc_List_Olist(X4090)),X4088),X4086)),c_List_Olexord(X4090,X4085)))|X4087!=X4089|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4090),tc_List_Olist(X4090))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4090),tc_List_Olist(X4090)),hAPP(hAPP(c_List_Olist_OCons(X4090),X4089),X4088)),hAPP(hAPP(c_List_Olist_OCons(X4090),X4087),X4086))),c_List_Olexord(X4090,X4085))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X4090,X4090)),hAPP(hAPP(c_Product__Type_OPair(X4090,X4090),X4089),X4087)),X4085))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4090),tc_List_Olist(X4090))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4090),tc_List_Olist(X4090)),hAPP(hAPP(c_List_Olist_OCons(X4090),X4089),X4088)),hAPP(hAPP(c_List_Olist_OCons(X4090),X4087),X4086))),c_List_Olexord(X4090,X4085)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__cons__cons])])])). 6.97/7.21 fof(c_0_4931, plain, ![X12018, X12019, X12020, X12021, X12022, X12023, X12024, X12025, X12026, X12027]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X12021,X12021)),hAPP(hAPP(c_Product__Type_OPair(X12021,X12021),hAPP(hAPP(c_List_Onth(X12021),X12020),X12023)),X12022)),X12018))|X12019!=hAPP(hAPP(c_List_Olist__update(X12021,X12020),X12023),X12022)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12023),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12021)),X12020)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X12021),tc_List_Olist(X12021))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X12021),tc_List_Olist(X12021)),X12020),X12019)),c_List_Olistrel1(X12021,X12018))))&(((hBOOL(hAPP(hAPP(c_member(tc_prod(X12027,X12027)),hAPP(hAPP(c_Product__Type_OPair(X12027,X12027),hAPP(hAPP(c_List_Onth(X12027),X12026),esk400_4(X12024,X12025,X12026,X12027))),esk399_4(X12024,X12025,X12026,X12027))),X12024))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X12027),tc_List_Olist(X12027))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X12027),tc_List_Olist(X12027)),X12026),X12025)),c_List_Olistrel1(X12027,X12024))))&(X12025=hAPP(hAPP(c_List_Olist__update(X12027,X12026),esk400_4(X12024,X12025,X12026,X12027)),esk399_4(X12024,X12025,X12026,X12027))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X12027),tc_List_Olist(X12027))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X12027),tc_List_Olist(X12027)),X12026),X12025)),c_List_Olistrel1(X12027,X12024)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk400_4(X12024,X12025,X12026,X12027)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12027)),X12026)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X12027),tc_List_Olist(X12027))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X12027),tc_List_Olist(X12027)),X12026),X12025)),c_List_Olistrel1(X12027,X12024)))))), 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])])])])])])). 6.97/7.21 fof(c_0_4932, plain, ![X2682, X2683, X2684, X2685, X2686, X2687]:(((X2684!=X2686|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2687),tc_List_Olist(X2687))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2687),tc_List_Olist(X2687)),X2685),X2683)),c_List_Olex(X2687,X2682)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2687),tc_List_Olist(X2687))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2687),tc_List_Olist(X2687)),hAPP(hAPP(c_List_Olist_OCons(X2687),X2686),X2685)),hAPP(hAPP(c_List_Olist_OCons(X2687),X2684),X2683))),c_List_Olex(X2687,X2682))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X2687,X2687)),hAPP(hAPP(c_Product__Type_OPair(X2687,X2687),X2686),X2684)),X2682))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2687)),X2683)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2687)),X2685)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2687),tc_List_Olist(X2687))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2687),tc_List_Olist(X2687)),hAPP(hAPP(c_List_Olist_OCons(X2687),X2686),X2685)),hAPP(hAPP(c_List_Olist_OCons(X2687),X2684),X2683))),c_List_Olex(X2687,X2682)))))&(((hBOOL(hAPP(hAPP(c_member(tc_prod(X2687,X2687)),hAPP(hAPP(c_Product__Type_OPair(X2687,X2687),X2686),X2684)),X2682))|X2684=X2686|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2687),tc_List_Olist(X2687))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2687),tc_List_Olist(X2687)),hAPP(hAPP(c_List_Olist_OCons(X2687),X2686),X2685)),hAPP(hAPP(c_List_Olist_OCons(X2687),X2684),X2683))),c_List_Olex(X2687,X2682))))&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2687)),X2683)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2687)),X2685)|X2684=X2686|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2687),tc_List_Olist(X2687))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2687),tc_List_Olist(X2687)),hAPP(hAPP(c_List_Olist_OCons(X2687),X2686),X2685)),hAPP(hAPP(c_List_Olist_OCons(X2687),X2684),X2683))),c_List_Olex(X2687,X2682)))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X2687,X2687)),hAPP(hAPP(c_Product__Type_OPair(X2687,X2687),X2686),X2684)),X2682))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2687),tc_List_Olist(X2687))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2687),tc_List_Olist(X2687)),X2685),X2683)),c_List_Olex(X2687,X2682)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2687),tc_List_Olist(X2687))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2687),tc_List_Olist(X2687)),hAPP(hAPP(c_List_Olist_OCons(X2687),X2686),X2685)),hAPP(hAPP(c_List_Olist_OCons(X2687),X2684),X2683))),c_List_Olex(X2687,X2682))))&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2687)),X2683)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2687)),X2685)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2687),tc_List_Olist(X2687))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2687),tc_List_Olist(X2687)),X2685),X2683)),c_List_Olex(X2687,X2682)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2687),tc_List_Olist(X2687))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2687),tc_List_Olist(X2687)),hAPP(hAPP(c_List_Olist_OCons(X2687),X2686),X2685)),hAPP(hAPP(c_List_Olist_OCons(X2687),X2684),X2683))),c_List_Olex(X2687,X2682))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__in__lex])])])). 6.97/7.21 fof(c_0_4933, plain, ![X8854, X8855]:(((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X8855)),esk288_2(X8854,X8855)),hAPP(c_List_Oset(tc_List_Olist(X8855)),X8854)))|hBOOL(hAPP(c_List_Odistinct(X8855),c_List_Oconcat(X8855,X8854)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X8855)),esk287_2(X8854,X8855)),hAPP(c_List_Oset(tc_List_Olist(X8855)),X8854)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X8855)),X8854)))&((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X8855)),esk289_2(X8854,X8855)),hAPP(c_List_Oset(tc_List_Olist(X8855)),X8854)))|hBOOL(hAPP(c_List_Odistinct(X8855),c_List_Oconcat(X8855,X8854)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X8855)),esk287_2(X8854,X8855)),hAPP(c_List_Oset(tc_List_Olist(X8855)),X8854)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X8855)),X8854)))&((esk289_2(X8854,X8855)!=esk288_2(X8854,X8855)|hBOOL(hAPP(c_List_Odistinct(X8855),c_List_Oconcat(X8855,X8854)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X8855)),esk287_2(X8854,X8855)),hAPP(c_List_Oset(tc_List_Olist(X8855)),X8854)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X8855)),X8854)))&(c_Orderings_Obot__class_Obot(tc_fun(X8855,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8855,tc_HOL_Obool)),hAPP(c_List_Oset(X8855),esk288_2(X8854,X8855))),hAPP(c_List_Oset(X8855),esk289_2(X8854,X8855)))|hBOOL(hAPP(c_List_Odistinct(X8855),c_List_Oconcat(X8855,X8854)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X8855)),esk287_2(X8854,X8855)),hAPP(c_List_Oset(tc_List_Olist(X8855)),X8854)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X8855)),X8854))))))&((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X8855)),esk288_2(X8854,X8855)),hAPP(c_List_Oset(tc_List_Olist(X8855)),X8854)))|hBOOL(hAPP(c_List_Odistinct(X8855),c_List_Oconcat(X8855,X8854)))|~hBOOL(hAPP(c_List_Odistinct(X8855),esk287_2(X8854,X8855)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X8855)),X8854)))&((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X8855)),esk289_2(X8854,X8855)),hAPP(c_List_Oset(tc_List_Olist(X8855)),X8854)))|hBOOL(hAPP(c_List_Odistinct(X8855),c_List_Oconcat(X8855,X8854)))|~hBOOL(hAPP(c_List_Odistinct(X8855),esk287_2(X8854,X8855)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X8855)),X8854)))&((esk289_2(X8854,X8855)!=esk288_2(X8854,X8855)|hBOOL(hAPP(c_List_Odistinct(X8855),c_List_Oconcat(X8855,X8854)))|~hBOOL(hAPP(c_List_Odistinct(X8855),esk287_2(X8854,X8855)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X8855)),X8854)))&(c_Orderings_Obot__class_Obot(tc_fun(X8855,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8855,tc_HOL_Obool)),hAPP(c_List_Oset(X8855),esk288_2(X8854,X8855))),hAPP(c_List_Oset(X8855),esk289_2(X8854,X8855)))|hBOOL(hAPP(c_List_Odistinct(X8855),c_List_Oconcat(X8855,X8854)))|~hBOOL(hAPP(c_List_Odistinct(X8855),esk287_2(X8854,X8855)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X8855)),X8854))))))), 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])])])])])). 6.97/7.21 cnf(c_0_4934, 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_4540])). 6.97/7.21 cnf(c_0_4935, plain, (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))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4541])). 6.97/7.21 fof(c_0_4936, plain, ![X15972, X15973, X15974, X15975, X15976]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X15976,X15976)),hAPP(hAPP(c_Product__Type_OPair(X15976,X15976),X15975),X15974)),c_Transitive__Closure_Ortrancl(X15976,X15973)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X15976,X15976)),hAPP(hAPP(c_Product__Type_OPair(X15976,X15976),X15974),X15972)),X15973))|hBOOL(hAPP(hAPP(c_member(tc_prod(X15976,X15976)),hAPP(hAPP(c_Product__Type_OPair(X15976,X15976),X15975),X15972)),c_Transitive__Closure_Otrancl(X15976,X15973))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl1])])). 6.97/7.21 cnf(c_0_4937, 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_4542])). 6.97/7.21 cnf(c_0_4938, 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_4543])). 6.97/7.21 fof(c_0_4939, plain, ![X2571, X2572]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2572))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2572),X2571))|c_Divides_Odivmod__nat(X2571,X2572)=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),X2571),X2572)),X2572))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2571),X2572),X2572)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__nat__step])])])). 6.97/7.21 fof(c_0_4940, plain, ![X10026, X10027, X10028]:((~c_Wellfounded_Owf(X10028,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10028,X10028),tc_HOL_Obool)),X10027),X10026))|c_Wellfounded_Owf(X10028,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10028,X10028),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10028,X10028),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10028,X10028,X10028),X10027),X10027)),hAPP(hAPP(c_Relation_Orel__comp(X10028,X10028,X10028),X10026),X10027))),X10026)))&(~c_Wellfounded_Owf(X10028,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10028,X10028),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10028,X10028),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10028,X10028,X10028),X10027),X10027)),hAPP(hAPP(c_Relation_Orel__comp(X10028,X10028,X10028),X10026),X10027))),X10026))|c_Wellfounded_Owf(X10028,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10028,X10028),tc_HOL_Obool)),X10027),X10026)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__union__merge])])). 6.97/7.21 fof(c_0_4941, plain, ![X10513, X10514, X10515, X10516]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10516,tc_HOL_Obool)),X10515),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10516,tc_HOL_Obool)),X10514),X10513))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10516,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10516,tc_HOL_Obool)),X10515),X10514)),X10513), inference(variable_rename,[status(thm)],[fact_Un__assoc])). 6.97/7.21 fof(c_0_4942, plain, ![X7702, X7703, X7704]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7704,tc_HOL_Obool)),X7702),X7703)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7704,tc_HOL_Obool)),X7703),X7702), inference(variable_rename,[status(thm)],[fact_Un__commute])). 6.97/7.21 fof(c_0_4943, plain, ![X7142, X7143, X7144, X7145]:((hBOOL(hAPP(hAPP(c_member(X7145),esk230_4(X7142,X7143,X7144,X7145)),hAPP(c_List_Oset(X7145),X7144)))|c_List_OdropWhile(X7145,X7143,hAPP(hAPP(c_List_Oappend(X7145),X7144),X7142))=c_List_OdropWhile(X7145,X7143,X7142))&(~hBOOL(hAPP(X7143,esk230_4(X7142,X7143,X7144,X7145)))|c_List_OdropWhile(X7145,X7143,hAPP(hAPP(c_List_Oappend(X7145),X7144),X7142))=c_List_OdropWhile(X7145,X7143,X7142))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dropWhile__append2])])])])])). 6.97/7.21 fof(c_0_4944, plain, ![X4970, X4971, X4972, X4973, X4974, X4975, X4976]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X4976,X4976)),hAPP(hAPP(c_Product__Type_OPair(X4976,X4976),X4971),X4970)),X4974))|X4972=X4973|~hBOOL(hAPP(hAPP(c_member(X4976),X4970),X4972))|~hBOOL(hAPP(hAPP(c_member(X4976),X4971),X4973))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X4976,tc_HOL_Obool)),X4972),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4976),X4975),X4974)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X4976,tc_HOL_Obool)),X4973),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4976),X4975),X4974)))|~c_Equiv__Relations_Oequiv(X4976,X4975,X4974))&(X4972!=X4973|hBOOL(hAPP(hAPP(c_member(tc_prod(X4976,X4976)),hAPP(hAPP(c_Product__Type_OPair(X4976,X4976),X4971),X4970)),X4974))|~hBOOL(hAPP(hAPP(c_member(X4976),X4970),X4972))|~hBOOL(hAPP(hAPP(c_member(X4976),X4971),X4973))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X4976,tc_HOL_Obool)),X4972),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4976),X4975),X4974)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X4976,tc_HOL_Obool)),X4973),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4976),X4975),X4974)))|~c_Equiv__Relations_Oequiv(X4976,X4975,X4974))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_quotient__eq__iff])])])])). 6.97/7.21 cnf(c_0_4945, 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))))=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_4426])). 6.97/7.21 fof(c_0_4946, plain, ![X1297, X1298, X1299, X1300, X1301]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X1301,X1301)),hAPP(hAPP(c_Product__Type_OPair(X1301,X1301),X1300),X1299)),X1298))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X1301,X1301)),hAPP(hAPP(c_Product__Type_OPair(X1301,X1301),X1299),X1297)),X1298))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1301,X1301)),hAPP(hAPP(c_Product__Type_OPair(X1301,X1301),X1300),X1297)),c_Transitive__Closure_Otrancl(X1301,X1298))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_r__r__into__trancl])])])). 6.97/7.21 fof(c_0_4947, plain, ![X791, X792, X793]:(((hBOOL(hAPP(hAPP(c_member(tc_fun(X793,tc_HOL_Obool)),esk22_3(X791,X792,X793)),X792))|hAPP(c_Finite__Set_Ocard(X793),c_Complete__Lattice_OSup__class_OSup(tc_fun(X793,tc_HOL_Obool),X792))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X791),hAPP(c_Finite__Set_Ocard(tc_fun(X793,tc_HOL_Obool)),X792))|hBOOL(hAPP(hAPP(c_member(tc_fun(X793,tc_HOL_Obool)),esk21_3(X791,X792,X793)),X792))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X793),c_Complete__Lattice_OSup__class_OSup(tc_fun(X793,tc_HOL_Obool),X792)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X793,tc_HOL_Obool)),X792)))&((hBOOL(hAPP(hAPP(c_member(tc_fun(X793,tc_HOL_Obool)),esk23_3(X791,X792,X793)),X792))|hAPP(c_Finite__Set_Ocard(X793),c_Complete__Lattice_OSup__class_OSup(tc_fun(X793,tc_HOL_Obool),X792))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X791),hAPP(c_Finite__Set_Ocard(tc_fun(X793,tc_HOL_Obool)),X792))|hBOOL(hAPP(hAPP(c_member(tc_fun(X793,tc_HOL_Obool)),esk21_3(X791,X792,X793)),X792))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X793),c_Complete__Lattice_OSup__class_OSup(tc_fun(X793,tc_HOL_Obool),X792)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X793,tc_HOL_Obool)),X792)))&((esk23_3(X791,X792,X793)!=esk22_3(X791,X792,X793)|hAPP(c_Finite__Set_Ocard(X793),c_Complete__Lattice_OSup__class_OSup(tc_fun(X793,tc_HOL_Obool),X792))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X791),hAPP(c_Finite__Set_Ocard(tc_fun(X793,tc_HOL_Obool)),X792))|hBOOL(hAPP(hAPP(c_member(tc_fun(X793,tc_HOL_Obool)),esk21_3(X791,X792,X793)),X792))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X793),c_Complete__Lattice_OSup__class_OSup(tc_fun(X793,tc_HOL_Obool),X792)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X793,tc_HOL_Obool)),X792)))&(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X793,tc_HOL_Obool)),esk22_3(X791,X792,X793)),esk23_3(X791,X792,X793))!=c_Orderings_Obot__class_Obot(tc_fun(X793,tc_HOL_Obool))|hAPP(c_Finite__Set_Ocard(X793),c_Complete__Lattice_OSup__class_OSup(tc_fun(X793,tc_HOL_Obool),X792))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X791),hAPP(c_Finite__Set_Ocard(tc_fun(X793,tc_HOL_Obool)),X792))|hBOOL(hAPP(hAPP(c_member(tc_fun(X793,tc_HOL_Obool)),esk21_3(X791,X792,X793)),X792))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X793),c_Complete__Lattice_OSup__class_OSup(tc_fun(X793,tc_HOL_Obool),X792)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X793,tc_HOL_Obool)),X792))))))&((hBOOL(hAPP(hAPP(c_member(tc_fun(X793,tc_HOL_Obool)),esk22_3(X791,X792,X793)),X792))|hAPP(c_Finite__Set_Ocard(X793),c_Complete__Lattice_OSup__class_OSup(tc_fun(X793,tc_HOL_Obool),X792))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X791),hAPP(c_Finite__Set_Ocard(tc_fun(X793,tc_HOL_Obool)),X792))|hAPP(c_Finite__Set_Ocard(X793),esk21_3(X791,X792,X793))!=X791|~hBOOL(hAPP(c_Finite__Set_Ofinite(X793),c_Complete__Lattice_OSup__class_OSup(tc_fun(X793,tc_HOL_Obool),X792)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X793,tc_HOL_Obool)),X792)))&((hBOOL(hAPP(hAPP(c_member(tc_fun(X793,tc_HOL_Obool)),esk23_3(X791,X792,X793)),X792))|hAPP(c_Finite__Set_Ocard(X793),c_Complete__Lattice_OSup__class_OSup(tc_fun(X793,tc_HOL_Obool),X792))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X791),hAPP(c_Finite__Set_Ocard(tc_fun(X793,tc_HOL_Obool)),X792))|hAPP(c_Finite__Set_Ocard(X793),esk21_3(X791,X792,X793))!=X791|~hBOOL(hAPP(c_Finite__Set_Ofinite(X793),c_Complete__Lattice_OSup__class_OSup(tc_fun(X793,tc_HOL_Obool),X792)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X793,tc_HOL_Obool)),X792)))&((esk23_3(X791,X792,X793)!=esk22_3(X791,X792,X793)|hAPP(c_Finite__Set_Ocard(X793),c_Complete__Lattice_OSup__class_OSup(tc_fun(X793,tc_HOL_Obool),X792))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X791),hAPP(c_Finite__Set_Ocard(tc_fun(X793,tc_HOL_Obool)),X792))|hAPP(c_Finite__Set_Ocard(X793),esk21_3(X791,X792,X793))!=X791|~hBOOL(hAPP(c_Finite__Set_Ofinite(X793),c_Complete__Lattice_OSup__class_OSup(tc_fun(X793,tc_HOL_Obool),X792)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X793,tc_HOL_Obool)),X792)))&(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X793,tc_HOL_Obool)),esk22_3(X791,X792,X793)),esk23_3(X791,X792,X793))!=c_Orderings_Obot__class_Obot(tc_fun(X793,tc_HOL_Obool))|hAPP(c_Finite__Set_Ocard(X793),c_Complete__Lattice_OSup__class_OSup(tc_fun(X793,tc_HOL_Obool),X792))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X791),hAPP(c_Finite__Set_Ocard(tc_fun(X793,tc_HOL_Obool)),X792))|hAPP(c_Finite__Set_Ocard(X793),esk21_3(X791,X792,X793))!=X791|~hBOOL(hAPP(c_Finite__Set_Ofinite(X793),c_Complete__Lattice_OSup__class_OSup(tc_fun(X793,tc_HOL_Obool),X792)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X793,tc_HOL_Obool)),X792))))))), 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])])])])])). 6.97/7.21 fof(c_0_4948, plain, ![X1841, X1842]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1842),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1842,tc_HOL_Obool),X1841)))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1842,tc_HOL_Obool)),X1841))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UnionD])])). 6.97/7.21 cnf(c_0_4949, plain, (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(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),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_4530])). 6.97/7.21 fof(c_0_4950, plain, ![X3617, X3618, X3621, X3623]:((((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk120_2(X3617,X3618)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3618)))|~hBOOL(hAPP(X3617,X3621))|(~hBOOL(hAPP(X3617,esk118_2(X3617,X3618)))|~hBOOL(hAPP(X3617,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk118_2(X3617,X3618)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk119_2(X3617,X3618)),X3618)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3618)))&(hBOOL(hAPP(X3617,esk120_2(X3617,X3618)))|~hBOOL(hAPP(X3617,X3621))|(~hBOOL(hAPP(X3617,esk118_2(X3617,X3618)))|~hBOOL(hAPP(X3617,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk118_2(X3617,X3618)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk119_2(X3617,X3618)),X3618)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3618))))&(~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3623),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3618)))|~hBOOL(hAPP(X3617,X3623))|hBOOL(hAPP(X3617,esk121_2(X3617,X3618)))|(~hBOOL(hAPP(X3617,esk118_2(X3617,X3618)))|~hBOOL(hAPP(X3617,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk118_2(X3617,X3618)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk119_2(X3617,X3618)),X3618)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3618))))&(((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk120_2(X3617,X3618)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3618)))|~hBOOL(hAPP(X3617,X3621))|(hBOOL(hAPP(X3617,esk118_2(X3617,X3618)))|hBOOL(hAPP(X3617,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk118_2(X3617,X3618)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk119_2(X3617,X3618)),X3618)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3618)))&(hBOOL(hAPP(X3617,esk120_2(X3617,X3618)))|~hBOOL(hAPP(X3617,X3621))|(hBOOL(hAPP(X3617,esk118_2(X3617,X3618)))|hBOOL(hAPP(X3617,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk118_2(X3617,X3618)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk119_2(X3617,X3618)),X3618)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3618))))&(~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3623),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3618)))|~hBOOL(hAPP(X3617,X3623))|hBOOL(hAPP(X3617,esk121_2(X3617,X3618)))|(hBOOL(hAPP(X3617,esk118_2(X3617,X3618)))|hBOOL(hAPP(X3617,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk118_2(X3617,X3618)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk119_2(X3617,X3618)),X3618)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3618))))), 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])])])])])])). 6.97/7.21 fof(c_0_4951, plain, ![X3945, X3946]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3945),X3946)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3946),X3945), inference(variable_rename,[status(thm)],[fact_zmult__commute])). 6.97/7.21 fof(c_0_4952, plain, ![X15582, X15583, X15584, X15585]:(((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15585)),X15584)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15585)),X15583)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X15585),tc_List_Olist(X15585))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X15585),tc_List_Olist(X15585)),X15584),X15583)),c_List_Olex(X15585,X15582))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X15585),tc_List_Olist(X15585))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X15585),tc_List_Olist(X15585)),X15584),X15583)),c_List_Olexord(X15585,X15582)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X15585),tc_List_Olist(X15585))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X15585),tc_List_Olist(X15585)),X15584),X15583)),c_List_Olex(X15585,X15582)))))&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15585)),X15584)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15585)),X15583)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X15585),tc_List_Olist(X15585))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X15585),tc_List_Olist(X15585)),X15584),X15583)),c_List_Olexord(X15585,X15582)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X15585),tc_List_Olist(X15585))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X15585),tc_List_Olist(X15585)),X15584),X15583)),c_List_Olex(X15585,X15582))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__lex])])])). 6.97/7.21 fof(c_0_4953, plain, ![X6847, X6848, X6849]:((((X6848=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|(X6848!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|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),X6847)),X6848)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X6847))!=X6849)|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X6849,X6848),X6847)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X6847)|(X6848!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|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),X6847)),X6848)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X6847))!=X6849)|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X6849,X6848),X6847))))&((((X6848=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)),X6848))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6848))|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),X6847)),X6848)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X6847))!=X6849)|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X6849,X6848),X6847)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X6847)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6848))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6848))|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),X6847)),X6848)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X6847))!=X6849)|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X6849,X6848),X6847))))&((X6848=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|(~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),X6847)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X6847)),X6848))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6848))|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),X6847)),X6848)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X6847))!=X6849)|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X6849,X6848),X6847)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X6847)|(~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),X6847)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X6847)),X6848))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6848))|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),X6847)),X6848)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X6847))!=X6849)|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X6849,X6848),X6847)))))&(((X6848=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)),X6848))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X6847)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6848),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X6847))))|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),X6847)),X6848)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X6847))!=X6849)|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X6849,X6848),X6847)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X6847)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6848))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X6847)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6848),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X6847))))|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),X6847)),X6848)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X6847))!=X6849)|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X6849,X6848),X6847))))&((X6848=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|(~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),X6847)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X6847)),X6848))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X6847)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6848),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X6847))))|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),X6847)),X6848)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X6847))!=X6849)|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X6849,X6848),X6847)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X6847)|(~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),X6847)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X6847)),X6848))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X6847)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6848),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X6847))))|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),X6847)),X6848)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X6847))!=X6849)|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X6849,X6848),X6847)))))))&(((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),X6847)),X6848)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X6847))=X6849|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X6849,X6848),X6847)))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X6847)),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)),X6848))|X6848=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X6849,X6848),X6847)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6848),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X6847)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6848))|X6848=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X6849,X6848),X6847))))&((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),X6847)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6848))|X6848=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X6849,X6848),X6847)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X6847)),X6848))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6848))|X6848=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X6849,X6848),X6847))))))&(X6848!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X6847)|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X6849,X6848),X6847))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__nat__rel__def])])])])). 6.97/7.21 fof(c_0_4954, plain, ![X3762]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3762)), inference(variable_rename,[status(thm)],[fact_le0])). 6.97/7.21 cnf(c_0_4955, plain, (X1=X2|hAPP(c_List_OremoveAll(X3,X2),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X4))=hAPP(hAPP(c_List_Olist_OCons(X3),X1),hAPP(c_List_OremoveAll(X3,X2),X4))), inference(split_conjunct,[status(thm)],[c_0_4544])). 6.97/7.21 fof(c_0_4956, plain, ![X6803, X6804, X6805, X6806, X6807]:((((X6803=hAPP(hAPP(c_List_Oappend(X6807),hAPP(hAPP(c_List_Odrop(X6807),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6807)),X6804)),X6806)),X6805)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6807)),X6806)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6807)),X6804)))|hAPP(hAPP(c_List_Oappend(X6807),X6804),X6803)!=hAPP(hAPP(c_List_Oappend(X6807),X6806),X6805))&(X6804=hAPP(hAPP(c_List_Otake(X6807),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6807)),X6804)),X6806)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6807)),X6806)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6807)),X6804)))|hAPP(hAPP(c_List_Oappend(X6807),X6804),X6803)!=hAPP(hAPP(c_List_Oappend(X6807),X6806),X6805)))&((X6805=hAPP(hAPP(c_List_Oappend(X6807),hAPP(hAPP(c_List_Odrop(X6807),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6807)),X6806)),X6804)),X6803)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6807)),X6806)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6807)),X6804)))|hAPP(hAPP(c_List_Oappend(X6807),X6804),X6803)!=hAPP(hAPP(c_List_Oappend(X6807),X6806),X6805))&(X6806=hAPP(hAPP(c_List_Otake(X6807),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6807)),X6806)),X6804)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6807)),X6806)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6807)),X6804)))|hAPP(hAPP(c_List_Oappend(X6807),X6804),X6803)!=hAPP(hAPP(c_List_Oappend(X6807),X6806),X6805))))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6807)),X6806)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6807)),X6804)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6807)),X6806)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6807)),X6804)))|hAPP(hAPP(c_List_Oappend(X6807),X6804),X6803)=hAPP(hAPP(c_List_Oappend(X6807),X6806),X6805))&(X6805!=hAPP(hAPP(c_List_Oappend(X6807),hAPP(hAPP(c_List_Odrop(X6807),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6807)),X6806)),X6804)),X6803)|X6806!=hAPP(hAPP(c_List_Otake(X6807),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6807)),X6806)),X6804)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6807)),X6806)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6807)),X6804)))|hAPP(hAPP(c_List_Oappend(X6807),X6804),X6803)=hAPP(hAPP(c_List_Oappend(X6807),X6806),X6805)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6807)),X6806)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6807)),X6804)))|(X6803!=hAPP(hAPP(c_List_Oappend(X6807),hAPP(hAPP(c_List_Odrop(X6807),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6807)),X6804)),X6806)),X6805)|X6804!=hAPP(hAPP(c_List_Otake(X6807),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6807)),X6804)),X6806))|hAPP(hAPP(c_List_Oappend(X6807),X6804),X6803)=hAPP(hAPP(c_List_Oappend(X6807),X6806),X6805))&(X6805!=hAPP(hAPP(c_List_Oappend(X6807),hAPP(hAPP(c_List_Odrop(X6807),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6807)),X6806)),X6804)),X6803)|X6806!=hAPP(hAPP(c_List_Otake(X6807),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6807)),X6806)),X6804)|(X6803!=hAPP(hAPP(c_List_Oappend(X6807),hAPP(hAPP(c_List_Odrop(X6807),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6807)),X6804)),X6806)),X6805)|X6804!=hAPP(hAPP(c_List_Otake(X6807),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6807)),X6804)),X6806))|hAPP(hAPP(c_List_Oappend(X6807),X6804),X6803)=hAPP(hAPP(c_List_Oappend(X6807),X6806),X6805))))), 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])])])])). 6.97/7.21 fof(c_0_4957, plain, ![X1134, X1135, X1136, X1137, X1138, X1139, X1140]:(~c_Fun_Oinj__on(X1140,X1139,X1138,hAPP(c_Set_Oimage(X1137,X1140,X1136),X1135))|(~c_Fun_Oinj__on(X1137,X1140,X1136,X1135)|(~hBOOL(hAPP(hAPP(c_member(X1139),X1134),hAPP(c_Set_Oimage(X1140,X1139,X1138),hAPP(c_Set_Oimage(X1137,X1140,X1136),X1135))))|hAPP(hAPP(c_Fun_Ocomp(X1140,X1137,X1139,c_Fun_Othe__inv__into(X1137,X1140,X1135,X1136)),c_Fun_Othe__inv__into(X1140,X1139,hAPP(c_Set_Oimage(X1137,X1140,X1136),X1135),X1138)),X1134)=hAPP(c_Fun_Othe__inv__into(X1137,X1139,X1135,hAPP(c_Fun_Ocomp(X1140,X1139,X1137,X1138),X1136)),X1134)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_the__inv__into__comp])])])). 6.97/7.21 fof(c_0_4958, plain, ![X3992, X3993, X3994, X3995, X3996, X3997, X3998]:(~c_Fun_Oinj__on(X3998,X3997,X3996,hAPP(c_Set_Oimage(X3995,X3998,X3994),X3993))|(~c_Fun_Oinj__on(X3995,X3998,X3994,X3993)|(~hBOOL(hAPP(hAPP(c_member(X3997),X3992),hAPP(c_Set_Oimage(X3998,X3997,X3996),hAPP(c_Set_Oimage(X3995,X3998,X3994),X3993))))|hAPP(c_Hilbert__Choice_Oinv__into(X3995,X3997,X3993,hAPP(c_Fun_Ocomp(X3998,X3997,X3995,X3996),X3994)),X3992)=hAPP(hAPP(c_Fun_Ocomp(X3998,X3995,X3997,c_Hilbert__Choice_Oinv__into(X3995,X3998,X3993,X3994)),c_Hilbert__Choice_Oinv__into(X3998,X3997,hAPP(c_Set_Oimage(X3995,X3998,X3994),X3993),X3996)),X3992)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inv__into__comp])])])). 6.97/7.21 fof(c_0_4959, plain, ![X14602, X14603, X14604, X14605]:((hBOOL(hAPP(hAPP(c_member(X14605),esk494_4(X14602,X14603,X14604,X14605)),hAPP(X14603,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14605,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X14605,tc_HOL_Obool),X14603)),hAPP(c_Set_OCollect(X14605),X14602)))))|hBOOL(hAPP(X14602,X14604))|~c_Orderings_Oorder__class_Omono(tc_fun(X14605,tc_HOL_Obool),tc_fun(X14605,tc_HOL_Obool),X14603)|~hBOOL(hAPP(hAPP(c_member(X14605),X14604),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X14605,tc_HOL_Obool),X14603))))&(~hBOOL(hAPP(X14602,esk494_4(X14602,X14603,X14604,X14605)))|hBOOL(hAPP(X14602,X14604))|~c_Orderings_Oorder__class_Omono(tc_fun(X14605,tc_HOL_Obool),tc_fun(X14605,tc_HOL_Obool),X14603)|~hBOOL(hAPP(hAPP(c_member(X14605),X14604),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X14605,tc_HOL_Obool),X14603))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lfp__induct__set])])])])])). 6.97/7.21 fof(c_0_4960, plain, ![X5628, X5629, X5630, X5631]:((hBOOL(hAPP(hAPP(c_member(X5631),esk187_4(X5628,X5629,X5630,X5631)),X5630))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5629),hAPP(c_Set_Oimage(X5631,X5629,X5628),X5630)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X5631),X5630)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5631),hAPP(c_Set_OCollect(X5631),hAPP(hAPP(c_COMBS(X5631,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5631),c_fconj),hAPP(hAPP(c_COMBC(X5631,tc_fun(X5631,tc_HOL_Obool),tc_HOL_Obool),c_member(X5631)),X5630))),hAPP(hAPP(c_COMBC(X5631,X5629,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X5629,tc_fun(X5629,tc_HOL_Obool),X5631),c_fequal),X5628)),hAPP(X5628,esk187_4(X5628,X5629,X5630,X5631)))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5629),hAPP(c_Set_Oimage(X5631,X5629,X5628),X5630)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X5631),X5630)))), 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])])])])])). 6.97/7.21 cnf(c_0_4961, 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_4545])). 6.97/7.21 fof(c_0_4962, plain, ![X8340, X8341, X8342, X8343, X8344, X8345, X8346, X8347, X8348, X8349]:((((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8340))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8344))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8340),X8343)),X8344)!=X8341|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8344),X8340))|hBOOL(hAPP(X8342,X8343)))|~hBOOL(hAPP(X8342,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8341),X8340))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8340),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X8346),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X8341!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8340),X8345)),X8346)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8340),X8346))|hBOOL(hAPP(X8342,X8345)))|~hBOOL(hAPP(X8342,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8341),X8340)))))&(X8340!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(X8342,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X8342,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8341),X8340)))))&((((X8347=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8347),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)),X8347)))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))&(~hBOOL(hAPP(X8349,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8347),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)),X8347)))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347)))))&(((((X8347=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_3(X8347,X8348,X8349)),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)),X8347)))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))&(~hBOOL(hAPP(X8349,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_3(X8347,X8348,X8349)),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)),X8347)))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347)))))&((X8347=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(X8348=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8347),esk275_3(X8347,X8348,X8349))),esk276_3(X8347,X8348,X8349))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8347)))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))&(~hBOOL(hAPP(X8349,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(X8348=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8347),esk275_3(X8347,X8348,X8349))),esk276_3(X8347,X8348,X8349))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8347)))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))))&((X8347=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8347),esk276_3(X8347,X8348,X8349)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8347)))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))&(~hBOOL(hAPP(X8349,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8347),esk276_3(X8347,X8348,X8349)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8347)))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))))&((X8347=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(~hBOOL(hAPP(X8349,esk275_3(X8347,X8348,X8349)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8347)))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))&(~hBOOL(hAPP(X8349,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(X8349,esk275_3(X8347,X8348,X8349)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8347)))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347)))))))&((((((X8347=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8347),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)),esk274_3(X8347,X8348,X8349))))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))&(~hBOOL(hAPP(X8349,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8347),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)),esk274_3(X8347,X8348,X8349))))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347)))))&(((((X8347=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_3(X8347,X8348,X8349)),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)),esk274_3(X8347,X8348,X8349))))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))&(~hBOOL(hAPP(X8349,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_3(X8347,X8348,X8349)),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)),esk274_3(X8347,X8348,X8349))))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347)))))&((X8347=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(X8348=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8347),esk275_3(X8347,X8348,X8349))),esk276_3(X8347,X8348,X8349))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk274_3(X8347,X8348,X8349))))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))&(~hBOOL(hAPP(X8349,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(X8348=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8347),esk275_3(X8347,X8348,X8349))),esk276_3(X8347,X8348,X8349))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk274_3(X8347,X8348,X8349))))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))))&((X8347=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8347),esk276_3(X8347,X8348,X8349)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk274_3(X8347,X8348,X8349))))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))&(~hBOOL(hAPP(X8349,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8347),esk276_3(X8347,X8348,X8349)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk274_3(X8347,X8348,X8349))))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))))&((X8347=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(~hBOOL(hAPP(X8349,esk275_3(X8347,X8348,X8349)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk274_3(X8347,X8348,X8349))))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))&(~hBOOL(hAPP(X8349,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(X8349,esk275_3(X8347,X8348,X8349)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk274_3(X8347,X8348,X8349))))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347)))))))&(((X8347=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8347),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),X8347),esk273_3(X8347,X8348,X8349))),esk274_3(X8347,X8348,X8349))=X8348)|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))&(~hBOOL(hAPP(X8349,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8347),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),X8347),esk273_3(X8347,X8348,X8349))),esk274_3(X8347,X8348,X8349))=X8348)|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347)))))&(((((X8347=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_3(X8347,X8348,X8349)),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),X8347),esk273_3(X8347,X8348,X8349))),esk274_3(X8347,X8348,X8349))=X8348)|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))&(~hBOOL(hAPP(X8349,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_3(X8347,X8348,X8349)),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),X8347),esk273_3(X8347,X8348,X8349))),esk274_3(X8347,X8348,X8349))=X8348)|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347)))))&((X8347=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(X8348=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8347),esk275_3(X8347,X8348,X8349))),esk276_3(X8347,X8348,X8349))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8347),esk273_3(X8347,X8348,X8349))),esk274_3(X8347,X8348,X8349))=X8348)|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))&(~hBOOL(hAPP(X8349,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(X8348=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8347),esk275_3(X8347,X8348,X8349))),esk276_3(X8347,X8348,X8349))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8347),esk273_3(X8347,X8348,X8349))),esk274_3(X8347,X8348,X8349))=X8348)|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))))&((X8347=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8347),esk276_3(X8347,X8348,X8349)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8347),esk273_3(X8347,X8348,X8349))),esk274_3(X8347,X8348,X8349))=X8348)|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))&(~hBOOL(hAPP(X8349,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8347),esk276_3(X8347,X8348,X8349)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8347),esk273_3(X8347,X8348,X8349))),esk274_3(X8347,X8348,X8349))=X8348)|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))))&((X8347=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(~hBOOL(hAPP(X8349,esk275_3(X8347,X8348,X8349)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8347),esk273_3(X8347,X8348,X8349))),esk274_3(X8347,X8348,X8349))=X8348)|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))&(~hBOOL(hAPP(X8349,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(X8349,esk275_3(X8347,X8348,X8349)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8347),esk273_3(X8347,X8348,X8349))),esk274_3(X8347,X8348,X8349))=X8348)|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))))))&(((X8347=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8347),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X8347,X8348,X8349)),X8347)))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))&(~hBOOL(hAPP(X8349,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8347),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X8347,X8348,X8349)),X8347)))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347)))))&(((((X8347=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_3(X8347,X8348,X8349)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X8347,X8348,X8349)),X8347)))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))&(~hBOOL(hAPP(X8349,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_3(X8347,X8348,X8349)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X8347,X8348,X8349)),X8347)))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347)))))&((X8347=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(X8348=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8347),esk275_3(X8347,X8348,X8349))),esk276_3(X8347,X8348,X8349))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X8347,X8348,X8349)),X8347)))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))&(~hBOOL(hAPP(X8349,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(X8348=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8347),esk275_3(X8347,X8348,X8349))),esk276_3(X8347,X8348,X8349))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X8347,X8348,X8349)),X8347)))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))))&((X8347=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8347),esk276_3(X8347,X8348,X8349)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X8347,X8348,X8349)),X8347)))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))&(~hBOOL(hAPP(X8349,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8347),esk276_3(X8347,X8348,X8349)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X8347,X8348,X8349)),X8347)))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))))&((X8347=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(~hBOOL(hAPP(X8349,esk275_3(X8347,X8348,X8349)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X8347,X8348,X8349)),X8347)))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))&(~hBOOL(hAPP(X8349,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(X8349,esk275_3(X8347,X8348,X8349)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X8347,X8348,X8349)),X8347)))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))))))&(((X8347=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8347),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X8349,esk273_3(X8347,X8348,X8349))))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))&(~hBOOL(hAPP(X8349,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8347),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X8349,esk273_3(X8347,X8348,X8349))))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347)))))&(((((X8347=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_3(X8347,X8348,X8349)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X8349,esk273_3(X8347,X8348,X8349))))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))&(~hBOOL(hAPP(X8349,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_3(X8347,X8348,X8349)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X8349,esk273_3(X8347,X8348,X8349))))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347)))))&((X8347=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(X8348=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8347),esk275_3(X8347,X8348,X8349))),esk276_3(X8347,X8348,X8349))|~hBOOL(hAPP(X8349,esk273_3(X8347,X8348,X8349))))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))&(~hBOOL(hAPP(X8349,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(X8348=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8347),esk275_3(X8347,X8348,X8349))),esk276_3(X8347,X8348,X8349))|~hBOOL(hAPP(X8349,esk273_3(X8347,X8348,X8349))))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))))&((X8347=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8347),esk276_3(X8347,X8348,X8349)))|~hBOOL(hAPP(X8349,esk273_3(X8347,X8348,X8349))))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))&(~hBOOL(hAPP(X8349,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8347),esk276_3(X8347,X8348,X8349)))|~hBOOL(hAPP(X8349,esk273_3(X8347,X8348,X8349))))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))))&((X8347=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(~hBOOL(hAPP(X8349,esk275_3(X8347,X8348,X8349)))|~hBOOL(hAPP(X8349,esk273_3(X8347,X8348,X8349))))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347))))&(~hBOOL(hAPP(X8349,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(X8349,esk275_3(X8347,X8348,X8349)))|~hBOOL(hAPP(X8349,esk273_3(X8347,X8348,X8349))))|hBOOL(hAPP(X8349,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8348),X8347)))))))))), 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__zdiv])])])])])])])). 6.97/7.21 fof(c_0_4963, plain, ![X16063, X16064, X16065]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X16065,X16065),tc_HOL_Obool)),X16064),X16063))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X16065,X16065),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X16065,X16065,X16065),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X16065,X16065),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X16065,X16064)),X16063)),X16064)),X16063))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X16065,X16065),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X16065,X16064)),X16063)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_trancl__Int__subset])])])). 6.97/7.21 cnf(c_0_4964, plain, (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_Oone__class_Oone(X2)|X1!=c_Groups_Oone__class_Oone(X2)|~class_Rings_Oring__1__no__zero__divisors(X2)), inference(split_conjunct,[status(thm)],[c_0_4426])). 6.97/7.21 cnf(c_0_4965, plain, (c_Groups_Ozero__class_Ozero(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_Ozero__class_Ozero(X2)|~class_Rings_Oring__1__no__zero__divisors(X2)), inference(split_conjunct,[status(thm)],[c_0_4546])). 6.97/7.21 cnf(c_0_4966, plain, (c_Groups_Oone__class_Oone(X1)=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))))|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_4547])). 6.97/7.21 cnf(c_0_4967, plain, (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),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_4548])). 6.97/7.21 fof(c_0_4968, plain, ![X14671, X14672, X14673]:((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),esk497_3(X14671,X14672,X14673)),esk498_3(X14671,X14672,X14673))))|hBOOL(hAPP(hAPP(X14671,X14673),X14672))|~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),X14673),X14672))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk497_3(X14671,X14672,X14673)),esk498_3(X14671,X14672,X14673)))|hBOOL(hAPP(hAPP(X14671,esk497_3(X14671,X14672,X14673)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk498_3(X14671,X14672,X14673)),c_Groups_Oone__class_Oone(tc_Int_Oint))))|hBOOL(hAPP(hAPP(X14671,X14673),X14672))|~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),X14673),X14672))))&(~hBOOL(hAPP(hAPP(X14671,esk497_3(X14671,X14672,X14673)),esk498_3(X14671,X14672,X14673)))|hBOOL(hAPP(hAPP(X14671,X14673),X14672))|~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),X14673),X14672)))))), 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])])])])])). 6.97/7.21 fof(c_0_4969, plain, ![X15391, X15392, X15393, X15394, X15395, X15396]:((hBOOL(hAPP(hAPP(c_member(X15396),esk517_6(X15391,X15392,X15393,X15394,X15395,X15396)),X15395))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15396,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X15396,X15392,X15394),X15391)),X15395)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15396,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X15396,X15392,X15393),X15391)),X15395))&(hAPP(X15394,esk517_6(X15391,X15392,X15393,X15394,X15395,X15396))!=hAPP(X15393,esk517_6(X15391,X15392,X15393,X15394,X15395,X15396))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15396,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X15396,X15392,X15394),X15391)),X15395)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15396,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X15396,X15392,X15393),X15391)),X15395))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__inter__cong])])])])). 6.97/7.21 fof(c_0_4970, plain, ![X6307, X6308, X6309, X6310, X6311, X6312, X6313, X6314]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6313),X6311),esk209_8(X6307,X6308,X6309,X6310,X6311,X6312,X6313,X6314)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6313,X6314),X6307),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X6313,X6311),X6309))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6313,X6314),X6308),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X6313,X6312),X6310))|X6310!=X6309|X6312!=X6311|(~class_Groups_Ocomm__monoid__add(X6314)|~class_Orderings_Oord(X6313)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6313),esk209_8(X6307,X6308,X6309,X6310,X6311,X6312,X6313,X6314)),X6309))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6313,X6314),X6307),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X6313,X6311),X6309))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6313,X6314),X6308),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X6313,X6312),X6310))|X6310!=X6309|X6312!=X6311|(~class_Groups_Ocomm__monoid__add(X6314)|~class_Orderings_Oord(X6313)))&(hAPP(X6308,esk209_8(X6307,X6308,X6309,X6310,X6311,X6312,X6313,X6314))!=hAPP(X6307,esk209_8(X6307,X6308,X6309,X6310,X6311,X6312,X6313,X6314))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6313,X6314),X6307),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X6313,X6311),X6309))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6313,X6314),X6308),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X6313,X6312),X6310))|X6310!=X6309|X6312!=X6311|(~class_Groups_Ocomm__monoid__add(X6314)|~class_Orderings_Oord(X6313))))), 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])])])])])). 6.97/7.21 fof(c_0_4971, plain, ![X8076, X8077, X8078, X8079]:(((((X8076=hAPP(X8077,esk265_4(X8076,X8077,X8078,X8079))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X8076),hAPP(X8077,X8078)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X8077,X8079)),X8076))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8079),X8078))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8079),esk264_4(X8076,X8077,X8078,X8079))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk265_4(X8076,X8077,X8078,X8079)),X8078))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X8076),hAPP(X8077,X8078)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X8077,X8079)),X8076))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8079),X8078))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8079),esk264_4(X8076,X8077,X8078,X8079)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8079),esk265_4(X8076,X8077,X8078,X8079)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X8076),hAPP(X8077,X8078)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X8077,X8079)),X8076))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8079),X8078))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8079),esk264_4(X8076,X8077,X8078,X8079)))))&(((X8076=hAPP(X8077,esk265_4(X8076,X8077,X8078,X8079))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X8076),hAPP(X8077,X8078)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X8077,X8079)),X8076))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8079),X8078))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk264_4(X8076,X8077,X8078,X8079)),X8078)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk265_4(X8076,X8077,X8078,X8079)),X8078))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X8076),hAPP(X8077,X8078)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X8077,X8079)),X8076))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8079),X8078))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk264_4(X8076,X8077,X8078,X8079)),X8078))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8079),esk265_4(X8076,X8077,X8078,X8079)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X8076),hAPP(X8077,X8078)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X8077,X8079)),X8076))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8079),X8078))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk264_4(X8076,X8077,X8078,X8079)),X8078)))))&(((X8076=hAPP(X8077,esk265_4(X8076,X8077,X8078,X8079))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X8076),hAPP(X8077,X8078)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X8077,X8079)),X8076))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8079),X8078))|~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(X8077,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk264_4(X8076,X8077,X8078,X8079)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X8077,esk264_4(X8076,X8077,X8078,X8079))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk265_4(X8076,X8077,X8078,X8079)),X8078))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X8076),hAPP(X8077,X8078)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X8077,X8079)),X8076))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8079),X8078))|~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(X8077,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk264_4(X8076,X8077,X8078,X8079)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X8077,esk264_4(X8076,X8077,X8078,X8079))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8079),esk265_4(X8076,X8077,X8078,X8079)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X8076),hAPP(X8077,X8078)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X8077,X8079)),X8076))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8079),X8078))|~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(X8077,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk264_4(X8076,X8077,X8078,X8079)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X8077,esk264_4(X8076,X8077,X8078,X8079))))),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])])])])])). 6.97/7.21 fof(c_0_4972, plain, ![X2875, X2876, X2877, X2878]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2878),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2877)),X2876)))|hAPP(hAPP(c_List_Olist__update(X2877,hAPP(c_List_Orev(X2877),X2876)),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(X2877)),X2876)),X2878)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2875)=hAPP(c_List_Orev(X2877),hAPP(hAPP(c_List_Olist__update(X2877,X2876),X2878),X2875))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rev__update])])])). 6.97/7.21 fof(c_0_4973, plain, ![X13595, X13596, X13597]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X13597),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13596),X13595))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X13597),X13596)),X13595), inference(variable_rename,[status(thm)],[fact_diff__diff__left])). 6.97/7.21 fof(c_0_4974, plain, ![X12559, X12560, X12561, X12562, X12563]:((X12560!=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),X12562),X12563)),X12561)),X12559)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12562),X12561)),X12559)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12563),X12561)),X12560)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X12563),X12562)))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12562),X12561)),X12559)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12563),X12561)),X12560)|X12560=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),X12562),X12563)),X12561)),X12559)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X12563),X12562)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__eq__add__iff2])])])])). 6.97/7.21 fof(c_0_4975, plain, ![X16281, X16282, X16283, X16284]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16284),X16283)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16282),X16283)),X16281))=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),X16284),X16282)),X16283)),X16281), inference(variable_rename,[status(thm)],[fact_left__add__mult__distrib])). 6.97/7.21 cnf(c_0_4976, 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_4549])). 6.97/7.21 cnf(c_0_4977, 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_4550]), ['final']). 6.97/7.21 cnf(c_0_4978, plain, (c_Orderings_Oord__class_Omax(tc_Nat_Onat)=c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[fact_sup__nat__def]), ['final']). 6.97/7.21 fof(c_0_4979, plain, ![X1777, X1778, X1779, X1780, X1781]:((hBOOL(hAPP(hAPP(c_member(X1780),esk53_5(X1777,X1778,X1779,X1780,X1781)),hAPP(X1779,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1780,tc_HOL_Obool)),X1781),hAPP(c_Set_OCollect(X1780),X1777)))))|hBOOL(hAPP(X1777,X1778))|~hBOOL(hAPP(hAPP(c_member(X1780),X1778),X1781))|~c_Orderings_Oorder__class_Omono(tc_fun(X1780,tc_HOL_Obool),tc_fun(X1780,tc_HOL_Obool),X1779)|c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1780,tc_HOL_Obool),X1779)!=X1781)&(~hBOOL(hAPP(X1777,esk53_5(X1777,X1778,X1779,X1780,X1781)))|hBOOL(hAPP(X1777,X1778))|~hBOOL(hAPP(hAPP(c_member(X1780),X1778),X1781))|~c_Orderings_Oorder__class_Omono(tc_fun(X1780,tc_HOL_Obool),tc_fun(X1780,tc_HOL_Obool),X1779)|c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1780,tc_HOL_Obool),X1779)!=X1781)), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_def__lfp__induct__set])])])])])). 6.97/7.21 fof(c_0_4980, plain, ![X7849, X7850, X7851, X7856, X7857, X7858, X7859, X7860, X7861, X7862]:(((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7849),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)),X7849))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X7849)|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849))))&((((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7849),esk256_3(X7849,X7850,X7851))),esk257_3(X7849,X7850,X7851))=X7850|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7849))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X7849)|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_3(X7849,X7850,X7851)),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)),X7849))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X7849)|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7849),esk257_3(X7849,X7850,X7851)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7849))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X7849)|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849)))))&(~hBOOL(hAPP(X7851,esk257_3(X7849,X7850,X7851)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7849))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X7849)|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849))))))&(((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7849),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X7849,X7850,X7851)),X7849))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X7849)|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849))))&((((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7849),esk256_3(X7849,X7850,X7851))),esk257_3(X7849,X7850,X7851))=X7850|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X7849,X7850,X7851)),X7849))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X7849)|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_3(X7849,X7850,X7851)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X7849,X7850,X7851)),X7849))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X7849)|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7849),esk257_3(X7849,X7850,X7851)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X7849,X7850,X7851)),X7849))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X7849)|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849)))))&(~hBOOL(hAPP(X7851,esk257_3(X7849,X7850,X7851)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X7849,X7850,X7851)),X7849))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X7849)|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849))))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7849),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(X7850=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7849),esk254_3(X7849,X7850,X7851))),esk255_3(X7849,X7850,X7851))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X7849)|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849))))&((((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7849),esk256_3(X7849,X7850,X7851))),esk257_3(X7849,X7850,X7851))=X7850|(X7850=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7849),esk254_3(X7849,X7850,X7851))),esk255_3(X7849,X7850,X7851))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X7849)|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_3(X7849,X7850,X7851)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(X7850=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7849),esk254_3(X7849,X7850,X7851))),esk255_3(X7849,X7850,X7851))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X7849)|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7849),esk257_3(X7849,X7850,X7851)))|(X7850=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7849),esk254_3(X7849,X7850,X7851))),esk255_3(X7849,X7850,X7851))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X7849)|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849)))))&(~hBOOL(hAPP(X7851,esk257_3(X7849,X7850,X7851)))|(X7850=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7849),esk254_3(X7849,X7850,X7851))),esk255_3(X7849,X7850,X7851))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X7849)|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849)))))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7849),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)),esk255_3(X7849,X7850,X7851)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X7849)|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849))))&((((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7849),esk256_3(X7849,X7850,X7851))),esk257_3(X7849,X7850,X7851))=X7850|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk255_3(X7849,X7850,X7851)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X7849)|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_3(X7849,X7850,X7851)),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)),esk255_3(X7849,X7850,X7851)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X7849)|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7849),esk257_3(X7849,X7850,X7851)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk255_3(X7849,X7850,X7851)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X7849)|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849)))))&(~hBOOL(hAPP(X7851,esk257_3(X7849,X7850,X7851)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk255_3(X7849,X7850,X7851)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X7849)|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849)))))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7849),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(X7851,esk255_3(X7849,X7850,X7851)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X7849)|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849))))&((((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7849),esk256_3(X7849,X7850,X7851))),esk257_3(X7849,X7850,X7851))=X7850|(~hBOOL(hAPP(X7851,esk255_3(X7849,X7850,X7851)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X7849)|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_3(X7849,X7850,X7851)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(X7851,esk255_3(X7849,X7850,X7851)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X7849)|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7849),esk257_3(X7849,X7850,X7851)))|(~hBOOL(hAPP(X7851,esk255_3(X7849,X7850,X7851)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X7849)|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849)))))&(~hBOOL(hAPP(X7851,esk257_3(X7849,X7850,X7851)))|(~hBOOL(hAPP(X7851,esk255_3(X7849,X7850,X7851)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X7849)|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849))))))))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7849),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)),X7849))|~hBOOL(hAPP(X7851,X7850)))|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849))))&((((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7849),esk256_3(X7849,X7850,X7851))),esk257_3(X7849,X7850,X7851))=X7850|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7849))|~hBOOL(hAPP(X7851,X7850)))|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_3(X7849,X7850,X7851)),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)),X7849))|~hBOOL(hAPP(X7851,X7850)))|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7849),esk257_3(X7849,X7850,X7851)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7849))|~hBOOL(hAPP(X7851,X7850)))|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849)))))&(~hBOOL(hAPP(X7851,esk257_3(X7849,X7850,X7851)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7849))|~hBOOL(hAPP(X7851,X7850)))|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849))))))&(((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7849),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X7849,X7850,X7851)),X7849))|~hBOOL(hAPP(X7851,X7850)))|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849))))&((((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7849),esk256_3(X7849,X7850,X7851))),esk257_3(X7849,X7850,X7851))=X7850|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X7849,X7850,X7851)),X7849))|~hBOOL(hAPP(X7851,X7850)))|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_3(X7849,X7850,X7851)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X7849,X7850,X7851)),X7849))|~hBOOL(hAPP(X7851,X7850)))|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7849),esk257_3(X7849,X7850,X7851)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X7849,X7850,X7851)),X7849))|~hBOOL(hAPP(X7851,X7850)))|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849)))))&(~hBOOL(hAPP(X7851,esk257_3(X7849,X7850,X7851)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X7849,X7850,X7851)),X7849))|~hBOOL(hAPP(X7851,X7850)))|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849))))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7849),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(X7850=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7849),esk254_3(X7849,X7850,X7851))),esk255_3(X7849,X7850,X7851))|~hBOOL(hAPP(X7851,X7850)))|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849))))&((((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7849),esk256_3(X7849,X7850,X7851))),esk257_3(X7849,X7850,X7851))=X7850|(X7850=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7849),esk254_3(X7849,X7850,X7851))),esk255_3(X7849,X7850,X7851))|~hBOOL(hAPP(X7851,X7850)))|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_3(X7849,X7850,X7851)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(X7850=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7849),esk254_3(X7849,X7850,X7851))),esk255_3(X7849,X7850,X7851))|~hBOOL(hAPP(X7851,X7850)))|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7849),esk257_3(X7849,X7850,X7851)))|(X7850=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7849),esk254_3(X7849,X7850,X7851))),esk255_3(X7849,X7850,X7851))|~hBOOL(hAPP(X7851,X7850)))|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849)))))&(~hBOOL(hAPP(X7851,esk257_3(X7849,X7850,X7851)))|(X7850=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7849),esk254_3(X7849,X7850,X7851))),esk255_3(X7849,X7850,X7851))|~hBOOL(hAPP(X7851,X7850)))|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849)))))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7849),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)),esk255_3(X7849,X7850,X7851)))|~hBOOL(hAPP(X7851,X7850)))|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849))))&((((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7849),esk256_3(X7849,X7850,X7851))),esk257_3(X7849,X7850,X7851))=X7850|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk255_3(X7849,X7850,X7851)))|~hBOOL(hAPP(X7851,X7850)))|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_3(X7849,X7850,X7851)),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)),esk255_3(X7849,X7850,X7851)))|~hBOOL(hAPP(X7851,X7850)))|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7849),esk257_3(X7849,X7850,X7851)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk255_3(X7849,X7850,X7851)))|~hBOOL(hAPP(X7851,X7850)))|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849)))))&(~hBOOL(hAPP(X7851,esk257_3(X7849,X7850,X7851)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk255_3(X7849,X7850,X7851)))|~hBOOL(hAPP(X7851,X7850)))|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849)))))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7849),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(X7851,esk255_3(X7849,X7850,X7851)))|~hBOOL(hAPP(X7851,X7850)))|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849))))&((((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7849),esk256_3(X7849,X7850,X7851))),esk257_3(X7849,X7850,X7851))=X7850|(~hBOOL(hAPP(X7851,esk255_3(X7849,X7850,X7851)))|~hBOOL(hAPP(X7851,X7850)))|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_3(X7849,X7850,X7851)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(X7851,esk255_3(X7849,X7850,X7851)))|~hBOOL(hAPP(X7851,X7850)))|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7849),esk257_3(X7849,X7850,X7851)))|(~hBOOL(hAPP(X7851,esk255_3(X7849,X7850,X7851)))|~hBOOL(hAPP(X7851,X7850)))|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849)))))&(~hBOOL(hAPP(X7851,esk257_3(X7849,X7850,X7851)))|(~hBOOL(hAPP(X7851,esk255_3(X7849,X7850,X7851)))|~hBOOL(hAPP(X7851,X7850)))|hBOOL(hAPP(X7851,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7850,X7849)))))))))&(((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X7856|hBOOL(hAPP(X7858,X7857))|~hBOOL(hAPP(X7858,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7857,X7856))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7856))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7860),X7856))|X7857!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7856),X7859)),X7860)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7860))|hBOOL(hAPP(X7858,X7860)))|~hBOOL(hAPP(X7858,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7857,X7856)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7856),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),X7856),X7861)),X7862)!=X7857|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7862),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7856),X7862))|hBOOL(hAPP(X7858,X7862)))|~hBOOL(hAPP(X7858,c_Divides_Odiv__class_Omod(tc_Int_Oint,X7857,X7856)))))), 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__zmod])])])])])])])). 6.97/7.21 cnf(c_0_4981, 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_4551])). 6.97/7.21 fof(c_0_4982, plain, ![X10426, X10427, X10428, X10429]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk344_4(X10426,X10427,X10428,X10429)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X10428)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10429),X10427))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X10429),X10428)),X10427)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X10427),c_Groups_Oone__class_Oone(tc_Int_Oint))),X10426))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10428)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk345_4(X10426,X10427,X10428,X10429)),X10426))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10429),X10427))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X10429),X10428)),X10427)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X10427),c_Groups_Oone__class_Oone(tc_Int_Oint))),X10426))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10428)))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk345_4(X10426,X10427,X10428,X10429)),esk344_4(X10426,X10427,X10428,X10429))=X10429|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10429),X10427))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X10429),X10428)),X10427)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X10427),c_Groups_Oone__class_Oone(tc_Int_Oint))),X10426))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10428))))), 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])])])])])])). 6.97/7.21 fof(c_0_4983, plain, ![X4004, X4005, X4006, X4007]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk135_4(X4004,X4005,X4006,X4007)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4006)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4005),X4007))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4005),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4007),X4006))))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4005),c_Groups_Oone__class_Oone(tc_Int_Oint))),X4004))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4006)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk136_4(X4004,X4005,X4006,X4007)),X4004))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4005),X4007))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4005),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4007),X4006))))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4005),c_Groups_Oone__class_Oone(tc_Int_Oint))),X4004))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4006)))&(X4007=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk136_4(X4004,X4005,X4006,X4007)),esk135_4(X4004,X4005,X4006,X4007))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4005),X4007))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4005),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4007),X4006))))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4005),c_Groups_Oone__class_Oone(tc_Int_Oint))),X4004))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4006))))), 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])])])])])])). 6.97/7.21 fof(c_0_4984, plain, ![X11091, X11092, X11093, X11096]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X11093,X11093)),hAPP(hAPP(c_Product__Type_OPair(X11093,X11093),hAPP(X11092,hAPP(c_Nat_OSuc,esk369_3(X11091,X11092,X11093)))),hAPP(X11092,esk369_3(X11091,X11092,X11093)))),c_Transitive__Closure_Ortrancl(X11093,X11091)))|(~c_Wellfounded_Owf(X11093,c_Transitive__Closure_Otrancl(X11093,X11091))|hAPP(X11092,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk370_3(X11091,X11092,X11093)),X11096))=hAPP(X11092,esk370_3(X11091,X11092,X11093)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__weak__decr__stable])])])])). 6.97/7.21 fof(c_0_4985, plain, ![X3967, X3968, X3969]:(~class_Int_Onumber__ring(X3969)|hAPP(hAPP(c_Power_Opower__class_Opower(X3969),X3968),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X3967)))=hAPP(hAPP(c_HOL_OLet(X3969,X3969),hAPP(hAPP(c_Power_Opower__class_Opower(X3969),X3968),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3967))),hAPP(hAPP(c_COMBS(X3969,X3969,X3969),c_Groups_Otimes__class_Otimes(X3969)),c_COMBI(X3969)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__number__of__even])])). 6.97/7.21 cnf(c_0_4986, 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_4552])). 6.97/7.21 fof(c_0_4987, plain, ![X17288, X17289, X17290]:((~hBOOL(hAPP(X17290,X17289))|hAPP(c_Set_OCollect(X17288),hAPP(hAPP(c_COMBS(X17288,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X17288),c_fconj),hAPP(hAPP(c_COMBC(X17288,X17288,tc_HOL_Obool),c_fequal),X17289))),X17290))=hAPP(hAPP(c_Set_Oinsert(X17288),X17289),c_Orderings_Obot__class_Obot(tc_fun(X17288,tc_HOL_Obool))))&(hBOOL(hAPP(X17290,X17289))|c_Orderings_Obot__class_Obot(tc_fun(X17288,tc_HOL_Obool))=hAPP(c_Set_OCollect(X17288),hAPP(hAPP(c_COMBS(X17288,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X17288),c_fconj),hAPP(hAPP(c_COMBC(X17288,X17288,tc_HOL_Obool),c_fequal),X17289))),X17290)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Collect__conv__if])])])). 6.97/7.21 fof(c_0_4988, plain, ![X10188, X10189, X10190, X10191, X10192, X10193]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10193),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10193),X10189),X10191)),X10188)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10193),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10193),X10192),X10191)),X10190)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10193),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10193),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10193),X10192),X10189)),X10191)),X10190)=X10188|~class_Rings_Oring(X10193))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10193),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10193),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10193),X10192),X10189)),X10191)),X10190)!=X10188|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10193),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10193),X10189),X10191)),X10188)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10193),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10193),X10192),X10191)),X10190)|~class_Rings_Oring(X10193))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff1])])])). 6.97/7.21 fof(c_0_4989, plain, ![X10115, X10116, X10117]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10117))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X10116),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),X10116),X10115))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X10117))),X10115))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_decr__lemma])])])). 6.97/7.21 fof(c_0_4990, plain, ![X9197, X9198, X9199, X9200]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X9200,X9200)),hAPP(hAPP(c_Product__Type_OPair(X9200,X9200),X9199),esk302_4(X9197,X9198,X9199,X9200))),X9197))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X9200,X9200)),hAPP(hAPP(c_Product__Type_OPair(X9200,X9200),X9199),X9198)),c_Transitive__Closure_Otrancl(X9200,X9197))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X9200,X9200)),hAPP(hAPP(c_Product__Type_OPair(X9200,X9200),esk302_4(X9197,X9198,X9199,X9200)),X9198)),c_Transitive__Closure_Ortrancl(X9200,X9197)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X9200,X9200)),hAPP(hAPP(c_Product__Type_OPair(X9200,X9200),X9199),X9198)),c_Transitive__Closure_Otrancl(X9200,X9197))))), 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])])])])])). 6.97/7.21 fof(c_0_4991, plain, ![X10149, X10150, X10151, X10152]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X10152,X10152)),hAPP(hAPP(c_Product__Type_OPair(X10152,X10152),esk330_4(X10149,X10150,X10151,X10152)),X10150)),X10149))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X10152,X10152)),hAPP(hAPP(c_Product__Type_OPair(X10152,X10152),X10151),X10150)),c_Transitive__Closure_Otrancl(X10152,X10149))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X10152,X10152)),hAPP(hAPP(c_Product__Type_OPair(X10152,X10152),X10151),esk330_4(X10149,X10150,X10151,X10152))),c_Transitive__Closure_Ortrancl(X10152,X10149)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X10152,X10152)),hAPP(hAPP(c_Product__Type_OPair(X10152,X10152),X10151),X10150)),c_Transitive__Closure_Otrancl(X10152,X10149))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_tranclD2])])])])])). 6.97/7.21 fof(c_0_4992, plain, ![X11262, X11263, X11264, X11265]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X11265,X11265)),X11264),c_Transitive__Closure_Otrancl(X11265,X11263)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X11265,X11265),tc_HOL_Obool)),X11263),X11262))|hBOOL(hAPP(hAPP(c_member(tc_prod(X11265,X11265)),X11264),c_Transitive__Closure_Otrancl(X11265,X11262))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_trancl__mono])])])). 6.97/7.21 fof(c_0_4993, plain, ![X13211, X13212, X13213]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13213))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13212),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X13211),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),X13211),X13212))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X13213))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_incr__lemma])])). 6.97/7.21 fof(c_0_4994, plain, ![X6220]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X6220|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6220))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_gr0I])])])). 6.97/7.21 fof(c_0_4995, plain, ![X3869, X3870, X3871, X3872, X3873, X3874, X3875, X3877, X3878, X3879, X3880, X3881, X3884]:(((hBOOL(hAPP(hAPP(c_member(X3873),esk129_7(X3869,X3870,X3871,X3872,X3873,X3874,X3875)),hAPP(c_List_Oset(X3873),X3874)))|(X3871!=hAPP(c_List_Ofilter(X3873,X3870),X3875)|~hBOOL(hAPP(X3870,X3872)))|hAPP(hAPP(c_List_Oappend(X3873),X3874),hAPP(hAPP(c_List_Olist_OCons(X3873),X3872),X3875))!=X3869|hAPP(hAPP(c_List_Olist_OCons(X3873),X3872),X3871)=hAPP(c_List_Ofilter(X3873,X3870),X3869))&(hBOOL(hAPP(X3870,esk129_7(X3869,X3870,X3871,X3872,X3873,X3874,X3875)))|(X3871!=hAPP(c_List_Ofilter(X3873,X3870),X3875)|~hBOOL(hAPP(X3870,X3872)))|hAPP(hAPP(c_List_Oappend(X3873),X3874),hAPP(hAPP(c_List_Olist_OCons(X3873),X3872),X3875))!=X3869|hAPP(hAPP(c_List_Olist_OCons(X3873),X3872),X3871)=hAPP(c_List_Ofilter(X3873,X3870),X3869)))&((((X3879=hAPP(c_List_Ofilter(X3881,X3878),esk131_5(X3877,X3878,X3879,X3880,X3881))|hAPP(hAPP(c_List_Olist_OCons(X3881),X3880),X3879)!=hAPP(c_List_Ofilter(X3881,X3878),X3877))&(hBOOL(hAPP(X3878,X3880))|hAPP(hAPP(c_List_Olist_OCons(X3881),X3880),X3879)!=hAPP(c_List_Ofilter(X3881,X3878),X3877)))&(~hBOOL(hAPP(hAPP(c_member(X3881),X3884),hAPP(c_List_Oset(X3881),esk130_5(X3877,X3878,X3879,X3880,X3881))))|~hBOOL(hAPP(X3878,X3884))|hAPP(hAPP(c_List_Olist_OCons(X3881),X3880),X3879)!=hAPP(c_List_Ofilter(X3881,X3878),X3877)))&(hAPP(hAPP(c_List_Oappend(X3881),esk130_5(X3877,X3878,X3879,X3880,X3881)),hAPP(hAPP(c_List_Olist_OCons(X3881),X3880),esk131_5(X3877,X3878,X3879,X3880,X3881)))=X3877|hAPP(hAPP(c_List_Olist_OCons(X3881),X3880),X3879)!=hAPP(c_List_Ofilter(X3881,X3878),X3877)))), 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])])])])])])])). 6.97/7.21 fof(c_0_4996, plain, ![X2712, X2713, X2714, X2715, X2716, X2717, X2718, X2720, X2721, X2722, X2723, X2724, X2727]:(((hBOOL(hAPP(hAPP(c_member(X2716),esk86_7(X2712,X2713,X2714,X2715,X2716,X2717,X2718)),hAPP(c_List_Oset(X2716),X2717)))|X2714!=hAPP(hAPP(c_List_Oappend(X2716),X2717),hAPP(hAPP(c_List_Olist_OCons(X2716),X2713),X2718))|~hBOOL(hAPP(X2715,X2713))|X2712!=hAPP(c_List_Ofilter(X2716,X2715),X2718)|hAPP(hAPP(c_List_Olist_OCons(X2716),X2713),X2712)=hAPP(c_List_Ofilter(X2716,X2715),X2714))&(hBOOL(hAPP(X2715,esk86_7(X2712,X2713,X2714,X2715,X2716,X2717,X2718)))|X2714!=hAPP(hAPP(c_List_Oappend(X2716),X2717),hAPP(hAPP(c_List_Olist_OCons(X2716),X2713),X2718))|~hBOOL(hAPP(X2715,X2713))|X2712!=hAPP(c_List_Ofilter(X2716,X2715),X2718)|hAPP(hAPP(c_List_Olist_OCons(X2716),X2713),X2712)=hAPP(c_List_Ofilter(X2716,X2715),X2714)))&((((X2722=hAPP(hAPP(c_List_Oappend(X2724),esk87_5(X2720,X2721,X2722,X2723,X2724)),hAPP(hAPP(c_List_Olist_OCons(X2724),X2721),esk88_5(X2720,X2721,X2722,X2723,X2724)))|hAPP(hAPP(c_List_Olist_OCons(X2724),X2721),X2720)!=hAPP(c_List_Ofilter(X2724,X2723),X2722))&(~hBOOL(hAPP(hAPP(c_member(X2724),X2727),hAPP(c_List_Oset(X2724),esk87_5(X2720,X2721,X2722,X2723,X2724))))|~hBOOL(hAPP(X2723,X2727))|hAPP(hAPP(c_List_Olist_OCons(X2724),X2721),X2720)!=hAPP(c_List_Ofilter(X2724,X2723),X2722)))&(hBOOL(hAPP(X2723,X2721))|hAPP(hAPP(c_List_Olist_OCons(X2724),X2721),X2720)!=hAPP(c_List_Ofilter(X2724,X2723),X2722)))&(X2720=hAPP(c_List_Ofilter(X2724,X2723),esk88_5(X2720,X2721,X2722,X2723,X2724))|hAPP(hAPP(c_List_Olist_OCons(X2724),X2721),X2720)!=hAPP(c_List_Ofilter(X2724,X2723),X2722)))), 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])])])])])])])). 6.97/7.21 fof(c_0_4997, plain, ![X7684, X7685, X7686]:((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),esk250_3(X7684,X7685,X7686)),esk251_3(X7684,X7685,X7686))))|hBOOL(hAPP(hAPP(X7684,X7686),X7685))|~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),X7686),X7685))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk250_3(X7684,X7685,X7686)),esk251_3(X7684,X7685,X7686)))|hBOOL(hAPP(hAPP(X7684,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk250_3(X7684,X7685,X7686)),c_Groups_Oone__class_Oone(tc_Int_Oint))),esk251_3(X7684,X7685,X7686)))|hBOOL(hAPP(hAPP(X7684,X7686),X7685))|~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),X7686),X7685))))&(~hBOOL(hAPP(hAPP(X7684,esk250_3(X7684,X7685,X7686)),esk251_3(X7684,X7685,X7686)))|hBOOL(hAPP(hAPP(X7684,X7686),X7685))|~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),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_upto_Opinduct])])])])])). 6.97/7.21 fof(c_0_4998, plain, ![X3908, X3909, X3910]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3910),X3909))|hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X3910,X3909)),c_List_Oupt(X3909,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3909),X3908)))=c_List_Oupt(X3910,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3909),X3908))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__add__eq__append])])). 6.97/7.21 fof(c_0_4999, plain, ![X12244, X12245, X12246, X12247]:((~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X12246),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X12246),c_fNot),hAPP(hAPP(c_COMBS(X12246,X12247,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X12247,tc_fun(X12247,tc_HOL_Obool),X12246),c_fequal),X12245)),X12244))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12246,X12247)),X12245),X12244))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12246,X12247)),X12245),X12244))|(~class_Orderings_Oorder(X12247)|~class_Enum_Oenum(X12246)))&((hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X12246),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X12246),c_fNot),hAPP(hAPP(c_COMBS(X12246,X12247,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X12247,tc_fun(X12247,tc_HOL_Obool),X12246),c_fequal),X12245)),X12244))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12246,X12247)),X12245),X12244))|(~class_Orderings_Oorder(X12247)|~class_Enum_Oenum(X12246)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12246,X12247)),X12245),X12244))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12246,X12247)),X12245),X12244))|(~class_Orderings_Oorder(X12247)|~class_Enum_Oenum(X12246))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__fun_I2_J])])])])). 6.97/7.21 cnf(c_0_5000, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X1)=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))))|~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_4553])). 6.97/7.21 cnf(c_0_5001, 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])). 6.97/7.21 cnf(c_0_5002, plain, (hAPP(c_Int_Onat,X1)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)), inference(rw,[status(thm)],[c_0_4554, c_0_4415]), ['final']). 6.97/7.21 cnf(c_0_5003, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)), inference(split_conjunct,[status(thm)],[fact_semiring__norm_I113_J])). 6.97/7.21 fof(c_0_5004, plain, ![X12205, X12206, X12207, X12208]:((hBOOL(hAPP(X12208,X12207))|c_List_OdropWhile(X12206,X12208,hAPP(hAPP(c_List_Olist_OCons(X12206),X12207),X12205))=hAPP(hAPP(c_List_Olist_OCons(X12206),X12207),X12205))&(~hBOOL(hAPP(X12208,X12207))|c_List_OdropWhile(X12206,X12208,X12205)=c_List_OdropWhile(X12206,X12208,hAPP(hAPP(c_List_Olist_OCons(X12206),X12207),X12205)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dropWhile_Osimps_I2_J])])])). 6.97/7.21 fof(c_0_5005, plain, ![X3814, X3815, X3816]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk128_3(X3814,X3815,X3816)),X3816))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3814),hAPP(X3815,X3816)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X3815,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3814))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk127_3(X3814,X3815,X3816)),X3816)))&(X3814=hAPP(X3815,esk128_3(X3814,X3815,X3816))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3814),hAPP(X3815,X3816)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X3815,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3814))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk127_3(X3814,X3815,X3816)),X3816))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk128_3(X3814,X3815,X3816)),X3816))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3814),hAPP(X3815,X3816)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X3815,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3814))|~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(X3815,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk127_3(X3814,X3815,X3816)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X3815,esk127_3(X3814,X3815,X3816))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))&(X3814=hAPP(X3815,esk128_3(X3814,X3815,X3816))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3814),hAPP(X3815,X3816)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X3815,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3814))|~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(X3815,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk127_3(X3814,X3815,X3816)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X3815,esk127_3(X3814,X3815,X3816))))),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])])])])])). 6.97/7.21 fof(c_0_5006, plain, ![X1836, X1837, X1838]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk58_3(X1836,X1837,X1838)),X1838))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1836),hAPP(X1837,X1838)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1837,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1836))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk57_3(X1836,X1837,X1838)),X1838)))&(X1836=hAPP(X1837,esk58_3(X1836,X1837,X1838))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1836),hAPP(X1837,X1838)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1837,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1836))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk57_3(X1836,X1837,X1838)),X1838))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk58_3(X1836,X1837,X1838)),X1838))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1836),hAPP(X1837,X1838)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1837,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1836))|~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(X1837,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk57_3(X1836,X1837,X1838)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X1837,esk57_3(X1836,X1837,X1838))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))&(X1836=hAPP(X1837,esk58_3(X1836,X1837,X1838))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1836),hAPP(X1837,X1838)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1837,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1836))|~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(X1837,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk57_3(X1836,X1837,X1838)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X1837,esk57_3(X1836,X1837,X1838))))),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])])])])])). 6.97/7.21 fof(c_0_5007, plain, ![X16506, X16507, X16508, X16509, X16510]:hAPP(hAPP(c_List_Otake(tc_prod(X16510,X16509)),X16508),hAPP(hAPP(c_List_Ozip(X16510,X16509),X16507),X16506))=hAPP(hAPP(c_List_Ozip(X16510,X16509),hAPP(hAPP(c_List_Otake(X16510),X16508),X16507)),hAPP(hAPP(c_List_Otake(X16509),X16508),X16506)), inference(variable_rename,[status(thm)],[fact_take__zip])). 6.97/7.21 fof(c_0_5008, plain, ![X9929, X9930]:(~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X9930),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X9930))),X9929)))|c_List_OtakeWhile(tc_List_Olist(X9930),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X9930)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X9930),tc_List_Olist(X9930),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X9930))),X9929)=c_List_Otranspose(X9930,c_List_Otranspose(X9930,X9929))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transpose__transpose])])])). 6.97/7.21 fof(c_0_5009, plain, ![X7000, X7001, X7002, X7003]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X7003,X7003)),hAPP(hAPP(c_Product__Type_OPair(X7003,X7003),X7002),X7001)),c_Transitive__Closure_Otrancl(X7003,X7000)))|X7002=X7001|~hBOOL(hAPP(hAPP(c_member(tc_prod(X7003,X7003)),hAPP(hAPP(c_Product__Type_OPair(X7003,X7003),X7002),X7001)),c_Transitive__Closure_Ortrancl(X7003,X7000))))&(X7002!=X7001|X7002=X7001|~hBOOL(hAPP(hAPP(c_member(tc_prod(X7003,X7003)),hAPP(hAPP(c_Product__Type_OPair(X7003,X7003),X7002),X7001)),c_Transitive__Closure_Ortrancl(X7003,X7000))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtranclD])])])). 6.97/7.21 cnf(c_0_5010, 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_4555])). 6.97/7.21 fof(c_0_5011, plain, ![X16240, X16241, X16242]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16242)),X16240)),X16241)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16242)),hAPP(hAPP(c_List_Odrop(X16242),X16241),X16240)), inference(variable_rename,[status(thm)],[fact_length__drop])). 6.97/7.21 cnf(c_0_5012, 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_4556])). 6.97/7.21 cnf(c_0_5013, 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_4557])). 6.97/7.21 cnf(c_0_5014, plain, (X2=c_Groups_Oone__class_Oone(X1)|hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))=X2|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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))!=c_Groups_Oone__class_Oone(X1)|~class_Rings_Oring__1__no__zero__divisors(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4558, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.21 cnf(c_0_5015, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[c_0_4559, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.21 cnf(c_0_5016, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[c_0_4560, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.21 cnf(c_0_5017, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[c_0_4561, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.21 fof(c_0_5018, plain, ![X9997, X9998, X9999, X10000]:(~class_Int_Onumber__ring(X10000)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10000),hAPP(c_Int_Onumber__class_Onumber__of(X10000),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X9999),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X9997)))),X9998)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10000),hAPP(c_Int_Onumber__class_Onumber__of(X10000),X9999)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10000),X9998),hAPP(c_Int_Onumber__class_Onumber__of(X10000),X9997)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__number__of__diff2])])])). 6.97/7.21 fof(c_0_5019, plain, ![X8495, X8496, X8497]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8495),X8496))|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)),X8497)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X8495),X8496))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8497),X8496)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8495),X8496))|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)),X8497)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X8495),X8496))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8497),X8496))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8497),X8496))|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)),X8497)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X8495),X8496))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X8495),X8497)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X8496),X8497)))), 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])])])])). 6.97/7.21 cnf(c_0_5020, 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_4562])). 6.97/7.21 fof(c_0_5021, plain, ![X1147, X1148, X1149]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1149,X1149),tc_HOL_Obool)),c_Relation_OId(X1149)),X1148))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1149,X1149),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1149,X1149,X1149),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1149,X1149),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1149,X1147)),X1148)),X1147)),X1148))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1149,X1149),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1149,X1147)),X1148)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rtrancl__Int__subset])])])). 6.97/7.21 fof(c_0_5022, plain, ![X11254, X11255, X11256, X11257, X11258]:(~class_Orderings_Olinorder(X11258)|(~c_Fun_Oinj__on(X11257,X11258,X11256,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11257,tc_HOL_Obool)),hAPP(c_List_Oset(X11257),X11255)),hAPP(c_List_Oset(X11257),X11254)))|(~c_List_Olinorder__class_Osorted(X11258,hAPP(hAPP(c_List_Omap(X11257,X11258),X11256),X11255))|(~hBOOL(hAPP(c_List_Odistinct(X11258),hAPP(hAPP(c_List_Omap(X11257,X11258),X11256),X11255)))|(~c_List_Olinorder__class_Osorted(X11258,hAPP(hAPP(c_List_Omap(X11257,X11258),X11256),X11254))|(~hBOOL(hAPP(c_List_Odistinct(X11258),hAPP(hAPP(c_List_Omap(X11257,X11258),X11256),X11254)))|(hAPP(c_List_Oset(X11257),X11255)!=hAPP(c_List_Oset(X11257),X11254)|X11255=X11254))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__sorted__distinct__set__unique])])])). 6.97/7.21 fof(c_0_5023, plain, ![X12566, X12567, X12568]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12568,tc_HOL_Obool)),hAPP(c_List_Oset(X12568),X12567)),hAPP(c_List_Oset(X12568),X12566))=hAPP(c_List_Oset(X12568),hAPP(hAPP(c_List_Oappend(X12568),X12567),X12566)), inference(variable_rename,[status(thm)],[fact_set__append])). 6.97/7.21 fof(c_0_5024, plain, ![X14993, X14994, X14995, X14996]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14995),X14994))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X14996),X14993),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X14994),hAPP(c_Nat_OSuc,X14995)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14996),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X14996),X14993),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X14994),X14995))),hAPP(X14993,X14995))|~class_Groups_Ocomm__monoid__add(X14996))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14995),X14994))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X14996),X14993),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X14994),hAPP(c_Nat_OSuc,X14995)))=c_Groups_Ozero__class_Ozero(X14996)|~class_Groups_Ocomm__monoid__add(X14996))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__op__ivl__Suc])])])])). 6.97/7.21 fof(c_0_5025, plain, ![X16643, X16644, X16645]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X16645)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X16645)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X16644)),X16643))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X16644)),X16643))&((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X16644)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X16645)),X16643)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X16645)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X16644)),X16643))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X16645))))&(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X16644)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X16645)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X16644)),X16643))=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),X16645),X16644))),X16643)|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X16645)))))), 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])])])])). 6.97/7.21 fof(c_0_5026, plain, ![X5007, X5008, X5009]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5009))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5007),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X5008),X5007),X5009))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5008,X5007))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X5008,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5007),X5009))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zmult2__eq])])). 6.97/7.21 fof(c_0_5027, plain, ![X13537, X13538, X13539, X13541, X13542, X13543, X13544]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk451_3(X13537,X13538,X13539)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X13539,X13539)),X13538),c_Transitive__Closure_Otrancl(X13539,X13537))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X13539,X13539)),X13538),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X13539,X13539),tc_HOL_Obool),esk451_3(X13537,X13538,X13539)),X13537)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X13539,X13539)),X13538),c_Transitive__Closure_Otrancl(X13539,X13537)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13544))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X13543,X13543)),X13542),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X13543,X13543),tc_HOL_Obool),X13544),X13541)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X13543,X13543)),X13542),c_Transitive__Closure_Otrancl(X13543,X13541))))), 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])])])])])])). 6.97/7.21 fof(c_0_5028, plain, ![X11828, X11829, X11830, X11831, X11832]:((X11830!=hAPP(hAPP(c_List_Oappend(X11832),c_List_OtakeWhile(X11832,X11831,X11830)),hAPP(hAPP(c_List_Olist_OCons(X11832),X11829),X11828))|hBOOL(hAPP(X11831,X11829))|hAPP(hAPP(c_List_Olist_OCons(X11832),X11829),X11828)=c_List_OdropWhile(X11832,X11831,X11830))&((X11830=hAPP(hAPP(c_List_Oappend(X11832),c_List_OtakeWhile(X11832,X11831,X11830)),hAPP(hAPP(c_List_Olist_OCons(X11832),X11829),X11828))|hAPP(hAPP(c_List_Olist_OCons(X11832),X11829),X11828)!=c_List_OdropWhile(X11832,X11831,X11830))&(~hBOOL(hAPP(X11831,X11829))|hAPP(hAPP(c_List_Olist_OCons(X11832),X11829),X11828)!=c_List_OdropWhile(X11832,X11831,X11830)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dropWhile__eq__Cons__conv])])])])). 6.97/7.21 fof(c_0_5029, plain, ![X17123, X17124, X17125, X17126]:(((X17124=X17125|~hBOOL(hAPP(hAPP(c_member(tc_prod(X17126,X17126)),hAPP(hAPP(c_Product__Type_OPair(X17126,X17126),X17125),X17124)),hAPP(c_List_Oset(tc_prod(X17126,X17126)),hAPP(hAPP(c_List_Ozip(X17126,X17126),X17123),X17123)))))&(hBOOL(hAPP(hAPP(c_member(X17126),X17125),hAPP(c_List_Oset(X17126),X17123)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X17126,X17126)),hAPP(hAPP(c_Product__Type_OPair(X17126,X17126),X17125),X17124)),hAPP(c_List_Oset(tc_prod(X17126,X17126)),hAPP(hAPP(c_List_Ozip(X17126,X17126),X17123),X17123))))))&(X17124!=X17125|~hBOOL(hAPP(hAPP(c_member(X17126),X17125),hAPP(c_List_Oset(X17126),X17123)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X17126,X17126)),hAPP(hAPP(c_Product__Type_OPair(X17126,X17126),X17125),X17124)),hAPP(c_List_Oset(tc_prod(X17126,X17126)),hAPP(hAPP(c_List_Ozip(X17126,X17126),X17123),X17123)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__same])])])). 6.97/7.21 fof(c_0_5030, plain, ![X12474, X12475]:(~c_Nat__Transfer_Onat__set(X12475)|(~c_Nat__Transfer_Onat__set(X12474)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X12475),X12474)=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),X12475)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X12474))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J])])). 6.97/7.21 fof(c_0_5031, plain, ![X11565, X11566, X11567, X11568, X11569]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11568,tc_HOL_Obool)),hAPP(c_Set_Oimage(X11569,X11568,X11567),X11566)),hAPP(c_Set_Oimage(X11569,X11568,X11567),X11565))=hAPP(c_Set_Oimage(X11569,X11568,X11567),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11569,tc_HOL_Obool)),X11566),X11565)), inference(variable_rename,[status(thm)],[fact_image__Un])). 6.97/7.21 fof(c_0_5032, plain, ![X5405, X5406, X5407, X5408, X5409, X5410]:hAPP(c_Set_Oimage(X5410,X5409,X5408),hAPP(c_Set_Oimage(X5407,X5410,X5406),X5405))=hAPP(c_Set_Oimage(X5407,X5409,hAPP(hAPP(c_COMBB(X5410,X5409,X5407),X5408),X5406)),X5405), inference(variable_rename,[status(thm)],[fact_image__image])). 6.97/7.21 fof(c_0_5033, plain, ![X7391, X7392]:(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7392))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=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)),X7392))),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,X7391)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__less])])). 6.97/7.21 fof(c_0_5034, plain, ![X8171, X8172, X8173, X8176, X8177]:(((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk268_3(X8171,X8172,X8173)),X8173))|hBOOL(hAPP(hAPP(X8172,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8171),X8173)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X8171,X8173)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8173)))&(X8171=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8173),esk267_3(X8171,X8172,X8173))),esk268_3(X8171,X8172,X8173))|hBOOL(hAPP(hAPP(X8172,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8171),X8173)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X8171,X8173)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8173))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk268_3(X8171,X8172,X8173)))|hBOOL(hAPP(hAPP(X8172,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8171),X8173)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X8171,X8173)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8173))))&(~hBOOL(hAPP(hAPP(X8172,esk267_3(X8171,X8172,X8173)),esk268_3(X8171,X8172,X8173)))|hBOOL(hAPP(hAPP(X8172,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8171),X8173)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X8171,X8173)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8173))))&(~hBOOL(hAPP(hAPP(X8172,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8171),X8173)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X8171,X8173)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8177),X8173))|X8171!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8173),X8176)),X8177)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8177))|hBOOL(hAPP(hAPP(X8172,X8176),X8177)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8173)))), 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_split__pos__lemma])])])])])])). 6.97/7.21 fof(c_0_5035, plain, ![X14641, X14642, X14643, X14644, X14645]:((~hBOOL(hAPP(hAPP(X14642,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14641),X14643)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X14641,X14643)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14643),X14645))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14643),X14644)),X14645)!=X14641|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X14645),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(X14642,X14644),X14645)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14643),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14643),esk496_3(X14641,X14642,X14643)))|hBOOL(hAPP(hAPP(X14642,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14641),X14643)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X14641,X14643)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14643),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),X14643),esk495_3(X14641,X14642,X14643))),esk496_3(X14641,X14642,X14643))=X14641|hBOOL(hAPP(hAPP(X14642,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14641),X14643)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X14641,X14643)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14643),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk496_3(X14641,X14642,X14643)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(X14642,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14641),X14643)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X14641,X14643)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14643),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))&(~hBOOL(hAPP(hAPP(X14642,esk495_3(X14641,X14642,X14643)),esk496_3(X14641,X14642,X14643)))|hBOOL(hAPP(hAPP(X14642,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14641),X14643)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X14641,X14643)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14643),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)],[inference(fof_simplification,[status(thm)],[fact_split__neg__lemma])])])])])])). 6.97/7.21 fof(c_0_5036, plain, ![X488]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X488)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|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),X488))=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),X488)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__pos__neg__1__number__of])])])). 6.97/7.21 cnf(c_0_5037, plain, (c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X1)=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)))), inference(split_conjunct,[status(thm)],[c_0_4563])). 6.97/7.21 cnf(c_0_5038, 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)), inference(rw,[status(thm)],[c_0_4564, c_0_4565]), ['final']). 6.97/7.21 fof(c_0_5039, plain, ![X10758, X10759]:hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X10759),X10758))=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X10759),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X10758)), inference(variable_rename,[status(thm)],[fact_negateSnd__eq])). 6.97/7.21 cnf(c_0_5040, plain, (X5=X3|hAPP(c_Product__Type_Ofst(X1,X2),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4))!=X5), inference(split_conjunct,[status(thm)],[c_0_4566])). 6.97/7.21 fof(c_0_5041, plain, ![X4589, X4590]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4590),X4589))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X4590)),c_Int_OBit1(X4589))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X4590)),c_Int_OBit1(X4589)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4590),X4589)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I16_J])])). 6.97/7.21 fof(c_0_5042, plain, ![X3038, X3039, X3040, X3042]:((hBOOL(hAPP(X3039,esk100_3(X3038,X3039,X3040)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3038))|(~hBOOL(hAPP(X3039,X3042))|hBOOL(hAPP(X3039,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3042),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3038),X3040))))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3040)))&(~hBOOL(hAPP(X3039,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk100_3(X3038,X3039,X3040)),X3040)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3038))|(~hBOOL(hAPP(X3039,X3042))|hBOOL(hAPP(X3039,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3042),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3038),X3040))))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3040)))), 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])])])])])])). 6.97/7.21 fof(c_0_5043, plain, ![X14150, X14151, X14152]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14152),c_Int_OPls))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X14152)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X14151)),X14150)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14152),c_Int_OPls))|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),X14152),X14151))),X14150)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X14152)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X14151)),X14150)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__number__of__mult__left])])])). 6.97/7.21 fof(c_0_5044, plain, ![X4612, X4613]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4613),X4612))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X4613)),c_Int_OBit1(X4612))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X4613)),c_Int_OBit1(X4612)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4613),X4612)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I34_J])])). 6.97/7.21 fof(c_0_5045, plain, ![X10533, X10534, X10535, X10536, X10537]:((~c_Wellfounded_Oacyclic(X10534,X10533)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X10534,X10534)),hAPP(hAPP(c_Product__Type_OPair(X10534,X10534),X10535),X10535)),c_Transitive__Closure_Otrancl(X10534,X10533))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X10537,X10537)),hAPP(hAPP(c_Product__Type_OPair(X10537,X10537),esk346_2(X10536,X10537)),esk346_2(X10536,X10537))),c_Transitive__Closure_Otrancl(X10537,X10536)))|c_Wellfounded_Oacyclic(X10537,X10536))), 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])])])])])])). 6.97/7.21 fof(c_0_5046, plain, ![X1731, X1732]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X1732,X1732)),hAPP(hAPP(c_Product__Type_OPair(X1732,X1732),esk51_2(X1731,X1732)),esk51_2(X1731,X1732))),c_Transitive__Closure_Otrancl(X1732,X1731)))|c_Wellfounded_Oacyclic(X1732,X1731)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_acyclicI])])])])). 6.97/7.21 cnf(c_0_5047, 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_4567])). 6.97/7.21 cnf(c_0_5048, plain, (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)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),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_4568])). 6.97/7.21 cnf(c_0_5049, 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(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_4569])). 6.97/7.21 cnf(c_0_5050, 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_4570]), ['final']). 6.97/7.21 fof(c_0_5051, plain, ![X1224, X1225, X1226]:((hBOOL(hAPP(hAPP(c_member(X1226),esk36_3(X1224,X1225,X1226)),hAPP(c_List_Oset(X1226),c_List_OdropWhile(X1226,X1225,X1224))))|hAPP(c_List_Ofilter(X1226,X1225),X1224)=c_List_OtakeWhile(X1226,X1225,X1224))&(hBOOL(hAPP(X1225,esk36_3(X1224,X1225,X1226)))|hAPP(c_List_Ofilter(X1226,X1225),X1224)=c_List_OtakeWhile(X1226,X1225,X1224))), 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])])])])])). 6.97/7.21 fof(c_0_5052, plain, ![X5678, X5679, X5680, X5681]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5680))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5680))|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X5681,X5680),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X5679),X5678)))|X5681!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5680),X5679)),X5678))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5678),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5680),X5678))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5680))|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X5681,X5680),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X5679),X5678)))|X5681!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5680),X5679)),X5678)))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5680))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5678))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5678),X5680)))|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X5681,X5680),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X5679),X5678)))|X5681!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5680),X5679)),X5678))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5678),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5680),X5678))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5678))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5678),X5680)))|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X5681,X5680),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X5679),X5678)))|X5681!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5680),X5679)),X5678)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__int__relI])])])])). 6.97/7.21 fof(c_0_5053, plain, ![X1006, X1007, X1008, X1009]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1008))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1008))|(X1008=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1009),X1008)=X1007)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1008),X1007)),X1006)!=X1009)&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1006),X1008))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1006))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1008))|(X1008=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1009),X1008)=X1007)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1008),X1007)),X1006)!=X1009))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1008))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1008),X1006))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1006),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))|(X1008=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1009),X1008)=X1007)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1008),X1007)),X1006)!=X1009)&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1006),X1008))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1006))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1008),X1006))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1006),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))|(X1008=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1009),X1008)=X1007)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1008),X1007)),X1006)!=X1009))), 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])])])])). 6.97/7.21 fof(c_0_5054, plain, ![X8676, X8677]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X8677))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8676))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X8676),X8677)),X8676)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X8676),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X8677),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__power__div__base])])). 6.97/7.21 fof(c_0_5055, plain, ![X16870, X16871, X16872, X16873, X16874, X16875, X16876, X16877]:((hBOOL(hAPP(hAPP(c_member(X16876),esk568_8(X16870,X16871,X16872,X16873,X16874,X16875,X16876,X16877)),X16873))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16876,X16877),X16871),X16873)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16875,X16877),X16870),X16872)|X16872!=hAPP(c_Set_Oimage(X16876,X16875,X16874),X16873)|~c_Fun_Oinj__on(X16876,X16875,X16874,X16873)|~class_Groups_Ocomm__monoid__mult(X16877))&(hAPP(hAPP(c_Fun_Ocomp(X16875,X16877,X16876,X16870),X16874),esk568_8(X16870,X16871,X16872,X16873,X16874,X16875,X16876,X16877))!=hAPP(X16871,esk568_8(X16870,X16871,X16872,X16873,X16874,X16875,X16876,X16877))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16876,X16877),X16871),X16873)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16875,X16877),X16870),X16872)|X16872!=hAPP(c_Set_Oimage(X16876,X16875,X16874),X16873)|~c_Fun_Oinj__on(X16876,X16875,X16874,X16873)|~class_Groups_Ocomm__monoid__mult(X16877))), 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])])])])])). 6.97/7.21 fof(c_0_5056, plain, ![X9191, X9192, X9193]:(X9193=c_List_Olist_ONil(X9192)|hAPP(hAPP(c_List_Onth(X9192),X9193),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X9191,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9192)),X9193)))=hAPP(c_List_Ohd(X9192),hAPP(c_List_Orotate(X9192,X9191),X9193))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__rotate__conv__nth])])). 6.97/7.21 fof(c_0_5057, plain, ![X3359, X3360, X3361, X3362, X3363, X3364, X3365, X3366]:((hBOOL(hAPP(hAPP(c_member(X3365),esk106_8(X3359,X3360,X3361,X3362,X3363,X3364,X3365,X3366)),X3362))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3365,X3366),X3360),X3362)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3364,X3366),X3359),X3361)|X3361!=hAPP(c_Set_Oimage(X3365,X3364,X3363),X3362)|~c_Fun_Oinj__on(X3365,X3364,X3363,X3362)|~class_Groups_Ocomm__monoid__add(X3366))&(hAPP(X3360,esk106_8(X3359,X3360,X3361,X3362,X3363,X3364,X3365,X3366))!=hAPP(X3359,hAPP(X3363,esk106_8(X3359,X3360,X3361,X3362,X3363,X3364,X3365,X3366)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3365,X3366),X3360),X3362)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3364,X3366),X3359),X3361)|X3361!=hAPP(c_Set_Oimage(X3365,X3364,X3363),X3362)|~c_Fun_Oinj__on(X3365,X3364,X3363,X3362)|~class_Groups_Ocomm__monoid__add(X3366))), 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])])])])])). 6.97/7.21 fof(c_0_5058, plain, ![X16769, X16770, X16771]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16771),X16770)),X16769))|c_List_Oupt(X16771,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16771),X16770))=hAPP(hAPP(c_List_Otake(tc_Nat_Onat),X16770),c_List_Oupt(X16771,X16769))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__upt])])). 6.97/7.21 fof(c_0_5059, plain, ![X700, X701, X702, X703, X704]:(X704!=c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X703,tc_HOL_Obool),X702)|(~c_Orderings_Oorder__class_Omono(tc_fun(X703,tc_HOL_Obool),tc_fun(X703,tc_HOL_Obool),X702)|(~hBOOL(hAPP(hAPP(c_member(X703),X701),X700))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X703,tc_HOL_Obool)),X700),hAPP(X702,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X703,tc_HOL_Obool)),X700),X704))))|hBOOL(hAPP(hAPP(c_member(X703),X701),X704)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_def__coinduct__set])])])). 6.97/7.21 fof(c_0_5060, plain, ![X857]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X857)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|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),X857)))))=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),X857))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__neg__1__number__of])])). 6.97/7.21 cnf(c_0_5061, plain, (X5=X1|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_4571])). 6.97/7.21 fof(c_0_5062, plain, ![X3964, X3965, X3966]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3966),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3965)),X3964)))|hAPP(c_Random_Opick(X3965,hAPP(hAPP(c_List_Omap(X3965,tc_prod(tc_Code__Numeral_Ocode__numeral,X3965)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X3965),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X3964)),hAPP(c_Code__Numeral_Oof__nat,X3966))=hAPP(hAPP(c_List_Onth(X3965),X3964),X3966)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pick__same])])])). 6.97/7.21 fof(c_0_5063, plain, ![X7047, X7048, X7049, X7050, X7051]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7051,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X7051,X7050,X7049),X7048)),X7047))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7050,tc_HOL_Obool)),X7048),hAPP(c_Set_Oimage(X7051,X7050,X7049),X7047)))|~c_Fun_Obij__betw(X7051,X7050,X7049,c_Orderings_Otop__class_Otop(tc_fun(X7051,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X7050,tc_HOL_Obool))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7050,tc_HOL_Obool)),X7048),hAPP(c_Set_Oimage(X7051,X7050,X7049),X7047)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7051,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X7051,X7050,X7049),X7048)),X7047))|~c_Fun_Obij__betw(X7051,X7050,X7049,c_Orderings_Otop__class_Otop(tc_fun(X7051,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X7050,tc_HOL_Obool))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__subset__eq])])])). 6.97/7.21 cnf(c_0_5064, 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_4572, c_0_4573])). 6.97/7.21 cnf(c_0_5065, 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_4574, c_0_4467]), c_0_4467]), ['final']). 6.97/7.21 cnf(c_0_5066, plain, (hAPP(c_List_Ofilter(X1,X2),hAPP(c_List_Ofilter(X1,X3),X4))=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),X3)),X2)),X4)), inference(split_conjunct,[status(thm)],[c_0_4575])). 6.97/7.21 fof(c_0_5067, plain, ![X15019, X15020, X15021, X15022]:(~class_Groups_Ocomm__monoid__add(X15022)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X15022),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X15022,tc_Nat_Onat),X15021),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X15020),X15019))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X15022),X15021),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X15020)),hAPP(c_Nat_OSuc,X15019)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__shift__bounds__Suc__ivl])])])). 6.97/7.21 fof(c_0_5068, plain, ![X5663, X5664, X5665, X5666]:(~c_Fun_Obij__betw(X5666,X5665,X5664,c_Orderings_Otop__class_Otop(tc_fun(X5666,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5665,tc_HOL_Obool)))|hAPP(c_Set_Oimage(X5666,X5665,X5664),hAPP(c_Set_OCollect(X5666),X5663))=hAPP(c_Set_OCollect(X5665),hAPP(hAPP(c_COMBB(X5666,tc_HOL_Obool,X5665),X5663),c_Hilbert__Choice_Oinv__into(X5666,X5665,c_Orderings_Otop__class_Otop(tc_fun(X5666,tc_HOL_Obool)),X5664)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bij__image__Collect__eq])])])). 6.97/7.21 cnf(c_0_5069, 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_4576])). 6.97/7.21 fof(c_0_5070, plain, ![X12070, X12071, X12072, X12073]:(((hBOOL(hAPP(c_List_Olistsp(X12073,X12072),X12070))|~hBOOL(hAPP(c_List_Olistsp(X12073,hAPP(hAPP(c_COMBS(X12073,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X12073),c_fconj),X12072)),X12071)),X12070)))&(hBOOL(hAPP(c_List_Olistsp(X12073,X12071),X12070))|~hBOOL(hAPP(c_List_Olistsp(X12073,hAPP(hAPP(c_COMBS(X12073,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X12073),c_fconj),X12072)),X12071)),X12070))))&(~hBOOL(hAPP(c_List_Olistsp(X12073,X12072),X12070))|~hBOOL(hAPP(c_List_Olistsp(X12073,X12071),X12070))|hBOOL(hAPP(c_List_Olistsp(X12073,hAPP(hAPP(c_COMBS(X12073,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X12073),c_fconj),X12072)),X12071)),X12070)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__conj__eq])])])). 6.97/7.21 fof(c_0_5071, plain, ![X13230, X13231, X13232]:((c_List_Olist_ONil(X13232)=X13231|hAPP(hAPP(c_Orderings_Oord__class_Omax(X13232),hAPP(hAPP(c_List_Onth(X13232),X13231),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X13230)=c_List_Ofoldr(X13232,X13232,c_Orderings_Oord__class_Omax(X13232),X13231,X13230)|~c_List_Olinorder__class_Osorted(X13232,hAPP(c_List_Orev(X13232),X13231))|~class_Orderings_Olinorder(X13232))&(X13231!=c_List_Olist_ONil(X13232)|X13230=c_List_Ofoldr(X13232,X13232,c_Orderings_Oord__class_Omax(X13232),X13231,X13230)|~c_List_Olinorder__class_Osorted(X13232,hAPP(c_List_Orev(X13232),X13231))|~class_Orderings_Olinorder(X13232))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_foldr__max__sorted])])])])). 6.97/7.21 fof(c_0_5072, plain, ![X12864, X12865, X12866, X12867, X12868]:(((X12864!=X12866|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12868),X12867),X12864)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12868),X12865),X12866))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12868),X12867),X12866)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12868),X12865),X12864))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X12868))&(X12865!=X12867|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12868),X12867),X12864)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12868),X12865),X12866))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12868),X12867),X12866)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12868),X12865),X12864))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X12868)))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12868),X12867),X12864)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12868),X12865),X12866))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12868),X12867),X12866)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12868),X12865),X12864))|(X12864=X12866|X12865=X12867)|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X12868))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__eq])])])). 6.97/7.21 cnf(c_0_5073, 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_4577])). 6.97/7.21 cnf(c_0_5074, 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_4577])). 6.97/7.21 fof(c_0_5075, plain, ![X14716, X14717, X14718, X14719, X14720]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14720),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14719),X14718)))|hAPP(hAPP(c_List_Onth(X14717),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X14717),X14716),c_List_Oupt(X14718,X14719))),X14720)=hAPP(X14716,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14718),X14720))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__map__upt])])])). 6.97/7.21 cnf(c_0_5076, 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)))|c_Groups_Oone__class_Oone(X2)=hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X1)))|~class_Int_Onumber__ring(X2)), inference(split_conjunct,[status(thm)],[c_0_4516])). 6.97/7.21 fof(c_0_5077, plain, ![X2483, X2484, X2485, X2486]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2483,X2485)),hAPP(X2483,X2484)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X2486,X2486)),hAPP(hAPP(c_Product__Type_OPair(X2486,X2486),X2485),X2484)),hAPP(c_Wellfounded_Omeasure(X2486),X2483))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X2486,X2486)),hAPP(hAPP(c_Product__Type_OPair(X2486,X2486),X2485),X2484)),hAPP(c_Wellfounded_Omeasure(X2486),X2483)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2483,X2485)),hAPP(X2483,X2484))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measure])])). 6.97/7.21 fof(c_0_5078, plain, ![X17405]:hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X17405),c_Wellfounded_Oless__than)=c_Wellfounded_Omeasure(X17405), inference(variable_rename,[status(thm)],[fact_measure__def])). 6.97/7.21 fof(c_0_5079, plain, ![X15255, X15256]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15256),X15255))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X15256,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(X15256,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X15256,tc_HOL_Obool),tc_fun(X15256,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X15256,tc_HOL_Obool))),X15255))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__subsets])])). 6.97/7.21 fof(c_0_5080, plain, ![X11629, X11630, X11631]:(~class_Groups_Omonoid__add(X11631)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11631),X11630),c_List_Ofoldr(X11631,X11631,c_Groups_Oplus__class_Oplus(X11631),X11629,c_Groups_Ozero__class_Ozero(X11631)))=hAPP(c_List_Ofoldl(X11631,X11631,c_Groups_Oplus__class_Oplus(X11631),X11630),X11629)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__foldr1__lemma])])). 6.97/7.21 fof(c_0_5081, plain, ![X10297, X10298, X10299]:(~class_Groups_Ocomm__monoid__add(X10299)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10299),X10298),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X10297)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10299),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10299),X10298),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X10297))),hAPP(X10298,X10297))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__lessThan__Suc])])])). 6.97/7.21 fof(c_0_5082, plain, ![X16861, X16862]:(~class_Int_Onumber__ring(X16862)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16862),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16862),c_Groups_Oone__class_Oone(X16862)),hAPP(c_Int_Onumber__class_Onumber__of(X16862),X16861))),hAPP(c_Int_Onumber__class_Onumber__of(X16862),X16861))=hAPP(c_Int_Onumber__class_Onumber__of(X16862),c_Int_OBit1(X16861))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Bit1])])). 6.97/7.21 fof(c_0_5083, plain, ![X9589, X9590, X9591]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk314_3(X9589,X9590,X9591)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X9591)))|X9590=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X9590),X9591)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X9590),c_Groups_Oone__class_Oone(tc_Int_Oint))),X9589))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9591)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk315_3(X9589,X9590,X9591)),X9589))|X9590=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X9590),X9591)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X9590),c_Groups_Oone__class_Oone(tc_Int_Oint))),X9589))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9591)))&(X9590=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk315_3(X9589,X9590,X9591)),esk314_3(X9589,X9590,X9591))|X9590=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X9590),X9591)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X9590),c_Groups_Oone__class_Oone(tc_Int_Oint))),X9589))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9591))))), 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])])])])])). 6.97/7.21 fof(c_0_5084, plain, ![X7540, X7541, X7542]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk248_3(X7540,X7541,X7542)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X7542)))|X7541=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7541),X7542)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7541),c_Groups_Oone__class_Oone(tc_Int_Oint))),X7540))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7542)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk249_3(X7540,X7541,X7542)),X7540))|X7541=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7541),X7542)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7541),c_Groups_Oone__class_Oone(tc_Int_Oint))),X7540))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7542)))&(X7541=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk249_3(X7540,X7541,X7542)),esk248_3(X7540,X7541,X7542))|X7541=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7541),X7542)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7541),c_Groups_Oone__class_Oone(tc_Int_Oint))),X7540))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7542))))), 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])])])])])). 6.97/7.21 cnf(c_0_5085, 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_4578])). 6.97/7.21 fof(c_0_5086, plain, ![X16667, X16668, X16669]:(~class_Groups_Ocomm__monoid__add(X16669)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16669),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X16669),X16668),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X16667))),hAPP(X16668,hAPP(c_Nat_OSuc,X16667)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X16669),X16668),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X16667)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__atMost__Suc])])). 6.97/7.21 fof(c_0_5087, plain, ![X15572]:hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X15572)=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15572), inference(variable_rename,[status(thm)],[fact_atLeast0AtMost])). 6.97/7.21 cnf(c_0_5088, 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_4579])). 6.97/7.21 cnf(c_0_5089, 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_4580])). 6.97/7.21 fof(c_0_5090, plain, ![X7676, X7677, X7678, X7679, X7680]:(~class_Complete__Lattice_Ocomplete__lattice(X7680)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7679),X7678))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7680),X7677),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7679,X7680),X7678),X7676))=hAPP(hAPP(c_Finite__Set_Ofold(X7679,X7680,hAPP(hAPP(c_COMBB(X7680,tc_fun(X7680,X7680),X7679),c_Lattices_Osemilattice__inf__class_Oinf(X7680)),X7676)),X7677),X7678))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__INFI__fold__inf])])])). 6.97/7.21 fof(c_0_5091, plain, ![X8416, X8417, X8418, X8419, X8420]:(~class_Complete__Lattice_Ocomplete__lattice(X8420)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8419),X8418))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8420),X8417),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8419,X8420),X8418),X8416))=hAPP(hAPP(c_Finite__Set_Ofold(X8419,X8420,hAPP(hAPP(c_COMBB(X8420,tc_fun(X8420,X8420),X8419),c_Lattices_Osemilattice__sup__class_Osup(X8420)),X8416)),X8417),X8418))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__SUPR__fold__sup])])])). 6.97/7.21 fof(c_0_5092, plain, ![X13897, X13898, X13899, X13900]:(~class_Groups_Ocomm__monoid__add(X13900)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13899),X13898))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X13900),X13897),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X13899,X13898))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13900),hAPP(X13897,X13899)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X13900),X13897),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X13899,X13898))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__head])])])). 6.97/7.21 cnf(c_0_5093, 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))))|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_4581])). 6.97/7.21 cnf(c_0_5094, 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_4582])). 6.97/7.21 cnf(c_0_5095, 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_4583])). 6.97/7.21 cnf(c_0_5096, 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_4584])). 6.97/7.21 fof(c_0_5097, plain, ![X5084, X5085, X5086, X5087, X5088, X5089]:((hBOOL(hAPP(hAPP(c_member(X5088),esk165_6(X5084,X5085,X5086,X5087,X5088,X5089)),X5087))|(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5088,X5089),X5086),X5087)!=X5085|(~hBOOL(hAPP(hAPP(c_member(X5088),X5084),X5087))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5089),hAPP(X5086,X5084)),X5085))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5088),X5087))|~class_Groups_Oordered__ab__group__add(X5089))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5089),c_Groups_Ozero__class_Ozero(X5089)),hAPP(X5086,esk165_6(X5084,X5085,X5086,X5087,X5088,X5089))))|(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5088,X5089),X5086),X5087)!=X5085|(~hBOOL(hAPP(hAPP(c_member(X5088),X5084),X5087))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5089),hAPP(X5086,X5084)),X5085))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5088),X5087))|~class_Groups_Oordered__ab__group__add(X5089))), 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])])])])])). 6.97/7.21 fof(c_0_5098, plain, ![X7359, X7360, X7361, X7362]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7362,tc_HOL_Obool)),X7361),X7360))|(~hBOOL(hAPP(hAPP(c_member(X7362),X7359),X7361))|hBOOL(hAPP(hAPP(c_member(X7362),X7359),X7360)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__mp])])). 6.97/7.21 fof(c_0_5099, plain, ![X6134, X6135, X6136, X6137, X6138, X6139]:((hAPP(X6134,hAPP(c_Product__Type_Osnd(X6137,X6139),X6135))!=hAPP(X6136,hAPP(c_Product__Type_Osnd(X6137,X6139),X6135))|hAPP(c_Product__Type_Oapsnd(X6139,X6138,X6137,X6134),X6135)=hAPP(c_Product__Type_Oapsnd(X6139,X6138,X6137,X6136),X6135))&(hAPP(c_Product__Type_Oapsnd(X6139,X6138,X6137,X6134),X6135)!=hAPP(c_Product__Type_Oapsnd(X6139,X6138,X6137,X6136),X6135)|hAPP(X6134,hAPP(c_Product__Type_Osnd(X6137,X6139),X6135))=hAPP(X6136,hAPP(c_Product__Type_Osnd(X6137,X6139),X6135)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_apsnd__eq__conv])])). 6.97/7.21 fof(c_0_5100, plain, ![X14454, X14455, X14456, X14457, X14458, X14459]:((hAPP(X14456,hAPP(c_Product__Type_Ofst(X14459,X14457),X14455))!=hAPP(X14454,hAPP(c_Product__Type_Ofst(X14459,X14457),X14455))|hAPP(c_Product__Type_Oapfst(X14459,X14458,X14457,X14456),X14455)=hAPP(c_Product__Type_Oapfst(X14459,X14458,X14457,X14454),X14455))&(hAPP(c_Product__Type_Oapfst(X14459,X14458,X14457,X14456),X14455)!=hAPP(c_Product__Type_Oapfst(X14459,X14458,X14457,X14454),X14455)|hAPP(X14456,hAPP(c_Product__Type_Ofst(X14459,X14457),X14455))=hAPP(X14454,hAPP(c_Product__Type_Ofst(X14459,X14457),X14455)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_apfst__eq__conv])])). 6.97/7.21 fof(c_0_5101, plain, ![X15665, X15666, X15667, X15668]:c_Product__Type_Oapfst(X15668,X15667,X15666,X15665)=c_Product__Type_Omap__pair(X15668,X15667,X15666,X15666,X15665,c_Fun_Oid(X15666)), inference(variable_rename,[status(thm)],[fact_apfst__def])). 6.97/7.21 fof(c_0_5102, plain, ![X5936, X5937, X5938, X5939]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5938))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5938))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X5938|c_Divides_Odiv__class_Omod(tc_Int_Oint,X5939,X5938)=X5936)|X5939!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5938),X5937)),X5936))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5936),X5938))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5936))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5938))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X5938|c_Divides_Odiv__class_Omod(tc_Int_Oint,X5939,X5938)=X5936)|X5939!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5938),X5937)),X5936)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5938))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5936),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5938),X5936)))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X5938|c_Divides_Odiv__class_Omod(tc_Int_Oint,X5939,X5938)=X5936)|X5939!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5938),X5937)),X5936))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5936),X5938))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5936))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5936),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5938),X5936)))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X5938|c_Divides_Odiv__class_Omod(tc_Int_Oint,X5939,X5938)=X5936)|X5939!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5938),X5937)),X5936)))), 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])])])])). 6.97/7.21 fof(c_0_5103, plain, ![X11325, X11326, X11327]:((c_Groups_Ozero__class_Ozero(X11327)!=X11326|c_Groups_Ozero__class_Ozero(X11327)!=X11325|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11327),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11327),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11327),X11326),X11326)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11327),X11325),X11325))),c_Groups_Ozero__class_Ozero(X11327)))|~class_Rings_Olinordered__ring__strict(X11327))&((c_Groups_Ozero__class_Ozero(X11327)=X11326|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11327),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11327),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11327),X11326),X11326)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11327),X11325),X11325))),c_Groups_Ozero__class_Ozero(X11327)))|~class_Rings_Olinordered__ring__strict(X11327))&(c_Groups_Ozero__class_Ozero(X11327)=X11325|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11327),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11327),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11327),X11326),X11326)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11327),X11325),X11325))),c_Groups_Ozero__class_Ozero(X11327)))|~class_Rings_Olinordered__ring__strict(X11327)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sum__squares__le__zero__iff])])])])). 6.97/7.21 cnf(c_0_5104, 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)))|c_Groups_Oone__class_Oone(tc_Int_Oint)=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)))), inference(split_conjunct,[status(thm)],[c_0_4517])). 6.97/7.21 cnf(c_0_5105, plain, (c_List_Oupt(X1,hAPP(c_Nat_OSuc,X2))=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)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4585])). 6.97/7.21 fof(c_0_5106, plain, ![X6257, X6258, X6259, X6260, X6261]:(c_Orderings_Otop__class_Otop(tc_fun(X6260,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X6261,X6260,X6259),c_Orderings_Otop__class_Otop(tc_fun(X6261,tc_HOL_Obool)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6261,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X6261,X6260,X6259),X6258)),X6257))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6260,tc_HOL_Obool)),X6258),hAPP(c_Set_Oimage(X6261,X6260,X6259),X6257))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__subsetD])])). 6.97/7.21 cnf(c_0_5107, 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_4586])). 6.97/7.21 cnf(c_0_5108, 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_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_4587])). 6.97/7.21 cnf(c_0_5109, 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_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_4588])). 6.97/7.21 cnf(c_0_5110, 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_4589])). 6.97/7.21 fof(c_0_5111, plain, ![X4205, X4206, X4207, X4208, X4209]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4209),X4206),X4205))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4209,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4209,X4208,X4207)),c_SetInterval_Oord__class_OatLeastAtMost(X4209,X4206,X4205)))|~class_Orderings_Oorder(X4209))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4209),X4207),X4205))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4209),X4208),X4207))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4209,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4209,X4208,X4207)),c_SetInterval_Oord__class_OatLeastAtMost(X4209,X4206,X4205)))|~class_Orderings_Oorder(X4209))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4209),X4207),X4205))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4209),X4206),X4208))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4209),X4208),X4207))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4209,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4209,X4208,X4207)),c_SetInterval_Oord__class_OatLeastAtMost(X4209,X4206,X4205)))|~class_Orderings_Oorder(X4209)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4209),X4206),X4208))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4209),X4208),X4207))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4209,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4209,X4208,X4207)),c_SetInterval_Oord__class_OatLeastAtMost(X4209,X4206,X4205)))|~class_Orderings_Oorder(X4209))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4209),X4208),X4207))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4209),X4206),X4205))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4209,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4209,X4208,X4207)),c_SetInterval_Oord__class_OatLeastAtMost(X4209,X4206,X4205)))|~class_Orderings_Oorder(X4209))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4209),X4207),X4205))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4209),X4207),X4205))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4209),X4206),X4208))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4209),X4206),X4205))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4209,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4209,X4208,X4207)),c_SetInterval_Oord__class_OatLeastAtMost(X4209,X4206,X4205)))|~class_Orderings_Oorder(X4209))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4209),X4206),X4208))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4209),X4207),X4205))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4209),X4206),X4208))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4209),X4206),X4205))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4209,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4209,X4208,X4207)),c_SetInterval_Oord__class_OatLeastAtMost(X4209,X4206,X4205)))|~class_Orderings_Oorder(X4209))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastatMost__psubset__iff])])])])). 6.97/7.21 fof(c_0_5112, plain, ![X9076, X9077, X9078]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9078),X9077),X9076))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9078),X9077),X9076))|X9077=X9076)|~class_Orderings_Oorder(X9078))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9078),X9077),X9076))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9078),X9077),X9076))|~class_Orderings_Oorder(X9078))&(X9077!=X9076|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9078),X9077),X9076))|~class_Orderings_Oorder(X9078)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__le__less])])])])). 6.97/7.21 fof(c_0_5113, plain, ![X17291, X17292, X17293]:(~class_Orderings_Olinorder(X17293)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17293),X17292),X17291))|c_SetInterval_Oord__class_OatLeastAtMost(X17293,X17292,X17291)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17293,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X17293,X17292),X17291)),hAPP(hAPP(c_Set_Oinsert(X17293),X17291),c_Orderings_Obot__class_Obot(tc_fun(X17293,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I6_J])])). 6.97/7.21 fof(c_0_5114, plain, ![X15938, X15939, X15940, X15941]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15941,tc_HOL_Obool)),X15940),hAPP(hAPP(c_Set_Oinsert(X15941),X15939),X15938))=hAPP(hAPP(c_Set_Oinsert(X15941),X15939),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15941,tc_HOL_Obool)),X15940),X15938)), inference(variable_rename,[status(thm)],[fact_Un__insert__right])). 6.97/7.21 fof(c_0_5115, plain, ![X8931, X8932]:X8931=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8932,tc_HOL_Obool)),X8931),c_Orderings_Obot__class_Obot(tc_fun(X8932,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Un__empty__right])). 6.97/7.21 fof(c_0_5116, plain, ![X9957, X9958, X9959, X9960]:(~class_Complete__Lattice_Ocomplete__lattice(X9960)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9959),X9958))|hAPP(hAPP(c_Finite__Set_Ofold(X9959,X9960,hAPP(hAPP(c_COMBB(X9960,tc_fun(X9960,X9960),X9959),c_Lattices_Osemilattice__inf__class_Oinf(X9960)),X9957)),c_Orderings_Otop__class_Otop(X9960)),X9958)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X9959,X9960),X9958),X9957))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INFI__fold__inf])])). 6.97/7.21 fof(c_0_5117, plain, ![X10391, X10392, X10393, X10394]:(~class_Complete__Lattice_Ocomplete__lattice(X10394)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10393),X10392))|hAPP(hAPP(c_Finite__Set_Ofold(X10393,X10394,hAPP(hAPP(c_COMBB(X10394,tc_fun(X10394,X10394),X10393),c_Lattices_Osemilattice__sup__class_Osup(X10394)),X10391)),c_Orderings_Obot__class_Obot(X10394)),X10392)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10393,X10394),X10392),X10391))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SUPR__fold__sup])])])). 6.97/7.21 fof(c_0_5118, plain, ![X1928, X1929, X1930]:(~class_Orderings_Olinorder(X1930)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1930),X1929),X1928))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1930,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1930),X1929),c_Orderings_Obot__class_Obot(tc_fun(X1930,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(X1930,X1929,X1928))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1930,X1929),X1928))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I3_J])])). 6.97/7.21 fof(c_0_5119, plain, ![X1430, X1431, X1432, X1433]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1433,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1433),X1432),X1431)),X1430)=hAPP(hAPP(c_Set_Oinsert(X1433),X1432),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1433,tc_HOL_Obool)),X1431),X1430)), inference(variable_rename,[status(thm)],[fact_Un__insert__left])). 6.97/7.21 fof(c_0_5120, plain, ![X15486, X15487]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15487,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X15487,tc_HOL_Obool))),X15486)=X15486, inference(variable_rename,[status(thm)],[fact_Un__empty__left])). 6.97/7.21 fof(c_0_5121, plain, ![X12974, X12975, X12976, X12977, X12978, X12979, X12980, X12981]:(~class_Groups_Ocomm__monoid__mult(X12981)|(~c_Fun_Oinj__on(X12980,X12979,X12978,X12977)|(hAPP(c_Set_Oimage(X12980,X12979,X12978),X12977)!=X12976|(hAPP(c_Fun_Ocomp(X12979,X12981,X12980,X12974),X12978)!=X12975|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12980,X12981),X12975),X12977)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12979,X12981),X12974),X12976))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__reindex__cong])])])). 6.97/7.21 fof(c_0_5122, plain, ![X10287, X10288, X10289, X10290]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk338_4(X10287,X10288,X10289,X10290)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X10289)))|(X10290=X10288|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X10290),X10289)!=X10288)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X10288),X10287))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10289)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk339_4(X10287,X10288,X10289,X10290)),X10287))|(X10290=X10288|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X10290),X10289)!=X10288)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X10288),X10287))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10289)))&(X10290=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk339_4(X10287,X10288,X10289,X10290)),esk338_4(X10287,X10288,X10289,X10290))|(X10290=X10288|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X10290),X10289)!=X10288)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X10288),X10287))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10289))))), 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])])])])])])). 6.97/7.21 fof(c_0_5123, plain, ![X13683, X13684, X13685]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13685),X13684))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13685),X13683))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X13684),X13685)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X13683),X13685))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X13684),X13683))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat_Odiff__diff__eq])])])). 6.97/7.21 fof(c_0_5124, plain, ![X6519, X6520, X6521, X6522]:(~class_Groups_Oab__group__add(X6522)|hAPP(c_Groups_Ouminus__class_Ouminus(X6522),hAPP(c_List_Omonoid__add__class_Olistsum(X6522),hAPP(hAPP(c_List_Omap(X6521,X6522),X6520),X6519)))=hAPP(c_List_Omonoid__add__class_Olistsum(X6522),hAPP(hAPP(c_List_Omap(X6521,X6522),hAPP(c_Fun_Ocomp(X6522,X6522,X6521,c_Groups_Ouminus__class_Ouminus(X6522)),X6520)),X6519))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__listsum__map])])). 6.97/7.21 fof(c_0_5125, plain, ![X15961, X15962, X15963, X15964, X15965, X15966]:hAPP(hAPP(c_List_Omap(X15963,X15965),hAPP(c_Fun_Ocomp(X15966,X15965,X15963,X15964),X15962)),X15961)=hAPP(hAPP(c_List_Omap(X15966,X15965),X15964),hAPP(hAPP(c_List_Omap(X15963,X15966),X15962),X15961)), inference(variable_rename,[status(thm)],[fact_List_Omap_Ocompositionality])). 6.97/7.21 fof(c_0_5126, plain, ![X3727, X3728, X3729, X3730]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk125_4(X3727,X3728,X3729,X3730)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3729)))|(X3728=X3730|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3730),X3729)!=X3728)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3728),X3727))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3729)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk126_4(X3727,X3728,X3729,X3730)),X3727))|(X3728=X3730|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3730),X3729)!=X3728)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3728),X3727))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3729)))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk126_4(X3727,X3728,X3729,X3730)),esk125_4(X3727,X3728,X3729,X3730))=X3730|(X3728=X3730|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3730),X3729)!=X3728)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3728),X3727))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3729))))), 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])])])])])])). 6.97/7.21 fof(c_0_5127, plain, ![X12036, X12037]:(c_List_Olist_ONil(X12036)=X12037|(~hBOOL(hAPP(c_List_Odistinct(X12036),X12037))|c_List_OtakeWhile(X12036,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X12036),c_fNot),hAPP(hAPP(c_COMBC(X12036,X12036,tc_HOL_Obool),c_fequal),c_List_Olast(X12036,X12037))),X12037)=c_List_Obutlast(X12036,X12037))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_takeWhile__not__last])])])). 6.97/7.21 fof(c_0_5128, plain, ![X14827, X14828, X14829, X14830, X14831, X14833]:((~c_Fun_Oinj__on(X14829,X14828,X14831,X14830)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14828,tc_HOL_Obool)),hAPP(c_Set_Oimage(X14829,X14828,X14831),X14830)),X14827))|hAPP(c_Set_Oimage(X14828,X14829,esk501_4(X14827,X14828,X14829,X14830)),X14827)=X14830|X14830=c_Orderings_Obot__class_Obot(tc_fun(X14829,tc_HOL_Obool)))&((c_Fun_Oinj__on(X14829,X14828,esk502_4(X14827,X14828,X14829,X14830),X14830)|hAPP(c_Set_Oimage(X14828,X14829,X14833),X14827)!=X14830|X14830=c_Orderings_Obot__class_Obot(tc_fun(X14829,tc_HOL_Obool)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14828,tc_HOL_Obool)),hAPP(c_Set_Oimage(X14829,X14828,esk502_4(X14827,X14828,X14829,X14830)),X14830)),X14827))|hAPP(c_Set_Oimage(X14828,X14829,X14833),X14827)!=X14830|X14830=c_Orderings_Obot__class_Obot(tc_fun(X14829,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_inj__on__iff__surj])])])])])])). 6.97/7.21 fof(c_0_5129, plain, ![X17334, X17335, X17336, X17337, X17338]:((c_List_Oconcat(X17335,X17334)!=c_List_Olist_ONil(X17335)|(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X17335)),X17336),hAPP(c_List_Oset(tc_List_Olist(X17335)),X17334)))|X17336=c_List_Olist_ONil(X17335)))&((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X17338)),esk590_2(X17337,X17338)),hAPP(c_List_Oset(tc_List_Olist(X17338)),X17337)))|c_List_Oconcat(X17338,X17337)=c_List_Olist_ONil(X17338))&(esk590_2(X17337,X17338)!=c_List_Olist_ONil(X17338)|c_List_Oconcat(X17338,X17337)=c_List_Olist_ONil(X17338)))), 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_concat__eq__Nil__conv])])])])])])). 6.97/7.21 fof(c_0_5130, plain, ![X13782, X13783, X13785, X13786, X13787]:(((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X13783)),esk462_2(X13782,X13783)),hAPP(c_List_Oset(tc_List_Olist(X13783)),X13782)))|c_List_Oconcat(X13783,X13782)=c_List_Olist_ONil(X13783))&(c_List_Olist_ONil(X13783)!=esk462_2(X13782,X13783)|c_List_Oconcat(X13783,X13782)=c_List_Olist_ONil(X13783)))&(c_List_Oconcat(X13786,X13785)!=c_List_Olist_ONil(X13786)|(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X13786)),X13787),hAPP(c_List_Oset(tc_List_Olist(X13786)),X13785)))|c_List_Olist_ONil(X13786)=X13787))), 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])])])])])])])). 6.97/7.21 fof(c_0_5131, plain, ![X15655, X15656, X15657, X15658, X15659]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk529_5(X15655,X15656,X15657,X15658,X15659)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X15659),X15656),X15658)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X15659),X15655),X15657)|~c_Nat__Transfer_Onat__set(X15657)|X15657!=X15658|(~class_Groups_Ocomm__monoid__add(X15659)|~class_Groups_Ocomm__monoid__mult(X15659)))&(hAPP(X15656,esk529_5(X15655,X15656,X15657,X15658,X15659))!=hAPP(X15655,esk529_5(X15655,X15656,X15657,X15658,X15659))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X15659),X15656),X15658)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X15659),X15655),X15657)|~c_Nat__Transfer_Onat__set(X15657)|X15657!=X15658|(~class_Groups_Ocomm__monoid__add(X15659)|~class_Groups_Ocomm__monoid__mult(X15659)))), 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])])])])])). 6.97/7.21 fof(c_0_5132, plain, ![X11612, X11613, X11614, X11615, X11616]:(~c_Fun_Oinj__on(X11616,X11615,X11614,c_Orderings_Otop__class_Otop(tc_fun(X11616,tc_HOL_Obool)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11615,tc_HOL_Obool)),X11613),hAPP(c_Set_Oimage(X11616,X11615,X11614),X11612)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11616,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X11616,X11615,X11614),X11613)),X11612)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_vimage__subsetI])])])). 6.97/7.21 fof(c_0_5133, plain, ![X16748, X16749, X16750, X16751, X16752]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk561_5(X16748,X16749,X16750,X16751,X16752)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X16752),X16748),X16750)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X16752),X16749),X16751)|~c_Nat__Transfer_Onat__set(X16750)|X16751!=X16750|(~class_Groups_Ocomm__monoid__mult(X16752)|~class_Groups_Ocomm__monoid__add(X16752)))&(hAPP(X16748,esk561_5(X16748,X16749,X16750,X16751,X16752))!=hAPP(X16749,esk561_5(X16748,X16749,X16750,X16751,X16752))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X16752),X16748),X16750)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X16752),X16749),X16751)|~c_Nat__Transfer_Onat__set(X16750)|X16751!=X16750|(~class_Groups_Ocomm__monoid__mult(X16752)|~class_Groups_Ocomm__monoid__add(X16752)))), 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])])])])])). 6.97/7.21 fof(c_0_5134, plain, ![X7200, X7201, X7202, X7204, X7205]:((((hBOOL(hAPP(hAPP(c_member(X7202),esk231_3(X7200,X7201,X7202)),X7201))|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7202,tc_Nat_Onat),X7200),X7201)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7202),X7201)))&(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(X7200,esk231_3(X7200,X7201,X7202))|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7202,tc_Nat_Onat),X7200),X7201)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7202),X7201))))&(~hBOOL(hAPP(hAPP(c_member(X7202),X7204),X7201))|(X7204=esk231_3(X7200,X7201,X7202)|hAPP(X7200,X7204)=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(X7202,tc_Nat_Onat),X7200),X7201)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7202),X7201))))&((hBOOL(hAPP(hAPP(c_member(X7202),esk232_4(X7200,X7201,X7202,X7205)),X7201))|(~hBOOL(hAPP(hAPP(c_member(X7202),X7205),X7201))|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(X7200,X7205))|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7202,tc_Nat_Onat),X7200),X7201)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7202),X7201)))&((esk232_4(X7200,X7201,X7202,X7205)!=X7205|(~hBOOL(hAPP(hAPP(c_member(X7202),X7205),X7201))|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(X7200,X7205))|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7202,tc_Nat_Onat),X7200),X7201)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7202),X7201)))&(hAPP(X7200,esk232_4(X7200,X7201,X7202,X7205))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|(~hBOOL(hAPP(hAPP(c_member(X7202),X7205),X7201))|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(X7200,X7205))|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7202,tc_Nat_Onat),X7200),X7201)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7202),X7201)))))), 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])])])])])])). 6.97/7.21 fof(c_0_5135, plain, ![X8178, X8179, X8180, X8183, X8184, X8185, X8186, X8187]:((((X8178!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X8178|hBOOL(hAPP(X8180,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X8179),X8178))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk270_3(X8178,X8179,X8180)),X8178))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X8178|hBOOL(hAPP(X8180,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X8179),X8178))))&((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8178),esk269_3(X8178,X8179,X8180))),esk270_3(X8178,X8179,X8180))=X8179|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X8178|hBOOL(hAPP(X8180,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X8179),X8178))))&(~hBOOL(hAPP(X8180,esk269_3(X8178,X8179,X8180)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X8178|hBOOL(hAPP(X8180,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X8179),X8178)))))))&((X8178!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(X8180,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(X8180,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X8179),X8178))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk270_3(X8178,X8179,X8180)),X8178))|~hBOOL(hAPP(X8180,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(X8180,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X8179),X8178))))&((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8178),esk269_3(X8178,X8179,X8180))),esk270_3(X8178,X8179,X8180))=X8179|~hBOOL(hAPP(X8180,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(X8180,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X8179),X8178))))&(~hBOOL(hAPP(X8180,esk269_3(X8178,X8179,X8180)))|~hBOOL(hAPP(X8180,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(X8180,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X8179),X8178))))))))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X8183|hBOOL(hAPP(X8185,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X8185,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X8184),X8183))))&(X8183=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8187),X8183))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8183),X8186)),X8187)!=X8184|hBOOL(hAPP(X8185,X8186))))|~hBOOL(hAPP(X8185,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X8184),X8183)))))), 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])])])])])])])). 6.97/7.21 fof(c_0_5136, plain, ![X16974, X16975, X16976, X16977, X16978, X16979]:((hBOOL(hAPP(hAPP(c_member(X16977),esk570_6(X16974,X16975,X16976,X16977,X16978,X16979)),X16978))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16977,tc_fun(X16974,tc_HOL_Obool)),X16978),X16975)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16977,tc_fun(X16974,tc_HOL_Obool)),X16979),X16976)|X16979!=X16978)&(hAPP(X16976,esk570_6(X16974,X16975,X16976,X16977,X16978,X16979))!=hAPP(X16975,esk570_6(X16974,X16975,X16976,X16977,X16978,X16979))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16977,tc_fun(X16974,tc_HOL_Obool)),X16978),X16975)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16977,tc_fun(X16974,tc_HOL_Obool)),X16979),X16976)|X16979!=X16978)), 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__cong])])])])])). 6.97/7.21 fof(c_0_5137, plain, ![X17310, X17311, X17312]:(~hBOOL(hAPP(c_List_Odistinct(X17312),X17311))|c_List_Osublist(X17312,X17311,X17310)=hAPP(c_List_Ofilter(X17312,hAPP(hAPP(c_COMBC(X17312,tc_fun(X17312,tc_HOL_Obool),tc_HOL_Obool),c_member(X17312)),hAPP(c_List_Oset(X17312),c_List_Osublist(X17312,X17311,X17310)))),X17311)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_filter__in__sublist])])])). 6.97/7.21 fof(c_0_5138, plain, ![X8882, X8883, X8884]:(~class_Orderings_Olinorder(X8884)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8884),X8883),X8882))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8884,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X8884),X8883),c_Orderings_Obot__class_Obot(tc_fun(X8884,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(X8884,X8883,X8882))=c_SetInterval_Oord__class_OatLeastAtMost(X8884,X8883,X8882))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I5_J])])])). 6.97/7.21 fof(c_0_5139, plain, ![X4773, X4774, X4775]:(~class_Orderings_Olinorder(X4775)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4775),X4774),X4773))|c_SetInterval_Oord__class_OgreaterThanAtMost(X4775,X4774,X4773)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4775,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4775,X4774,X4773)),hAPP(hAPP(c_Set_Oinsert(X4775),X4773),c_Orderings_Obot__class_Obot(tc_fun(X4775,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I4_J])])])). 6.97/7.21 fof(c_0_5140, plain, ![X9317, X9318]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X9318))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X9317))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9318),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9318),X9317))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__less__n__mult__m])])). 6.97/7.21 fof(c_0_5141, plain, ![X13843, X13844]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X13844))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X13843))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13844),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13843),X13844))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_n__less__m__mult__n])])])). 6.97/7.21 fof(c_0_5142, plain, ![X14594, X14595]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk493_2(X14594,X14595)),hAPP(X14595,esk493_2(X14594,X14595))))|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)),X14595)),X14594))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__less__ub])])])). 6.97/7.21 fof(c_0_5143, plain, ![X5421, X5422]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X5422)),c_Int_OBit0(X5421)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5422),X5421)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5422),X5421))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X5422)),c_Int_OBit0(X5421))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I15_J])])). 6.97/7.21 fof(c_0_5144, plain, ![X5127, X5128]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X5128)),c_Int_OBit0(X5127)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5128),X5127)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5128),X5127))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X5128)),c_Int_OBit0(X5127))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I15_J])])). 6.97/7.21 fof(c_0_5145, plain, ![X1771, X1772]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1772),X1771))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1772)),c_Int_OBit1(X1771))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1772)),c_Int_OBit1(X1771)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1772),X1771)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I15_J])])). 6.97/7.21 fof(c_0_5146, plain, ![X2063, X2064]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X2064)),c_Int_OBit1(X2063)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2064),X2063)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2064),X2063))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X2064)),c_Int_OBit1(X2063))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I14_J])])). 6.97/7.21 fof(c_0_5147, plain, ![X3319, X3320, X3321, X3322]:((c_Orderings_Obot__class_Obot(tc_fun(X3321,tc_HOL_Obool))=X3322|hAPP(c_Set_Oimage(tc_prod(X3321,X3320),X3320,c_Product__Type_Osnd(X3321,X3320)),hAPP(hAPP(c_Product__Type_OSigma(X3321,X3320),X3322),hAPP(c_COMBK(tc_fun(X3320,tc_HOL_Obool),X3321),X3319)))=X3319)&(X3322!=c_Orderings_Obot__class_Obot(tc_fun(X3321,tc_HOL_Obool))|hAPP(c_Set_Oimage(tc_prod(X3321,X3320),X3320,c_Product__Type_Osnd(X3321,X3320)),hAPP(hAPP(c_Product__Type_OSigma(X3321,X3320),X3322),hAPP(c_COMBK(tc_fun(X3320,tc_HOL_Obool),X3321),X3319)))=c_Orderings_Obot__class_Obot(tc_fun(X3320,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_snd__image__times])])])). 6.97/7.21 fof(c_0_5148, plain, ![X14690, X14691, X14692]:hAPP(c_Relation_ORange(X14692,X14691),X14690)=hAPP(c_Set_Oimage(tc_prod(X14692,X14691),X14691,c_Product__Type_Osnd(X14692,X14691)),X14690), inference(variable_rename,[status(thm)],[fact_snd__eq__Range])). 6.97/7.21 fof(c_0_5149, plain, ![X1686, X1687]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1686,X1687)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1686),X1687))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1686),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1687))|X1687=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1686,X1687)|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),X1686),X1687))),c_Groups_Oone__class_Oone(tc_Int_Oint))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1686),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1687))|X1687=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_zdiv__zminus2__eq__if])])])])). 6.97/7.21 fof(c_0_5150, plain, ![X16375, X16376, X16377, X16378]:((X16378=c_Orderings_Obot__class_Obot(tc_fun(X16377,tc_HOL_Obool))|hAPP(c_Set_Oimage(tc_prod(X16376,X16377),X16376,c_Product__Type_Ofst(X16376,X16377)),hAPP(hAPP(c_Product__Type_OSigma(X16376,X16377),X16375),hAPP(c_COMBK(tc_fun(X16377,tc_HOL_Obool),X16376),X16378)))=X16375)&(X16378!=c_Orderings_Obot__class_Obot(tc_fun(X16377,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X16376,tc_HOL_Obool))=hAPP(c_Set_Oimage(tc_prod(X16376,X16377),X16376,c_Product__Type_Ofst(X16376,X16377)),hAPP(hAPP(c_Product__Type_OSigma(X16376,X16377),X16375),hAPP(c_COMBK(tc_fun(X16377,tc_HOL_Obool),X16376),X16378))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fst__image__times])])). 6.97/7.21 fof(c_0_5151, plain, ![X12007, X12008, X12009]:hAPP(c_Relation_ODomain(X12009,X12008),X12007)=hAPP(c_Set_Oimage(tc_prod(X12009,X12008),X12009,c_Product__Type_Ofst(X12009,X12008)),X12007), inference(variable_rename,[status(thm)],[fact_fst__eq__Domain])). 6.97/7.21 fof(c_0_5152, plain, ![X5216, X5217, X5218, X5219, X5220]:(c_List_Opartition(X5220,X5219,X5218)!=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5220),tc_List_Olist(X5220)),X5217),X5216)|hAPP(c_List_Oset(X5220),X5218)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5220,tc_HOL_Obool)),hAPP(c_List_Oset(X5220),X5217)),hAPP(c_List_Oset(X5220),X5216))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_partition__set])])). 6.97/7.21 fof(c_0_5153, plain, ![X13799, X13800]:(~class_Orderings_Olinorder(X13800)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13800,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X13800),X13799)),hAPP(hAPP(c_Set_Oinsert(X13800),X13799),c_Orderings_Obot__class_Obot(tc_fun(X13800,tc_HOL_Obool))))=hAPP(c_SetInterval_Oord__class_OatMost(X13800),X13799)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I2_J])])). 6.97/7.21 fof(c_0_5154, plain, ![X3158, X3159]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3159),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),X3159))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3158)))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3159),X3158))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__mult__distrib__neg])])])). 6.97/7.21 fof(c_0_5155, plain, ![X4620, X4621, X4622, X4623]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X4623,X4623)),hAPP(hAPP(c_Product__Type_OPair(X4623,X4623),X4622),X4621)),c_Transitive__Closure_Otrancl(X4623,X4620)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X4623,X4623)),hAPP(hAPP(c_Product__Type_OPair(X4623,X4623),X4622),X4621)),c_Transitive__Closure_Ortrancl(X4623,X4620)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__into__rtrancl])])). 6.97/7.21 fof(c_0_5156, plain, ![X1761, X1762]:(~class_Int_Onumber__ring(X1762)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1762),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1762),c_Groups_Ozero__class_Ozero(X1762)),hAPP(c_Int_Onumber__class_Onumber__of(X1762),X1761))),hAPP(c_Int_Onumber__class_Onumber__of(X1762),X1761))=hAPP(c_Int_Onumber__class_Onumber__of(X1762),c_Int_OBit0(X1761))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_number__of__Bit0])])])). 6.97/7.21 fof(c_0_5157, plain, ![X7264, X7265]:(((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X7264)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7265)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7265),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7264))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X7265))))&(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X7264)))|hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X7265),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X7264)))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7265),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7264))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X7265)))))&(~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X7265)))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7265),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7264))=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])])])])). 6.97/7.21 fof(c_0_5158, plain, ![X10740, X10741, X10742, X10743, X10744, X10745]:(hAPP(c_Set_Oimage(X10745,X10744,X10743),X10742)!=X10741|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10744,tc_HOL_Obool)),X10740),X10741))|X10740=hAPP(c_Set_Oimage(X10745,X10744,X10743),hAPP(c_Set_Oimage(X10744,X10745,c_Hilbert__Choice_Oinv__into(X10745,X10744,X10742,X10743)),X10740)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__inv__into__cancel])])])). 6.97/7.21 cnf(c_0_5159, 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_4586])). 6.97/7.21 cnf(c_0_5160, 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_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(X2)), inference(split_conjunct,[status(thm)],[c_0_4587])). 6.97/7.21 cnf(c_0_5161, 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_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(X2)), inference(split_conjunct,[status(thm)],[c_0_4588])). 6.97/7.21 cnf(c_0_5162, 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_4589])). 6.97/7.21 fof(c_0_5163, plain, ![X10046, X10047]:((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X10047)))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X10047)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X10046))=hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X10047)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X10046))))&(~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X10047)))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X10047)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X10046))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__nat__number__of])])])). 6.97/7.21 fof(c_0_5164, plain, ![X10879, X10880, X10881, X10884, X10885, X10886, X10887, X10888]:((((X10879!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X10879=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X10881,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X10880,X10879))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk361_3(X10879,X10880,X10881)),X10879))|X10879=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X10881,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X10880,X10879))))&((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10879),esk360_3(X10879,X10880,X10881))),esk361_3(X10879,X10880,X10881))=X10880|X10879=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X10881,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X10880,X10879))))&(~hBOOL(hAPP(X10881,esk361_3(X10879,X10880,X10881)))|X10879=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X10881,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X10880,X10879)))))))&((X10879!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(X10881,X10880))|hBOOL(hAPP(X10881,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X10880,X10879))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk361_3(X10879,X10880,X10881)),X10879))|~hBOOL(hAPP(X10881,X10880))|hBOOL(hAPP(X10881,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X10880,X10879))))&((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10879),esk360_3(X10879,X10880,X10881))),esk361_3(X10879,X10880,X10881))=X10880|~hBOOL(hAPP(X10881,X10880))|hBOOL(hAPP(X10881,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X10880,X10879))))&(~hBOOL(hAPP(X10881,esk361_3(X10879,X10880,X10881)))|~hBOOL(hAPP(X10881,X10880))|hBOOL(hAPP(X10881,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X10880,X10879))))))))&((X10884!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X10886,X10885))|~hBOOL(hAPP(X10886,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X10885,X10884))))&(X10884=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10888),X10884))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10884),X10887)),X10888)!=X10885|hBOOL(hAPP(X10886,X10888))))|~hBOOL(hAPP(X10886,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X10885,X10884)))))), 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])])])])])])])). 6.97/7.21 fof(c_0_5165, plain, ![X7408, X7409]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X7409))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X7408))|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),X7408),X7409))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_one__less__mult])])])). 6.97/7.21 fof(c_0_5166, plain, ![X3867, X3868]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3868))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3867))|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),X3868),X3867))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3868))|~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),X3868),X3867))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3867))|~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),X3868),X3867)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__mult__iff])])])). 6.97/7.21 fof(c_0_5167, plain, ![X8956, X8957, X8958, X8959, X8960, X8961]:((X8956!=hAPP(c_Set_Oimage(tc_Nat_Onat,X8957,X8959),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)),X8958)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X8957),X8956)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8961),X8960))|X8960=hAPP(c_Set_Oimage(tc_Nat_Onat,X8961,esk293_2(X8960,X8961)),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)),esk292_2(X8960,X8961)))))), 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])])])])])). 6.97/7.21 fof(c_0_5168, plain, ![X9584, X9585]:(~class_Groups_Omonoid__add(X9585)|hAPP(c_List_Ofoldl(X9585,X9585,c_Groups_Oplus__class_Oplus(X9585),c_Groups_Ozero__class_Ozero(X9585)),X9584)=c_List_Ofoldr(X9585,X9585,c_Groups_Oplus__class_Oplus(X9585),X9584,c_Groups_Ozero__class_Ozero(X9585))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__foldr1])])). 6.97/7.21 cnf(c_0_5169, plain, (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))=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)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1))), inference(split_conjunct,[status(thm)],[c_0_4590])). 6.97/7.21 fof(c_0_5170, plain, ![X13827, X13828]:(~class_Int_Onumber__ring(X13828)|hAPP(c_Int_Onumber__class_Onumber__of(X13828),c_Int_OBit0(X13827))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13828),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13828),c_Groups_Oone__class_Oone(X13828)),c_Groups_Oone__class_Oone(X13828))),hAPP(c_Int_Onumber__class_Onumber__of(X13828),X13827))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__number__of__Bit0])])). 6.97/7.21 fof(c_0_5171, plain, ![X3949, X3950, X3951]:(~class_Groups_Ocomm__monoid__add(X3951)|(hAPP(X3950,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Ozero__class_Ozero(X3951)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3951),X3950),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3949))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3951),X3950),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3949)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__shift__lb__Suc0__0__upt])])])). 6.97/7.21 fof(c_0_5172, plain, ![X1847]:(~c_Nat__Transfer_Onat__set(X1847)|X1847=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),X1847))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transfer__nat__int__set__return__embed])])])). 6.97/7.21 cnf(c_0_5173, 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_4591])). 6.97/7.21 cnf(c_0_5174, plain, (c_Transitive__Closure_Otrancl(X1,X2)=hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_4592])). 6.97/7.21 fof(c_0_5175, plain, ![X17017, X17018, X17019, X17020, X17021]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17021,tc_HOL_Obool)),X17020),X17019))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17018,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X17018,X17021,X17017),X17020)),hAPP(c_Set_Ovimage(X17018,X17021,X17017),X17019)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_vimage__mono])])])). 6.97/7.21 fof(c_0_5176, plain, ![X1958, X1959]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1959,X1958)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1959,X1958),tc_HOL_Obool))))|(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(c_Finite__Set_Ocard(X1958),c_Orderings_Otop__class_Otop(tc_fun(X1958,tc_HOL_Obool)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X1959),c_Orderings_Otop__class_Otop(tc_fun(X1959,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__fun__UNIVD1])])])). 6.97/7.21 fof(c_0_5177, plain, ![X12723, X12724]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12723),c_Int_OPls))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X12724)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X12724)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X12723))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12724),c_Int_OPls)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12723),c_Int_OPls))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X12724)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X12723))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X12724),X12723))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12724),c_Int_OPls))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12724),c_Int_OPls))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X12723)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X12724)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X12723)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__nat__number__of])])])])). 6.97/7.21 fof(c_0_5178, plain, ![X3597, X3598]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(X3598,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X3598),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3597))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X3598),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3597))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__shift__lb__Suc0__0])])])). 6.97/7.21 fof(c_0_5179, plain, ![X13956]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13956),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_mult__0__right])). 6.97/7.21 fof(c_0_5180, plain, ![X16050]:X16050=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16050),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right])). 6.97/7.21 cnf(c_0_5181, 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)|hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X4),X1)!=c_List_Oupt(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_4593])). 6.97/7.21 fof(c_0_5182, plain, ![X17360]:(~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),X17360)))|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),X17360)))=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),X17360))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__pos__1__number__of])])). 6.97/7.21 cnf(c_0_5183, plain, (c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X1|c_Code__Numeral_Onat__of__aux(X1,X2)=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))), inference(split_conjunct,[status(thm)],[c_0_4594])). 6.97/7.21 cnf(c_0_5184, 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_4595])). 6.97/7.21 cnf(c_0_5185, 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_4596])). 6.97/7.21 cnf(c_0_5186, 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))), inference(split_conjunct,[status(thm)],[c_0_4597]), ['final']). 6.97/7.21 fof(c_0_5187, plain, ![X1793, X1794]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1794))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1793))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X1794)),hAPP(c_Int_Onat,X1793))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1794),X1793)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__add__distrib])])])). 6.97/7.21 fof(c_0_5188, plain, ![X6160, X6161]:(~class_Orderings_Olinorder(X6161)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6161,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X6161),X6160),c_Orderings_Obot__class_Obot(tc_fun(X6161,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(X6161),X6160))=hAPP(c_SetInterval_Oord__class_OatLeast(X6161),X6160)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I1_J])])])). 6.97/7.21 fof(c_0_5189, plain, ![X16631, X16632, X16633]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X16633,X16633)),X16632),X16631))|hBOOL(hAPP(hAPP(c_member(tc_prod(X16633,X16633)),X16632),c_Transitive__Closure_Otrancl(X16633,X16631)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_r__into__trancl_H])])])). 6.97/7.21 fof(c_0_5190, plain, ![X10403, X10404]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10404))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10404),X10403))|hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X10403),X10404))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X10403)),hAPP(c_Int_Onat,X10404)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__diff__distrib])])])). 6.97/7.21 fof(c_0_5191, plain, ![X7655, X7656, X7657, X7658]:(((hBOOL(hAPP(hAPP(c_member(X7658),X7657),X7656))|~hBOOL(hAPP(hAPP(c_member(X7658),X7657),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7658,tc_HOL_Obool)),X7656),hAPP(c_Set_OCollect(X7658),X7655)))))&(hBOOL(hAPP(X7655,X7657))|~hBOOL(hAPP(hAPP(c_member(X7658),X7657),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7658,tc_HOL_Obool)),X7656),hAPP(c_Set_OCollect(X7658),X7655))))))&(~hBOOL(hAPP(hAPP(c_member(X7658),X7657),X7656))|~hBOOL(hAPP(X7655,X7657))|hBOOL(hAPP(hAPP(c_member(X7658),X7657),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7658,tc_HOL_Obool)),X7656),hAPP(c_Set_OCollect(X7658),X7655)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__Collect])])])). 6.97/7.21 fof(c_0_5192, plain, ![X7070, X7071, X7072, X7073]:(~c_Fun_Obij__betw(X7073,X7072,X7071,c_Orderings_Otop__class_Otop(tc_fun(X7073,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X7072,tc_HOL_Obool)))|hAPP(c_Set_Oimage(X7072,X7073,c_Hilbert__Choice_Oinv__into(X7073,X7072,c_Orderings_Otop__class_Otop(tc_fun(X7073,tc_HOL_Obool)),X7071)),X7070)=hAPP(c_Set_Ovimage(X7073,X7072,X7071),X7070)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bij__vimage__eq__inv__image])])])). 6.97/7.21 fof(c_0_5193, plain, ![X12210, X12211]:((~c_Wellfounded_Oacyclic(X12211,hAPP(c_Set_OCollect(tc_prod(X12211,X12211)),hAPP(c_Product__Type_Oprod_Oprod__case(X12211,X12211,tc_HOL_Obool),X12210)))|c_Wellfounded_Oacyclic(X12211,hAPP(c_Set_OCollect(tc_prod(X12211,X12211)),hAPP(c_Product__Type_Oprod_Oprod__case(X12211,X12211,tc_HOL_Obool),c_Predicate_Oconversep(X12211,X12211,X12210)))))&(~c_Wellfounded_Oacyclic(X12211,hAPP(c_Set_OCollect(tc_prod(X12211,X12211)),hAPP(c_Product__Type_Oprod_Oprod__case(X12211,X12211,tc_HOL_Obool),c_Predicate_Oconversep(X12211,X12211,X12210))))|c_Wellfounded_Oacyclic(X12211,hAPP(c_Set_OCollect(tc_prod(X12211,X12211)),hAPP(c_Product__Type_Oprod_Oprod__case(X12211,X12211,tc_HOL_Obool),X12210))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclicP__converse])])). 6.97/7.21 fof(c_0_5194, plain, ![X17436, X17437, X17438]:((~c_Relation_Ototal__on(X17438,X17437,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X17438,X17438),tc_HOL_Obool)),X17436),c_Relation_OId(X17438)))|c_Relation_Ototal__on(X17438,X17437,X17436))&(~c_Relation_Ototal__on(X17438,X17437,X17436)|c_Relation_Ototal__on(X17438,X17437,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X17438,X17438),tc_HOL_Obool)),X17436),c_Relation_OId(X17438))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_total__on__diff__Id])])). 6.97/7.21 fof(c_0_5195, plain, ![X1427, X1428, X1429]:(~class_Groups_Oab__semigroup__add(X1429)|c_List_Ofoldr(X1429,X1429,c_Groups_Oplus__class_Oplus(X1429),X1428,X1427)=hAPP(c_List_Ofoldl(X1429,X1429,c_Groups_Oplus__class_Oplus(X1429),X1427),X1428)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldr__conv__foldl])])). 6.97/7.21 fof(c_0_5196, plain, ![X2620, X2621]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2621),X2620))|c_List_Oupt(X2621,X2620)=hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X2621),c_List_Oupt(hAPP(c_Nat_OSuc,X2621),X2620)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2621),X2620))|c_List_Olist_ONil(tc_Nat_Onat)=c_List_Oupt(X2621,X2620))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_upt__rec])])])). 6.97/7.21 fof(c_0_5197, plain, ![X948, X949, X950, X952, X953, X954, X955]:(((hBOOL(hAPP(hAPP(c_member(X950),esk27_3(X948,X949,X950)),hAPP(c_List_Oset(X950),X948)))|c_List_Olist_ONil(X950)=c_List_OdropWhile(X950,X949,X948))&(~hBOOL(hAPP(X949,esk27_3(X948,X949,X950)))|c_List_Olist_ONil(X950)=c_List_OdropWhile(X950,X949,X948)))&(c_List_Olist_ONil(X954)!=c_List_OdropWhile(X954,X953,X952)|(~hBOOL(hAPP(hAPP(c_member(X954),X955),hAPP(c_List_Oset(X954),X952)))|hBOOL(hAPP(X953,X955))))), 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_dropWhile__eq__Nil__conv])])])])])])])). 6.97/7.21 fof(c_0_5198, plain, ![X15276, X15277]:(~c_Relation_Otrans(X15277,X15276)|(~c_Relation_Oantisym(X15277,X15276)|c_Relation_Otrans(X15277,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X15277,X15277),tc_HOL_Obool)),X15276),c_Relation_OId(X15277))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__diff__Id])])). 6.97/7.21 fof(c_0_5199, plain, ![X7117, X7118]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X7118,X7118)),X7117),c_Relation_OId(X7118)))|hAPP(hAPP(c_Product__Type_OPair(X7118,X7118),esk229_2(X7117,X7118)),esk229_2(X7117,X7118))=X7117), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_IdE])])])])). 6.97/7.21 fof(c_0_5200, plain, ![X14295]:(hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X14295|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,X14295)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,X14295)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_code__numeral__decr])])])). 6.97/7.21 cnf(c_0_5201, plain, (c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[fact_zero__code__numeral__def])). 6.97/7.21 cnf(c_0_5202, plain, (c_Code__Numeral_Oof__nat=c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[fact_Code__Numeral_Oof__nat__code]), ['final']). 6.97/7.21 fof(c_0_5203, plain, ![X7179, X7180]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7180),X7179))|c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X7179,X7180)=c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7180),X7179))|c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X7179,X7180)=hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X7179),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7179),c_Groups_Oone__class_Oone(tc_Int_Oint)),X7180)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_simp__from__to])])])). 6.97/7.21 cnf(c_0_5204, 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_Fields_Ofield(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4598])). 6.97/7.21 fof(c_0_5205, plain, ![X5932, X5933, X5934, X5935]:((hAPP(hAPP(c_List_Olist_OCons(X5935),X5933),X5932)!=hAPP(c_List_Orev(X5935),X5934)|hAPP(hAPP(c_List_Oappend(X5935),hAPP(c_List_Orev(X5935),X5932)),hAPP(hAPP(c_List_Olist_OCons(X5935),X5933),c_List_Olist_ONil(X5935)))=X5934)&(hAPP(hAPP(c_List_Oappend(X5935),hAPP(c_List_Orev(X5935),X5932)),hAPP(hAPP(c_List_Olist_OCons(X5935),X5933),c_List_Olist_ONil(X5935)))!=X5934|hAPP(hAPP(c_List_Olist_OCons(X5935),X5933),X5932)=hAPP(c_List_Orev(X5935),X5934))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__eq__Cons__iff])])). 6.97/7.21 fof(c_0_5206, plain, ![X13057, X13058, X13059]:hAPP(hAPP(c_List_Oappend(X13059),hAPP(c_List_Orev(X13059),X13057)),hAPP(hAPP(c_List_Olist_OCons(X13059),X13058),c_List_Olist_ONil(X13059)))=hAPP(c_List_Orev(X13059),hAPP(hAPP(c_List_Olist_OCons(X13059),X13058),X13057)), inference(variable_rename,[status(thm)],[fact_rev_Osimps_I2_J])). 6.97/7.21 fof(c_0_5207, plain, ![X1173, X1174, X1175, X1176, X1177]:((hAPP(hAPP(c_List_Omap(tc_prod(X1177,X1175),X1177),c_Product__Type_Ofst(X1177,X1175)),X1173)!=X1176|hAPP(hAPP(c_List_Omap(tc_prod(X1177,X1175),X1175),c_Product__Type_Osnd(X1177,X1175)),X1173)!=X1174|X1173=hAPP(hAPP(c_List_Ozip(X1177,X1175),X1176),X1174)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1175)),X1174)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1177)),X1176))&((hAPP(hAPP(c_List_Omap(tc_prod(X1177,X1175),X1177),c_Product__Type_Ofst(X1177,X1175)),X1173)=X1176|X1173!=hAPP(hAPP(c_List_Ozip(X1177,X1175),X1176),X1174)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1175)),X1174)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1177)),X1176))&(hAPP(hAPP(c_List_Omap(tc_prod(X1177,X1175),X1175),c_Product__Type_Osnd(X1177,X1175)),X1173)=X1174|X1173!=hAPP(hAPP(c_List_Ozip(X1177,X1175),X1176),X1174)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1175)),X1174)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1177)),X1176)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zip__eq__conv])])])])). 6.97/7.21 fof(c_0_5208, plain, ![X9491, X9492, X9493]:((~hBOOL(hAPP(hAPP(c_member(tc_fun(X9493,tc_HOL_Obool)),X9491),hAPP(c_Set_OPow(X9493),X9492)))|hBOOL(hAPP(c_Predicate_OPowp(X9493,hAPP(hAPP(c_COMBC(X9493,tc_fun(X9493,tc_HOL_Obool),tc_HOL_Obool),c_member(X9493)),X9492)),X9491)))&(~hBOOL(hAPP(c_Predicate_OPowp(X9493,hAPP(hAPP(c_COMBC(X9493,tc_fun(X9493,tc_HOL_Obool),tc_HOL_Obool),c_member(X9493)),X9492)),X9491))|hBOOL(hAPP(hAPP(c_member(tc_fun(X9493,tc_HOL_Obool)),X9491),hAPP(c_Set_OPow(X9493),X9492))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Powp__Pow__eq])])). 6.97/7.21 fof(c_0_5209, plain, ![X6712, X6713, X6714, X6715]:(~c_Fun_Oinj__on(X6715,X6714,X6713,c_Complete__Lattice_OSup__class_OSup(tc_fun(X6715,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(X6715),tc_fun(X6715,tc_HOL_Obool),c_List_Oset(X6715)),X6712)))|c_Fun_Oinj__on(tc_List_Olist(X6715),tc_List_Olist(X6714),hAPP(c_List_Omap(X6715,X6714),X6713),X6712)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__mapI])])). 6.97/7.21 fof(c_0_5210, plain, ![X17203, X17204, X17205, X17206]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17206,tc_fun(X17205,tc_HOL_Obool)),X17204),X17203)=c_Complete__Lattice_OSup__class_OSup(tc_fun(X17205,tc_HOL_Obool),hAPP(c_Set_Oimage(X17206,tc_fun(X17205,tc_HOL_Obool),X17203),X17204)), inference(variable_rename,[status(thm)],[fact_UNION__eq__Union__image])). 6.97/7.21 fof(c_0_5211, plain, ![X6162, X6163, X6164]:(((X6163=c_Groups_Ozero__class_Ozero(X6164)|c_Groups_Ozero__class_Ozero(X6164)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6164),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6164),X6163),X6163)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6164),X6162),X6162))|~class_Rings_Olinordered__ring__strict(X6164))&(X6162=c_Groups_Ozero__class_Ozero(X6164)|c_Groups_Ozero__class_Ozero(X6164)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6164),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6164),X6163),X6163)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6164),X6162),X6162))|~class_Rings_Olinordered__ring__strict(X6164)))&(X6163!=c_Groups_Ozero__class_Ozero(X6164)|X6162!=c_Groups_Ozero__class_Ozero(X6164)|c_Groups_Ozero__class_Ozero(X6164)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6164),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6164),X6163),X6163)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6164),X6162),X6162))|~class_Rings_Olinordered__ring__strict(X6164))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__eq__zero__iff])])])). 6.97/7.21 fof(c_0_5212, plain, ![X13584, X13585, X13588, X13589, X13590]:((((~hBOOL(hAPP(hAPP(c_member(X13585),X13588),hAPP(c_List_Oset(X13585),esk452_2(X13584,X13585))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13585),esk453_2(X13584,X13585)),X13588))|X13584=c_List_Olist_ONil(X13585)|~c_List_Olinorder__class_Osorted(X13585,X13584)|~class_Orderings_Olinorder(X13585))&(c_List_Olinorder__class_Osorted(X13585,esk452_2(X13584,X13585))|X13584=c_List_Olist_ONil(X13585)|~c_List_Olinorder__class_Osorted(X13585,X13584)|~class_Orderings_Olinorder(X13585)))&(hAPP(hAPP(c_List_Olist_OCons(X13585),esk453_2(X13584,X13585)),esk452_2(X13584,X13585))=X13584|X13584=c_List_Olist_ONil(X13585)|~c_List_Olinorder__class_Osorted(X13585,X13584)|~class_Orderings_Olinorder(X13585)))&((X13584!=c_List_Olist_ONil(X13585)|c_List_Olinorder__class_Osorted(X13585,X13584)|~class_Orderings_Olinorder(X13585))&((hBOOL(hAPP(hAPP(c_member(X13585),esk454_4(X13584,X13585,X13589,X13590)),hAPP(c_List_Oset(X13585),X13589)))|~c_List_Olinorder__class_Osorted(X13585,X13589)|hAPP(hAPP(c_List_Olist_OCons(X13585),X13590),X13589)!=X13584|c_List_Olinorder__class_Osorted(X13585,X13584)|~class_Orderings_Olinorder(X13585))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13585),X13590),esk454_4(X13584,X13585,X13589,X13590)))|~c_List_Olinorder__class_Osorted(X13585,X13589)|hAPP(hAPP(c_List_Olist_OCons(X13585),X13590),X13589)!=X13584|c_List_Olinorder__class_Osorted(X13585,X13584)|~class_Orderings_Olinorder(X13585))))), 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])])])])])). 6.97/7.21 fof(c_0_5213, plain, ![X5043, X5044, X5045]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5045),X5044)),X5043))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5045),X5044)=hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(X5045,X5043)),X5044)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__upt])])])). 6.97/7.21 fof(c_0_5214, plain, ![X5808, X5809]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X5809)))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X5809)),X5808)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5808))&(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X5809)))|hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X5809)),X5808))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X5809)),X5808))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__nat__number__of])])])). 6.97/7.21 fof(c_0_5215, plain, ![X2361, X2362]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2362),X2361))|c_Lazy__Sequence_Oempty(tc_Int_Oint)=c_Lazy__Sequence_Osmall__lazy_H(X2362,X2361))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2362),X2361))|c_Lazy__Sequence_Osmall__lazy_H(X2362,X2361)=c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X2361),c_Lazy__Sequence_Osmall__lazy_H(X2362,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2361),c_Groups_Oone__class_Oone(tc_Int_Oint)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_small__lazy_H_Osimps])])])). 6.97/7.21 fof(c_0_5216, plain, ![X6982]:(~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),X6982)))|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),X6982))=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),X6982)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__pos__1__number__of])])). 6.97/7.21 fof(c_0_5217, plain, ![X2730, X2731, X2732]:(c_List_OdropWhile(X2732,X2731,X2730)=c_List_Olist_ONil(X2732)|~hBOOL(hAPP(X2731,hAPP(c_List_Ohd(X2732),c_List_OdropWhile(X2732,X2731,X2730))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_hd__dropWhile])])])). 6.97/7.21 fof(c_0_5218, plain, ![X8922, X8923]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8923),c_Int_OPls))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8923),X8922))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8923)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8922)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8923),c_Int_OPls))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8923)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8922))=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__nat__number__of])])])). 6.97/7.21 fof(c_0_5219, plain, ![X17350, X17351]:(((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17351)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17350)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17351)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17350))&((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17350)))|X17350=X17351|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17351)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17351)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17350))&(~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17350)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17351)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17351)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17351)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17350))))&(((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17351)))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17351)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17351)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17350))&(((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17350)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17350)))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17351)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17351)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17350))&(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17351)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17350)))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17351)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17351)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17350)))&((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17350)))|X17350!=X17351|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17351)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17351)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17350))&(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17351)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X17350!=X17351|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17351)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17351)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17350)))))&((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17351)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17350)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17351)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17350))&(((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17350)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17350)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17350)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17351)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17350))&(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17351)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17350)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17350)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17351)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17350)))&((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17350)))|X17350!=X17351|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17350)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17351)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17350))&(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17351)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X17350!=X17351|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17350)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17351)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17350))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__nat__number__of])])])])). 6.97/7.21 fof(c_0_5220, plain, ![X4717, X4718, X4719, X4720]:(X4719!=X4720|(~hBOOL(hAPP(hAPP(c_member(X4718),X4720),X4717))|hBOOL(hAPP(hAPP(c_member(tc_prod(X4718,X4718)),hAPP(hAPP(c_Product__Type_OPair(X4718,X4718),X4720),X4719)),c_Relation_OId__on(X4718,X4717))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Id__on__eqI])])])). 6.97/7.21 fof(c_0_5221, plain, ![X16021, X16022, X16023]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16021),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16023),hAPP(c_Nat_OSuc,X16022))))|X16022!=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X16021),X16023)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X16023)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16023),X16022)),X16021))|X16022!=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X16021),X16023)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X16023))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16021),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16023),hAPP(c_Nat_OSuc,X16022))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16023),X16022)),X16021))|X16022=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X16021),X16023)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X16023)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_split__div__lemma])])])])). 6.97/7.21 cnf(c_0_5222, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|hAPP(c_List_OremoveAll(X1,X2),X3)=X3), inference(split_conjunct,[status(thm)],[c_0_4599])). 6.97/7.21 fof(c_0_5223, plain, ![X16502, X16503, X16504, X16505]:((((X16503!=c_Groups_Ozero__class_Ozero(X16505)|X16503=c_Groups_Ozero__class_Ozero(X16505)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16505),X16504),X16503)=hAPP(c_Int_Onumber__class_Onumber__of(X16505),X16502)|(~class_Fields_Ofield__inverse__zero(X16505)|~class_Int_Onumber(X16505)))&(X16504!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16505),hAPP(c_Int_Onumber__class_Onumber__of(X16505),X16502)),X16503)|X16503=c_Groups_Ozero__class_Ozero(X16505)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16505),X16504),X16503)=hAPP(c_Int_Onumber__class_Onumber__of(X16505),X16502)|(~class_Fields_Ofield__inverse__zero(X16505)|~class_Int_Onumber(X16505))))&((X16503!=c_Groups_Ozero__class_Ozero(X16505)|c_Groups_Ozero__class_Ozero(X16505)!=hAPP(c_Int_Onumber__class_Onumber__of(X16505),X16502)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16505),X16504),X16503)=hAPP(c_Int_Onumber__class_Onumber__of(X16505),X16502)|(~class_Fields_Ofield__inverse__zero(X16505)|~class_Int_Onumber(X16505)))&(X16504!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16505),hAPP(c_Int_Onumber__class_Onumber__of(X16505),X16502)),X16503)|c_Groups_Ozero__class_Ozero(X16505)!=hAPP(c_Int_Onumber__class_Onumber__of(X16505),X16502)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16505),X16504),X16503)=hAPP(c_Int_Onumber__class_Onumber__of(X16505),X16502)|(~class_Fields_Ofield__inverse__zero(X16505)|~class_Int_Onumber(X16505)))))&((X16503!=c_Groups_Ozero__class_Ozero(X16505)|c_Groups_Ozero__class_Ozero(X16505)=hAPP(c_Int_Onumber__class_Onumber__of(X16505),X16502)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16505),X16504),X16503)!=hAPP(c_Int_Onumber__class_Onumber__of(X16505),X16502)|(~class_Fields_Ofield__inverse__zero(X16505)|~class_Int_Onumber(X16505)))&(X16503=c_Groups_Ozero__class_Ozero(X16505)|X16504=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16505),hAPP(c_Int_Onumber__class_Onumber__of(X16505),X16502)),X16503)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16505),X16504),X16503)!=hAPP(c_Int_Onumber__class_Onumber__of(X16505),X16502)|(~class_Fields_Ofield__inverse__zero(X16505)|~class_Int_Onumber(X16505))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__eq__eq__number__of])])])])). 6.97/7.21 fof(c_0_5224, plain, ![X13550, X13551, X13552]:(((X13551=c_Groups_Ozero__class_Ozero(X13552)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13552),X13551),X13550)!=c_Groups_Ozero__class_Ozero(X13552)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13552),c_Groups_Ozero__class_Ozero(X13552)),X13550))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13552),c_Groups_Ozero__class_Ozero(X13552)),X13551))|~class_Groups_Oordered__comm__monoid__add(X13552))&(c_Groups_Ozero__class_Ozero(X13552)=X13550|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13552),X13551),X13550)!=c_Groups_Ozero__class_Ozero(X13552)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13552),c_Groups_Ozero__class_Ozero(X13552)),X13550))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13552),c_Groups_Ozero__class_Ozero(X13552)),X13551))|~class_Groups_Oordered__comm__monoid__add(X13552)))&(X13551!=c_Groups_Ozero__class_Ozero(X13552)|c_Groups_Ozero__class_Ozero(X13552)!=X13550|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13552),X13551),X13550)=c_Groups_Ozero__class_Ozero(X13552)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13552),c_Groups_Ozero__class_Ozero(X13552)),X13550))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13552),c_Groups_Ozero__class_Ozero(X13552)),X13551))|~class_Groups_Oordered__comm__monoid__add(X13552))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__nonneg__eq__0__iff])])])])). 6.97/7.21 fof(c_0_5225, plain, ![X12319, X12320]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12320),X12319))|hAPP(c_Finite__Set_Ocard(tc_fun(X12320,tc_HOL_Obool)),hAPP(c_Set_OPow(X12320),X12319))=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(X12320),X12319))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Pow])])])). 6.97/7.21 fof(c_0_5226, plain, ![X1228, X1229, X1230, X1231]:(~class_Groups_Ocomm__monoid__add(X1231)|hAPP(c_List_Omonoid__add__class_Olistsum(X1231),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X1231),X1230),c_List_Oupto(X1229,X1228)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X1231),X1230),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X1229,X1228)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__set__upto__conv__listsum__int])])). 6.97/7.21 fof(c_0_5227, plain, ![X1150, X1151]:hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X1151,X1150))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1151,X1150), inference(variable_rename,[status(thm)],[fact_atLeastAtMost__upto])). 6.97/7.21 fof(c_0_5228, plain, ![X1524, X1525, X1526]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1524),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1525),X1526)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1524),X1526)),X1525))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1526),X1525)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1524),X1526)),X1525))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1524),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1525),X1526)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1526),X1525)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv2])])])). 6.97/7.21 fof(c_0_5229, plain, ![X8589, X8590, X8591]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X8591),X8590)),X8589))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8590),X8589))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__leD2])])])). 6.97/7.21 fof(c_0_5230, plain, ![X10539, X10540, X10541]:((~hBOOL(hAPP(c_List_Olistsp(X10541,hAPP(hAPP(c_COMBC(X10541,tc_fun(X10541,tc_HOL_Obool),tc_HOL_Obool),c_member(X10541)),X10540)),X10539))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10541)),X10539),c_List_Olists(X10541,X10540))))&(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10541)),X10539),c_List_Olists(X10541,X10540)))|hBOOL(hAPP(c_List_Olistsp(X10541,hAPP(hAPP(c_COMBC(X10541,tc_fun(X10541,tc_HOL_Obool),tc_HOL_Obool),c_member(X10541)),X10540)),X10539)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__lists__eq])])). 6.97/7.21 fof(c_0_5231, plain, ![X1469]:((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1469)))|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),X1469)))=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),X1469)))&(~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1469)))|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=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),X1469)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_one__mod__nat__number__of])])])). 6.97/7.21 fof(c_0_5232, plain, ![X9776, X9777]:((~c_Relation_Oantisym(X9777,X9776)|c_Relation_Oantisym(X9777,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X9777,X9777),tc_HOL_Obool)),X9776),c_Relation_OId(X9777))))&(~c_Relation_Oantisym(X9777,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X9777,X9777),tc_HOL_Obool)),X9776),c_Relation_OId(X9777)))|c_Relation_Oantisym(X9777,X9776))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_antisym__reflcl])])). 6.97/7.21 fof(c_0_5233, plain, ![X15376, X15377]:(~c_Relation_Otrans(X15377,X15376)|c_Relation_Otrans(X15377,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X15377,X15377),tc_HOL_Obool)),X15376),c_Relation_OId(X15377)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__reflclI])])). 6.97/7.21 fof(c_0_5234, plain, ![X11367]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X11367)=hAPP(c_Nat_OSuc,X11367), inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left])). 6.97/7.21 cnf(c_0_5235, 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_4600])). 6.97/7.21 cnf(c_0_5236, plain, (X2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),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_4601])). 6.97/7.21 fof(c_0_5237, plain, ![X4471, X4472, X4473, X4474]:(((X4473=hAPP(hAPP(c_List_Otake(X4474),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4474)),X4473)),X4471)|X4471!=hAPP(hAPP(c_List_Oappend(X4474),X4473),X4472))&(X4472=hAPP(hAPP(c_List_Odrop(X4474),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4474)),X4473)),X4471)|X4471!=hAPP(hAPP(c_List_Oappend(X4474),X4473),X4472)))&(X4473!=hAPP(hAPP(c_List_Otake(X4474),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4474)),X4473)),X4471)|X4472!=hAPP(hAPP(c_List_Odrop(X4474),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4474)),X4473)),X4471)|X4471=hAPP(hAPP(c_List_Oappend(X4474),X4473),X4472))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__eq__conv__conj])])])). 6.97/7.21 fof(c_0_5238, plain, ![X17078]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17078),c_Int_OMin))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X17078)),c_Int_OMin)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X17078)),c_Int_OMin))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17078),c_Int_OMin)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I13_J])])). 6.97/7.21 cnf(c_0_5239, 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_4602])). 6.97/7.21 cnf(c_0_5240, 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_4582])). 6.97/7.21 fof(c_0_5241, plain, ![X1949]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1949),c_Int_OMin))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1949)),c_Int_OMin)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1949)),c_Int_OMin))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1949),c_Int_OMin)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I30_J])])). 6.97/7.21 cnf(c_0_5242, 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_4603])). 6.97/7.21 cnf(c_0_5243, 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_4604])). 6.97/7.21 cnf(c_0_5244, plain, (c_Groups_Oone__class_Oone(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_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_4581])). 6.97/7.21 fof(c_0_5245, plain, ![X10982]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X10982))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X10982))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X10982)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X10982)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I9_J])])). 6.97/7.21 cnf(c_0_5246, 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_4605])). 6.97/7.21 fof(c_0_5247, plain, ![X9123]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X9123)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X9123)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X9123))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X9123))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I26_J])])). 6.97/7.21 cnf(c_0_5248, 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_4606])). 6.97/7.21 fof(c_0_5249, plain, ![X3057, X3058]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3058),X3057))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X3058)),c_Int_OBit0(X3057))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X3058)),c_Int_OBit0(X3057)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3058),X3057)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I13_J])])). 6.97/7.21 cnf(c_0_5250, 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_4607])). 6.97/7.21 fof(c_0_5251, plain, ![X5423, X5424]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X5424)),c_Int_OBit0(X5423)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5424),X5423)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5424),X5423))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X5424)),c_Int_OBit0(X5423))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I31_J])])). 6.97/7.21 fof(c_0_5252, plain, ![X11738, X11739, X11740, X11741]:((c_Groups_Ozero__class_Ozero(X11741)=X11740|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X11741),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11741),X11740),X11739)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11741),X11740),X11738))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X11741),X11739),X11738)|~class_Divides_Osemiring__div(X11741))&(c_Groups_Ozero__class_Ozero(X11741)!=X11740|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X11741),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11741),X11740),X11739)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11741),X11740),X11738))=c_Groups_Ozero__class_Ozero(X11741)|~class_Divides_Osemiring__div(X11741))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__mult__mult1__if])])])])). 6.97/7.21 cnf(c_0_5253, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(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),X1)))), inference(split_conjunct,[status(thm)],[c_0_4535])). 6.97/7.21 fof(c_0_5254, plain, ![X12421, X12422, X12423, X12424]:((~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X12424),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12424),X12423),X12422)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12424),X12423),X12421)))|(c_Groups_Ozero__class_Ozero(X12424)=X12423|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X12424),X12422),X12421)))|~class_Rings_Oidom(X12424))&((c_Groups_Ozero__class_Ozero(X12424)!=X12423|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X12424),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12424),X12423),X12422)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12424),X12423),X12421)))|~class_Rings_Oidom(X12424))&(~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X12424),X12422),X12421))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X12424),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12424),X12423),X12422)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12424),X12423),X12421)))|~class_Rings_Oidom(X12424)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel__left])])])). 6.97/7.21 fof(c_0_5255, plain, ![X9855, X9856]:(~class_Int_Onumber__ring(X9856)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9856),hAPP(c_Groups_Ouminus__class_Ouminus(X9856),c_Groups_Oone__class_Oone(X9856))),hAPP(c_Int_Onumber__class_Onumber__of(X9856),X9855))=hAPP(c_Int_Onumber__class_Onumber__of(X9856),c_Int_Opred(X9855))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__pred])])). 6.97/7.21 fof(c_0_5256, plain, ![X5556, X5557, X5558, X5559]:((~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5559),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5559),X5558),X5557)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5559),X5556),X5557)))|(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5559),X5558),X5556))|c_Groups_Ozero__class_Ozero(X5559)=X5557)|~class_Rings_Oidom(X5559))&((~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5559),X5558),X5556))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5559),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5559),X5558),X5557)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5559),X5556),X5557)))|~class_Rings_Oidom(X5559))&(c_Groups_Ozero__class_Ozero(X5559)!=X5557|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5559),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5559),X5558),X5557)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5559),X5556),X5557)))|~class_Rings_Oidom(X5559)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dvd__mult__cancel__right])])])])). 6.97/7.21 fof(c_0_5257, plain, ![X10775, X10776, X10777, X10778, X10779, X10782]:(((hAPP(X10776,esk357_5(X10775,X10776,X10777,X10778,X10779))=X10775|X10775!=hAPP(X10776,X10779)|hBOOL(hAPP(hAPP(c_member(X10777),X10775),hAPP(c_Set_Oimage(X10778,X10777,X10776),c_Orderings_Otop__class_Otop(tc_fun(X10778,tc_HOL_Obool)))))|~c_Fun_Oinj__on(X10778,X10777,X10776,c_Orderings_Otop__class_Otop(tc_fun(X10778,tc_HOL_Obool))))&(X10779!=esk357_5(X10775,X10776,X10777,X10778,X10779)|X10775!=hAPP(X10776,X10779)|hBOOL(hAPP(hAPP(c_member(X10777),X10775),hAPP(c_Set_Oimage(X10778,X10777,X10776),c_Orderings_Otop__class_Otop(tc_fun(X10778,tc_HOL_Obool)))))|~c_Fun_Oinj__on(X10778,X10777,X10776,c_Orderings_Otop__class_Otop(tc_fun(X10778,tc_HOL_Obool)))))&((X10775=hAPP(X10776,esk358_4(X10775,X10776,X10777,X10778))|~hBOOL(hAPP(hAPP(c_member(X10777),X10775),hAPP(c_Set_Oimage(X10778,X10777,X10776),c_Orderings_Otop__class_Otop(tc_fun(X10778,tc_HOL_Obool)))))|~c_Fun_Oinj__on(X10778,X10777,X10776,c_Orderings_Otop__class_Otop(tc_fun(X10778,tc_HOL_Obool))))&(hAPP(X10776,X10782)!=X10775|esk358_4(X10775,X10776,X10777,X10778)=X10782|~hBOOL(hAPP(hAPP(c_member(X10777),X10775),hAPP(c_Set_Oimage(X10778,X10777,X10776),c_Orderings_Otop__class_Otop(tc_fun(X10778,tc_HOL_Obool)))))|~c_Fun_Oinj__on(X10778,X10777,X10776,c_Orderings_Otop__class_Otop(tc_fun(X10778,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)],[fact_range__ex1__eq])])])])])). 6.97/7.21 fof(c_0_5258, plain, ![X1712, X1713, X1714, X1715]:hBOOL(hAPP(hAPP(c_member(X1715),hAPP(X1714,X1713)),hAPP(c_Set_Oimage(X1712,X1715,X1714),c_Orderings_Otop__class_Otop(tc_fun(X1712,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[fact_rangeI])). 6.97/7.21 fof(c_0_5259, plain, ![X13633, X13634, X13636, X13637, X13638]:(((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk457_2(X13633,X13634)),hAPP(c_List_Oset(tc_Nat_Onat),X13633)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X13634|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),X13634),X13633))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=esk457_2(X13633,X13634)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X13634|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),X13634),X13633)))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X13637|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),X13637),X13636))&(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X13638),hAPP(c_List_Oset(tc_Nat_Onat),X13636)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X13638|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),X13637),X13636)))), 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_sum__eq__0__conv])])])])])])). 6.97/7.21 fof(c_0_5260, plain, ![X6969, X6970, X6971, X6972]:(hAPP(c_Set_Oimage(X6972,X6971,X6970),c_Orderings_Otop__class_Otop(tc_fun(X6972,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X6971,tc_HOL_Obool))|X6969=hAPP(c_Set_Oimage(X6972,X6971,X6970),hAPP(c_Set_Ovimage(X6972,X6971,X6970),X6969))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__image__vimage__eq])])). 6.97/7.21 fof(c_0_5261, plain, ![X2282, X2283, X2284, X2285]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2285),X2284))|(~c_Fun_Oinj__on(X2283,X2285,X2282,c_Orderings_Otop__class_Otop(tc_fun(X2283,tc_HOL_Obool)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X2283),hAPP(c_Set_Ovimage(X2283,X2285,X2282),X2284))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__vimageI])])])). 6.97/7.21 fof(c_0_5262, plain, ![X6409, X6410, X6411, X6412]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X6412),hAPP(c_Set_Ovimage(X6412,X6411,X6410),X6409)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X6411),X6409))|~c_Fun_Obij__betw(X6412,X6411,X6410,c_Orderings_Otop__class_Otop(tc_fun(X6412,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X6411,tc_HOL_Obool))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6411),X6409))|hBOOL(hAPP(c_Finite__Set_Ofinite(X6412),hAPP(c_Set_Ovimage(X6412,X6411,X6410),X6409)))|~c_Fun_Obij__betw(X6412,X6411,X6410,c_Orderings_Otop__class_Otop(tc_fun(X6412,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X6411,tc_HOL_Obool))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__vimage__iff])])])). 6.97/7.21 fof(c_0_5263, plain, ![X11197, X11198, X11199, X11200]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11200),hAPP(c_Set_Ovimage(X11200,X11199,X11198),X11197)))|(hAPP(c_Set_Oimage(X11200,X11199,X11198),c_Orderings_Otop__class_Otop(tc_fun(X11200,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X11199,tc_HOL_Obool))|hBOOL(hAPP(c_Finite__Set_Ofinite(X11199),X11197)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__vimageD])])). 6.97/7.21 fof(c_0_5264, plain, ![X14306, X14307, X14308, X14309]:((hBOOL(hAPP(hAPP(c_member(X14309),X14308),X14307))|hAPP(c_Set_Ovimage(X14306,X14309,hAPP(c_COMBK(X14309,X14306),X14308)),X14307)=c_Orderings_Obot__class_Obot(tc_fun(X14306,tc_HOL_Obool)))&(~hBOOL(hAPP(hAPP(c_member(X14309),X14308),X14307))|hAPP(c_Set_Ovimage(X14306,X14309,hAPP(c_COMBK(X14309,X14306),X14308)),X14307)=c_Orderings_Otop__class_Otop(tc_fun(X14306,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_vimage__const])])])). 6.97/7.21 fof(c_0_5265, plain, ![X11321, X11322, X11323, X11324]:(~c_Fun_Oinj__on(X11324,X11323,X11322,c_Orderings_Otop__class_Otop(tc_fun(X11324,tc_HOL_Obool)))|X11321=hAPP(c_Set_Ovimage(X11324,X11323,X11322),hAPP(c_Set_Oimage(X11324,X11323,X11322),X11321))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__vimage__image__eq])])). 6.97/7.21 fof(c_0_5266, plain, ![X997, X998, X999, X1000, X1001]:(~hBOOL(hAPP(hAPP(c_member(X1001),hAPP(X1000,X999)),X998))|hBOOL(hAPP(hAPP(c_member(X997),X999),hAPP(c_Set_Ovimage(X997,X1001,X1000),X998)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_vimageI2])])])). 6.97/7.21 fof(c_0_5267, plain, ![X8638, X8639, X8640, X8641, X8642]:((X8638!=hAPP(X8639,X8641)|hBOOL(hAPP(hAPP(c_member(X8642),X8641),hAPP(c_Set_Ovimage(X8642,X8640,X8639),hAPP(hAPP(c_Set_Oinsert(X8640),X8638),c_Orderings_Obot__class_Obot(tc_fun(X8640,tc_HOL_Obool)))))))&(~hBOOL(hAPP(hAPP(c_member(X8642),X8641),hAPP(c_Set_Ovimage(X8642,X8640,X8639),hAPP(hAPP(c_Set_Oinsert(X8640),X8638),c_Orderings_Obot__class_Obot(tc_fun(X8640,tc_HOL_Obool))))))|X8638=hAPP(X8639,X8641))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__singleton__eq])])). 6.97/7.21 fof(c_0_5268, plain, ![X1944, X1945, X1946, X1947, X1948]:(~hBOOL(hAPP(hAPP(c_member(X1948),X1947),hAPP(c_Set_Ovimage(X1948,X1946,X1945),X1944)))|hBOOL(hAPP(hAPP(c_member(X1946),hAPP(X1945,X1947)),X1944))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimageD])])). 6.97/7.21 fof(c_0_5269, plain, ![X16615]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16615))|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,X16615)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16615)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__atLeastZeroLessThan__int])])). 6.97/7.21 fof(c_0_5270, plain, ![X5049, X5050]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X5050))|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),X5050),X5049)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__one__le__power])])). 6.97/7.21 fof(c_0_5271, plain, ![X17243, X17244, X17245, X17246]:(~c_Hoare__Mirabelle_Ohoare__derivs(X17246,X17245,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17246)),X17244),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17246),tc_HOL_Obool))))|(~c_Hoare__Mirabelle_Ohoare__derivs(X17246,X17245,X17243)|c_Hoare__Mirabelle_Ohoare__derivs(X17246,X17245,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17246)),X17244),X17243)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_hoare__derivs_Oinsert])])])). 6.97/7.21 fof(c_0_5272, plain, ![X13606, X13607, X13608, X13609, X13610]:((hAPP(hAPP(c_List_Omap(X13610,X13609),X13608),X13606)!=hAPP(hAPP(c_List_Omap(X13610,X13609),X13608),X13607)|X13606=X13607|~c_Fun_Oinj__on(X13610,X13609,X13608,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13610,tc_HOL_Obool)),hAPP(c_List_Oset(X13610),X13607)),hAPP(c_List_Oset(X13610),X13606))))&(X13606!=X13607|hAPP(hAPP(c_List_Omap(X13610,X13609),X13608),X13606)=hAPP(hAPP(c_List_Omap(X13610,X13609),X13608),X13607)|~c_Fun_Oinj__on(X13610,X13609,X13608,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13610,tc_HOL_Obool)),hAPP(c_List_Oset(X13610),X13607)),hAPP(c_List_Oset(X13610),X13606))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__map__eq__map])])])). 6.97/7.21 fof(c_0_5273, plain, ![X3774, X3775]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X3775,X3775)),X3774))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X3775,X3775)),c_Transitive__Closure_Otrancl(X3775,X3774))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X3775,X3775)),c_Transitive__Closure_Otrancl(X3775,X3774)))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X3775,X3775)),X3774)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__trancl])])). 6.97/7.21 fof(c_0_5274, plain, ![X12248, X12249]:(~c_Wellfounded_Owf(X12249,hAPP(c_Relation_Oconverse(X12249,X12249),X12248))|c_Wellfounded_Owf(X12249,hAPP(c_Relation_Oconverse(X12249,X12249),c_Transitive__Closure_Otrancl(X12249,X12248)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__converse__trancl])])). 6.97/7.21 fof(c_0_5275, plain, ![X1652, X1653]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1653))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1652))|hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1653,X1652))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X1653),hAPP(c_Int_Onat,X1652)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Divides_Otransfer__nat__int__functions_I2_J])])])). 6.97/7.21 fof(c_0_5276, plain, ![X1938, X1939]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1938),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Oring__1__class_Oof__int(X1939),X1938)=hAPP(c_Groups_Ouminus__class_Ouminus(X1939),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1939),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1938))))|~class_Rings_Oring__1(X1939))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1938),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1939),hAPP(c_Int_Onat,X1938))=hAPP(c_Int_Oring__1__class_Oof__int(X1939),X1938)|~class_Rings_Oring__1(X1939))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__of__nat])])])])). 6.97/7.21 fof(c_0_5277, plain, ![X11839, X11840]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11840),X11839))|c_List_Oupto(X11840,X11839)=hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X11840),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11840),c_Groups_Oone__class_Oone(tc_Int_Oint)),X11839)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11840),X11839))|c_List_Oupto(X11840,X11839)=c_List_Olist_ONil(tc_Int_Oint))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_upto_Osimps])])])). 6.97/7.21 fof(c_0_5278, plain, ![X2301, X2302, X2303]:(~class_Orderings_Olinorder(X2303)|c_Big__Operators_Olattice_OInf__fin(X2303,c_Orderings_Oord__class_Omin(X2303),hAPP(c_List_Oset(X2303),hAPP(hAPP(c_List_Olist_OCons(X2303),X2302),X2301)))=hAPP(c_List_Ofoldl(X2303,X2303,c_Orderings_Oord__class_Omin(X2303),X2302),X2301)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin__set__fold])])])). 6.97/7.21 fof(c_0_5279, plain, ![X14533, X14534, X14535]:hAPP(c_List_Oset(X14535),hAPP(hAPP(c_List_Olist_OCons(X14535),X14534),X14533))=hAPP(hAPP(c_Set_Oinsert(X14535),X14534),hAPP(c_List_Oset(X14535),X14533)), inference(variable_rename,[status(thm)],[fact_List_Oset_Osimps_I2_J])). 6.97/7.21 fof(c_0_5280, plain, ![X16289, X16290, X16291]:(~class_Orderings_Olinorder(X16291)|hAPP(c_List_Ofoldl(X16291,X16291,c_Orderings_Oord__class_Omax(X16291),X16290),X16289)=c_Big__Operators_Olattice_OSup__fin(X16291,c_Orderings_Oord__class_Omax(X16291),hAPP(c_List_Oset(X16291),hAPP(hAPP(c_List_Olist_OCons(X16291),X16290),X16289)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin__set__fold])])). 6.97/7.21 fof(c_0_5281, plain, ![X13382, X13383]:((~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X13383),X13382))|hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X13383)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X13382)))|~c_Nat__Transfer_Onat__set(X13382)|~c_Nat__Transfer_Ois__nat(X13383))&(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X13383)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X13382)))|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X13383),X13382))|~c_Nat__Transfer_Onat__set(X13382)|~c_Nat__Transfer_Ois__nat(X13383))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I2_J])])])). 6.97/7.21 fof(c_0_5282, plain, ![X5990, X5991]:(~c_Nat__Transfer_Onat__set(X5991)|(~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X5990),X5991))|c_Nat__Transfer_Ois__nat(X5990))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J])])). 6.97/7.21 cnf(c_0_5283, 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_4608])). 6.97/7.21 cnf(c_0_5284, plain, (c_List_Oremove1(X1,X3,X2)=hAPP(c_List_OremoveAll(X1,X3),X2)|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4609])). 6.97/7.21 fof(c_0_5285, plain, ![X14431, X14432]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14432))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X14432)),hAPP(c_Int_Onat,X14431))=hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14432),X14431))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__div__distrib])])])). 6.97/7.21 fof(c_0_5286, plain, ![X10951, X10952]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10952))|hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X10952),X10951))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X10952)),hAPP(c_Int_Onat,X10951))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__mult__distrib])])])). 6.97/7.21 fof(c_0_5287, plain, ![X11475, X11476]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11476))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11475))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X11476)),hAPP(c_Int_Onat,X11475))=hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(X11476,X11475)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J])])). 6.97/7.21 fof(c_0_5288, plain, ![X14257, X14258, X14259, X14260, X14261, X14262, X14263]:((c_Orderings_Obot__class_Obot(tc_fun(X14259,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14259,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X14259,tc_HOL_Obool),X14258)),X14257)|(~hBOOL(hAPP(hAPP(c_member(tc_fun(X14259,tc_HOL_Obool)),X14260),X14258))|c_Orderings_Obot__class_Obot(tc_fun(X14259,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14259,tc_HOL_Obool)),X14260),X14257)))&((hBOOL(hAPP(hAPP(c_member(tc_fun(X14263,tc_HOL_Obool)),esk485_3(X14261,X14262,X14263)),X14262))|c_Orderings_Obot__class_Obot(tc_fun(X14263,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14263,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X14263,tc_HOL_Obool),X14262)),X14261))&(c_Orderings_Obot__class_Obot(tc_fun(X14263,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14263,tc_HOL_Obool)),esk485_3(X14261,X14262,X14263)),X14261)|c_Orderings_Obot__class_Obot(tc_fun(X14263,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14263,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X14263,tc_HOL_Obool),X14262)),X14261)))), 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__disjoint])])])])])])])). 6.97/7.21 fof(c_0_5289, plain, ![X895, X896, X897]:((hAPP(c_Int_Onumber__class_Onumber__of(X897),X895)!=hAPP(c_Int_Onumber__class_Onumber__of(X897),X896)|c_Int_Oiszero(X897,hAPP(c_Int_Onumber__class_Onumber__of(X897),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X896),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X895))))|~class_Int_Onumber__ring(X897))&(~c_Int_Oiszero(X897,hAPP(c_Int_Onumber__class_Onumber__of(X897),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X896),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X895))))|hAPP(c_Int_Onumber__class_Onumber__of(X897),X895)=hAPP(c_Int_Onumber__class_Onumber__of(X897),X896)|~class_Int_Onumber__ring(X897))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of__eq])])])). 6.97/7.21 fof(c_0_5290, plain, ![X9893, X9894]:(~c_Nat__Transfer_Ois__nat(X9894)|(~c_Nat__Transfer_Ois__nat(X9893)|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,X9894),hAPP(c_Int_Onat,X9893)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X9894,X9893))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__int__nat__set__functions])])). 6.97/7.21 fof(c_0_5291, plain, ![X4704, X4705, X4706, X4707, X4708, X4709, X4710]:(((~hBOOL(hAPP(hAPP(c_member(tc_prod(X4704,X4704)),X4707),hAPP(c_List_Oset(tc_prod(X4704,X4704)),hAPP(hAPP(c_List_Ozip(X4704,X4704),X4706),X4705))))|hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4704,X4704,tc_HOL_Obool),c_fequal),X4707))|X4706!=X4705)&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4704)),X4705)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4704)),X4706)|X4706!=X4705))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X4708,X4708)),esk157_3(X4708,X4709,X4710)),hAPP(c_List_Oset(tc_prod(X4708,X4708)),hAPP(hAPP(c_List_Ozip(X4708,X4708),X4710),X4709))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4708)),X4709)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4708)),X4710)|X4710=X4709)&(~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4708,X4708,tc_HOL_Obool),c_fequal),esk157_3(X4708,X4709,X4710)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4708)),X4709)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4708)),X4710)|X4710=X4709))), 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])])])])])])). 6.97/7.21 fof(c_0_5292, plain, ![X8421, X8422]:((~c_Predicate_Oreflp(X8422,X8421)|c_Relation_Orefl__on(X8422,c_Orderings_Otop__class_Otop(tc_fun(X8422,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X8422,X8422)),hAPP(c_Product__Type_Oprod_Oprod__case(X8422,X8422,tc_HOL_Obool),X8421))))&(~c_Relation_Orefl__on(X8422,c_Orderings_Otop__class_Otop(tc_fun(X8422,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X8422,X8422)),hAPP(c_Product__Type_Oprod_Oprod__case(X8422,X8422,tc_HOL_Obool),X8421)))|c_Predicate_Oreflp(X8422,X8421))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reflp__def])])). 6.97/7.21 fof(c_0_5293, plain, ![X2470, X2471, X2472]:((~hBOOL(hAPP(c_List_Odistinct(X2472),X2470))|hBOOL(hAPP(c_List_Odistinct(X2472),hAPP(c_List_Orotate(X2472,X2471),X2470))))&(~hBOOL(hAPP(c_List_Odistinct(X2472),hAPP(c_List_Orotate(X2472,X2471),X2470)))|hBOOL(hAPP(c_List_Odistinct(X2472),X2470)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__rotate])])). 6.97/7.21 fof(c_0_5294, plain, ![X6373, X6374]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6374),X6373))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X6374)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X6373))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6374),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),X6374)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X6373)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X6374)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X6373)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6374),X6373))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6374),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])])])])). 6.97/7.21 fof(c_0_5295, plain, ![X17399, X17400, X17401, X17402, X17403, X17404]:(~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X17404)|(X17403=c_Groups_Ozero__class_Ozero(X17404)|(X17400=X17399|X17401!=X17402|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17404),X17402),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17404),X17403),X17400))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17404),X17401),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17404),X17403),X17399))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__scale__eq__noteq])])])). 6.97/7.21 fof(c_0_5296, plain, ![X13708, X13709, X13710]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13710)),X13709)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))|X13709=hAPP(c_List_Orotate(X13710,X13708),X13709)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rotate__length01])])])). 6.97/7.21 cnf(c_0_5297, 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_4580])). 6.97/7.21 cnf(c_0_5298, 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_4579])). 6.97/7.21 fof(c_0_5299, plain, ![X13739, X13740]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13740),X13739))|hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X13740),hAPP(c_Nat_OSuc,X13739))=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),X13740),X13739))|hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X13740),hAPP(c_Nat_OSuc,X13739))=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X13739),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X13740),X13739)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastLessThanSuc])])])). 6.97/7.21 fof(c_0_5300, plain, ![X8027, X8028]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X8028)),hAPP(c_Int_Onat,X8027)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8028),X8027))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8028)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8028),X8027))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X8028)),hAPP(c_Int_Onat,X8027)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8028)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__eq__zless])])])). 6.97/7.21 fof(c_0_5301, plain, ![X7468, X7469]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7469))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7469),X7468)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X7469),X7468))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__pos__neg__trivial])])])). 6.97/7.21 fof(c_0_5302, plain, ![X11276, X11277]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11276))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X11277)),hAPP(c_Int_Onat,X11276))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11277),X11276))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X11277)),hAPP(c_Int_Onat,X11276)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11276))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11277),X11276))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X11277)),hAPP(c_Int_Onat,X11276))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__nat__conj])])])). 6.97/7.21 fof(c_0_5303, plain, ![X2411, X2412, X2413, X2416, X2417, X2418, X2419, X2420]:(((((hAPP(hAPP(c_Set_Oinsert(X2413),esk80_3(X2411,X2412,X2413)),esk81_3(X2411,X2412,X2413))=X2412|hAPP(c_Finite__Set_Ocard(X2413),X2412)!=hAPP(c_Nat_OSuc,X2411))&(~hBOOL(hAPP(hAPP(c_member(X2413),esk80_3(X2411,X2412,X2413)),esk81_3(X2411,X2412,X2413)))|hAPP(c_Finite__Set_Ocard(X2413),X2412)!=hAPP(c_Nat_OSuc,X2411)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X2411|c_Orderings_Obot__class_Obot(tc_fun(X2413,tc_HOL_Obool))=esk81_3(X2411,X2412,X2413)|hAPP(c_Finite__Set_Ocard(X2413),X2412)!=hAPP(c_Nat_OSuc,X2411)))&(hAPP(c_Finite__Set_Ocard(X2413),esk81_3(X2411,X2412,X2413))=X2411|hAPP(c_Finite__Set_Ocard(X2413),X2412)!=hAPP(c_Nat_OSuc,X2411)))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2416|(hAPP(hAPP(c_Set_Oinsert(X2418),X2419),X2420)!=X2417|hBOOL(hAPP(hAPP(c_member(X2418),X2419),X2420)))|hAPP(c_Finite__Set_Ocard(X2418),X2420)!=X2416|hAPP(c_Finite__Set_Ocard(X2418),X2417)=hAPP(c_Nat_OSuc,X2416))&(c_Orderings_Obot__class_Obot(tc_fun(X2418,tc_HOL_Obool))!=X2420|(hAPP(hAPP(c_Set_Oinsert(X2418),X2419),X2420)!=X2417|hBOOL(hAPP(hAPP(c_member(X2418),X2419),X2420)))|hAPP(c_Finite__Set_Ocard(X2418),X2420)!=X2416|hAPP(c_Finite__Set_Ocard(X2418),X2417)=hAPP(c_Nat_OSuc,X2416)))), 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])])])])])])])). 6.97/7.21 fof(c_0_5304, plain, ![X4931, X4932]:((c_Groups_Ozero__class_Ozero(X4932)!=hAPP(c_Int_Onumber__class_Onumber__of(X4932),X4931)|c_Int_Oiszero(X4932,hAPP(c_Int_Onumber__class_Onumber__of(X4932),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4931))))|~class_Int_Onumber__ring(X4932))&(~c_Int_Oiszero(X4932,hAPP(c_Int_Onumber__class_Onumber__of(X4932),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4931))))|c_Groups_Ozero__class_Ozero(X4932)=hAPP(c_Int_Onumber__class_Onumber__of(X4932),X4931)|~class_Int_Onumber__ring(X4932))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I1_J])])])). 6.97/7.21 fof(c_0_5305, plain, ![X6478, X6479]:((c_Groups_Ozero__class_Ozero(X6479)!=hAPP(c_Int_Onumber__class_Onumber__of(X6479),X6478)|c_Int_Oiszero(X6479,hAPP(c_Int_Onumber__class_Onumber__of(X6479),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6478),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))|~class_Int_Onumber__ring(X6479))&(~c_Int_Oiszero(X6479,hAPP(c_Int_Onumber__class_Onumber__of(X6479),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6478),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))|c_Groups_Ozero__class_Ozero(X6479)=hAPP(c_Int_Onumber__class_Onumber__of(X6479),X6478)|~class_Int_Onumber__ring(X6479))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__special_I3_J])])])])). 6.97/7.21 cnf(c_0_5306, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)=c_Int_OPls), inference(split_conjunct,[status(thm)],[fact_minus__Pls])). 6.97/7.21 cnf(c_0_5307, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OPls)=X1), inference(split_conjunct,[status(thm)],[c_0_4610])). 6.97/7.21 fof(c_0_5308, plain, ![X3805, X3806, X3807]:(~class_Lattices_Olattice(X3807)|c_Big__Operators_Olattice__class_OSup__fin(X3807,hAPP(c_List_Oset(X3807),hAPP(hAPP(c_List_Olist_OCons(X3807),X3806),X3805)))=hAPP(c_List_Ofoldl(X3807,X3807,c_Lattices_Osemilattice__sup__class_Osup(X3807),X3806),X3805)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin__set__fold])])). 6.97/7.21 fof(c_0_5309, plain, ![X5773, X5774, X5775]:(~class_Lattices_Olattice(X5775)|c_Big__Operators_Olattice__class_OInf__fin(X5775,hAPP(c_List_Oset(X5775),hAPP(hAPP(c_List_Olist_OCons(X5775),X5774),X5773)))=hAPP(c_List_Ofoldl(X5775,X5775,c_Lattices_Osemilattice__inf__class_Oinf(X5775),X5774),X5773)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin__set__fold])])). 6.97/7.21 fof(c_0_5310, plain, ![X6242, X6243, X6244]:(~class_Orderings_Olinorder(X6244)|hAPP(c_List_Ofoldl(X6244,X6244,c_Orderings_Oord__class_Omax(X6244),X6243),X6242)=c_Big__Operators_Olinorder__class_OMax(X6244,hAPP(c_List_Oset(X6244),hAPP(hAPP(c_List_Olist_OCons(X6244),X6243),X6242)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__fin__set__fold])])). 6.97/7.21 fof(c_0_5311, plain, ![X2023, X2024, X2025]:(~class_Orderings_Olinorder(X2025)|hAPP(c_List_Ofoldl(X2025,X2025,c_Orderings_Oord__class_Omin(X2025),X2024),X2023)=c_Big__Operators_Olinorder__class_OMin(X2025,hAPP(c_List_Oset(X2025),hAPP(hAPP(c_List_Olist_OCons(X2025),X2024),X2023)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min__fin__set__fold])])])). 6.97/7.21 fof(c_0_5312, plain, ![X7404, X7405, X7407]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk238_2(X7404,X7405)),X7404))|~hBOOL(hAPP(X7405,X7404))|hBOOL(hAPP(X7405,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))&(hBOOL(hAPP(X7405,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk238_2(X7404,X7405)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|~hBOOL(hAPP(X7405,X7404))|hBOOL(hAPP(X7405,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7407),esk238_2(X7404,X7405)))|~hBOOL(hAPP(X7405,X7407))|~hBOOL(hAPP(X7405,X7404))|hBOOL(hAPP(X7405,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])])])])])])). 6.97/7.21 fof(c_0_5313, plain, ![X2680, X2681]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X2681)),X2680))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2681),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2680)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2681)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2681),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2680)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X2681)),X2680))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2681)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__less__iff])])])])). 6.97/7.21 fof(c_0_5314, plain, ![X15857, X15858]:((~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),X15857)))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15858),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15857))=hAPP(c_Int_Onumber__class_Onumber__of(X15858),X15857)|~class_Int_Onumber__ring(X15858))&(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),X15857)))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15858),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15857))=c_Groups_Ozero__class_Ozero(X15858)|~class_Int_Onumber__ring(X15858))), 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])])])])). 6.97/7.21 fof(c_0_5315, plain, ![X4721, X4722, X4723, X4724]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4723)),X4724)),c_Groups_Oone__class_Oone(tc_Nat_Onat))!=X4722|X4721=c_List_Olast(X4723,hAPP(hAPP(c_List_Olist__update(X4723,X4724),X4722),X4721))|c_List_Olist_ONil(X4723)=X4724)&(X4722=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4723)),X4724)),c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_List_Olast(X4723,X4724)=c_List_Olast(X4723,hAPP(hAPP(c_List_Olist__update(X4723,X4724),X4722),X4721))|c_List_Olist_ONil(X4723)=X4724)), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_last__list__update])])])])). 6.97/7.21 fof(c_0_5316, plain, ![X3939, X3940, X3941]:(~class_Orderings_Olinorder(X3941)|c_List_Olinorder__class_Osorted(X3941,hAPP(c_List_Ofilter(X3941,hAPP(hAPP(c_COMBC(X3941,X3941,tc_HOL_Obool),c_fequal),hAPP(X3940,X3939))),X3939))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__same])])])). 6.97/7.21 fof(c_0_5317, plain, ![X17523, X17524]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17524))|hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X17524),X17523))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X17524)),X17523)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J])])])). 6.97/7.21 fof(c_0_5318, plain, ![X10064, X10065, X10066]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X10066,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10065)),X10064))|hAPP(c_List_Orotate(X10065,X10066),X10064)=X10064), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate__id])])). 6.97/7.21 fof(c_0_5319, plain, ![X6897, X6898]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6898),X6897))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6897),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_List_Olast(tc_Nat_Onat,c_List_Oupt(X6898,X6897))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__upt])])). 6.97/7.21 fof(c_0_5320, plain, ![X13159, X13160, X13161]:((~c_List_Olist__ex(tc_Nat_Onat,X13161,c_List_Oupt(X13160,X13159))|~c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),X13161),X13160,X13159))&(c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),X13161),X13160,X13159)|c_List_Olist__ex(tc_Nat_Onat,X13161,c_List_Oupt(X13160,X13159)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__ex__iff__not__all__inverval__nat])])])). 6.97/7.21 fof(c_0_5321, plain, ![X2576, X2577]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2576),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2577),hAPP(c_Int_Onumber__class_Onumber__of(X2577),X2576)),c_Groups_Ozero__class_Ozero(X2577)))|(~class_Int_Onumber__ring(X2577)|~class_Rings_Olinordered__idom(X2577)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2577),hAPP(c_Int_Onumber__class_Onumber__of(X2577),X2576)),c_Groups_Ozero__class_Ozero(X2577)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2576),c_Int_OPls))|(~class_Int_Onumber__ring(X2577)|~class_Rings_Olinordered__idom(X2577)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__special_I3_J])])])])). 6.97/7.21 fof(c_0_5322, plain, ![X10531, X10532]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10532),hAPP(c_Int_Onumber__class_Onumber__of(X10532),X10531)),c_Groups_Ozero__class_Ozero(X10532)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10531),c_Int_OPls))|(~class_Rings_Olinordered__idom(X10532)|~class_Int_Onumber__ring(X10532)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10531),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10532),hAPP(c_Int_Onumber__class_Onumber__of(X10532),X10531)),c_Groups_Ozero__class_Ozero(X10532)))|(~class_Rings_Olinordered__idom(X10532)|~class_Int_Onumber__ring(X10532)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I3_J])])])). 6.97/7.21 fof(c_0_5323, plain, ![X4400, X4401]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4401),c_Groups_Ozero__class_Ozero(X4401)),hAPP(c_Int_Onumber__class_Onumber__of(X4401),X4400)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X4400))|(~class_Int_Onumber__ring(X4401)|~class_Rings_Olinordered__idom(X4401)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X4400))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4401),c_Groups_Ozero__class_Ozero(X4401)),hAPP(c_Int_Onumber__class_Onumber__of(X4401),X4400)))|(~class_Int_Onumber__ring(X4401)|~class_Rings_Olinordered__idom(X4401)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__special_I1_J])])])])). 6.97/7.21 fof(c_0_5324, plain, ![X16625, X16626]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16626),c_Groups_Ozero__class_Ozero(X16626)),hAPP(c_Int_Onumber__class_Onumber__of(X16626),X16625)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X16625))|(~class_Rings_Olinordered__idom(X16626)|~class_Int_Onumber__ring(X16626)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X16625))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16626),c_Groups_Ozero__class_Ozero(X16626)),hAPP(c_Int_Onumber__class_Onumber__of(X16626),X16625)))|(~class_Rings_Olinordered__idom(X16626)|~class_Int_Onumber__ring(X16626)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I1_J])])])). 6.97/7.21 fof(c_0_5325, plain, ![X5748, X5749]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5749),c_Groups_Oone__class_Oone(tc_Int_Oint))),X5748))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5749),X5748)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5749),X5748))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5749),c_Groups_Oone__class_Oone(tc_Int_Oint))),X5748)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add1__zle__eq])])). 6.97/7.21 cnf(c_0_5326, 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_4611])). 6.97/7.21 fof(c_0_5327, plain, ![X9447, X9448, X9449]:(((c_Groups_Ozero__class_Ozero(X9449)=X9447|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9449),c_Groups_Ozero__class_Ozero(X9449)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9449),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9449),X9448),X9448)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9449),X9447),X9447))))|~class_Rings_Olinordered__ring__strict(X9449))&(X9448=c_Groups_Ozero__class_Ozero(X9449)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9449),c_Groups_Ozero__class_Ozero(X9449)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9449),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9449),X9448),X9448)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9449),X9447),X9447))))|~class_Rings_Olinordered__ring__strict(X9449)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9449),c_Groups_Ozero__class_Ozero(X9449)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9449),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9449),X9448),X9448)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9449),X9447),X9447))))|(c_Groups_Ozero__class_Ozero(X9449)!=X9447|X9448!=c_Groups_Ozero__class_Ozero(X9449))|~class_Rings_Olinordered__ring__strict(X9449))), 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])])])])). 6.97/7.21 fof(c_0_5328, plain, ![X375, X376]:(((X375!=X376|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X376),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X375),c_Groups_Oone__class_Oone(tc_Int_Oint)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X376),X375))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X376),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X375),c_Groups_Oone__class_Oone(tc_Int_Oint))))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X376),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X375),c_Groups_Oone__class_Oone(tc_Int_Oint))))|(X375=X376|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X376),X375))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__add1__eq])])])). 6.97/7.21 fof(c_0_5329, plain, ![X7915, X7916]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7916),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7915),c_Groups_Oone__class_Oone(tc_Int_Oint))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7916),X7915)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7916),X7915))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7916),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7915),c_Groups_Oone__class_Oone(tc_Int_Oint)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__add1__eq__le])])). 6.97/7.21 fof(c_0_5330, plain, ![X4277, X4278]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4278),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4277),c_Groups_Oone__class_Oone(tc_Int_Oint))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4278),X4277)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4278),X4277))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4278),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4277),c_Groups_Oone__class_Oone(tc_Int_Oint)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__diff1__eq])])). 6.97/7.21 fof(c_0_5331, plain, ![X14391, X14392, X14393, X14394]:((((X14391!=c_List_Olist_ONil(X14394)|hAPP(hAPP(c_List_Oappend(X14394),X14393),hAPP(hAPP(c_List_Olist_OCons(X14394),X14392),c_List_Olist_ONil(X14394)))!=X14391)&(c_List_Olast(X14394,X14391)=X14392|hAPP(hAPP(c_List_Oappend(X14394),X14393),hAPP(hAPP(c_List_Olist_OCons(X14394),X14392),c_List_Olist_ONil(X14394)))!=X14391))&(c_List_Obutlast(X14394,X14391)=X14393|hAPP(hAPP(c_List_Oappend(X14394),X14393),hAPP(hAPP(c_List_Olist_OCons(X14394),X14392),c_List_Olist_ONil(X14394)))!=X14391))&(X14391=c_List_Olist_ONil(X14394)|c_List_Olast(X14394,X14391)!=X14392|c_List_Obutlast(X14394,X14391)!=X14393|hAPP(hAPP(c_List_Oappend(X14394),X14393),hAPP(hAPP(c_List_Olist_OCons(X14394),X14392),c_List_Olist_ONil(X14394)))=X14391)), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snoc__eq__iff__butlast])])])). 6.97/7.21 fof(c_0_5332, plain, ![X10699, X10700]:(~class_Int_Onumber__ring(X10700)|hAPP(c_Int_Onumber__class_Onumber__of(X10700),c_Int_Osucc(X10699))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10700),c_Groups_Oone__class_Oone(X10700)),hAPP(c_Int_Onumber__class_Onumber__of(X10700),X10699))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__succ])])). 6.97/7.21 cnf(c_0_5333, 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_4602])). 6.97/7.21 cnf(c_0_5334, 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_4603])). 6.97/7.21 cnf(c_0_5335, 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_4604])). 6.97/7.21 fof(c_0_5336, plain, ![X1645, X1646, X1647, X1648, X1649, X1650, X1651]:(~c_Fun_Obij__betw(X1651,X1650,X1649,X1648,X1647)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1651,tc_HOL_Obool)),X1646),X1648))|(hAPP(c_Set_Oimage(X1651,X1650,X1649),X1646)!=X1645|c_Fun_Obij__betw(X1651,X1650,X1649,X1646,X1645)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bij__betw__subset])])])). 6.97/7.21 cnf(c_0_5337, 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_4605])). 6.97/7.21 cnf(c_0_5338, 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_4606])). 6.97/7.21 fof(c_0_5339, plain, ![X3588, X3589, X3591, X3592, X3593]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3588),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X3588=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk116_2(X3588,X3589))|hBOOL(hAPP(X3589,hAPP(c_Int_Onat,X3588))))&(~hBOOL(hAPP(X3589,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|X3588=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk116_2(X3588,X3589))|hBOOL(hAPP(X3589,hAPP(c_Int_Onat,X3588)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3588),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X3589,esk116_2(X3588,X3589)))|hBOOL(hAPP(X3589,hAPP(c_Int_Onat,X3588))))&(~hBOOL(hAPP(X3589,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X3589,esk116_2(X3588,X3589)))|hBOOL(hAPP(X3589,hAPP(c_Int_Onat,X3588))))))&((X3591!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3593)|hBOOL(hAPP(X3592,X3593))|~hBOOL(hAPP(X3592,hAPP(c_Int_Onat,X3591))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3591),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X3592,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X3592,hAPP(c_Int_Onat,X3591)))))), 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__nat])])])])])])])). 6.97/7.21 fof(c_0_5340, plain, ![X7648, X7649, X7650, X7651]:((X7649=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X7650!=X7648|hBOOL(hAPP(hAPP(c_member(X7651),X7650),hAPP(c_List_Oset(X7651),c_List_Oreplicate(X7651,X7649,X7648)))))&((X7649!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X7651),X7650),hAPP(c_List_Oset(X7651),c_List_Oreplicate(X7651,X7649,X7648)))))&(X7650=X7648|~hBOOL(hAPP(hAPP(c_member(X7651),X7650),hAPP(c_List_Oset(X7651),c_List_Oreplicate(X7651,X7649,X7648))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__replicate])])])). 6.97/7.21 fof(c_0_5341, plain, ![X7644]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7644))|hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,X7644))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X7644))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__nat__eq__nat__zadd1])])). 6.97/7.21 fof(c_0_5342, plain, ![X9950, X9951]:((((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X9951|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))=c_Nitpick_Onorm__frac(X9950,X9951)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9951),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X9950|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))=c_Nitpick_Onorm__frac(X9950,X9951)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9951),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X9951|X9950=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Nitpick_Onorm__frac(X9950,X9951)=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X9950),X9951)),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),X9950))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X9951)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9951),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9951),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X9950),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X9951))=c_Nitpick_Onorm__frac(X9950,X9951))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_norm__frac_Osimps])])])])). 6.97/7.21 fof(c_0_5343, plain, ![X9527]:((~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,X9527)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X9527)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X9527))|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,X9527))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__nat__eq])])). 6.97/7.21 fof(c_0_5344, plain, ![X10127, X10128]:((~c_Int_Oiszero(X10128,hAPP(c_Int_Onumber__class_Onumber__of(X10128),X10127))|c_Int_Oiszero(X10128,hAPP(c_Int_Onumber__class_Onumber__of(X10128),c_Int_OBit0(X10127)))|(~class_Int_Oring__char__0(X10128)|~class_Int_Onumber__ring(X10128)))&(~c_Int_Oiszero(X10128,hAPP(c_Int_Onumber__class_Onumber__of(X10128),c_Int_OBit0(X10127)))|c_Int_Oiszero(X10128,hAPP(c_Int_Onumber__class_Onumber__of(X10128),X10127))|(~class_Int_Oring__char__0(X10128)|~class_Int_Onumber__ring(X10128)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_iszero__number__of__Bit0])])])])). 6.97/7.21 fof(c_0_5345, plain, ![X1083]:(~c_List_Onat__list(X1083)|c_List_Oembed__list(c_List_Oreturn__list(X1083))=X1083), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transfer__nat__int__list__return__embed])])])). 6.97/7.21 cnf(c_0_5346, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X1))), inference(split_conjunct,[status(thm)],[c_0_4612])). 6.97/7.21 fof(c_0_5347, plain, ![X5970, X5971]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X5971)),hAPP(c_Int_Onat,X5970)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5971),X5970))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5970)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5971),X5970))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X5971)),hAPP(c_Int_Onat,X5970)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5970))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X5971)),hAPP(c_Int_Onat,X5970)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5971),X5970))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5971)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5971),X5970))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X5971)),hAPP(c_Int_Onat,X5970)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5971))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__le__eq__zle])])])])). 6.97/7.21 fof(c_0_5348, plain, ![X17490]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17490))|c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X17490)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X17490),c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__minus1])])). 6.97/7.21 fof(c_0_5349, plain, ![X14447]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14447))|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)),X14447)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__eq__minus1])])). 6.97/7.21 fof(c_0_5350, plain, ![X2544]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2544),c_Int_OMin))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X2544)),c_Int_OMin)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X2544)),c_Int_OMin))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2544),c_Int_OMin)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I11_J])])). 6.97/7.21 cnf(c_0_5351, 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_4613])). 6.97/7.21 fof(c_0_5352, plain, ![X11570]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X11570)),c_Int_OMin))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11570),c_Int_OMin)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11570),c_Int_OMin))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X11570)),c_Int_OMin)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I28_J])])). 6.97/7.21 cnf(c_0_5353, 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_4614])). 6.97/7.21 cnf(c_0_5354, 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_4615])). 6.97/7.21 fof(c_0_5355, plain, ![X14246, X14247]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X14247),X14246))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X14247)),X14246)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X14247)),X14246))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X14247),X14246)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__pred__less])])). 6.97/7.21 fof(c_0_5356, plain, ![X13604, X13605]:((c_Int_OBit1(X13604)!=c_Int_OBit1(X13605)|X13604=X13605)&(X13604!=X13605|c_Int_OBit1(X13604)=c_Int_OBit1(X13605))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I51_J])])). 6.97/7.21 fof(c_0_5357, plain, ![X11286]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X11286)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X11286)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X11286))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X11286))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I8_J])])). 6.97/7.21 cnf(c_0_5358, 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_4616])). 6.97/7.21 fof(c_0_5359, plain, ![X1046]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X1046)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1046)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1046))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X1046))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I25_J])])). 6.97/7.21 cnf(c_0_5360, 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_4617])). 6.97/7.21 fof(c_0_5361, plain, ![X15719, X15720]:(~class_Int_Onumber__ring(X15720)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X15719))|hBOOL(hAPP(hAPP(c_member(X15720),hAPP(c_Int_Onumber__class_Onumber__of(X15720),X15719)),c_Nat_Osemiring__1__class_ONats(X15720))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nats__number__of])])])). 6.97/7.21 fof(c_0_5362, plain, ![X16572]:(~class_Orderings_Owellorder(X16572)|c_Wellfounded_Owf(X16572,hAPP(c_Set_OCollect(tc_prod(X16572,X16572)),hAPP(c_Product__Type_Oprod_Oprod__case(X16572,X16572,tc_HOL_Obool),c_Orderings_Oord__class_Oless(X16572))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf])])])). 6.97/7.21 fof(c_0_5363, plain, ![X4010, X4011, X4012, X4015, X4016, X4017, X4018, X4019]:(((hBOOL(hAPP(hAPP(c_member(X4012),esk137_3(X4010,X4011,X4012)),X4011))|c_Orderings_Obot__class_Obot(tc_fun(X4012,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4012,tc_HOL_Obool)),X4011),X4010))&((hBOOL(hAPP(hAPP(c_member(X4012),esk138_3(X4010,X4011,X4012)),X4010))|c_Orderings_Obot__class_Obot(tc_fun(X4012,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4012,tc_HOL_Obool)),X4011),X4010))&(esk137_3(X4010,X4011,X4012)=esk138_3(X4010,X4011,X4012)|c_Orderings_Obot__class_Obot(tc_fun(X4012,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4012,tc_HOL_Obool)),X4011),X4010))))&(c_Orderings_Obot__class_Obot(tc_fun(X4017,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4017,tc_HOL_Obool)),X4016),X4015)|(~hBOOL(hAPP(hAPP(c_member(X4017),X4018),X4016))|(~hBOOL(hAPP(hAPP(c_member(X4017),X4019),X4015))|X4018!=X4019)))), 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])])])])])])])). 6.97/7.21 cnf(c_0_5364, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|c_List_Olist_ONil(tc_Nat_Onat)=c_List_Oupt(X1,hAPP(c_Nat_OSuc,X2))), inference(split_conjunct,[status(thm)],[c_0_4618])). 6.97/7.21 fof(c_0_5365, plain, ![X7045, X7046]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X7045)))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7046),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7045))=c_Groups_Ozero__class_Ozero(X7046)|~class_Int_Onumber__ring(X7046))&(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X7045)))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7046),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7045))=hAPP(c_Int_Onumber__class_Onumber__of(X7046),X7045)|~class_Int_Onumber__ring(X7046))), 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])])])])). 6.97/7.21 fof(c_0_5366, plain, ![X14911, X14912]:((hBOOL(hAPP(hAPP(c_member(X14912),esk504_2(X14911,X14912)),X14911))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(X14912),X14911)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14912),X14911)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(X14912),X14911)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14912),X14911)))), 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])])])])])). 6.97/7.21 fof(c_0_5367, plain, ![X2524, X2525]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X2525),X2524))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X2525,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X2525),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2524)=hAPP(c_Finite__Set_Ocard(X2525),X2524))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X2525),X2524))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(X2525),X2524))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__def])])])). 6.97/7.21 fof(c_0_5368, plain, ![X9692, X9693, X9694]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9692),X9694)!=X9693|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X9693),X9694)=X9692|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X9694),X9693)))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X9693),X9694)!=X9692|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9692),X9694)=X9693|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X9694),X9693)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__diff__is__add])])])). 6.97/7.21 fof(c_0_5369, plain, ![X5391, X5392]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5392),X5391),X5391)!=c_Groups_Ozero__class_Ozero(X5392)|c_Groups_Ozero__class_Ozero(X5392)=X5391|~hBOOL(hAPP(hAPP(c_member(X5392),X5391),c_Int_Oring__1__class_OInts(X5392)))|~class_Int_Oring__char__0(X5392))&(c_Groups_Ozero__class_Ozero(X5392)!=X5391|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5392),X5391),X5391)=c_Groups_Ozero__class_Ozero(X5392)|~hBOOL(hAPP(hAPP(c_member(X5392),X5391),c_Int_Oring__1__class_OInts(X5392)))|~class_Int_Oring__char__0(X5392))), 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])])])])). 6.97/7.21 cnf(c_0_5370, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(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_4619])). 6.97/7.21 fof(c_0_5371, plain, ![X12935, X12936]:(~c_Wellfounded_OwfP(X12936,X12935)|c_Wellfounded_Oacyclic(X12936,hAPP(c_Set_OCollect(tc_prod(X12936,X12936)),hAPP(c_Product__Type_Oprod_Oprod__case(X12936,X12936,tc_HOL_Obool),X12935)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wfP__acyclicP])])])). 6.97/7.21 fof(c_0_5372, plain, ![X16654, X16655]:((~c_Relation_Otrans(X16655,hAPP(c_Set_OCollect(tc_prod(X16655,X16655)),hAPP(c_Product__Type_Oprod_Oprod__case(X16655,X16655,tc_HOL_Obool),X16654)))|c_Predicate_Otransp(X16655,X16654))&(~c_Predicate_Otransp(X16655,X16654)|c_Relation_Otrans(X16655,hAPP(c_Set_OCollect(tc_prod(X16655,X16655)),hAPP(c_Product__Type_Oprod_Oprod__case(X16655,X16655,tc_HOL_Obool),X16654))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transp__def])])). 6.97/7.21 fof(c_0_5373, plain, ![X2449, X2450]:((~c_Relation_Osym(X2450,hAPP(c_Set_OCollect(tc_prod(X2450,X2450)),hAPP(c_Product__Type_Oprod_Oprod__case(X2450,X2450,tc_HOL_Obool),X2449)))|c_Predicate_Osymp(X2450,X2449))&(~c_Predicate_Osymp(X2450,X2449)|c_Relation_Osym(X2450,hAPP(c_Set_OCollect(tc_prod(X2450,X2450)),hAPP(c_Product__Type_Oprod_Oprod__case(X2450,X2450,tc_HOL_Obool),X2449))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_symp__def])])). 6.97/7.21 fof(c_0_5374, plain, ![X5306, X5307]:((~c_Wellfounded_OwfP(X5307,X5306)|c_Wellfounded_Owf(X5307,hAPP(c_Set_OCollect(tc_prod(X5307,X5307)),hAPP(c_Product__Type_Oprod_Oprod__case(X5307,X5307,tc_HOL_Obool),X5306))))&(~c_Wellfounded_Owf(X5307,hAPP(c_Set_OCollect(tc_prod(X5307,X5307)),hAPP(c_Product__Type_Oprod_Oprod__case(X5307,X5307,tc_HOL_Obool),X5306)))|c_Wellfounded_OwfP(X5307,X5306))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__def])])). 6.97/7.21 fof(c_0_5375, plain, ![X5231, X5232, X5233, X5234]:((((c_Groups_Ozero__class_Ozero(X5234)!=X5232|X5232=c_Groups_Ozero__class_Ozero(X5234)|X5231=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5234),X5233),X5232)|~class_Fields_Ofield__inverse__zero(X5234))&(X5233!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5234),X5231),X5232)|X5232=c_Groups_Ozero__class_Ozero(X5234)|X5231=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5234),X5233),X5232)|~class_Fields_Ofield__inverse__zero(X5234)))&((c_Groups_Ozero__class_Ozero(X5234)!=X5232|c_Groups_Ozero__class_Ozero(X5234)!=X5231|X5231=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5234),X5233),X5232)|~class_Fields_Ofield__inverse__zero(X5234))&(X5233!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5234),X5231),X5232)|c_Groups_Ozero__class_Ozero(X5234)!=X5231|X5231=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5234),X5233),X5232)|~class_Fields_Ofield__inverse__zero(X5234))))&((X5232!=c_Groups_Ozero__class_Ozero(X5234)|c_Groups_Ozero__class_Ozero(X5234)=X5231|X5231!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5234),X5233),X5232)|~class_Fields_Ofield__inverse__zero(X5234))&(c_Groups_Ozero__class_Ozero(X5234)=X5232|X5233=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5234),X5231),X5232)|X5231!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5234),X5233),X5232)|~class_Fields_Ofield__inverse__zero(X5234)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__eq__eq])])])])). 6.97/7.21 fof(c_0_5376, plain, ![X12758, X12759, X12760, X12761]:((X12759!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12761),X12758),X12760)|X12758=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12761),X12759),X12760)|c_Groups_Ozero__class_Ozero(X12761)=X12760|~class_Rings_Odivision__ring(X12761))&(X12758!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12761),X12759),X12760)|X12759=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12761),X12758),X12760)|c_Groups_Ozero__class_Ozero(X12761)=X12760|~class_Rings_Odivision__ring(X12761))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__eq__divide__eq])])])). 6.97/7.21 fof(c_0_5377, plain, ![X2532, X2533, X2534]:(hAPP(hAPP(c_Relation_Orel__comp(X2534,X2534,X2534),hAPP(c_Relation_Oconverse(X2534,X2534),X2533)),X2533)!=X2533|(hAPP(c_Relation_ODomain(X2534,X2534),X2533)!=X2532|c_Equiv__Relations_Oequiv(X2534,X2532,X2533))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comp__equivI])])])). 6.97/7.21 fof(c_0_5378, plain, ![X379, X380]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X380),X379))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X380)),hAPP(c_Code__Numeral_Oof__nat,X379))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X380)),hAPP(c_Code__Numeral_Oof__nat,X379)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X380),X379)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__code__numeral__code])])). 6.97/7.21 fof(c_0_5379, plain, ![X15440, X15441]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X15441)),hAPP(c_Code__Numeral_Oof__nat,X15440)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15441),X15440)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15441),X15440))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X15441)),hAPP(c_Code__Numeral_Oof__nat,X15440))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__code__numeral__code])])). 6.97/7.21 fof(c_0_5380, plain, ![X12719, X12720, X12721, X12722]:(((X12719!=c_Groups_Ozero__class_Ozero(X12722)|c_Groups_Ozero__class_Ozero(X12722)=X12721|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12722),X12720),X12719)!=X12721|~class_Fields_Ofield__inverse__zero(X12722))&(X12719=c_Groups_Ozero__class_Ozero(X12722)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12722),X12721),X12719)=X12720|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12722),X12720),X12719)!=X12721|~class_Fields_Ofield__inverse__zero(X12722)))&(((X12719!=c_Groups_Ozero__class_Ozero(X12722)|X12719=c_Groups_Ozero__class_Ozero(X12722)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12722),X12720),X12719)=X12721|~class_Fields_Ofield__inverse__zero(X12722))&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12722),X12721),X12719)!=X12720|X12719=c_Groups_Ozero__class_Ozero(X12722)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12722),X12720),X12719)=X12721|~class_Fields_Ofield__inverse__zero(X12722)))&((X12719!=c_Groups_Ozero__class_Ozero(X12722)|c_Groups_Ozero__class_Ozero(X12722)!=X12721|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12722),X12720),X12719)=X12721|~class_Fields_Ofield__inverse__zero(X12722))&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12722),X12721),X12719)!=X12720|c_Groups_Ozero__class_Ozero(X12722)!=X12721|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12722),X12720),X12719)=X12721|~class_Fields_Ofield__inverse__zero(X12722))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq])])])). 6.97/7.21 fof(c_0_5381, plain, ![X14633, X14634, X14635]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X14635,X14635)),hAPP(hAPP(c_Product__Type_OPair(X14635,X14635),X14634),X14633)),c_Relation_OId(X14635)))|X14634=X14633)&(X14634!=X14633|hBOOL(hAPP(hAPP(c_member(tc_prod(X14635,X14635)),hAPP(hAPP(c_Product__Type_OPair(X14635,X14635),X14634),X14633)),c_Relation_OId(X14635))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__in__Id__conv])])). 6.97/7.21 fof(c_0_5382, plain, ![X15589, X15590]:((~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),X15590)),X15589)))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X15590|X15589=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X15590|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),X15590)),X15589))))&(X15589!=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),X15590)),X15589)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__zpower__abs__iff])])])). 6.97/7.21 fof(c_0_5383, plain, ![X16425, X16426, X16427, X16428]:(~class_Rings_Odivision__ring(X16428)|(X16427=c_Groups_Ozero__class_Ozero(X16428)|(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16428),X16425),X16427)!=X16426|X16425=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16428),X16426),X16427)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__eq__imp])])])). 6.97/7.21 fof(c_0_5384, plain, ![X14714, X14715]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14715),X14714))|hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(X14715,X14714))=X14715), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__upt])])). 6.97/7.21 fof(c_0_5385, plain, ![X15799, X15800]:((X15799!=c_Groups_Ozero__class_Ozero(X15800)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15800),hAPP(c_Groups_Oabs__class_Oabs(X15800),X15799)),c_Groups_Ozero__class_Ozero(X15800)))|~class_Groups_Oordered__ab__group__add__abs(X15800))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15800),hAPP(c_Groups_Oabs__class_Oabs(X15800),X15799)),c_Groups_Ozero__class_Ozero(X15800)))|X15799=c_Groups_Ozero__class_Ozero(X15800)|~class_Groups_Oordered__ab__group__add__abs(X15800))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__zero__iff])])])). 6.97/7.21 fof(c_0_5386, plain, ![X2589]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2589))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X2589))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X2589)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2589)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__nat__eq])])). 6.97/7.21 fof(c_0_5387, plain, ![X13373, X13374]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13374),hAPP(c_Int_Onat,X13373)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X13374)),X13373)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X13374)),X13373))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13374),hAPP(c_Int_Onat,X13373))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__nat__eq__int__zless])])). 6.97/7.21 fof(c_0_5388, plain, ![X9189, X9190]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X9189)),X9190))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X9190),X9189)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X9190),X9189))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X9189)),X9190)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__less__eq__eq])])])). 6.97/7.21 fof(c_0_5389, plain, ![X17207, X17208, X17209, X17211, X17212, X17213]:((~hBOOL(hAPP(hAPP(c_member(X17208),X17209),c_Orderings_Otop__class_Otop(tc_fun(X17208,tc_HOL_Obool))))|~hBOOL(hAPP(X17207,X17209))|hBOOL(hAPP(X17207,esk586_1(X17207))))&((hBOOL(hAPP(hAPP(c_member(X17213),esk587_2(X17211,X17213)),c_Orderings_Otop__class_Otop(tc_fun(X17213,tc_HOL_Obool))))|~hBOOL(hAPP(X17211,X17212)))&(hBOOL(hAPP(X17211,esk587_2(X17211,X17213)))|~hBOOL(hAPP(X17211,X17212))))), 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__UNIV])])])])])])). 6.97/7.21 fof(c_0_5390, plain, ![X7661, X7662]:hBOOL(hAPP(hAPP(c_member(X7662),X7661),c_Orderings_Otop__class_Otop(tc_fun(X7662,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_UNIV__I])). 6.97/7.21 fof(c_0_5391, plain, ![X1550, X1551, X1552, X1553]:(hBOOL(hAPP(X1553,X1552))|c_List_Oremove1(X1551,X1552,hAPP(c_List_Ofilter(X1551,X1553),X1550))=hAPP(c_List_Ofilter(X1551,X1553),X1550)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_remove1__filter__not])])])). 6.97/7.21 fof(c_0_5392, plain, ![X11545, X11546, X11547, X11548]:hAPP(c_List_Ofilter(X11548,X11547),c_List_Oremove1(X11548,X11546,X11545))=c_List_Oremove1(X11548,X11546,hAPP(c_List_Ofilter(X11548,X11547),X11545)), inference(variable_rename,[status(thm)],[fact_filter__remove1])). 6.97/7.21 fof(c_0_5393, plain, ![X9883, X9884]:(~c_Relation_Osym(X9884,X9883)|c_Relation_Osym(X9884,c_Transitive__Closure_Otrancl(X9884,X9883))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sym__trancl])])])). 6.97/7.21 fof(c_0_5394, plain, ![X11821, X11822, X11823]:((X11822!=X11823|X11822!=X11821|c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X11823,X11822)=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X11821),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))&((X11822=X11823|c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X11823,X11822)!=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X11821),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))&(X11822=X11821|c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X11823,X11822)!=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X11821),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastAtMost__singleton__iff])])])). 6.97/7.21 fof(c_0_5395, plain, ![X711, X712]:(~c_Wellfounded_Owf(X712,X711)|c_Wellfounded_Owf(X712,c_Transitive__Closure_Otrancl(X712,X711))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__trancl])])])). 6.97/7.21 fof(c_0_5396, plain, ![X13845, X13846, X13848]:((((c_List_Olinorder__class_Osorted(X13846,esk469_2(X13845,X13846))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13846),X13845))|~class_Orderings_Olinorder(X13846))&(hBOOL(hAPP(c_List_Odistinct(X13846),esk469_2(X13845,X13846)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13846),X13845))|~class_Orderings_Olinorder(X13846)))&(X13845!=hAPP(c_List_Oset(X13846),X13848)|~hBOOL(hAPP(c_List_Odistinct(X13846),X13848))|~c_List_Olinorder__class_Osorted(X13846,X13848)|esk469_2(X13845,X13846)=X13848|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13846),X13845))|~class_Orderings_Olinorder(X13846)))&(X13845=hAPP(c_List_Oset(X13846),esk469_2(X13845,X13846))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13846),X13845))|~class_Orderings_Olinorder(X13846))), 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])])])])])])). 6.97/7.21 fof(c_0_5397, plain, ![X3508, X3509]:hBOOL(hAPP(c_Finite__Set_Ofinite(X3509),hAPP(c_List_Oset(X3509),X3508))), inference(variable_rename,[status(thm)],[fact_finite__set])). 6.97/7.21 fof(c_0_5398, plain, ![X3433, X3434, X3435]:((hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3435),X3433),X3433)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3435),X3434),X3434)|(X3434=hAPP(c_Groups_Ouminus__class_Ouminus(X3435),X3433)|X3433=X3434)|~class_Rings_Oidom(X3435))&((X3434!=hAPP(c_Groups_Ouminus__class_Ouminus(X3435),X3433)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3435),X3433),X3433)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3435),X3434),X3434)|~class_Rings_Oidom(X3435))&(X3433!=X3434|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3435),X3433),X3433)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3435),X3434),X3434)|~class_Rings_Oidom(X3435)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__iff])])])). 6.97/7.21 fof(c_0_5399, plain, ![X2820]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X2820|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Groups_Osgn__class_Osgn(tc_Int_Oint,X2820))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2820))|c_Groups_Osgn__class_Osgn(tc_Int_Oint,X2820)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2820)&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2820))|c_Groups_Oone__class_Oone(tc_Int_Oint)=c_Groups_Osgn__class_Osgn(tc_Int_Oint,X2820)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2820))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zsgn__def])])])])). 6.97/7.21 fof(c_0_5400, plain, ![X4200, X4201]:(((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X4201|X4200!=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_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4201),X4200))&(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=X4201|X4200!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4201),X4200)))&(((hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X4201|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X4201|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4201),X4200))&(X4200=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X4201|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4201),X4200)))&((hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X4201|X4200=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_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4201),X4200))&(X4200=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X4200=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_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4201),X4200))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__is__add])])])). 6.97/7.21 fof(c_0_5401, plain, ![X7599, X7600]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X7600)),X7599))|hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7600),X7599)))&(~hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7600),X7599))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X7600)),X7599)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__nat_Osimps_I2_J])])). 6.97/7.21 cnf(c_0_5402, plain, (~class_Int_Onumber__ring(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4620, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.21 fof(c_0_5403, plain, ![X767, X769, X770, X772]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk18_1(X767)))|hBOOL(hAPP(X767,X769)))&(~hBOOL(hAPP(X767,hAPP(c_Int_Onat,esk18_1(X767))))|hBOOL(hAPP(X767,X769))))&(~hBOOL(hAPP(X770,esk19_1(X770)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X772))|hBOOL(hAPP(X770,hAPP(c_Int_Onat,X772)))))), 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])])])])])])])). 6.97/7.21 fof(c_0_5404, plain, ![X9784, X9785, X9786, X9787]:(~class_Rings_Odvd(X9787)|(X9786!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9787),X9785),X9784)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9787),X9785),X9786)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dvdI])])])). 6.97/7.21 fof(c_0_5405, plain, ![X5815, X5816]:(~class_Rings_Oring__1(X5816)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5815))|hAPP(c_Int_Oring__1__class_Oof__int(X5816),X5815)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5816),hAPP(c_Int_Onat,X5815)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__nat])])])). 6.97/7.21 cnf(c_0_5406, 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_4613])). 6.97/7.21 cnf(c_0_5407, 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_4614])). 6.97/7.21 cnf(c_0_5408, 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_4615])). 6.97/7.21 cnf(c_0_5409, 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_4616])). 6.97/7.21 cnf(c_0_5410, 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_4617])). 6.97/7.21 fof(c_0_5411, plain, ![X2843]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X2843))|hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=X2843)&(hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X2843|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X2843)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral__not__eq__zero])])). 6.97/7.21 fof(c_0_5412, plain, ![X4844, X4845]:((hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4845),X4844),X4844)!=c_Groups_Oone__class_Oone(X4845)|(X4844=hAPP(c_Groups_Ouminus__class_Ouminus(X4845),c_Groups_Oone__class_Oone(X4845))|X4844=c_Groups_Oone__class_Oone(X4845))|~class_Rings_Oring__1__no__zero__divisors(X4845))&((X4844!=hAPP(c_Groups_Ouminus__class_Ouminus(X4845),c_Groups_Oone__class_Oone(X4845))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4845),X4844),X4844)=c_Groups_Oone__class_Oone(X4845)|~class_Rings_Oring__1__no__zero__divisors(X4845))&(X4844!=c_Groups_Oone__class_Oone(X4845)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4845),X4844),X4844)=c_Groups_Oone__class_Oone(X4845)|~class_Rings_Oring__1__no__zero__divisors(X4845)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__1__iff])])])). 6.97/7.21 fof(c_0_5413, plain, ![X8476, X8477]:(~class_Int_Onumber__ring(X8477)|~class_Fields_Ofield__inverse__zero(X8477)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8477),X8476),hAPP(c_Int_Onumber__class_Onumber__of(X8477),c_Int_OPls))=c_Groups_Ozero__class_Ozero(X8477)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__Numeral0])])])). 6.97/7.21 fof(c_0_5414, plain, ![X14601]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14601))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X14601))=X14601)&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14601))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X14601))=c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_int__nat__eq])])])). 6.97/7.21 fof(c_0_5415, plain, ![X3653, X3654]:((c_List_Oupt(X3654,X3653)!=c_List_Olist_ONil(tc_Nat_Onat)|(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X3653|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3653),X3654))))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X3653|c_List_Oupt(X3654,X3653)=c_List_Olist_ONil(tc_Nat_Onat))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3653),X3654))|c_List_Oupt(X3654,X3653)=c_List_Olist_ONil(tc_Nat_Onat)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__eq__Nil__conv])])])). 6.97/7.21 fof(c_0_5416, plain, ![X10648, X10649, X10650]:(((X10649=c_Groups_Ozero__class_Ozero(X10650)|hAPP(hAPP(c_Power_Opower__class_Opower(X10650),X10649),X10648)!=c_Groups_Ozero__class_Ozero(X10650)|(~class_Rings_Omult__zero(X10650)|~class_Rings_Ono__zero__divisors(X10650)|~class_Rings_Ozero__neq__one(X10650)|~class_Power_Opower(X10650)))&(X10648!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(X10650),X10649),X10648)!=c_Groups_Ozero__class_Ozero(X10650)|(~class_Rings_Omult__zero(X10650)|~class_Rings_Ono__zero__divisors(X10650)|~class_Rings_Ozero__neq__one(X10650)|~class_Power_Opower(X10650))))&(X10649!=c_Groups_Ozero__class_Ozero(X10650)|X10648=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(X10650),X10649),X10648)=c_Groups_Ozero__class_Ozero(X10650)|(~class_Rings_Omult__zero(X10650)|~class_Rings_Ono__zero__divisors(X10650)|~class_Rings_Ozero__neq__one(X10650)|~class_Power_Opower(X10650)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__eq__0__iff])])])])). 6.97/7.21 fof(c_0_5417, plain, ![X1830, X1831, X1833, X1834]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk55_1(X1830)))|~hBOOL(hAPP(X1830,X1831)))&(hBOOL(hAPP(X1830,hAPP(c_Int_Onat,esk55_1(X1830))))|~hBOOL(hAPP(X1830,X1831))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1834))|~hBOOL(hAPP(X1833,hAPP(c_Int_Onat,X1834)))|hBOOL(hAPP(X1833,esk56_1(X1833))))), 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])])])])])])). 6.97/7.21 fof(c_0_5418, plain, ![X11894, X11895, X11896]:(~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X11896,X11895),X11894))|X11894=c_Divides_Odivmod__nat(X11896,X11895)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__nat__eq])])])). 6.97/7.21 fof(c_0_5419, plain, ![X11946, X11947]:(~c_Relation_Otrans(X11947,X11946)|X11946=c_Transitive__Closure_Otrancl(X11947,X11946)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__id])])). 6.97/7.21 fof(c_0_5420, plain, ![X6953, X6954]:((((hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X6953|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X6953|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6954),X6953)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&(X6954=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X6953|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6954),X6953)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))&((hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X6953|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X6954|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6954),X6953)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&(X6954=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X6954|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6954),X6953)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X6953|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=X6954|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6954),X6953)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=X6953|X6954!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6954),X6953)=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])])])). 6.97/7.21 fof(c_0_5421, plain, ![X4311, X4312, X4313]:((~c_List_Olist__all(tc_Nat_Onat,X4313,c_List_Oupt(X4312,X4311))|c_List_Oall__interval__nat(X4313,X4312,X4311))&(~c_List_Oall__interval__nat(X4313,X4312,X4311)|c_List_Olist__all(tc_Nat_Onat,X4313,c_List_Oupt(X4312,X4311)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__iff__all__interval__nat])])). 6.97/7.21 fof(c_0_5422, plain, ![X11048, X11049]:((X11048!=X11049|hAPP(c_Int_Onat,X11049)=hAPP(c_Int_Onat,X11048)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11048))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11049)))&(hAPP(c_Int_Onat,X11049)!=hAPP(c_Int_Onat,X11048)|X11048=X11049|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11048))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11049)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__nat__nat__iff])])])])). 6.97/7.21 fof(c_0_5423, plain, ![X4320, X4321, X4322, X4323]:((((hAPP(c_Int_Onumber__class_Onumber__of(X4323),X4320)!=c_Groups_Ozero__class_Ozero(X4323)|hAPP(c_Int_Onumber__class_Onumber__of(X4323),X4320)=c_Groups_Ozero__class_Ozero(X4323)|X4322=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4323),X4321),hAPP(c_Int_Onumber__class_Onumber__of(X4323),X4320))|(~class_Fields_Ofield__inverse__zero(X4323)|~class_Int_Onumber(X4323)))&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4323),X4322),hAPP(c_Int_Onumber__class_Onumber__of(X4323),X4320))!=X4321|hAPP(c_Int_Onumber__class_Onumber__of(X4323),X4320)=c_Groups_Ozero__class_Ozero(X4323)|X4322=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4323),X4321),hAPP(c_Int_Onumber__class_Onumber__of(X4323),X4320))|(~class_Fields_Ofield__inverse__zero(X4323)|~class_Int_Onumber(X4323))))&((hAPP(c_Int_Onumber__class_Onumber__of(X4323),X4320)!=c_Groups_Ozero__class_Ozero(X4323)|c_Groups_Ozero__class_Ozero(X4323)!=X4322|X4322=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4323),X4321),hAPP(c_Int_Onumber__class_Onumber__of(X4323),X4320))|(~class_Fields_Ofield__inverse__zero(X4323)|~class_Int_Onumber(X4323)))&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4323),X4322),hAPP(c_Int_Onumber__class_Onumber__of(X4323),X4320))!=X4321|c_Groups_Ozero__class_Ozero(X4323)!=X4322|X4322=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4323),X4321),hAPP(c_Int_Onumber__class_Onumber__of(X4323),X4320))|(~class_Fields_Ofield__inverse__zero(X4323)|~class_Int_Onumber(X4323)))))&((hAPP(c_Int_Onumber__class_Onumber__of(X4323),X4320)!=c_Groups_Ozero__class_Ozero(X4323)|c_Groups_Ozero__class_Ozero(X4323)=X4322|X4322!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4323),X4321),hAPP(c_Int_Onumber__class_Onumber__of(X4323),X4320))|(~class_Fields_Ofield__inverse__zero(X4323)|~class_Int_Onumber(X4323)))&(hAPP(c_Int_Onumber__class_Onumber__of(X4323),X4320)=c_Groups_Ozero__class_Ozero(X4323)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4323),X4322),hAPP(c_Int_Onumber__class_Onumber__of(X4323),X4320))=X4321|X4322!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4323),X4321),hAPP(c_Int_Onumber__class_Onumber__of(X4323),X4320))|(~class_Fields_Ofield__inverse__zero(X4323)|~class_Int_Onumber(X4323))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__divide__eq__number__of1])])])])). 6.97/7.21 cnf(c_0_5424, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=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),c_Int_Opred(X1))))), inference(split_conjunct,[status(thm)],[c_0_4619])). 6.97/7.21 fof(c_0_5425, plain, ![X16999, X17000]:(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X17000),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))|(~hBOOL(hAPP(X16999,hAPP(c_Code__Numeral_Onat__of,esk573_2(X16999,X17000))))|hBOOL(hAPP(X16999,X17000)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__of__induct])])])). 6.97/7.21 fof(c_0_5426, plain, ![X9371, X9373, X9374, X9375, X9376]:((hBOOL(hAPP(X9371,esk307_1(X9371)))|c_Orderings_Obot__class_Obot(tc_fun(X9373,tc_HOL_Obool))=hAPP(c_Set_OCollect(X9373),X9371))&(c_Orderings_Obot__class_Obot(tc_fun(X9375,tc_HOL_Obool))!=hAPP(c_Set_OCollect(X9375),X9374)|~hBOOL(hAPP(X9374,X9376)))), 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])])])])])])). 6.97/7.21 fof(c_0_5427, plain, ![X2372, X2374, X2375, X2376, X2377]:((hBOOL(hAPP(X2372,esk77_1(X2372)))|hAPP(c_Set_OCollect(X2374),X2372)=c_Orderings_Obot__class_Obot(tc_fun(X2374,tc_HOL_Obool)))&(hAPP(c_Set_OCollect(X2376),X2375)!=c_Orderings_Obot__class_Obot(tc_fun(X2376,tc_HOL_Obool))|~hBOOL(hAPP(X2375,X2377)))), 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])])])])])])). 6.97/7.21 fof(c_0_5428, plain, ![X11669, X11670]:(((hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=X11670|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X11670),X11669)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&(X11669!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X11670),X11669)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))&(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X11670),X11669)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X11670|X11669=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])])])). 6.97/7.21 fof(c_0_5429, plain, ![X15900, X15901]:(~class_Int_Onumber__ring(X15901)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15901),hAPP(c_Int_Onumber__class_Onumber__of(X15901),c_Int_OPls)),X15900)=X15900), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__numeral__0])])])). 6.97/7.21 fof(c_0_5430, plain, ![X4437, X4438]:(~class_Int_Onumber__ring(X4438)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4438),X4437),hAPP(c_Int_Onumber__class_Onumber__of(X4438),c_Int_OPls))=X4437), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__numeral__0__right])])])). 6.97/7.21 fof(c_0_5431, plain, ![X568, X569]:(~class_Int_Onumber__ring(X569)|~class_Int_Oring__char__0(X569)|~c_Int_Oiszero(X569,hAPP(c_Int_Onumber__class_Onumber__of(X569),c_Int_OBit1(X568)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_iszero__number__of__Bit1])])])). 6.97/7.21 fof(c_0_5432, plain, ![X11343, X11344]:((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11344)),X11343)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11344)),c_List_Oremdups(X11344,X11343))|X11343=c_List_Oremdups(X11344,X11343))&(X11343!=c_List_Oremdups(X11344,X11343)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11344)),X11343)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11344)),c_List_Oremdups(X11344,X11343)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__remdups__eq])])). 6.97/7.21 fof(c_0_5433, plain, ![X16958, X16959]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16959)),c_List_Oremdups(X16959,X16958))=hAPP(c_Finite__Set_Ocard(X16959),hAPP(c_List_Oset(X16959),X16958)), inference(variable_rename,[status(thm)],[fact_length__remdups__card__conv])). 6.97/7.21 cnf(c_0_5434, plain, (X1=X2|c_Code__Numeral_OSuc__code__numeral(X1)!=c_Code__Numeral_OSuc__code__numeral(X2)), inference(split_conjunct,[status(thm)],[c_0_4621])). 6.97/7.21 cnf(c_0_5435, 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_4622])). 6.97/7.21 fof(c_0_5436, plain, ![X2813, X2814, X2815, X2816, X2817]:((X2815!=X2816|X2814=X2813|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2817),X2816),X2815)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2817),X2814),X2813)|~class_Groups_Oab__group__add(X2817))&(X2814!=X2813|X2815=X2816|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2817),X2816),X2815)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2817),X2814),X2813)|~class_Groups_Oab__group__add(X2817))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq])])])). 6.97/7.21 fof(c_0_5437, plain, ![X10841]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X10841)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X10841)))&(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X10841)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X10841)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X10841)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_int__nat__number__of])])])). 6.97/7.21 fof(c_0_5438, plain, ![X10974]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10974))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X10974))=X10974), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__le])])). 6.97/7.21 fof(c_0_5439, plain, ![X11995, X11996]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11996))|X11996=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X11995)|hAPP(c_Int_Onat,X11996)!=X11995)&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11996))|X11995=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Int_Onat,X11996)!=X11995))&(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11996))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11996))|hAPP(c_Int_Onat,X11996)=X11995)&(X11995!=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)),X11996))|hAPP(c_Int_Onat,X11996)=X11995))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11996))|X11996!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X11995)|hAPP(c_Int_Onat,X11996)=X11995)&(X11995!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X11996!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X11995)|hAPP(c_Int_Onat,X11996)=X11995)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__eq__iff])])])])). 6.97/7.21 fof(c_0_5440, plain, ![X2560, X2561, X2562, X2563, X2564]:((~c_Fun_Oinj__on(X2564,X2563,X2562,X2561)|hAPP(c_Set_Oimage(X2564,X2563,X2562),X2561)!=X2560|c_Fun_Obij__betw(X2564,X2563,X2562,X2561,X2560))&((c_Fun_Oinj__on(X2564,X2563,X2562,X2561)|~c_Fun_Obij__betw(X2564,X2563,X2562,X2561,X2560))&(hAPP(c_Set_Oimage(X2564,X2563,X2562),X2561)=X2560|~c_Fun_Obij__betw(X2564,X2563,X2562,X2561,X2560)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__def])])])). 6.97/7.21 fof(c_0_5441, plain, ![X15690, X15691]:((c_Groups_Ozero__class_Ozero(X15691)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15691),X15690),X15690)|c_Groups_Ozero__class_Ozero(X15691)=X15690|~class_Groups_Olinordered__ab__group__add(X15691))&(c_Groups_Ozero__class_Ozero(X15691)!=X15690|c_Groups_Ozero__class_Ozero(X15691)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15691),X15690),X15690)|~class_Groups_Olinordered__ab__group__add(X15691))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])])). 6.97/7.21 fof(c_0_5442, plain, ![X2279, X2280, X2281]:(((c_Groups_Ozero__class_Ozero(X2281)!=X2280|c_Groups_Ozero__class_Ozero(X2281)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2281),X2280),X2279)|~class_Rings_Oring__no__zero__divisors(X2281))&(X2279!=c_Groups_Ozero__class_Ozero(X2281)|c_Groups_Ozero__class_Ozero(X2281)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2281),X2280),X2279)|~class_Rings_Oring__no__zero__divisors(X2281)))&(c_Groups_Ozero__class_Ozero(X2281)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2281),X2280),X2279)|(c_Groups_Ozero__class_Ozero(X2281)=X2280|X2279=c_Groups_Ozero__class_Ozero(X2281))|~class_Rings_Oring__no__zero__divisors(X2281))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff])])])). 6.97/7.21 fof(c_0_5443, plain, ![X16490, X16491, X16492]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(X16492),X16491),X16490)!=c_Groups_Ozero__class_Ozero(X16492)|X16491=X16490|~class_Groups_Oab__group__add(X16492))&(X16491!=X16490|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X16492),X16491),X16490)=c_Groups_Ozero__class_Ozero(X16492)|~class_Groups_Oab__group__add(X16492))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__iff__diff__eq__0])])])). 6.97/7.21 fof(c_0_5444, plain, ![X14733, X14734, X14735]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14735),X14734),X14733)!=X14734|c_Groups_Ozero__class_Ozero(X14735)=X14733|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X14735))&(c_Groups_Ozero__class_Ozero(X14735)!=X14733|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14735),X14734),X14733)=X14734|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X14735))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])])). 6.97/7.21 fof(c_0_5445, plain, ![X8530]:(hBOOL(hAPP(c_Nat__Numeral_Oneg,X8530))|X8530=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X8530))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__neg__nat])])])). 6.97/7.21 fof(c_0_5446, plain, ![X11637]:((c_Int_OBit1(X11637)!=c_Int_OMin|X11637=c_Int_OMin)&(X11637!=c_Int_OMin|c_Int_OBit1(X11637)=c_Int_OMin)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I43_J])])). 6.97/7.21 fof(c_0_5447, plain, ![X5202, X5203, X5204]:(~class_Complete__Lattice_Ocomplete__lattice(X5204)|(X5203!=c_Inductive_Ocomplete__lattice__class_Olfp(X5204,X5202)|(~c_Orderings_Oorder__class_Omono(X5204,X5204,X5202)|hAPP(X5202,X5203)=X5203))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_def__lfp__unfold])])])). 6.97/7.21 fof(c_0_5448, plain, ![X3961, X3962, X3963]:(~class_Complete__Lattice_Ocomplete__lattice(X3963)|(X3962!=c_Inductive_Ocomplete__lattice__class_Ogfp(X3963,X3961)|(~c_Orderings_Oorder__class_Omono(X3963,X3963,X3961)|hAPP(X3961,X3962)=X3962))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_def__gfp__unfold])])])). 6.97/7.21 fof(c_0_5449, plain, ![X4664, X4665]:((c_Int_OBit0(X4664)!=c_Int_OBit0(X4665)|X4665=X4664)&(X4665!=X4664|c_Int_OBit0(X4664)=c_Int_OBit0(X4665))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I48_J])])). 6.97/7.21 fof(c_0_5450, plain, ![X3594, X3595, X3596]:((X3594!=hAPP(c_Groups_Ouminus__class_Ouminus(X3596),X3595)|X3595=hAPP(c_Groups_Ouminus__class_Ouminus(X3596),X3594)|~class_Groups_Ogroup__add(X3596))&(X3595!=hAPP(c_Groups_Ouminus__class_Ouminus(X3596),X3594)|X3594=hAPP(c_Groups_Ouminus__class_Ouminus(X3596),X3595)|~class_Groups_Ogroup__add(X3596))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equation__minus__iff])])])). 6.97/7.21 fof(c_0_5451, plain, ![X8231]:((X8231!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8231),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8231),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|X8231=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc0])])). 6.97/7.21 fof(c_0_5452, plain, ![X8313, X8314]:((c_Groups_Ozero__class_Ozero(X8314)=X8313|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8314),c_Groups_Ozero__class_Ozero(X8314)),hAPP(c_Groups_Oabs__class_Oabs(X8314),X8313)))|~class_Groups_Oordered__ab__group__add__abs(X8314))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8314),c_Groups_Ozero__class_Ozero(X8314)),hAPP(c_Groups_Oabs__class_Oabs(X8314),X8313)))|c_Groups_Ozero__class_Ozero(X8314)!=X8313|~class_Groups_Oordered__ab__group__add__abs(X8314))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__less__abs__iff])])])])). 6.97/7.21 fof(c_0_5453, plain, ![X7342]:((hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7342)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7342),c_Int_OPls)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7342),c_Int_OPls))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7342)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__0__number__of])])). 6.97/7.21 fof(c_0_5454, plain, ![X5655]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5655),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onat,X5655)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(hAPP(c_Int_Onat,X5655)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5655),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__iff])])). 6.97/7.21 fof(c_0_5455, plain, ![X16612]:(~hBOOL(hAPP(c_Nat__Numeral_Oneg,X16612))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onat,X16612)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__nat])])). 6.97/7.21 fof(c_0_5456, plain, ![X14485, X14486]:((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk488_2(X14485,X14486)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))|hBOOL(hAPP(X14486,X14485)))&(~hBOOL(hAPP(X14486,hAPP(c_Code__Numeral_Oof__nat,esk488_2(X14485,X14486))))|hBOOL(hAPP(X14486,X14485)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__induct])])])])). 6.97/7.21 fof(c_0_5457, plain, ![X9528, X9529]:((c_Groups_Ozero__class_Ozero(X9529)!=hAPP(c_Int_Oring__1__class_Oof__int(X9529),X9528)|X9528=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~class_Int_Oring__char__0(X9529))&(X9528!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Groups_Ozero__class_Ozero(X9529)=hAPP(c_Int_Oring__1__class_Oof__int(X9529),X9528)|~class_Int_Oring__char__0(X9529))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__eq__0__iff])])])). 6.97/7.21 fof(c_0_5458, plain, ![X1634]:(~class_Int_Onumber__ring(X1634)|c_Int_Oiszero(X1634,hAPP(c_Int_Onumber__class_Onumber__of(X1634),c_Int_OPls))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__Numeral0])])). 6.97/7.21 fof(c_0_5459, plain, ![X6366, X6367]:((hAPP(c_Groups_Ouminus__class_Ouminus(X6367),X6366)!=X6366|c_Groups_Ozero__class_Ozero(X6367)=X6366|~class_Groups_Olinordered__ab__group__add(X6367))&(c_Groups_Ozero__class_Ozero(X6367)!=X6366|hAPP(c_Groups_Ouminus__class_Ouminus(X6367),X6366)=X6366|~class_Groups_Olinordered__ab__group__add(X6367))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equal__neg__zero])])])). 6.97/7.21 fof(c_0_5460, plain, ![X2535, X2536]:((c_Groups_Ozero__class_Ozero(X2536)!=c_Groups_Osgn__class_Osgn(X2536,X2535)|c_Groups_Ozero__class_Ozero(X2536)=X2535|~class_Rings_Olinordered__idom(X2536))&(c_Groups_Ozero__class_Ozero(X2536)!=X2535|c_Groups_Ozero__class_Ozero(X2536)=c_Groups_Osgn__class_Osgn(X2536,X2535)|~class_Rings_Olinordered__idom(X2536))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__0__0])])])). 6.97/7.21 fof(c_0_5461, plain, ![X4144, X4145, X4146]:(~class_Orderings_Oorder(X4146)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4146),X4145),X4144))|X4144!=X4145)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__eq2])])])). 6.97/7.21 fof(c_0_5462, plain, ![X2999, X3000, X3001]:((X2999=X3000|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3001),X2999),X3000))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3001),X3000),X2999)))|~class_Orderings_Olinorder(X3001))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3001),X2999),X3000))|X2999!=X3000|~class_Orderings_Olinorder(X3001))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3001),X3000),X2999))|X2999!=X3000|~class_Orderings_Olinorder(X3001)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__neq__iff])])])])). 6.97/7.21 cnf(c_0_5463, plain, (c_Int_OPls=X1|c_Int_OPls!=c_Int_OBit0(X1)), inference(split_conjunct,[status(thm)],[c_0_4623])). 6.97/7.21 fof(c_0_5464, plain, ![X11824, X11825]:((X11825!=X11824|hAPP(c_Code__Numeral_Oof__nat,X11825)=hAPP(c_Code__Numeral_Oof__nat,X11824))&(hAPP(c_Code__Numeral_Oof__nat,X11825)!=hAPP(c_Code__Numeral_Oof__nat,X11824)|X11825=X11824)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Code__Numeral_Oof__nat__inject])])). 6.97/7.21 fof(c_0_5465, plain, ![X5473]:(~class_Int_Onumber__ring(X5473)|c_Groups_Ozero__class_Ozero(X5473)=hAPP(c_Int_Onumber__class_Onumber__of(X5473),c_Int_OPls)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_semiring__norm_I112_J])])])). 6.97/7.21 fof(c_0_5466, plain, ![X2381, X2382, X2383, X2384, X2386, X2387, X2388, X2389, X2390, X2391]:(((hBOOL(hAPP(hAPP(c_member(X2384),esk78_4(X2381,X2382,X2383,X2384)),X2383))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2384),X2383))|X2382=c_Orderings_Obot__class_Obot(tc_fun(X2384,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2384),X2382))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2384,tc_HOL_Obool),tc_fun(X2384,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2384,tc_HOL_Obool),tc_fun(X2384,tc_HOL_Obool)),X2383),X2382)),c_Wellfounded_Omax__ext(X2384,X2381))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X2384,X2384)),hAPP(hAPP(c_Product__Type_OPair(X2384,X2384),esk78_4(X2381,X2382,X2383,X2384)),X2386)),X2381))|~hBOOL(hAPP(hAPP(c_member(X2384),X2386),X2382))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2384),X2383))|X2382=c_Orderings_Obot__class_Obot(tc_fun(X2384,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2384),X2382))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2384,tc_HOL_Obool),tc_fun(X2384,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2384,tc_HOL_Obool),tc_fun(X2384,tc_HOL_Obool)),X2383),X2382)),c_Wellfounded_Omax__ext(X2384,X2381)))))&((((hBOOL(hAPP(c_Finite__Set_Ofinite(X2390),X2389))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2390,tc_HOL_Obool),tc_fun(X2390,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2390,tc_HOL_Obool),tc_fun(X2390,tc_HOL_Obool)),X2389),X2388)),c_Wellfounded_Omax__ext(X2390,X2387))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X2390,X2390)),hAPP(hAPP(c_Product__Type_OPair(X2390,X2390),X2391),esk79_5(X2387,X2388,X2389,X2390,X2391))),X2387))|~hBOOL(hAPP(hAPP(c_member(X2390),X2391),X2389))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2390,tc_HOL_Obool),tc_fun(X2390,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2390,tc_HOL_Obool),tc_fun(X2390,tc_HOL_Obool)),X2389),X2388)),c_Wellfounded_Omax__ext(X2390,X2387))))&(hBOOL(hAPP(hAPP(c_member(X2390),esk79_5(X2387,X2388,X2389,X2390,X2391)),X2388))|~hBOOL(hAPP(hAPP(c_member(X2390),X2391),X2389))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2390,tc_HOL_Obool),tc_fun(X2390,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2390,tc_HOL_Obool),tc_fun(X2390,tc_HOL_Obool)),X2389),X2388)),c_Wellfounded_Omax__ext(X2390,X2387))))))&(X2388!=c_Orderings_Obot__class_Obot(tc_fun(X2390,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2390,tc_HOL_Obool),tc_fun(X2390,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2390,tc_HOL_Obool),tc_fun(X2390,tc_HOL_Obool)),X2389),X2388)),c_Wellfounded_Omax__ext(X2390,X2387)))))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X2390),X2388))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2390,tc_HOL_Obool),tc_fun(X2390,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2390,tc_HOL_Obool),tc_fun(X2390,tc_HOL_Obool)),X2389),X2388)),c_Wellfounded_Omax__ext(X2390,X2387)))))), 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_max__ext_Osimps])])])])])])). 6.97/7.21 fof(c_0_5467, plain, ![X4441, X4442, X4443]:((X4441=X4442|hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X4443,X4443,hAPP(hAPP(c_COMBB(tc_fun(X4443,tc_HOL_Obool),tc_fun(X4443,tc_HOL_Obool),X4443),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4443),c_fNot)),c_fequal)),X4442),X4441)))&(~hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X4443,X4443,hAPP(hAPP(c_COMBB(tc_fun(X4443,tc_HOL_Obool),tc_fun(X4443,tc_HOL_Obool),X4443),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4443),c_fNot)),c_fequal)),X4442),X4441))|X4441!=X4442)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep__noteq])])). 6.97/7.21 fof(c_0_5468, plain, ![X7492, X7493]:c_Int_OBit1(X7492)!=c_Int_OBit0(X7493), inference(variable_rename,[status(thm)],[fact_rel__simps_I49_J])). 6.97/7.21 cnf(c_0_5469, plain, (c_Int_OPls!=c_Int_OBit1(X1)), inference(split_conjunct,[status(thm)],[c_0_4624])). 6.97/7.21 cnf(c_0_5470, 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_4625])). 6.97/7.21 fof(c_0_5471, plain, ![X11990, X11991]:((X11991=X11990|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11991),X11990))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11991),X11990)))&((X11991!=X11990|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11991),X11990)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11991),X11990))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11991),X11990))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__le])])])). 6.97/7.21 fof(c_0_5472, plain, ![X2188, X2189, X2190, X2191, X2193, X2194, X2195, X2196, X2197, X2198]:(((hBOOL(hAPP(hAPP(c_member(X2191),esk67_4(X2188,X2189,X2190,X2191)),X2189))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2191),X2189))|X2188=c_Orderings_Obot__class_Obot(tc_fun(X2191,tc_HOL_Obool)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2191),X2188))|c_Wellfounded_Omax__extp(X2191,X2190,X2189,X2188))&(~hBOOL(hAPP(hAPP(X2190,esk67_4(X2188,X2189,X2190,X2191)),X2193))|~hBOOL(hAPP(hAPP(c_member(X2191),X2193),X2188))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2191),X2189))|X2188=c_Orderings_Obot__class_Obot(tc_fun(X2191,tc_HOL_Obool)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2191),X2188))|c_Wellfounded_Omax__extp(X2191,X2190,X2189,X2188)))&((((hBOOL(hAPP(c_Finite__Set_Ofinite(X2197),X2195))|~c_Wellfounded_Omax__extp(X2197,X2196,X2195,X2194))&(X2194!=c_Orderings_Obot__class_Obot(tc_fun(X2197,tc_HOL_Obool))|~c_Wellfounded_Omax__extp(X2197,X2196,X2195,X2194)))&((hBOOL(hAPP(hAPP(X2196,X2198),esk68_5(X2194,X2195,X2196,X2197,X2198)))|~hBOOL(hAPP(hAPP(c_member(X2197),X2198),X2195))|~c_Wellfounded_Omax__extp(X2197,X2196,X2195,X2194))&(hBOOL(hAPP(hAPP(c_member(X2197),esk68_5(X2194,X2195,X2196,X2197,X2198)),X2194))|~hBOOL(hAPP(hAPP(c_member(X2197),X2198),X2195))|~c_Wellfounded_Omax__extp(X2197,X2196,X2195,X2194))))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X2197),X2194))|~c_Wellfounded_Omax__extp(X2197,X2196,X2195,X2194)))), 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])])])])])])])). 6.97/7.21 fof(c_0_5473, 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])). 6.97/7.21 fof(c_0_5474, 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])). 6.97/7.21 fof(c_0_5475, plain, ![X8535]:c_Int_OMin!=c_Int_OBit0(X8535), inference(variable_rename,[status(thm)],[fact_rel__simps_I42_J])). 6.97/7.21 fof(c_0_5476, negated_conjecture, ~(c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts)), inference(assume_negation,[status(cth)],[conj_2])). 6.97/7.21 cnf(c_0_5477, 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_4626])). 6.97/7.21 cnf(c_0_5478, 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_4627])). 6.97/7.21 fof(c_0_5479, plain, ![X7781, X7782, X7783, X7784, X7785, X7786]:hAPP(X7783,hAPP(c_Set_OCollect(X7786),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7784,X7786),tc_HOL_Obool),tc_HOL_Obool,X7786),c_HOL_OEx(tc_fun(X7784,X7786))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7784,X7786),tc_HOL_Obool),tc_fun(tc_fun(X7784,X7786),tc_HOL_Obool),X7786),hAPP(c_COMBS(tc_fun(X7784,X7786),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X7784,X7786)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X7784,X7786),tc_fun(tc_fun(X7784,X7786),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X7784,X7786))),X7782)))),hAPP(hAPP(c_COMBC(X7786,tc_fun(tc_fun(X7784,X7786),X7786),tc_fun(tc_fun(X7784,X7786),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7786,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X7784,X7786),X7786),tc_fun(tc_fun(X7784,X7786),tc_HOL_Obool)),X7786),c_COMBB(X7786,tc_HOL_Obool,tc_fun(X7784,X7786))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X7784,X7786),X7784,X7786),c_COMBI(tc_fun(X7784,X7786))),X7781))))))=c_Partial__Function_Ofun__lub(X7786,X7785,X7784,X7783,X7782,X7781), inference(variable_rename,[status(thm)],[fact_fun__lub__def])). 6.97/7.21 fof(c_0_5480, plain, ![X7595, X7596, X7597, X7598]: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),X7598),X7597)),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),X7596),X7595)),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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7598),X7596)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7597),X7595))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7598),X7595)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7597),X7596)))),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])). 6.97/7.21 cnf(c_0_5481, 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_4628])). 6.97/7.21 fof(c_0_5482, plain, ![X16968, X16969, X16970, X16971, X16972, X16973]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16972,tc_HOL_Obool)),hAPP(c_Set_Oimage(X16973,X16972,X16970),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16973,tc_HOL_Obool)),X16968),hAPP(c_Set_OCollect(X16973),X16971)))),hAPP(c_Set_Oimage(X16973,X16972,X16969),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16973,tc_HOL_Obool)),X16968),hAPP(c_Set_OCollect(X16973),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X16973),c_fNot),X16971)))))=hAPP(c_Set_Oimage(X16973,X16972,hAPP(hAPP(c_COMBS(X16973,X16972,X16972),hAPP(hAPP(c_COMBS(X16973,X16972,tc_fun(X16972,X16972)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X16972,tc_fun(X16972,X16972)),X16973),c_If(X16972)),X16971)),X16970)),X16969)),X16968), inference(variable_rename,[status(thm)],[fact_if__image__distrib])). 6.97/7.21 cnf(c_0_5483, plain, (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)))=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)))), inference(split_conjunct,[status(thm)],[c_0_4629])). 6.97/7.21 fof(c_0_5484, plain, ![X1532, X1533, X1534]: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),X1534)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),X1533))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X1532)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1532),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1534),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1534),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1532),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1533)))), inference(variable_rename,[status(thm)],[fact_arith__series__nat])). 6.97/7.21 cnf(c_0_5485, 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_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_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))), inference(split_conjunct,[status(thm)],[c_0_4630])). 6.97/7.21 cnf(c_0_5486, 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_4631, c_0_4632])). 6.97/7.21 fof(c_0_5487, plain, ![X8413, X8414, X8415]: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(X8415)),X8414)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X8413))))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8415)),c_List_Osublist(X8415,X8414,X8413)), inference(variable_rename,[status(thm)],[fact_length__sublist])). 6.97/7.21 fof(c_0_5488, plain, ![X3183, X3184, X3185, X3186, X3187, X3188, X3189, X3190, X3191, X3192]:(hAPP(c_Set_Oimage(X3192,X3191,X3190),X3189)!=X3188|(X3183!=hAPP(c_Set_Oimage(X3187,X3186,X3185),X3184)|hAPP(hAPP(c_Product__Type_OSigma(X3191,X3186),X3188),hAPP(c_COMBK(tc_fun(X3186,tc_HOL_Obool),X3191),X3183))=hAPP(c_Set_Oimage(tc_prod(X3192,X3187),tc_prod(X3191,X3186),c_Product__Type_Omap__pair(X3192,X3191,X3187,X3186,X3190,X3185)),hAPP(hAPP(c_Product__Type_OSigma(X3192,X3187),X3189),hAPP(c_COMBK(tc_fun(X3187,tc_HOL_Obool),X3192),X3184))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__pair__surj__on])])). 6.97/7.21 fof(c_0_5489, plain, ![X7607, X7608, X7609, X7610, X7611]:hAPP(hAPP(c_List_Omap(X7609,X7611),X7608),c_List_OdropWhile(X7609,hAPP(c_Fun_Ocomp(X7611,tc_HOL_Obool,X7609,X7610),X7608),X7607))=c_List_OdropWhile(X7611,X7610,hAPP(hAPP(c_List_Omap(X7609,X7611),X7608),X7607)), inference(variable_rename,[status(thm)],[fact_dropWhile__map])). 6.97/7.21 fof(c_0_5490, plain, ![X12269, X12270, X12271, X12272]:hAPP(c_Relation_OImage(X12272,X12271,X12270),hAPP(hAPP(c_Set_Oinsert(X12272),X12269),c_Orderings_Obot__class_Obot(tc_fun(X12272,tc_HOL_Obool))))=hAPP(c_Set_OCollect(X12271),hAPP(hAPP(c_COMBC(X12271,tc_fun(tc_prod(X12272,X12271),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X12272,X12271),tc_fun(tc_fun(tc_prod(X12272,X12271),tc_HOL_Obool),tc_HOL_Obool),X12271),c_member(tc_prod(X12272,X12271))),hAPP(c_Product__Type_OPair(X12272,X12271),X12269))),X12270)), inference(variable_rename,[status(thm)],[fact_Image__singleton])). 6.97/7.21 fof(c_0_5491, plain, ![X9246, X9247, X9248, X9249]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X9249,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X9248)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X9249,tc_HOL_Obool),tc_Nat_Onat),X9247),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X9246)))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X9249,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X9246,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9248),X9246))),X9247), inference(variable_rename,[status(thm)],[fact_UN__le__add__shift])). 6.97/7.21 fof(c_0_5492, plain, ![X7393, X7394, X7395, X7396, X7397, X7398, X7399]:c_List_Ofoldr(X7396,X7398,hAPP(c_Fun_Ocomp(X7399,tc_fun(X7398,X7398),X7396,X7397),X7395),X7394,X7393)=c_List_Ofoldr(X7399,X7398,X7397,hAPP(hAPP(c_List_Omap(X7396,X7399),X7395),X7394),X7393), inference(variable_rename,[status(thm)],[fact_foldr__map])). 6.97/7.21 cnf(c_0_5493, 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_4633])). 6.97/7.21 cnf(c_0_5494, 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_4634])). 6.97/7.21 cnf(c_0_5495, 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_4635])). 6.97/7.21 fof(c_0_5496, plain, ![X17560, X17561, X17562, X17563, X17564, X17565]:c_List_Ofoldr(X17565,X17564,X17563,hAPP(hAPP(c_List_Olist_OCons(X17565),X17562),X17561),X17560)=hAPP(hAPP(X17563,X17562),c_List_Ofoldr(X17565,X17564,X17563,X17561,X17560)), inference(variable_rename,[status(thm)],[fact_foldr_Osimps_I2_J])). 6.97/7.21 fof(c_0_5497, plain, ![X12425, X12426, X12427, X12428, X12429, X12430, X12431]:hAPP(hAPP(c_Product__Type_OPair(X12429,X12430),hAPP(X12426,hAPP(c_Product__Type_Ofst(X12427,X12431),X12425))),hAPP(X12428,hAPP(c_Product__Type_Osnd(X12427,X12431),X12425)))=hAPP(c_Product__Type_Oapsnd(X12431,X12430,X12429,X12428),hAPP(c_Product__Type_Oapfst(X12427,X12429,X12431,X12426),X12425)), inference(variable_rename,[status(thm)],[fact_apsnd__apfst])). 6.97/7.21 fof(c_0_5498, plain, ![X2397, X2398, X2399, X2400, X2401, X2402, X2403]:hAPP(hAPP(c_Product__Type_OPair(X2402,X2401),hAPP(X2400,hAPP(c_Product__Type_Ofst(X2403,X2399),X2397))),hAPP(X2398,hAPP(c_Product__Type_Osnd(X2403,X2399),X2397)))=hAPP(c_Product__Type_Oapfst(X2403,X2402,X2401,X2400),hAPP(c_Product__Type_Oapsnd(X2399,X2401,X2403,X2398),X2397)), inference(variable_rename,[status(thm)],[fact_apfst__apsnd])). 6.97/7.21 fof(c_0_5499, plain, ![X16274, X16275, X16276, X16277, X16278, X16279, X16280]:hAPP(c_Product__Type_Oapsnd(X16280,X16279,X16278,X16277),hAPP(c_Product__Type_Oapfst(X16276,X16278,X16280,X16275),X16274))=hAPP(c_Product__Type_Oapfst(X16276,X16278,X16279,X16275),hAPP(c_Product__Type_Oapsnd(X16280,X16279,X16276,X16277),X16274)), inference(variable_rename,[status(thm)],[fact_apsnd__apfst__commute])). 6.97/7.21 cnf(c_0_5500, plain, (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)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_4636])). 6.97/7.21 fof(c_0_5501, plain, ![X5614, X5615, X5616]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5616),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5615),X5614))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5616),X5615)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5616),X5614)), inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib2])). 6.97/7.21 fof(c_0_5502, plain, ![X9163, X9164, X9165, X9166, X9167]:hAPP(hAPP(c_List_Omap(X9165,X9167),X9164),hAPP(c_List_Orotate(X9165,X9166),X9163))=hAPP(c_List_Orotate(X9167,X9166),hAPP(hAPP(c_List_Omap(X9165,X9167),X9164),X9163)), inference(variable_rename,[status(thm)],[fact_rotate__map])). 6.97/7.21 fof(c_0_5503, plain, ![X5871, X5872, X5873, X5874, X5875, X5876, X5877]:hAPP(c_Product__Type_Oapsnd(X5877,X5876,X5875,X5874),hAPP(c_Product__Type_Oapsnd(X5873,X5877,X5875,X5872),X5871))=hAPP(c_Product__Type_Oapsnd(X5873,X5876,X5875,hAPP(c_Fun_Ocomp(X5877,X5876,X5873,X5874),X5872)),X5871), inference(variable_rename,[status(thm)],[fact_apsnd__compose])). 6.97/7.21 fof(c_0_5504, plain, ![X12143, X12144, X12145, X12146, X12147, X12148, X12149]:hAPP(c_Product__Type_Oapfst(X12145,X12148,X12147,hAPP(c_Fun_Ocomp(X12149,X12148,X12145,X12146),X12144)),X12143)=hAPP(c_Product__Type_Oapfst(X12149,X12148,X12147,X12146),hAPP(c_Product__Type_Oapfst(X12145,X12149,X12147,X12144),X12143)), inference(variable_rename,[status(thm)],[fact_apfst__compose])). 6.97/7.21 cnf(c_0_5505, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2))=c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4637])). 6.97/7.21 fof(c_0_5506, plain, ![X13744, X13745]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X13745),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X13744)))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X13745),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X13744))),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])). 6.97/7.21 fof(c_0_5507, plain, ![X15210, X15211]:hAPP(c_Set_Oimage(X15211,tc_List_Olist(X15211),hAPP(hAPP(c_COMBC(X15211,tc_List_Olist(X15211),tc_List_Olist(X15211)),c_List_Olist_OCons(X15211)),c_List_Olist_ONil(X15211))),X15210)=c_List_Oset__Cons(X15211,X15210,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X15211)),c_List_Olist_ONil(X15211)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X15211),tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_set__Cons__sing__Nil])). 6.97/7.21 fof(c_0_5508, plain, ![X6973, X6974]:hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X6974),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X6974))),X6973))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6974)),c_List_Oconcat(X6974,X6973)), inference(variable_rename,[status(thm)],[fact_length__concat])). 6.97/7.21 fof(c_0_5509, plain, ![X11782, X11783, X11784, X11785]:c_List_Olist_Olist__size(X11785,X11784,hAPP(hAPP(c_List_Olist_OCons(X11785),X11783),X11782))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X11784,X11783)),c_List_Olist_Olist__size(X11785,X11784,X11782))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_list_Osize_I2_J])). 6.97/7.21 fof(c_0_5510, plain, ![X8427, X8428, X8429, X8430]:hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X8430,X8429),c_Lazy__Sequence_Olazy__sequence_OInsert(X8430,X8428,X8427))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X8429,X8428)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X8430,X8429),X8427))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osize_I2_J])). 6.97/7.21 fof(c_0_5511, plain, ![X3012]:hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3012)),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(X3012)), inference(variable_rename,[status(thm)],[fact_nat__number__of__Bit0])). 6.97/7.21 fof(c_0_5512, plain, ![X4602, X4603, X4604]:hAPP(c_Relation_ORange(X4604,X4603),hAPP(c_Set_OCollect(tc_prod(X4604,X4603)),hAPP(c_Product__Type_Oprod_Oprod__case(X4604,X4603,tc_HOL_Obool),X4602)))=hAPP(c_Set_OCollect(X4603),hAPP(hAPP(c_COMBB(tc_fun(X4604,tc_HOL_Obool),tc_HOL_Obool,X4603),c_HOL_OEx(X4604)),hAPP(c_COMBC(X4604,X4603,tc_HOL_Obool),X4602))), inference(variable_rename,[status(thm)],[fact_Range__Collect__split])). 6.97/7.21 fof(c_0_5513, plain, ![X582, X583]:hAPP(c_Relation_OField(X583),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X583,X583),tc_HOL_Obool),X582))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X583,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(X583,X583),tc_HOL_Obool),tc_fun(X583,tc_HOL_Obool),c_Relation_OField(X583)),X582)), inference(variable_rename,[status(thm)],[fact_Field__Union])). 6.97/7.21 cnf(c_0_5514, 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_4638])). 6.97/7.21 fof(c_0_5515, plain, ![X5439, X5440, X5441, X5442, X5443, X5444]:hAPP(c_Set_Ovimage(X5444,X5442,X5440),hAPP(c_Set_Ovimage(X5442,X5443,X5441),X5439))=hAPP(c_Set_Ovimage(X5444,X5443,hAPP(c_Fun_Ocomp(X5442,X5443,X5444,X5441),X5440)),X5439), inference(variable_rename,[status(thm)],[fact_vimage__compose])). 6.97/7.21 fof(c_0_5516, plain, ![X4032, X4033]:hAPP(c_Set_OPow(X4033),X4032)=hAPP(c_Set_OCollect(tc_fun(X4033,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X4033,tc_HOL_Obool),tc_fun(X4033,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X4033,tc_HOL_Obool))),X4032)), inference(variable_rename,[status(thm)],[fact_Pow__def])). 6.97/7.21 fof(c_0_5517, plain, ![X4176, X4177, X4178, X4179]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4179,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X4179,X4178,X4177),X4176))=hAPP(c_Set_Ovimage(X4179,X4178,X4177),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4178,tc_HOL_Obool)),X4176)), inference(variable_rename,[status(thm)],[fact_vimage__Compl])). 6.97/7.21 fof(c_0_5518, plain, ![X11319, X11320]:hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X11320),X11319)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X11320,X11319))=c_Divides_Odivmod__nat(X11320,X11319), inference(variable_rename,[status(thm)],[fact_divmod__nat__div__mod])). 6.97/7.21 fof(c_0_5519, plain, ![X11083, X11084, X11085, X11086]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11085,tc_HOL_Obool)),X11083),hAPP(c_Set_Oimage(X11086,X11085,X11084),c_Orderings_Otop__class_Otop(tc_fun(X11086,tc_HOL_Obool))))=hAPP(c_Set_Oimage(X11086,X11085,X11084),hAPP(c_Set_Ovimage(X11086,X11085,X11084),X11083)), inference(variable_rename,[status(thm)],[fact_image__vimage__eq])). 6.97/7.21 cnf(c_0_5520, plain, (c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X1,X2,X3,c_Code__Numeral_OSuc__code__numeral(X4))=hAPP(hAPP(X3,X4),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X1,X2,X3,X4))), inference(split_conjunct,[status(thm)],[c_0_4639])). 6.97/7.21 fof(c_0_5521, plain, ![X8972, X8973, X8974, X8975, X8976]:((X8976!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X8975,X8974,X8973),X8976),X8972)=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X8974),X8975),c_List_Olist_ONil(X8974)),X8972))&(X8976=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(X8974),X8975),tc_prod(X8974,X8975),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X8974),X8975),c_List_Olist_ONil(X8974)),X8972),hAPP(c_Product__Type_Oprod_Oprod__case(X8974,X8975,tc_prod(tc_List_Olist(X8974),X8975)),hAPP(hAPP(c_COMBC(X8974,tc_fun(X8975,tc_prod(tc_List_Olist(X8974),X8975)),tc_fun(X8975,tc_prod(tc_List_Olist(X8974),X8975))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(X8974),X8975),tc_prod(tc_List_Olist(X8974),X8975)),tc_fun(tc_fun(X8975,tc_prod(tc_List_Olist(X8974),X8975)),tc_fun(X8975,tc_prod(tc_List_Olist(X8974),X8975))),X8974),c_COMBB(tc_prod(tc_List_Olist(X8974),X8975),tc_prod(tc_List_Olist(X8974),X8975),X8975)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X8974),tc_fun(X8975,tc_prod(tc_List_Olist(X8974),X8975))),tc_fun(tc_prod(tc_List_Olist(X8974),X8975),tc_prod(tc_List_Olist(X8974),X8975)),X8974),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X8974),X8975,tc_prod(tc_List_Olist(X8974),X8975))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X8974),tc_List_Olist(X8974)),tc_fun(tc_List_Olist(X8974),tc_fun(X8975,tc_prod(tc_List_Olist(X8974),X8975))),X8974),hAPP(c_COMBB(tc_List_Olist(X8974),tc_fun(X8975,tc_prod(tc_List_Olist(X8974),X8975)),tc_List_Olist(X8974)),c_Product__Type_OPair(tc_List_Olist(X8974),X8975))),c_List_Olist_OCons(X8974))))),hAPP(c_Lazy__Sequence_Oanamorph(X8975,X8974,X8973),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X8976),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))),hAPP(X8973,X8972))=hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X8975,X8974,X8973),X8976),X8972))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_anamorph_Osimps])])). 6.97/7.21 fof(c_0_5522, plain, ![X16417, X16418]:c_Relation_OId(X16418)=hAPP(hAPP(c_Nat_Ocompow(tc_prod(X16418,X16418),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X16417), inference(variable_rename,[status(thm)],[fact_relpow_Osimps_I1_J])). 6.97/7.21 fof(c_0_5523, plain, ![X15010, X15011]:hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X15011),tc_List_Olist(X15011))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X15011),tc_List_Olist(X15011),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(X15011),tc_fun(tc_List_Olist(X15011),tc_HOL_Obool),tc_fun(tc_List_Olist(X15011),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X15011),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X15011),tc_HOL_Obool),tc_fun(tc_List_Olist(X15011),tc_HOL_Obool)),tc_List_Olist(X15011)),c_COMBS(tc_List_Olist(X15011),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X15011),tc_HOL_Obool),tc_fun(tc_List_Olist(X15011),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X15011)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X15011)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X15011),tc_fun(tc_List_Olist(X15011),tc_Nat_Onat),tc_fun(tc_List_Olist(X15011),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X15011),tc_Nat_Onat),tc_fun(tc_List_Olist(X15011),tc_HOL_Obool)),tc_List_Olist(X15011)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X15011))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X15011)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X15011))))),c_Nat_Osize__class_Osize(tc_List_Olist(X15011)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(X15011),tc_fun(tc_List_Olist(X15011),tc_HOL_Obool),tc_fun(tc_List_Olist(X15011),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X15011),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X15011),tc_HOL_Obool),tc_fun(tc_List_Olist(X15011),tc_HOL_Obool)),tc_List_Olist(X15011)),c_COMBS(tc_List_Olist(X15011),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X15011),tc_HOL_Obool),tc_fun(tc_List_Olist(X15011),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X15011)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X15011)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X15011),tc_fun(tc_List_Olist(X15011),tc_Nat_Onat),tc_fun(tc_List_Olist(X15011),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X15011),tc_Nat_Onat),tc_fun(tc_List_Olist(X15011),tc_HOL_Obool)),tc_List_Olist(X15011)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X15011))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X15011)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X15011))))),c_Nat_Osize__class_Osize(tc_List_Olist(X15011)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X15011),tc_fun(tc_prod(tc_List_Olist(X15011),tc_List_Olist(X15011)),tc_HOL_Obool),tc_fun(tc_List_Olist(X15011),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X15011),tc_fun(tc_fun(tc_prod(tc_List_Olist(X15011),tc_List_Olist(X15011)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X15011),tc_List_Olist(X15011)),tc_HOL_Obool),tc_fun(tc_List_Olist(X15011),tc_HOL_Obool)),tc_List_Olist(X15011)),c_COMBC(tc_List_Olist(X15011),tc_fun(tc_prod(tc_List_Olist(X15011),tc_List_Olist(X15011)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X15011),tc_prod(tc_List_Olist(X15011),tc_List_Olist(X15011))),tc_fun(tc_List_Olist(X15011),tc_fun(tc_fun(tc_prod(tc_List_Olist(X15011),tc_List_Olist(X15011)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(X15011)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X15011),tc_List_Olist(X15011)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X15011),tc_List_Olist(X15011)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X15011)),c_member(tc_prod(tc_List_Olist(X15011),tc_List_Olist(X15011))))),c_Product__Type_OPair(tc_List_Olist(X15011),tc_List_Olist(X15011))))),c_List_Olex(X15011,X15010))))))=c_List_Olenlex(X15011,X15010), inference(variable_rename,[status(thm)],[fact_lenlex__conv])). 6.97/7.21 fof(c_0_5524, plain, ![X6690, X6691, X6692]:hAPP(c_Set_OCollect(tc_List_Olist(X6692)),hAPP(hAPP(c_COMBB(tc_fun(X6692,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(X6692)),c_HOL_OEx(X6692)),hAPP(hAPP(c_COMBB(tc_fun(X6692,tc_fun(tc_List_Olist(X6692),tc_HOL_Obool)),tc_fun(X6692,tc_HOL_Obool),tc_List_Olist(X6692)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X6692),tc_HOL_Obool),tc_HOL_Obool,X6692),c_HOL_OEx(tc_List_Olist(X6692)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X6692),tc_fun(X6692,tc_fun(tc_List_Olist(X6692),tc_HOL_Obool)),tc_fun(X6692,tc_fun(tc_List_Olist(X6692),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X6692,tc_fun(tc_fun(tc_List_Olist(X6692),tc_HOL_Obool),tc_fun(tc_List_Olist(X6692),tc_HOL_Obool))),tc_fun(tc_fun(X6692,tc_fun(tc_List_Olist(X6692),tc_HOL_Obool)),tc_fun(X6692,tc_fun(tc_List_Olist(X6692),tc_HOL_Obool))),tc_List_Olist(X6692)),c_COMBS(X6692,tc_fun(tc_List_Olist(X6692),tc_HOL_Obool),tc_fun(tc_List_Olist(X6692),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X6692,tc_fun(tc_List_Olist(X6692),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X6692,tc_fun(tc_fun(tc_List_Olist(X6692),tc_HOL_Obool),tc_fun(tc_List_Olist(X6692),tc_HOL_Obool))),tc_List_Olist(X6692)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X6692),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X6692),tc_HOL_Obool),tc_fun(tc_List_Olist(X6692),tc_HOL_Obool)),X6692),c_COMBS(tc_List_Olist(X6692),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X6692,tc_fun(tc_List_Olist(X6692),tc_HOL_Obool)),tc_fun(X6692,tc_fun(tc_List_Olist(X6692),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(X6692)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X6692),tc_HOL_Obool),tc_fun(tc_List_Olist(X6692),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X6692),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X6692)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(X6692),tc_fun(X6692,tc_fun(tc_List_Olist(X6692),tc_List_Olist(X6692))),tc_fun(X6692,tc_fun(tc_List_Olist(X6692),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(X6692),tc_List_Olist(X6692)),tc_fun(tc_List_Olist(X6692),tc_HOL_Obool)),tc_fun(tc_fun(X6692,tc_fun(tc_List_Olist(X6692),tc_List_Olist(X6692))),tc_fun(X6692,tc_fun(tc_List_Olist(X6692),tc_HOL_Obool))),tc_List_Olist(X6692)),c_COMBB(tc_fun(tc_List_Olist(X6692),tc_List_Olist(X6692)),tc_fun(tc_List_Olist(X6692),tc_HOL_Obool),X6692)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X6692),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X6692),tc_List_Olist(X6692)),tc_fun(tc_List_Olist(X6692),tc_HOL_Obool)),tc_List_Olist(X6692)),c_COMBB(tc_List_Olist(X6692),tc_HOL_Obool,tc_List_Olist(X6692))),c_fequal))),c_List_Olist_OCons(X6692)))))),hAPP(hAPP(c_COMBC(X6692,tc_fun(tc_List_Olist(X6692),tc_HOL_Obool),tc_fun(tc_List_Olist(X6692),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X6692),tc_HOL_Obool),tc_fun(tc_List_Olist(X6692),tc_HOL_Obool)),X6692),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X6692))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X6692),c_fconj),hAPP(hAPP(c_COMBC(X6692,tc_fun(X6692,tc_HOL_Obool),tc_HOL_Obool),c_member(X6692)),X6691)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X6692),tc_fun(tc_List_Olist(X6692),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X6692))),X6690))))))=c_List_Oset__Cons(X6692,X6691,X6690), inference(variable_rename,[status(thm)],[fact_set__Cons__def])). 6.97/7.21 fof(c_0_5525, plain, ![X11289, X11290, X11291, X11292, X11293]:hAPP(hAPP(c_Relation_Orel__comp(X11293,X11292,X11291),X11290),X11289)=hAPP(c_Set_OCollect(tc_prod(X11293,X11291)),hAPP(c_Product__Type_Oprod_Oprod__case(X11293,X11291,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X11291,tc_fun(X11292,tc_HOL_Obool)),tc_fun(X11291,tc_HOL_Obool),X11293),hAPP(c_COMBB(tc_fun(X11292,tc_HOL_Obool),tc_HOL_Obool,X11291),c_HOL_OEx(X11292))),hAPP(hAPP(c_COMBC(X11293,tc_fun(X11291,tc_fun(X11292,tc_HOL_Obool)),tc_fun(X11291,tc_fun(X11292,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X11292,tc_HOL_Obool),tc_fun(X11292,tc_HOL_Obool)),tc_fun(tc_fun(X11291,tc_fun(X11292,tc_HOL_Obool)),tc_fun(X11291,tc_fun(X11292,tc_HOL_Obool))),X11293),c_COMBB(tc_fun(X11292,tc_HOL_Obool),tc_fun(X11292,tc_HOL_Obool),X11291)),hAPP(hAPP(c_COMBB(tc_fun(X11292,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X11292,tc_HOL_Obool),tc_fun(X11292,tc_HOL_Obool)),X11293),c_COMBS(X11292,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X11292,tc_HOL_Obool),tc_fun(X11292,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X11293),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X11292),c_fconj)),hAPP(hAPP(c_COMBC(X11293,tc_fun(tc_prod(X11293,X11292),tc_HOL_Obool),tc_fun(X11292,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X11292,tc_fun(tc_fun(tc_prod(X11293,X11292),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X11293,X11292),tc_HOL_Obool),tc_fun(X11292,tc_HOL_Obool)),X11293),c_COMBC(X11292,tc_fun(tc_prod(X11293,X11292),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X11292,tc_prod(X11293,X11292)),tc_fun(X11292,tc_fun(tc_fun(tc_prod(X11293,X11292),tc_HOL_Obool),tc_HOL_Obool)),X11293),hAPP(c_COMBB(tc_prod(X11293,X11292),tc_fun(tc_fun(tc_prod(X11293,X11292),tc_HOL_Obool),tc_HOL_Obool),X11292),c_member(tc_prod(X11293,X11292)))),c_Product__Type_OPair(X11293,X11292)))),X11290))))),hAPP(hAPP(c_COMBC(X11291,tc_fun(tc_prod(X11292,X11291),tc_HOL_Obool),tc_fun(X11292,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X11292,tc_fun(tc_fun(tc_prod(X11292,X11291),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X11292,X11291),tc_HOL_Obool),tc_fun(X11292,tc_HOL_Obool)),X11291),c_COMBC(X11292,tc_fun(tc_prod(X11292,X11291),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X11292,tc_prod(X11292,X11291)),tc_fun(X11292,tc_fun(tc_fun(tc_prod(X11292,X11291),tc_HOL_Obool),tc_HOL_Obool)),X11291),hAPP(c_COMBB(tc_prod(X11292,X11291),tc_fun(tc_fun(tc_prod(X11292,X11291),tc_HOL_Obool),tc_HOL_Obool),X11292),c_member(tc_prod(X11292,X11291)))),hAPP(c_COMBC(X11292,X11291,tc_prod(X11292,X11291)),c_Product__Type_OPair(X11292,X11291))))),X11289))))), inference(variable_rename,[status(thm)],[fact_rel__comp__def])). 6.97/7.21 cnf(c_0_5526, 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_4640])). 6.97/7.21 fof(c_0_5527, plain, ![X9194, X9195, X9196]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(X9196),tc_List_Olist(X9196)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(X9196,tc_List_Olist(X9196)),tc_prod(X9196,tc_List_Olist(X9196))),tc_prod(tc_List_Olist(X9196),tc_List_Olist(X9196)),c_Product__Type_Omap__pair(tc_prod(X9196,tc_List_Olist(X9196)),tc_List_Olist(X9196),tc_prod(X9196,tc_List_Olist(X9196)),tc_List_Olist(X9196),hAPP(c_Product__Type_Oprod_Oprod__case(X9196,tc_List_Olist(X9196),tc_List_Olist(X9196)),c_List_Olist_OCons(X9196)),hAPP(c_Product__Type_Oprod_Oprod__case(X9196,tc_List_Olist(X9196),tc_List_Olist(X9196)),c_List_Olist_OCons(X9196)))),c_Wellfounded_Olex__prod(X9196,tc_List_Olist(X9196),X9195,hAPP(c_List_Olexn(X9196,X9195),X9194)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X9196),tc_List_Olist(X9196))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X9196),tc_List_Olist(X9196),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X9196),tc_fun(tc_List_Olist(X9196),tc_HOL_Obool),tc_fun(tc_List_Olist(X9196),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X9196),tc_HOL_Obool),tc_fun(tc_List_Olist(X9196),tc_HOL_Obool)),tc_List_Olist(X9196)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X9196))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X9196)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X9196),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X9196)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X9196)))),hAPP(c_Nat_OSuc,X9194))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X9196),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X9196)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X9196)))),hAPP(c_Nat_OSuc,X9194))))))=hAPP(c_List_Olexn(X9196,X9195),hAPP(c_Nat_OSuc,X9194)), inference(variable_rename,[status(thm)],[fact_lexn_Osimps_I2_J])). 6.97/7.21 fof(c_0_5528, plain, ![X14337, X14338]:hAPP(c_Set_OPow(X14338),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X14338,tc_HOL_Obool)),X14337))=hAPP(c_Set_OCollect(tc_fun(X14338,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X14338,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X14338,tc_HOL_Obool)),c_HOL_OEx(tc_fun(X14338,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X14338,tc_HOL_Obool),tc_fun(tc_fun(X14338,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X14338,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X14338,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X14338,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X14338,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X14338,tc_HOL_Obool)),c_COMBS(tc_fun(X14338,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X14338,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X14338,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X14338,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X14338,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(X14338,tc_HOL_Obool),tc_fun(tc_fun(X14338,tc_HOL_Obool),tc_fun(X14338,tc_HOL_Obool)),tc_fun(tc_fun(X14338,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X14338,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X14338,tc_HOL_Obool),tc_fun(X14338,tc_HOL_Obool)),tc_fun(tc_fun(X14338,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X14338,tc_HOL_Obool)),c_COMBB(tc_fun(X14338,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X14338,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(X14338,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X14338,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X14338,tc_HOL_Obool)),hAPP(c_member(tc_fun(X14338,tc_HOL_Obool)),X14337)),c_Set_OPow(X14338))))), inference(variable_rename,[status(thm)],[fact_Pow__Compl])). 6.97/7.21 fof(c_0_5529, plain, ![X3235, X3236, X3237, X3238]:hAPP(c_List_Oset(tc_prod(X3238,X3237)),hAPP(hAPP(c_List_Ozip(X3238,X3237),X3236),X3235))=hAPP(c_Set_OCollect(tc_prod(X3238,X3237)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X3238,X3237)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X3238,X3237),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(X3238,X3237)),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(X3238,X3237)),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(X3238,X3237),tc_fun(tc_Nat_Onat,tc_prod(X3238,X3237)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X3238,X3237),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(X3238,X3237)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X3238,X3237)),c_COMBB(tc_prod(X3238,X3237),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X3237,tc_prod(X3238,X3237)),hAPP(hAPP(c_COMBB(X3238,tc_fun(X3237,tc_prod(X3238,X3237)),tc_Nat_Onat),c_Product__Type_OPair(X3238,X3237)),hAPP(c_List_Onth(X3238),X3236))),hAPP(c_List_Onth(X3237),X3235)))))),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(X3238)),X3236)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3237)),X3235)))))), inference(variable_rename,[status(thm)],[fact_set__zip])). 6.97/7.22 cnf(c_0_5530, plain, (c_Nitpick_Oplus__frac(X1,X2,X3)=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)))), inference(split_conjunct,[status(thm)],[c_0_4641])). 6.97/7.22 cnf(c_0_5531, 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),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)))),X3)),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)))),X3)),X1)))=hAPP(c_Divides_Oadjust(X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X1))), inference(split_conjunct,[status(thm)],[c_0_4642])). 6.97/7.22 fof(c_0_5532, plain, ![X17441, X17442]: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,X17442))),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),X17441)))))),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)),X17441))),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)),X17441))))),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)),X17441)))),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),X17441))),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(X17442,X17441), inference(variable_rename,[status(thm)],[fact_divmod__int__rel__def])). 6.97/7.22 fof(c_0_5533, plain, ![X2689, X2690, X2691]:hAPP(c_List_Oset(X2691),c_List_Osublist(X2691,X2690,X2689))=hAPP(c_Set_OCollect(X2691),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X2691),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X2691,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)),X2691),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)),X2691),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X2691,tc_fun(tc_Nat_Onat,X2691),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2691,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X2691),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X2691),c_COMBB(X2691,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X2691),X2690))))),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(X2691)),X2690)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X2689))))), inference(variable_rename,[status(thm)],[fact_set__sublist])). 6.97/7.22 fof(c_0_5534, plain, ![X15989, X15990, X15991, X15992]:hAPP(hAPP(c_Relation_Oinv__image(X15992,X15991),X15990),X15989)=hAPP(c_Set_OCollect(tc_prod(X15991,X15991)),hAPP(c_Product__Type_Oprod_Oprod__case(X15991,X15991,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X15991,tc_fun(tc_prod(X15992,X15992),tc_HOL_Obool),tc_fun(X15991,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X15991,tc_fun(tc_fun(tc_prod(X15992,X15992),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X15992,X15992),tc_HOL_Obool),tc_fun(X15991,tc_HOL_Obool)),X15991),c_COMBC(X15991,tc_fun(tc_prod(X15992,X15992),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X15991,tc_prod(X15992,X15992)),tc_fun(X15991,tc_fun(tc_fun(tc_prod(X15992,X15992),tc_HOL_Obool),tc_HOL_Obool)),X15991),hAPP(c_COMBB(tc_prod(X15992,X15992),tc_fun(tc_fun(tc_prod(X15992,X15992),tc_HOL_Obool),tc_HOL_Obool),X15991),c_member(tc_prod(X15992,X15992)))),hAPP(hAPP(c_COMBC(X15991,tc_fun(X15991,X15992),tc_fun(X15991,tc_prod(X15992,X15992))),hAPP(hAPP(c_COMBB(tc_fun(X15992,tc_prod(X15992,X15992)),tc_fun(tc_fun(X15991,X15992),tc_fun(X15991,tc_prod(X15992,X15992))),X15991),c_COMBB(X15992,tc_prod(X15992,X15992),X15991)),hAPP(hAPP(c_COMBB(X15992,tc_fun(X15992,tc_prod(X15992,X15992)),X15991),c_Product__Type_OPair(X15992,X15992)),X15989))),X15989)))),X15990))), inference(variable_rename,[status(thm)],[fact_inv__image__def])). 6.97/7.22 cnf(c_0_5535, 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_4643])). 6.97/7.22 cnf(c_0_5536, plain, (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))=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))), inference(rw,[status(thm)],[c_0_4644, c_0_4645])). 6.97/7.22 cnf(c_0_5537, 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)), inference(rw,[status(thm)],[c_0_4646, c_0_4645]), ['final']). 6.97/7.22 cnf(c_0_5538, 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_4647, c_0_4467]), ['final']). 6.97/7.22 cnf(c_0_5539, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=hAPP(c_fequal,X2)), inference(rw,[status(thm)],[c_0_4648, c_0_4467]), ['final']). 6.97/7.22 cnf(c_0_5540, 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_4649, c_0_4645])). 6.97/7.22 cnf(c_0_5541, plain, (hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4)),X5))=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)),hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),X5))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,X1),tc_Int_Oint),X3),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,X2,X3)),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)))))), inference(split_conjunct,[status(thm)],[c_0_4650])). 6.97/7.22 cnf(c_0_5542, plain, (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))))=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)))), inference(split_conjunct,[status(thm)],[c_0_4651])). 6.97/7.22 fof(c_0_5543, plain, ![X10424, X10425]:hAPP(c_List_Oset(X10425),X10424)=hAPP(c_Set_OCollect(X10425),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X10425),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X10425,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)),X10425),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)),X10425),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X10425,tc_fun(tc_Nat_Onat,X10425),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10425,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X10425),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X10425),c_COMBB(X10425,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X10425),X10424))))),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(X10425)),X10424))))), inference(variable_rename,[status(thm)],[fact_set__conv__nth])). 6.97/7.22 fof(c_0_5544, plain, ![X756, X757, X758, X759]:c_Complete__Lattice_OInf__class_OInf(tc_fun(X758,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(X758,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X759,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X758,tc_HOL_Obool)),c_HOL_OEx(X759)),hAPP(hAPP(c_COMBB(tc_fun(X759,tc_HOL_Obool),tc_fun(X759,tc_HOL_Obool),tc_fun(X758,tc_HOL_Obool)),hAPP(c_COMBS(X759,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X759),c_fconj),hAPP(hAPP(c_COMBC(X759,tc_fun(X759,tc_HOL_Obool),tc_HOL_Obool),c_member(X759)),X757)))),hAPP(hAPP(c_COMBC(tc_fun(X758,tc_HOL_Obool),tc_fun(X759,tc_fun(X758,tc_HOL_Obool)),tc_fun(X759,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X758,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X759,tc_fun(X758,tc_HOL_Obool)),tc_fun(X759,tc_HOL_Obool)),tc_fun(X758,tc_HOL_Obool)),c_COMBB(tc_fun(X758,tc_HOL_Obool),tc_HOL_Obool,X759)),c_fequal)),X756)))))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X759,tc_fun(X758,tc_HOL_Obool)),X757),X756), inference(variable_rename,[status(thm)],[fact_INT__eq])). 6.97/7.22 fof(c_0_5545, plain, ![X13073, X13074, X13075, X13076]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13076,tc_fun(X13075,tc_HOL_Obool)),X13074),X13073)=c_Complete__Lattice_OSup__class_OSup(tc_fun(X13075,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(X13075,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13076,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X13075,tc_HOL_Obool)),c_HOL_OEx(X13076)),hAPP(hAPP(c_COMBB(tc_fun(X13076,tc_HOL_Obool),tc_fun(X13076,tc_HOL_Obool),tc_fun(X13075,tc_HOL_Obool)),hAPP(c_COMBS(X13076,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X13076),c_fconj),hAPP(hAPP(c_COMBC(X13076,tc_fun(X13076,tc_HOL_Obool),tc_HOL_Obool),c_member(X13076)),X13074)))),hAPP(hAPP(c_COMBC(tc_fun(X13075,tc_HOL_Obool),tc_fun(X13076,tc_fun(X13075,tc_HOL_Obool)),tc_fun(X13076,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X13075,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X13076,tc_fun(X13075,tc_HOL_Obool)),tc_fun(X13076,tc_HOL_Obool)),tc_fun(X13075,tc_HOL_Obool)),c_COMBB(tc_fun(X13075,tc_HOL_Obool),tc_HOL_Obool,X13076)),c_fequal)),X13073))))), inference(variable_rename,[status(thm)],[fact_UN__eq])). 6.97/7.22 fof(c_0_5546, plain, ![X4651, X4652, X4653]:hAPP(c_Set_OCollect(tc_prod(X4652,X4653)),hAPP(c_Product__Type_Oprod_Oprod__case(X4652,X4653,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4652,tc_fun(tc_prod(X4653,X4652),tc_HOL_Obool),tc_fun(X4653,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4653,tc_fun(tc_fun(tc_prod(X4653,X4652),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4653,X4652),tc_HOL_Obool),tc_fun(X4653,tc_HOL_Obool)),X4652),c_COMBC(X4653,tc_fun(tc_prod(X4653,X4652),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4653,tc_prod(X4653,X4652)),tc_fun(X4653,tc_fun(tc_fun(tc_prod(X4653,X4652),tc_HOL_Obool),tc_HOL_Obool)),X4652),hAPP(c_COMBB(tc_prod(X4653,X4652),tc_fun(tc_fun(tc_prod(X4653,X4652),tc_HOL_Obool),tc_HOL_Obool),X4653),c_member(tc_prod(X4653,X4652)))),hAPP(c_COMBC(X4653,X4652,tc_prod(X4653,X4652)),c_Product__Type_OPair(X4653,X4652))))),X4651)))=hAPP(c_Relation_Oconverse(X4653,X4652),X4651), inference(variable_rename,[status(thm)],[fact_converse__def])). 6.97/7.22 fof(c_0_5547, plain, ![X8490]: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,X8490)),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,X8490), inference(variable_rename,[status(thm)],[fact_nat__def])). 6.97/7.22 fof(c_0_5548, plain, ![X16441]:hAPP(c_Set_OCollect(tc_prod(tc_fun(X16441,tc_HOL_Obool),tc_fun(X16441,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(X16441,tc_HOL_Obool),tc_fun(X16441,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X16441,tc_HOL_Obool),tc_fun(tc_fun(X16441,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X16441,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X16441,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X16441,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X16441,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X16441,tc_HOL_Obool)),c_COMBS(tc_fun(X16441,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X16441,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X16441,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X16441,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X16441,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(X16441,tc_HOL_Obool))))),c_Finite__Set_Ofinite(X16441))))=c_Wellfounded_Ofinite__psubset(X16441), inference(variable_rename,[status(thm)],[fact_finite__psubset__def])). 6.97/7.22 fof(c_0_5549, plain, ![X15638, X15639, X15640, X15641]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X15641,tc_fun(X15640,tc_HOL_Obool)),X15639),X15638)=hAPP(c_Set_OCollect(X15640),hAPP(hAPP(c_COMBB(tc_fun(X15641,tc_HOL_Obool),tc_HOL_Obool,X15640),c_HOL_OAll(X15641)),hAPP(hAPP(c_COMBB(tc_fun(X15641,tc_HOL_Obool),tc_fun(X15641,tc_HOL_Obool),X15640),hAPP(c_COMBS(X15641,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X15641),c_fimplies),hAPP(hAPP(c_COMBC(X15641,tc_fun(X15641,tc_HOL_Obool),tc_HOL_Obool),c_member(X15641)),X15639)))),hAPP(hAPP(c_COMBC(X15640,tc_fun(X15641,tc_fun(X15640,tc_HOL_Obool)),tc_fun(X15641,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X15640,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X15641,tc_fun(X15640,tc_HOL_Obool)),tc_fun(X15641,tc_HOL_Obool)),X15640),c_COMBB(tc_fun(X15640,tc_HOL_Obool),tc_HOL_Obool,X15641)),c_member(X15640))),X15638)))), inference(variable_rename,[status(thm)],[fact_INTER__def])). 6.97/7.22 fof(c_0_5550, plain, ![X2917, X2918, X2919]:hAPP(hAPP(c_Equiv__Relations_Oquotient(X2919),X2918),X2917)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2919,tc_fun(tc_fun(X2919,tc_HOL_Obool),tc_HOL_Obool)),X2918),hAPP(hAPP(c_COMBC(X2919,tc_fun(tc_fun(X2919,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X2919,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2919,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X2919,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X2919,tc_HOL_Obool),tc_HOL_Obool)),X2919),c_Set_Oinsert(tc_fun(X2919,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2919,tc_HOL_Obool),tc_fun(X2919,tc_HOL_Obool),X2919),c_Relation_OImage(X2919,X2919,X2917)),hAPP(hAPP(c_COMBC(X2919,tc_fun(X2919,tc_HOL_Obool),tc_fun(X2919,tc_HOL_Obool)),c_Set_Oinsert(X2919)),c_Orderings_Obot__class_Obot(tc_fun(X2919,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X2919,tc_HOL_Obool),tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_quotient__def])). 6.97/7.22 fof(c_0_5551, plain, ![X6860, X6861, X6862, X6863]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6863,tc_fun(X6862,tc_HOL_Obool)),X6860),hAPP(hAPP(c_COMBC(X6863,tc_fun(X6862,tc_HOL_Obool),tc_fun(X6862,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X6862,tc_fun(tc_fun(X6862,tc_HOL_Obool),tc_fun(X6862,tc_HOL_Obool)),X6863),c_Set_Oinsert(X6862)),X6861)),c_Orderings_Obot__class_Obot(tc_fun(X6862,tc_HOL_Obool))))=hAPP(c_Set_Oimage(X6863,X6862,X6861),X6860), inference(variable_rename,[status(thm)],[fact_image__eq__UN])). 6.97/7.22 cnf(c_0_5552, 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_4652])). 6.97/7.22 fof(c_0_5553, plain, ![X9788, X9789, X9790]:hAPP(c_List_Oset(tc_List_Olist(X9790)),c_Enum_On__lists(X9790,X9789,X9788))=hAPP(c_Set_OCollect(tc_List_Olist(X9790)),hAPP(hAPP(c_COMBS(tc_List_Olist(X9790),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X9790)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X9790),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X9790)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X9790)))),X9789))),hAPP(hAPP(c_COMBC(tc_List_Olist(X9790),tc_fun(X9790,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X9790,tc_HOL_Obool),tc_fun(tc_fun(X9790,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X9790)),c_Orderings_Oord__class_Oless__eq(tc_fun(X9790,tc_HOL_Obool))),c_List_Oset(X9790))),hAPP(c_List_Oset(X9790),X9788)))), inference(variable_rename,[status(thm)],[fact_set__n__lists])). 6.97/7.22 fof(c_0_5554, plain, ![X8652, X8653, X8654, X8655, X8656, X8657, X8658, X8659]:hAPP(hAPP(c_List_Ozip(X8659,X8658),hAPP(hAPP(c_List_Omap(X8657,X8659),X8656),X8655)),hAPP(hAPP(c_List_Omap(X8654,X8658),X8653),X8652))=hAPP(hAPP(c_List_Omap(tc_prod(X8657,X8654),tc_prod(X8659,X8658)),hAPP(c_Product__Type_Oprod_Oprod__case(X8657,X8654,tc_prod(X8659,X8658)),hAPP(hAPP(c_COMBC(X8657,tc_fun(X8654,X8658),tc_fun(X8654,tc_prod(X8659,X8658))),hAPP(hAPP(c_COMBB(tc_fun(X8658,tc_prod(X8659,X8658)),tc_fun(tc_fun(X8654,X8658),tc_fun(X8654,tc_prod(X8659,X8658))),X8657),c_COMBB(X8658,tc_prod(X8659,X8658),X8654)),hAPP(hAPP(c_COMBB(X8659,tc_fun(X8658,tc_prod(X8659,X8658)),X8657),c_Product__Type_OPair(X8659,X8658)),X8656))),X8653))),hAPP(hAPP(c_List_Ozip(X8657,X8654),X8655),X8652)), inference(variable_rename,[status(thm)],[fact_zip__map__map])). 6.97/7.22 fof(c_0_5555, plain, ![X1202, X1203, X1204, X1205, X1206, X1207]:hAPP(c_Product__Type_Oprod_Oprod__case(X1207,X1205,tc_prod(X1206,X1204)),hAPP(hAPP(c_COMBC(X1207,tc_fun(X1205,X1204),tc_fun(X1205,tc_prod(X1206,X1204))),hAPP(hAPP(c_COMBB(tc_fun(X1204,tc_prod(X1206,X1204)),tc_fun(tc_fun(X1205,X1204),tc_fun(X1205,tc_prod(X1206,X1204))),X1207),c_COMBB(X1204,tc_prod(X1206,X1204),X1205)),hAPP(hAPP(c_COMBB(X1206,tc_fun(X1204,tc_prod(X1206,X1204)),X1207),c_Product__Type_OPair(X1206,X1204)),X1203))),X1202))=c_Product__Type_Omap__pair(X1207,X1206,X1205,X1204,X1203,X1202), inference(variable_rename,[status(thm)],[fact_map__pair__def])). 6.97/7.22 cnf(c_0_5556, 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_4653])). 6.97/7.22 cnf(c_0_5557, 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_4654])). 6.97/7.22 cnf(c_0_5558, plain, (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))=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))))), inference(split_conjunct,[status(thm)],[c_0_4655])). 6.97/7.22 cnf(c_0_5559, 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_4656])). 6.97/7.22 cnf(c_0_5560, 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_4657])). 6.97/7.22 fof(c_0_5561, plain, ![X14365, X14366, X14367, X14368]: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),X14368),X14367)),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),X14366),X14365)),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),X14368),X14366)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14367),X14365))),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])). 6.97/7.22 cnf(c_0_5562, 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_4658])). 6.97/7.22 fof(c_0_5563, plain, ![X9582, X9583]:c_Complete__Lattice_OSup__class_OSup(tc_fun(X9583,tc_HOL_Obool),X9582)=hAPP(c_Set_OCollect(X9583),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X9583,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X9583),c_HOL_OEx(tc_fun(X9583,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X9583,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X9583,tc_HOL_Obool),tc_HOL_Obool),X9583),hAPP(c_COMBS(tc_fun(X9583,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(X9583,tc_HOL_Obool)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X9583,tc_HOL_Obool),tc_fun(tc_fun(X9583,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X9583,tc_HOL_Obool))),X9582)))),c_member(X9583)))), inference(variable_rename,[status(thm)],[fact_Union__eq])). 6.97/7.22 cnf(c_0_5564, plain, (c_Nitpick_Otimes__frac(X1,X2,X3)=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)))), inference(split_conjunct,[status(thm)],[c_0_4659])). 6.97/7.22 cnf(c_0_5565, 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)),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_Orderings_Oord__class_Omax(tc_Nat_Onat),X2)),c_Int_Onat))))=hAPP(hAPP(c_Orderings_Oord__class_Omax(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_4660])). 6.97/7.22 cnf(c_0_5566, plain, (c_Enum_On__lists(X1,hAPP(c_Nat_OSuc,X2),X3)=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)))),X3)),c_Enum_On__lists(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_4661])). 6.97/7.22 cnf(c_0_5567, 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_4662])). 6.97/7.22 fof(c_0_5568, plain, ![X1920, X1921]:c_Relation_OId__on(X1921,X1920)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1921,tc_fun(tc_prod(X1921,X1921),tc_HOL_Obool)),X1920),hAPP(hAPP(c_COMBC(X1921,tc_fun(tc_prod(X1921,X1921),tc_HOL_Obool),tc_fun(tc_prod(X1921,X1921),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(X1921,X1921),tc_fun(tc_fun(tc_prod(X1921,X1921),tc_HOL_Obool),tc_fun(tc_prod(X1921,X1921),tc_HOL_Obool)),X1921),c_Set_Oinsert(tc_prod(X1921,X1921))),hAPP(hAPP(c_COMBS(X1921,X1921,tc_prod(X1921,X1921)),c_Product__Type_OPair(X1921,X1921)),c_COMBI(X1921)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1921,X1921),tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_Id__on__def])). 6.97/7.22 cnf(c_0_5569, plain, (c_Int_Oint__ge__less__than(X1)=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))))), inference(split_conjunct,[status(thm)],[c_0_4663])). 6.97/7.22 cnf(c_0_5570, 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_4664])). 6.97/7.22 fof(c_0_5571, plain, ![X13572, X13573, X13574, X13575]:hAPP(c_Set_OCollect(X13574),hAPP(hAPP(c_COMBB(tc_fun(X13575,tc_HOL_Obool),tc_HOL_Obool,X13574),c_HOL_OEx(X13575)),hAPP(hAPP(c_COMBB(tc_fun(X13575,tc_HOL_Obool),tc_fun(X13575,tc_HOL_Obool),X13574),hAPP(c_COMBS(X13575,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X13575),c_fconj),hAPP(hAPP(c_COMBC(X13575,tc_fun(X13575,tc_HOL_Obool),tc_HOL_Obool),c_member(X13575)),X13572)))),hAPP(c_COMBC(X13575,X13574,tc_HOL_Obool),X13573))))=hAPP(c_Relation_OImage(X13575,X13574,hAPP(c_Set_OCollect(tc_prod(X13575,X13574)),hAPP(c_Product__Type_Oprod_Oprod__case(X13575,X13574,tc_HOL_Obool),X13573))),X13572), inference(variable_rename,[status(thm)],[fact_Image__Collect__split])). 6.97/7.22 cnf(c_0_5572, 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_4665])). 6.97/7.22 cnf(c_0_5573, plain, (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)))))=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))))), inference(split_conjunct,[status(thm)],[c_0_4666])). 6.97/7.22 fof(c_0_5574, plain, ![X1931, X1932, X1933, X1934]:hAPP(hAPP(c_Product__Type_OPair(X1934,X1933),X1932),X1931)=c_Hilbert__Choice_OEps(tc_prod(X1934,X1933),hAPP(c_Product__Type_Oprod_Oprod__case(X1934,X1933,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1934,tc_fun(X1933,tc_HOL_Obool),tc_fun(X1933,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1933,tc_HOL_Obool),tc_fun(X1933,tc_HOL_Obool)),X1934),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1933)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1934),c_fconj),hAPP(c_fequal,X1932)))),hAPP(c_fequal,X1931)))), inference(variable_rename,[status(thm)],[fact_Eps__split__eq])). 6.97/7.22 fof(c_0_5575, plain, ![X3394, X3395, X3396, X3397]:hAPP(hAPP(c_Product__Type_OPair(X3397,X3396),X3395),X3394)=c_HOL_OThe(tc_prod(X3397,X3396),hAPP(c_Product__Type_Oprod_Oprod__case(X3397,X3396,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X3397,tc_fun(X3396,tc_HOL_Obool),tc_fun(X3396,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X3396,tc_HOL_Obool),tc_fun(X3396,tc_HOL_Obool)),X3397),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3396)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3397),c_fconj),hAPP(c_fequal,X3395)))),hAPP(c_fequal,X3394)))), inference(variable_rename,[status(thm)],[fact_The__split__eq])). 6.97/7.22 fof(c_0_5576, plain, ![X12250, X12251, X12252, X12253]:hAPP(hAPP(c_List_Oappend(X12253),hAPP(hAPP(hAPP(c_If(tc_List_Olist(X12253)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12250)),hAPP(hAPP(c_List_Olist_OCons(X12253),X12252),c_List_Olist_ONil(X12253))),c_List_Olist_ONil(X12253))),c_List_Osublist(X12253,X12251,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)),X12250))))=c_List_Osublist(X12253,hAPP(hAPP(c_List_Olist_OCons(X12253),X12252),X12251),X12250), inference(variable_rename,[status(thm)],[fact_sublist__Cons])). 6.97/7.22 cnf(c_0_5577, 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])). 6.97/7.22 fof(c_0_5578, plain, ![X8327, X8328, X8329]:c_List_Olistsp(X8329,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8329,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X8329,tc_fun(X8329,tc_HOL_Obool),tc_HOL_Obool),c_member(X8329)),X8328)),hAPP(hAPP(c_COMBC(X8329,tc_fun(X8329,tc_HOL_Obool),tc_HOL_Obool),c_member(X8329)),X8327)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X8329),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(X8329),tc_fun(tc_List_Olist(X8329),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X8329))),c_List_Olists(X8329,X8328))),hAPP(hAPP(c_COMBC(tc_List_Olist(X8329),tc_fun(tc_List_Olist(X8329),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X8329))),c_List_Olists(X8329,X8327))), inference(variable_rename,[status(thm)],[fact_lists__Int__eq])). 6.97/7.22 fof(c_0_5579, plain, ![X17317, X17318, X17319, X17320]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17320,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17320,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17320,tc_HOL_Obool)),X17319),X17318)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17320,tc_HOL_Obool)),X17318),X17317))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17320,tc_HOL_Obool)),X17317),X17319))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17320,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17320,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17320,tc_HOL_Obool)),X17319),X17318)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17320,tc_HOL_Obool)),X17318),X17317))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17320,tc_HOL_Obool)),X17317),X17319)), inference(variable_rename,[status(thm)],[fact_Un__Int__crazy])). 6.97/7.22 fof(c_0_5580, plain, ![X7557, X7558, X7559, X7560]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7560,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7560,tc_HOL_Obool)),X7559),X7558)),X7557)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7560,tc_HOL_Obool)),X7559),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7560,tc_HOL_Obool)),X7558),X7557)), inference(variable_rename,[status(thm)],[fact_Int__assoc])). 6.97/7.22 cnf(c_0_5581, 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_4667])). 6.97/7.22 fof(c_0_5582, plain, ![X3990, X3991]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X3991,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X3990)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X3991,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(X3991,tc_HOL_Obool)),tc_fun(X3991,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(X3991,tc_HOL_Obool)),tc_fun(X3991,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X3991,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X3990)), inference(variable_rename,[status(thm)],[fact_UN__UN__finite__eq])). 6.97/7.22 fof(c_0_5583, plain, ![X2882, X2883, X2884, X2885, X2886, X2887]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2887,tc_fun(X2886,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2885,tc_fun(X2887,tc_HOL_Obool)),X2884),X2883)),X2882)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2885,tc_fun(X2886,tc_HOL_Obool)),X2884),hAPP(hAPP(c_COMBC(X2885,tc_fun(X2887,tc_fun(X2886,tc_HOL_Obool)),tc_fun(X2886,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2887,tc_HOL_Obool),tc_fun(tc_fun(X2887,tc_fun(X2886,tc_HOL_Obool)),tc_fun(X2886,tc_HOL_Obool)),X2885),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2887,tc_fun(X2886,tc_HOL_Obool))),X2883)),X2882)), inference(variable_rename,[status(thm)],[fact_UN__simps_I9_J])). 6.97/7.22 cnf(c_0_5584, 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_4668])). 6.97/7.22 fof(c_0_5585, plain, ![X11232, X11233, X11234, X11235]:c_List_Osublist(X11235,hAPP(hAPP(c_List_Oappend(X11235),X11234),X11233),X11232)=hAPP(hAPP(c_List_Oappend(X11235),c_List_Osublist(X11235,X11234,X11232)),c_List_Osublist(X11235,X11233,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(X11235)),X11234)))),X11232)))), inference(variable_rename,[status(thm)],[fact_sublist__append])). 6.97/7.22 fof(c_0_5586, plain, ![X8330, X8331]:hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(X8331)),tc_List_Olist(X8331)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(X8331),c_Wellfounded_Oless__than,c_List_Olex(X8331,X8330))),hAPP(hAPP(c_COMBS(tc_List_Olist(X8331),tc_List_Olist(X8331),tc_prod(tc_Nat_Onat,tc_List_Olist(X8331))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(X8331),tc_prod(tc_Nat_Onat,tc_List_Olist(X8331))),tc_List_Olist(X8331)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(X8331))),c_Nat_Osize__class_Osize(tc_List_Olist(X8331)))),c_COMBI(tc_List_Olist(X8331))))=c_List_Olenlex(X8331,X8330), inference(variable_rename,[status(thm)],[fact_lenlex__def])). 6.97/7.22 fof(c_0_5587, plain, ![X16196, X16197, X16198]:hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X16198),X16198),c_Wellfounded_Olex__prod(tc_Nat_Onat,X16198,c_Wellfounded_Oless__than,X16196)),hAPP(hAPP(c_COMBS(X16198,X16198,tc_prod(tc_Nat_Onat,X16198)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X16198,tc_prod(tc_Nat_Onat,X16198)),X16198),c_Product__Type_OPair(tc_Nat_Onat,X16198)),X16197)),c_COMBI(X16198)))=c_Wellfounded_Omlex__prod(X16198,X16197,X16196), inference(variable_rename,[status(thm)],[fact_mlex__prod__def])). 6.97/7.22 fof(c_0_5588, plain, ![X4984, X4985]:c_Random_Oselect(X4985,X4984)=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(X4985,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(X4985)),X4984)))),hAPP(hAPP(c_COMBB(X4985,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X4985,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X4985,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4985,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(X4985),X4984)),c_Code__Numeral_Onat__of))), inference(variable_rename,[status(thm)],[fact_select__def])). 6.97/7.22 fof(c_0_5589, plain, ![X5521, X5522]: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),X5522),X5521)),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),X5521),X5522)),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])). 6.97/7.22 cnf(c_0_5590, 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])). 6.97/7.22 fof(c_0_5591, plain, ![X4567, X4568, X4569]: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(X4569)),X4567)))),hAPP(hAPP(c_COMBB(X4569,tc_HOL_Obool,tc_Nat_Onat),X4568),hAPP(c_List_Onth(X4569),X4567)))))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4569)),hAPP(c_List_Ofilter(X4569,X4568),X4567)), inference(variable_rename,[status(thm)],[fact_length__filter__conv__card])). 6.97/7.22 fof(c_0_5592, plain, ![X8445, X8446, X8447, X8448, X8449, X8450]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8450,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X8450,X8449,hAPP(c_Fun_Ocomp(tc_prod(X8449,X8448),X8449,X8450,c_Product__Type_Ofst(X8449,X8448)),X8447)),X8446)),hAPP(c_Set_Ovimage(X8450,X8448,hAPP(c_Fun_Ocomp(tc_prod(X8449,X8448),X8448,X8450,c_Product__Type_Osnd(X8449,X8448)),X8447)),X8445))=hAPP(c_Set_Ovimage(X8450,tc_prod(X8449,X8448),X8447),hAPP(hAPP(c_Product__Type_OSigma(X8449,X8448),X8446),hAPP(c_COMBK(tc_fun(X8448,tc_HOL_Obool),X8449),X8445))), inference(variable_rename,[status(thm)],[fact_vimage__Times])). 6.97/7.22 fof(c_0_5593, plain, ![X5725, X5726, X5727, X5728, X5729]:hAPP(c_Fun_Othe__inv__into(X5729,X5728,X5727,X5726),X5725)=c_HOL_OThe(X5729,hAPP(hAPP(c_COMBS(X5729,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5729),c_fconj),hAPP(hAPP(c_COMBC(X5729,tc_fun(X5729,tc_HOL_Obool),tc_HOL_Obool),c_member(X5729)),X5727))),hAPP(hAPP(c_COMBC(X5729,X5728,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X5728,tc_fun(X5728,tc_HOL_Obool),X5729),c_fequal),X5726)),X5725))), inference(variable_rename,[status(thm)],[fact_the__inv__into__def])). 6.97/7.22 fof(c_0_5594, plain, ![X13768, X13769, X13770, X13771]:c_List_Oset__Cons(X13771,hAPP(c_Relation_OImage(X13771,X13771,X13770),hAPP(hAPP(c_Set_Oinsert(X13771),X13769),c_Orderings_Obot__class_Obot(tc_fun(X13771,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(X13771),tc_List_Olist(X13771),c_List_Olistrel(X13771,X13770)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X13771)),X13768),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X13771),tc_HOL_Obool)))))=hAPP(c_Relation_OImage(tc_List_Olist(X13771),tc_List_Olist(X13771),c_List_Olistrel(X13771,X13770)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X13771)),hAPP(hAPP(c_List_Olist_OCons(X13771),X13769),X13768)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X13771),tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_listrel__Cons])). 6.97/7.22 cnf(c_0_5595, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2))=c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_Osucc(X2)))), inference(split_conjunct,[status(thm)],[c_0_4669])). 6.97/7.22 cnf(c_0_5596, 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_4670])). 6.97/7.22 cnf(c_0_5597, 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_4671])). 6.97/7.22 cnf(c_0_5598, plain, (c_List_Oconcat(X1,hAPP(hAPP(c_List_Omap(X2,tc_List_Olist(X1)),hAPP(hAPP(c_COMBC(X2,tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_COMBB(X1,tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_OCons(X1)),X3)),c_List_Olist_ONil(X1))),X4))=hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)), inference(split_conjunct,[status(thm)],[c_0_4672])). 6.97/7.22 fof(c_0_5599, plain, ![X4103, X4104, X4105]: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),X4105),X4103)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X4104),X4103))),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,X4105,X4103)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4104,X4103))),X4103))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4105),X4104)),X4103), inference(variable_rename,[status(thm)],[fact_zdiv__zadd1__eq])). 6.97/7.22 fof(c_0_5600, plain, ![X10419, X10420, X10421]: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),X10421),X10419)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X10420),X10419))),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,X10421,X10419)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X10420,X10419))),X10419))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10421),X10420)),X10419), inference(variable_rename,[status(thm)],[fact_div__add1__eq])). 6.97/7.22 fof(c_0_5601, plain, ![X14939, X14940, X14941, X14942, X14943]:((X14943=c_Orderings_Obot__class_Obot(tc_fun(X14942,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14942,tc_fun(X14941,tc_HOL_Obool)),X14943),hAPP(hAPP(c_COMBC(X14942,tc_fun(X14941,tc_HOL_Obool),tc_fun(X14941,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14941,tc_HOL_Obool),tc_fun(tc_fun(X14941,tc_HOL_Obool),tc_fun(X14941,tc_HOL_Obool)),X14942),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14941,tc_HOL_Obool))),X14940)),X14939))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14941,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14942,tc_fun(X14941,tc_HOL_Obool)),X14943),X14940)),X14939))&(c_Orderings_Obot__class_Obot(tc_fun(X14942,tc_HOL_Obool))!=X14943|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14942,tc_fun(X14941,tc_HOL_Obool)),X14943),hAPP(hAPP(c_COMBC(X14942,tc_fun(X14941,tc_HOL_Obool),tc_fun(X14941,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14941,tc_HOL_Obool),tc_fun(tc_fun(X14941,tc_HOL_Obool),tc_fun(X14941,tc_HOL_Obool)),X14942),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14941,tc_HOL_Obool))),X14940)),X14939))=c_Orderings_Obot__class_Obot(tc_fun(X14941,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__simps_I2_J])])). 6.97/7.22 cnf(c_0_5602, 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_4673])). 6.97/7.22 cnf(c_0_5603, 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_4674])). 6.97/7.22 cnf(c_0_5604, 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_4675])). 6.97/7.22 cnf(c_0_5605, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),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),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4676, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_5606, 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_4677]), ['final']). 6.97/7.22 cnf(c_0_5607, 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])). 6.97/7.22 fof(c_0_5608, plain, ![X8764]: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),X8764)))),c_Orderings_Oord__class_Oless(tc_Int_Oint))))=c_Int_Oint__ge__less__than2(X8764), inference(variable_rename,[status(thm)],[fact_int__ge__less__than2__def])). 6.97/7.22 fof(c_0_5609, plain, ![X8907, X8908, X8909]:hAPP(c_List_Orotate(X8909,X8908),hAPP(c_List_Orev(X8909),X8907))=hAPP(c_List_Orev(X8909),hAPP(c_List_Orotate(X8909,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8909)),X8907)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X8908,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8909)),X8907)))),X8907)), inference(variable_rename,[status(thm)],[fact_rotate__rev])). 6.97/7.22 cnf(c_0_5610, 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_4678])). 6.97/7.22 fof(c_0_5611, plain, ![X3073, X3074, X3075]:hAPP(hAPP(c_Set_Oinsert(X3075),X3074),hAPP(c_Set_OCollect(X3075),X3073))=hAPP(c_Set_OCollect(X3075),hAPP(hAPP(c_COMBS(X3075,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3075),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3075),c_fNot),hAPP(hAPP(c_COMBC(X3075,X3075,tc_HOL_Obool),c_fequal),X3074)))),X3073)), inference(variable_rename,[status(thm)],[fact_insert__Collect])). 6.97/7.22 cnf(c_0_5612, 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_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=X1), inference(split_conjunct,[status(thm)],[c_0_4679])). 6.97/7.22 fof(c_0_5613, plain, ![X11951]:hAPP(c_Set_OCollect(tc_Nat_Onat),X11951)=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),X11951),c_Int_Onat)))), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J])). 6.97/7.22 fof(c_0_5614, plain, ![X11307, X11308, X11309]:hAPP(c_List_Oset(X11309),hAPP(c_List_Ofilter(X11309,X11308),X11307))=hAPP(c_Set_OCollect(X11309),hAPP(hAPP(c_COMBS(X11309,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X11309),c_fconj),hAPP(hAPP(c_COMBC(X11309,tc_fun(X11309,tc_HOL_Obool),tc_HOL_Obool),c_member(X11309)),hAPP(c_List_Oset(X11309),X11307)))),X11308)), inference(variable_rename,[status(thm)],[fact_set__filter])). 6.97/7.22 fof(c_0_5615, plain, ![X14611, X14612]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X14612,X14612),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X14612,X14611)),hAPP(hAPP(c_Product__Type_OSigma(X14612,X14612),hAPP(c_Relation_OField(X14612),X14611)),hAPP(c_COMBK(tc_fun(X14612,tc_HOL_Obool),X14612),hAPP(c_Relation_OField(X14612),X14611))))), inference(variable_rename,[status(thm)],[fact_trancl__subset__Field2])). 6.97/7.22 fof(c_0_5616, plain, ![X1657, X1658, X1659]:hAPP(hAPP(c_List_Oappend(X1659),hAPP(hAPP(c_List_Odrop(X1659),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1658,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1659)),X1657))),X1657)),hAPP(hAPP(c_List_Otake(X1659),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1658,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1659)),X1657))),X1657))=hAPP(c_List_Orotate(X1659,X1658),X1657), inference(variable_rename,[status(thm)],[fact_rotate__drop__take])). 6.97/7.22 cnf(c_0_5617, 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_4680])). 6.97/7.22 cnf(c_0_5618, 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_4681])). 6.97/7.22 cnf(c_0_5619, 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_4682])). 6.97/7.22 cnf(c_0_5620, 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_4683])). 6.97/7.22 cnf(c_0_5621, 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_4684])). 6.97/7.22 cnf(c_0_5622, 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_4685])). 6.97/7.22 cnf(c_0_5623, 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_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)=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)],[c_0_4686, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411])). 6.97/7.22 cnf(c_0_5624, plain, (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))=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))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4687, c_0_4410]), c_0_4410]), c_0_4410]), ['final']). 6.97/7.22 cnf(c_0_5625, 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])). 6.97/7.22 fof(c_0_5626, plain, ![X4534, X4535]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4535),X4534)=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),X4535),X4534)),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])). 6.97/7.22 fof(c_0_5627, plain, ![X13426]: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),X13426),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))))=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)))),X13426)), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J])). 6.97/7.22 cnf(c_0_5628, 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])). 6.97/7.22 fof(c_0_5629, plain, ![X5157, X5158, X5159, X5160]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5160,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5160),X5159),hAPP(hAPP(c_Set_Oinsert(X5160),X5158),c_Orderings_Obot__class_Obot(tc_fun(X5160,tc_HOL_Obool))))),hAPP(c_Relation_OField(X5160),X5157))=hAPP(c_Relation_OField(X5160),hAPP(hAPP(c_Set_Oinsert(tc_prod(X5160,X5160)),hAPP(hAPP(c_Product__Type_OPair(X5160,X5160),X5159),X5158)),X5157)), inference(variable_rename,[status(thm)],[fact_Field__insert])). 6.97/7.22 fof(c_0_5630, plain, ![X9895, X9896, X9897]:hAPP(hAPP(c_Set_Oinsert(tc_fun(X9897,tc_HOL_Obool)),hAPP(c_Relation_OImage(X9897,X9897,X9895),hAPP(hAPP(c_Set_Oinsert(X9897),X9896),c_Orderings_Obot__class_Obot(tc_fun(X9897,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X9897,tc_HOL_Obool),tc_HOL_Obool)))=hAPP(hAPP(c_Equiv__Relations_Oquotient(X9897),hAPP(hAPP(c_Set_Oinsert(X9897),X9896),c_Orderings_Obot__class_Obot(tc_fun(X9897,tc_HOL_Obool)))),X9895), inference(variable_rename,[status(thm)],[fact_singleton__quotient])). 6.97/7.22 fof(c_0_5631, plain, ![X10845, X10846, X10847, X10848]:hAPP(c_List_Orotate(X10848,X10847),hAPP(c_List_Orotate(X10848,X10846),X10845))=hAPP(c_List_Orotate(X10848,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10847),X10846)),X10845), inference(variable_rename,[status(thm)],[fact_rotate__rotate])). 6.97/7.22 fof(c_0_5632, plain, ![X7486]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X7486)=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),X7486),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))))), inference(variable_rename,[status(thm)],[fact_int__def])). 6.97/7.22 cnf(c_0_5633, 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])). 6.97/7.22 cnf(c_0_5634, 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_4688])). 6.97/7.22 fof(c_0_5635, plain, ![X10248, X10249, X10250, X10251]:hAPP(c_List_Orev(X10251),hAPP(hAPP(c_List_Omap(X10250,X10251),X10249),X10248))=hAPP(hAPP(c_List_Omap(X10250,X10251),X10249),hAPP(c_List_Orev(X10250),X10248)), inference(variable_rename,[status(thm)],[fact_rev__map])). 6.97/7.22 cnf(c_0_5636, 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),c_Transitive__Closure_Otrancl(X1,X2)),X2))=c_Transitive__Closure_Otrancl(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_4689])). 6.97/7.22 fof(c_0_5637, plain, ![X11794, X11795, X11796, X11797, X11798, X11799, X11800]:hAPP(hAPP(c_Relation_Orel__comp(X11800,X11799,X11798),hAPP(hAPP(c_Relation_Orel__comp(X11800,X11797,X11799),X11796),X11795)),X11794)=hAPP(hAPP(c_Relation_Orel__comp(X11800,X11797,X11798),X11796),hAPP(hAPP(c_Relation_Orel__comp(X11797,X11799,X11798),X11795),X11794)), inference(variable_rename,[status(thm)],[fact_O__assoc])). 6.97/7.22 fof(c_0_5638, plain, ![X7787, X7788]:hAPP(hAPP(c_Relation_Orel__comp(X7788,X7788,X7788),X7787),c_Transitive__Closure_Ortrancl(X7788,X7787))=hAPP(hAPP(c_Relation_Orel__comp(X7788,X7788,X7788),c_Transitive__Closure_Ortrancl(X7788,X7787)),X7787), inference(variable_rename,[status(thm)],[fact_r__comp__rtrancl__eq])). 6.97/7.22 fof(c_0_5639, plain, ![X16845]:X16845=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),esk566_1(X16845)),esk567_1(X16845))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__Abs__Integ])])])). 6.97/7.22 fof(c_0_5640, plain, ![X7334, X7335, X7336]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7336)),X7334)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7336)),hAPP(c_List_Ofilter(X7336,X7335),X7334))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7336)),hAPP(c_List_Ofilter(X7336,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7336),c_fNot),X7335)),X7334))), inference(variable_rename,[status(thm)],[fact_sum__length__filter__compl])). 6.97/7.22 fof(c_0_5641, plain, ![X3655, X3656, X3657]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3657)),hAPP(hAPP(c_List_Oappend(X3657),X3656),X3655))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3657)),X3656)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3657)),X3655)), inference(variable_rename,[status(thm)],[fact_length__append])). 6.97/7.22 fof(c_0_5642, plain, ![X5287, X5288, X5289, X5290, X5291, X5292]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5289,tc_fun(X5292,tc_HOL_Obool)),X5288),hAPP(hAPP(c_COMBB(tc_fun(X5291,tc_HOL_Obool),tc_fun(X5292,tc_HOL_Obool),X5289),c_Set_Ovimage(X5292,X5291,X5290)),X5287))=hAPP(c_Set_Ovimage(X5292,X5291,X5290),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5289,tc_fun(X5291,tc_HOL_Obool)),X5288),X5287)), inference(variable_rename,[status(thm)],[fact_vimage__INT])). 6.97/7.22 fof(c_0_5643, plain, ![X15778, X15779, X15780, X15781, X15782, X15783]:hAPP(c_Set_Ovimage(X15783,X15782,X15781),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15780,tc_fun(X15782,tc_HOL_Obool)),X15779),X15778))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15780,tc_fun(X15783,tc_HOL_Obool)),X15779),hAPP(hAPP(c_COMBB(tc_fun(X15782,tc_HOL_Obool),tc_fun(X15783,tc_HOL_Obool),X15780),c_Set_Ovimage(X15783,X15782,X15781)),X15778)), inference(variable_rename,[status(thm)],[fact_vimage__UN])). 6.97/7.22 fof(c_0_5644, plain, ![X14084, X14085]: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),X14085)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X14084))))), inference(variable_rename,[status(thm)],[fact_finite__M__bounded__by__nat])). 6.97/7.22 fof(c_0_5645, plain, ![X16115, X16116, X16117, X16118]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16118,tc_HOL_Obool)),X16117),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16118,tc_HOL_Obool)),X16116),X16115))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16118,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16118,tc_HOL_Obool)),X16117),X16116)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16118,tc_HOL_Obool)),X16117),X16115)), inference(variable_rename,[status(thm)],[fact_Diff__Un])). 6.97/7.22 cnf(c_0_5646, 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_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_4690])). 6.97/7.22 cnf(c_0_5647, 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)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X4)),X3)), inference(rw,[status(thm)],[c_0_4691, c_0_4692])). 6.97/7.22 fof(c_0_5648, plain, ![X12333, X12334, X12335, X12336]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12336,tc_HOL_Obool)),X12335),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12336,tc_HOL_Obool)),X12334),X12333))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12336,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12336,tc_HOL_Obool)),X12335),X12334)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12336,tc_HOL_Obool)),X12335),X12333)), inference(variable_rename,[status(thm)],[fact_Diff__Int__distrib])). 6.97/7.22 cnf(c_0_5649, 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_4693])). 6.97/7.22 fof(c_0_5650, plain, ![X1911, X1912, X1913, X1914, X1915, X1916]:(hAPP(hAPP(c_List_Olist_OCons(X1913),X1915),X1916)!=X1914|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1913),tc_List_Olist(X1913))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1913),tc_List_Olist(X1913)),X1912),hAPP(hAPP(c_List_Oappend(X1913),X1912),X1914))),c_List_Olexord(X1913,X1911)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lexord__append__rightI])])])])). 6.97/7.22 cnf(c_0_5651, 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_4694])). 6.97/7.22 cnf(c_0_5652, 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])). 6.97/7.22 fof(c_0_5653, plain, ![X9301, X9302, X9303, X9304, X9305]:((X9305=c_Orderings_Obot__class_Obot(tc_fun(X9304,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9304,tc_fun(X9303,tc_HOL_Obool)),X9305),hAPP(hAPP(c_COMBB(tc_fun(X9303,tc_HOL_Obool),tc_fun(X9303,tc_HOL_Obool),X9304),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9303,tc_HOL_Obool)),X9302)),X9301))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9303,tc_HOL_Obool)),X9302),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9304,tc_fun(X9303,tc_HOL_Obool)),X9305),X9301)))&(c_Orderings_Obot__class_Obot(tc_fun(X9304,tc_HOL_Obool))!=X9305|c_Orderings_Obot__class_Obot(tc_fun(X9303,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9304,tc_fun(X9303,tc_HOL_Obool)),X9305),hAPP(hAPP(c_COMBB(tc_fun(X9303,tc_HOL_Obool),tc_fun(X9303,tc_HOL_Obool),X9304),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9303,tc_HOL_Obool)),X9302)),X9301)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__simps_I3_J])])). 6.97/7.22 fof(c_0_5654, plain, ![X12125, X12126, X12127, X12128, X12129]:c_Product__Type_Oprod_Oprod__size(X12129,X12128,X12127,X12126,X12125)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X12127,hAPP(c_Product__Type_Ofst(X12129,X12128),X12125))),hAPP(X12126,hAPP(c_Product__Type_Osnd(X12129,X12128),X12125)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_prod__size__simp])). 6.97/7.22 cnf(c_0_5655, plain, (hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),X1),X2)=c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(X1)),c_List_Oembed__list(X2)))), inference(split_conjunct,[status(thm)],[c_0_4695])). 6.97/7.22 cnf(c_0_5656, 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_4696])). 6.97/7.22 cnf(c_0_5657, plain, (hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)=c_List_Oembed__list(X1)), inference(split_conjunct,[status(thm)],[c_0_4697])). 6.97/7.22 fof(c_0_5658, plain, ![X3573, X3574, X3575, X3576, X3577]:hAPP(hAPP(c_List_Omap(X3577,X3576),X3575),hAPP(hAPP(c_List_Oappend(X3577),X3574),X3573))=hAPP(hAPP(c_List_Oappend(X3576),hAPP(hAPP(c_List_Omap(X3577,X3576),X3575),X3574)),hAPP(hAPP(c_List_Omap(X3577,X3576),X3575),X3573)), inference(variable_rename,[status(thm)],[fact_map__append])). 6.97/7.22 cnf(c_0_5659, 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_4698])). 6.97/7.22 cnf(c_0_5660, plain, (hAPP(c_List_OremoveAll(X3,X2),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X4))=hAPP(c_List_OremoveAll(X3,X2),X4)|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_4544])). 6.97/7.22 cnf(c_0_5661, 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_4699])). 6.97/7.22 fof(c_0_5662, plain, ![X9497, X9498, X9499]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9499,tc_HOL_Obool)),X9498),X9497)=c_Complete__Lattice_OInf__class_OInf(tc_fun(X9499,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X9499,tc_HOL_Obool)),X9498),hAPP(hAPP(c_Set_Oinsert(tc_fun(X9499,tc_HOL_Obool)),X9497),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X9499,tc_HOL_Obool),tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[fact_Int__eq__Inter])). 6.97/7.22 fof(c_0_5663, plain, ![X13392, X13393, X13394]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13394,tc_HOL_Obool)),X13393),X13392)=c_Complete__Lattice_OSup__class_OSup(tc_fun(X13394,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X13394,tc_HOL_Obool)),X13393),hAPP(hAPP(c_Set_Oinsert(tc_fun(X13394,tc_HOL_Obool)),X13392),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X13394,tc_HOL_Obool),tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[fact_Un__eq__Union])). 6.97/7.22 fof(c_0_5664, plain, ![X10078, X10079]:c_Divides_Opdivmod(X10079,X10078)=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),X10079)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X10078))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X10079),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X10078))), inference(variable_rename,[status(thm)],[fact_pdivmod__def])). 6.97/7.22 fof(c_0_5665, plain, ![X799, X800]:c_Divides_Odivmod__int(X800,X799)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X800),X799)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X800,X799)), inference(variable_rename,[status(thm)],[fact_divmod__int__mod__div])). 6.97/7.22 fof(c_0_5666, plain, ![X6498, X6499, X6500, X6501, X6502]:((X6502=c_Orderings_Obot__class_Obot(tc_fun(X6501,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6501,tc_fun(X6500,tc_HOL_Obool)),X6502),hAPP(hAPP(c_COMBB(tc_fun(X6500,tc_HOL_Obool),tc_fun(X6500,tc_HOL_Obool),X6501),hAPP(c_Set_Oinsert(X6500),X6499)),X6498))=hAPP(hAPP(c_Set_Oinsert(X6500),X6499),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6501,tc_fun(X6500,tc_HOL_Obool)),X6502),X6498)))&(X6502!=c_Orderings_Obot__class_Obot(tc_fun(X6501,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6501,tc_fun(X6500,tc_HOL_Obool)),X6502),hAPP(hAPP(c_COMBB(tc_fun(X6500,tc_HOL_Obool),tc_fun(X6500,tc_HOL_Obool),X6501),hAPP(c_Set_Oinsert(X6500),X6499)),X6498))=c_Orderings_Obot__class_Obot(tc_fun(X6500,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__simps_I1_J])])])). 6.97/7.22 fof(c_0_5667, plain, ![X3721, X3722]:hAPP(c_Relation_OImage(tc_List_Olist(X3722),tc_List_Olist(X3722),c_List_Olistrel(X3722,X3721)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X3722)),c_List_Olist_ONil(X3722)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X3722),tc_HOL_Obool))))=hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X3722)),c_List_Olist_ONil(X3722)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X3722),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_listrel__Nil])). 6.97/7.22 cnf(c_0_5668, 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_4700])). 6.97/7.22 fof(c_0_5669, plain, ![X7420, X7421, X7422]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7421),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X7422),X7421),X7420))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X7422,X7421))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X7422,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7421),X7420)), inference(variable_rename,[status(thm)],[fact_mod__mult2__eq])). 6.97/7.22 cnf(c_0_5670, 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_4701])). 6.97/7.22 fof(c_0_5671, plain, ![X9552, X9553]:hAPP(c_List_Orev(X9553),hAPP(c_List_Orev(X9553),X9552))=X9552, inference(variable_rename,[status(thm)],[fact_rev__rev__ident])). 6.97/7.22 cnf(c_0_5672, 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])). 6.97/7.22 fof(c_0_5673, plain, ![X17300, X17301, X17302, X17303, X17304, X17305, X17306, X17307]:((hAPP(hAPP(c_List_Olist_OCons(X17302),X17303),X17304)!=X17301|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17302),tc_List_Olist(X17302))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17302),tc_List_Olist(X17302)),c_List_Olist_ONil(X17302)),X17301)),c_List_Olexord(X17302,X17300))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17307),tc_List_Olist(X17307))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17307),tc_List_Olist(X17307)),c_List_Olist_ONil(X17307)),X17306)),c_List_Olexord(X17307,X17305)))|hAPP(hAPP(c_List_Olist_OCons(X17307),esk588_3(X17305,X17306,X17307)),esk589_3(X17305,X17306,X17307))=X17306)), 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])])])])])). 6.97/7.22 fof(c_0_5674, plain, ![X16405, X16406]:c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X16405),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)),X16405)),X16406)=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X16406),hAPP(c_Nat_OSuc,X16405)), inference(variable_rename,[status(thm)],[fact_max__Suc2])). 6.97/7.22 fof(c_0_5675, plain, ![X5602, X5603, X5604]:hAPP(c_List_Orotate(X5604,X5603),X5602)=hAPP(c_List_Orotate(X5604,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5603,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5604)),X5602))),X5602), inference(variable_rename,[status(thm)],[fact_rotate__conv__mod])). 6.97/7.22 fof(c_0_5676, plain, ![X10584, X10585, X10586, X10587, X10588]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10588,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X10588,X10587,X10586),X10585)),hAPP(c_Set_Ovimage(X10588,X10587,X10586),X10584))=hAPP(c_Set_Ovimage(X10588,X10587,X10586),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10587,tc_HOL_Obool)),X10585),X10584)), inference(variable_rename,[status(thm)],[fact_vimage__Un])). 6.97/7.22 fof(c_0_5677, plain, ![X11966, X11967, X11968, X11969, X11970]:hAPP(c_Set_Ovimage(X11970,X11969,X11968),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11969,tc_HOL_Obool)),X11967),X11966))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11970,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X11970,X11969,X11968),X11967)),hAPP(c_Set_Ovimage(X11970,X11969,X11968),X11966)), inference(variable_rename,[status(thm)],[fact_vimage__Diff])). 6.97/7.22 fof(c_0_5678, plain, ![X15929, X15930, X15931, X15932, X15933]:hAPP(c_Set_Ovimage(X15933,X15932,X15931),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15932,tc_HOL_Obool)),X15930),X15929))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15933,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X15933,X15932,X15931),X15930)),hAPP(c_Set_Ovimage(X15933,X15932,X15931),X15929)), inference(variable_rename,[status(thm)],[fact_vimage__Int])). 6.97/7.22 fof(c_0_5679, plain, ![X6150, X6151, X6152]:hAPP(hAPP(c_Relation_Orel__comp(X6152,X6152,X6152),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X6152,X6152),tc_HOL_Obool),X6150),X6151)),X6151)=hAPP(hAPP(c_Relation_Orel__comp(X6152,X6152,X6152),X6151),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X6152,X6152),tc_HOL_Obool),X6150),X6151)), inference(variable_rename,[status(thm)],[fact_rel__pow__commute])). 6.97/7.22 fof(c_0_5680, plain, ![X6601, X6602, X6603]:hAPP(hAPP(c_Nat_Ocompow(tc_prod(X6603,X6603),tc_HOL_Obool),hAPP(c_Nat_OSuc,X6602)),X6601)=hAPP(hAPP(c_Relation_Orel__comp(X6603,X6603,X6603),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X6603,X6603),tc_HOL_Obool),X6602),X6601)),X6601), inference(variable_rename,[status(thm)],[fact_relpow_Osimps_I2_J])). 6.97/7.22 cnf(c_0_5681, plain, (c_Int_Osucc(c_Int_OBit1(X1))=c_Int_OBit0(c_Int_Osucc(X1))), inference(split_conjunct,[status(thm)],[c_0_4702])). 6.97/7.22 fof(c_0_5682, plain, ![X17331, X17332, X17333]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17333,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X17333,tc_HOL_Obool)),X17332)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X17333,tc_HOL_Obool)),X17331))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X17333,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17333,tc_HOL_Obool)),X17332),X17331)), inference(variable_rename,[status(thm)],[fact_Compl__Un])). 6.97/7.22 cnf(c_0_5683, plain, (c_Int_OBit0(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_OBit1(X1))), inference(split_conjunct,[status(thm)],[c_0_4703])). 6.97/7.22 fof(c_0_5684, plain, ![X12121, X12122, X12123, X12124]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12123)),X12121)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12124)),hAPP(hAPP(c_List_Omap(X12123,X12124),X12122),X12121)), inference(variable_rename,[status(thm)],[fact_length__map])). 6.97/7.22 fof(c_0_5685, plain, ![X6610, X6611]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X6611),hAPP(c_Nat_OSuc,X6610))=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)),X6610)),X6611), inference(variable_rename,[status(thm)],[fact_min__Suc2])). 6.97/7.22 fof(c_0_5686, plain, ![X11879, X11880, X11881, X11882]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11882)),X11880)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11881)),X11879))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(X11882,X11881))),hAPP(hAPP(c_List_Ozip(X11882,X11881),X11880),X11879)), inference(variable_rename,[status(thm)],[fact_length__zip])). 6.97/7.22 fof(c_0_5687, plain, ![X10023, X10024, X10025]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10025,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10025,tc_HOL_Obool),X10024)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10025,tc_HOL_Obool),X10023))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X10025,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X10025,tc_HOL_Obool),tc_HOL_Obool)),X10024),X10023)), inference(variable_rename,[status(thm)],[fact_Inter__Un__distrib])). 6.97/7.22 fof(c_0_5688, plain, ![X13445, X13446, X13447]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13447,tc_HOL_Obool)),X13446),c_Complete__Lattice_OInf__class_OInf(tc_fun(X13447,tc_HOL_Obool),X13445))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X13447,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X13447,tc_HOL_Obool)),X13446),X13445)), inference(variable_rename,[status(thm)],[fact_Inter__insert])). 6.97/7.22 fof(c_0_5689, plain, ![X15543, X15544, X15545]:c_Complete__Lattice_OSup__class_OSup(tc_fun(X15545,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X15545,tc_HOL_Obool),tc_HOL_Obool)),X15544),X15543))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15545,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X15545,tc_HOL_Obool),X15544)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X15545,tc_HOL_Obool),X15543)), inference(variable_rename,[status(thm)],[fact_Union__Un__distrib])). 6.97/7.22 fof(c_0_5690, plain, ![X7139, X7140, X7141]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7141,tc_HOL_Obool)),X7140),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7141,tc_HOL_Obool),X7139))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X7141,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X7141,tc_HOL_Obool)),X7140),X7139)), inference(variable_rename,[status(thm)],[fact_Union__insert])). 6.97/7.22 fof(c_0_5691, plain, ![X6579, X6580, X6581, X6582, X6583]:(hAPP(c_Set_Oimage(X6583,X6582,X6581),X6580)!=X6579|hAPP(c_Set_Oimage(tc_fun(X6583,tc_HOL_Obool),tc_fun(X6582,tc_HOL_Obool),c_Set_Oimage(X6583,X6582,X6581)),hAPP(c_Set_OPow(X6583),X6580))=hAPP(c_Set_OPow(X6582),X6579)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__Pow__surj])])])). 6.97/7.22 fof(c_0_5692, plain, ![X7470, X7471, X7472, X7473, X7474, X7475]:hAPP(hAPP(X7472,X7471),X7470)=c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X7475,X7474,X7473,X7472,c_Lazy__Sequence_Olazy__sequence_OInsert(X7474,X7471,X7470)), inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osimps_I5_J])). 6.97/7.22 fof(c_0_5693, plain, ![X2763, X2764, X2765, X2766, X2767]:c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X2767,X2766,X2765,X2764,X2763)=c_Option_Ooption_Ooption__case(X2767,tc_prod(X2766,tc_Lazy__Sequence_Olazy__sequence(X2766)),X2765,hAPP(c_Product__Type_Oprod_Oprod__case(X2766,tc_Lazy__Sequence_Olazy__sequence(X2766),X2767),X2764),hAPP(c_Lazy__Sequence_Oyield(X2766),X2763)), inference(variable_rename,[status(thm)],[fact_seq__case])). 6.97/7.22 fof(c_0_5694, plain, ![X16855, X16856, X16857]:hAPP(c_Relation_ODomain(X16857,X16856),hAPP(c_Set_OCollect(tc_prod(X16857,X16856)),hAPP(c_Product__Type_Oprod_Oprod__case(X16857,X16856,tc_HOL_Obool),X16855)))=hAPP(c_Set_OCollect(X16857),hAPP(hAPP(c_COMBB(tc_fun(X16856,tc_HOL_Obool),tc_HOL_Obool,X16857),c_HOL_OEx(X16856)),X16855)), inference(variable_rename,[status(thm)],[fact_Domain__Collect__split])). 6.97/7.22 fof(c_0_5695, plain, ![X15372]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X15372)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X15372)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))=hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X15372)), inference(variable_rename,[status(thm)],[fact_greaterThan__Suc])). 6.97/7.22 fof(c_0_5696, plain, ![X6748, X6749, X6750]:hAPP(c_List_Orotate1(X6750),hAPP(c_List_Orotate(X6750,X6749),X6748))=hAPP(c_List_Orotate(X6750,hAPP(c_Nat_OSuc,X6749)),X6748), inference(variable_rename,[status(thm)],[fact_rotate__Suc])). 6.97/7.22 fof(c_0_5697, plain, ![X2593]:X2593=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)),X2593)), inference(variable_rename,[status(thm)],[fact_transfer__int__nat__set__return__embed])). 6.97/7.22 fof(c_0_5698, plain, ![X10503, X10504]:hAPP(c_List_Oset(X10504),c_List_Oconcat(X10504,X10503))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X10504),tc_fun(X10504,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X10504)),X10503)),c_List_Oset(X10504)), inference(variable_rename,[status(thm)],[fact_set__concat])). 6.97/7.22 fof(c_0_5699, plain, ![X2742, X2743, X2744, X2745]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X2744,tc_HOL_Obool),tc_fun(X2745,tc_HOL_Obool)),X2742),c_Set_Ovimage(X2745,X2744,X2743))=hAPP(c_Set_Ovimage(X2745,X2744,X2743),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2744,tc_HOL_Obool),X2742)), inference(variable_rename,[status(thm)],[fact_vimage__Union])). 6.97/7.22 fof(c_0_5700, plain, ![X13093, X13094, X13095, X13096, X13097, X13098]:hAPP(hAPP(c_List_Ozip(X13098,X13097),c_List_Oreplicate(X13098,X13096,X13095)),c_List_Oreplicate(X13097,X13094,X13093))=c_List_Oreplicate(tc_prod(X13098,X13097),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X13096),X13094),hAPP(hAPP(c_Product__Type_OPair(X13098,X13097),X13095),X13093)), inference(variable_rename,[status(thm)],[fact_zip__replicate])). 6.97/7.22 fof(c_0_5701, plain, ![X329, X330]:c_Relation_Orefl__on(X330,c_Orderings_Otop__class_Otop(tc_fun(X330,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X330,X330),tc_HOL_Obool)),X329),c_Relation_OId(X330))), inference(variable_rename,[status(thm)],[fact_refl__reflcl])). 6.97/7.22 fof(c_0_5702, plain, ![X6274, X6275, X6276]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6276),X6275)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6274),X6275))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X6276),X6274)),X6275), inference(variable_rename,[status(thm)],[fact_min__diff])). 6.97/7.22 fof(c_0_5703, plain, ![X15530, X15531, X15532, X15533, X15534]:((X15534=c_Orderings_Obot__class_Obot(tc_fun(X15533,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15533,tc_fun(X15532,tc_HOL_Obool)),X15534),hAPP(hAPP(c_COMBB(tc_fun(X15532,tc_HOL_Obool),tc_fun(X15532,tc_HOL_Obool),X15533),hAPP(c_Set_Oinsert(X15532),X15531)),X15530))=hAPP(hAPP(c_Set_Oinsert(X15532),X15531),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15533,tc_fun(X15532,tc_HOL_Obool)),X15534),X15530)))&(X15534!=c_Orderings_Obot__class_Obot(tc_fun(X15533,tc_HOL_Obool))|hAPP(hAPP(c_Set_Oinsert(X15532),X15531),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15533,tc_fun(X15532,tc_HOL_Obool)),X15534),X15530))=hAPP(hAPP(c_Set_Oinsert(X15532),X15531),c_Orderings_Obot__class_Obot(tc_fun(X15532,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__extend__simps_I1_J])])])). 6.97/7.22 fof(c_0_5704, plain, ![X491]:hAPP(c_Set_OPow(X491),c_Orderings_Obot__class_Obot(tc_fun(X491,tc_HOL_Obool)))=hAPP(hAPP(c_Set_Oinsert(tc_fun(X491,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X491,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X491,tc_HOL_Obool),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Pow__empty])). 6.97/7.22 fof(c_0_5705, plain, ![X4319]:hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X4319))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),X4319)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X4319),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_atLeast__Suc])). 6.97/7.22 fof(c_0_5706, plain, ![X7991]:hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X7991))=hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X7991), inference(variable_rename,[status(thm)],[fact_atLeast__Suc__greaterThan])). 6.97/7.22 fof(c_0_5707, plain, ![X777, X778, X779]:hAPP(c_List_Ofoldl(tc_List_Olist(X779),tc_List_Olist(X779),c_List_Oappend(X779),X778),X777)=hAPP(hAPP(c_List_Oappend(X779),X778),c_List_Oconcat(X779,X777)), inference(variable_rename,[status(thm)],[fact_foldl__conv__concat])). 6.97/7.22 fof(c_0_5708, plain, ![X5429, X5430]:hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X5430)),X5429)=c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X5430),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),X5430)),X5429), inference(variable_rename,[status(thm)],[fact_max__Suc1])). 6.97/7.22 fof(c_0_5709, plain, ![X4586, X4587, X4588]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4588),X4587)),X4586)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X4588)),X4587)),hAPP(c_Nat_OSuc,X4586)), inference(variable_rename,[status(thm)],[fact_Suc__diff__diff])). 6.97/7.22 fof(c_0_5710, plain, ![X7322, X7323, X7324]:hAPP(hAPP(c_List_Oappend(X7324),c_List_OtakeWhile(X7324,X7323,X7322)),c_List_OdropWhile(X7324,X7323,X7322))=X7322, inference(variable_rename,[status(thm)],[fact_takeWhile__dropWhile__id])). 6.97/7.22 fof(c_0_5711, plain, ![X1476, X1477, X1478]: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(X1478,tc_Nat_Onat),X1477),X1476))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1478)),X1476))=c_List_Olist_Olist__size(X1478,X1477,X1476), inference(variable_rename,[status(thm)],[fact_list__size__conv__listsum])). 6.97/7.22 fof(c_0_5712, plain, ![X3200, X3201, X3202]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3202)),hAPP(hAPP(c_List_Olist_OCons(X3202),X3201),X3200))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3202)),X3200)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_list_Osize_I4_J])). 6.97/7.22 fof(c_0_5713, plain, ![X12414, X12415]:hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X12415),hAPP(c_List_Onth(X12415),X12414)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12415)),X12414)))=X12414, inference(variable_rename,[status(thm)],[fact_map__nth])). 6.97/7.22 fof(c_0_5714, plain, ![X15713, X15714, X15715, X15716, X15717, X15718]:c_Nitpick_Opair__box_Opair__box__size(X15718,X15717,X15716,X15715,c_Nitpick_Opair__box_OPairBox(X15718,X15717,X15714,X15713))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X15716,X15714)),hAPP(X15715,X15713))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_pair__box_Osize_I1_J])). 6.97/7.22 fof(c_0_5715, plain, ![X6113, X6114]: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),X6114)),X6113)=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X6114)),X6113), inference(variable_rename,[status(thm)],[fact_min__Suc1])). 6.97/7.22 fof(c_0_5716, plain, ![X11268, X11269]:c_Transitive__Closure_Ortrancl(X11269,X11268)=c_Transitive__Closure_Ortrancl(X11269,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X11269,X11269),tc_HOL_Obool)),X11268),c_Relation_OId(X11269))), inference(variable_rename,[status(thm)],[fact_rtrancl__r__diff__Id])). 6.97/7.22 fof(c_0_5717, plain, ![X14177, X14178]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X14178,X14178),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X14178,X14177)),c_Relation_OId(X14178))=c_Transitive__Closure_Ortrancl(X14178,X14177), inference(variable_rename,[status(thm)],[fact_rtrancl__reflcl__absorb])). 6.97/7.22 fof(c_0_5718, plain, ![X10395, X10396, X10397]:c_List_Oreplicate(X10397,X10395,X10396)=hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X10397),hAPP(c_COMBK(X10397,tc_Nat_Onat),X10396)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X10395)), inference(variable_rename,[status(thm)],[fact_map__replicate__trivial])). 6.97/7.22 cnf(c_0_5719, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(X1),X2)|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=X2), inference(split_conjunct,[status(thm)],[c_0_4704])). 6.97/7.22 fof(c_0_5720, plain, ![X6874, X6875]:~hBOOL(hAPP(hAPP(c_member(X6875),X6874),c_Orderings_Obot__class_Obot(tc_fun(X6875,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_empty__iff])])). 6.97/7.22 fof(c_0_5721, plain, ![X14017, X14018, X14019]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14019)),c_List_Osplice(X14019,X14018,X14017))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14019)),X14018)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14019)),X14017)), inference(variable_rename,[status(thm)],[fact_length__splice])). 6.97/7.22 fof(c_0_5722, plain, ![X12438, X12439, X12440, X12441]:((c_Orderings_Obot__class_Obot(tc_fun(X12440,tc_HOL_Obool))!=X12441|c_Orderings_Obot__class_Obot(tc_fun(X12439,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12440,tc_fun(X12439,tc_HOL_Obool)),X12441),hAPP(c_COMBK(tc_fun(X12439,tc_HOL_Obool),X12440),X12438)))&(X12441=c_Orderings_Obot__class_Obot(tc_fun(X12440,tc_HOL_Obool))|X12438=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12440,tc_fun(X12439,tc_HOL_Obool)),X12441),hAPP(c_COMBK(tc_fun(X12439,tc_HOL_Obool),X12440),X12438)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__constant])])). 6.97/7.22 cnf(c_0_5723, 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_4705])). 6.97/7.22 fof(c_0_5724, plain, ![X4354, X4355, X4356, X4357]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4357,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4356,X4357,X4355),hAPP(c_Set_Ovimage(X4356,X4357,X4355),X4354))),X4354)), inference(variable_rename,[status(thm)],[fact_image__vimage__subset])). 6.97/7.22 cnf(c_0_5725, plain, (c_Int_Opred(c_Int_OBit1(X1))=c_Int_OBit0(X1)), inference(split_conjunct,[status(thm)],[c_0_4706])). 6.97/7.22 fof(c_0_5726, plain, ![X13162, X13163, X13164]:hAPP(c_Set_Ovimage(X13164,X13163,X13162),c_Orderings_Otop__class_Otop(tc_fun(X13163,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X13164,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_vimage__UNIV])). 6.97/7.22 fof(c_0_5727, plain, ![X3585, X3586, X3587]:hAPP(c_Set_Ovimage(X3587,X3586,X3585),c_Orderings_Obot__class_Obot(tc_fun(X3586,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X3587,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_vimage__empty])). 6.97/7.22 fof(c_0_5728, plain, ![X1218, X1219]:hAPP(c_Set_Ovimage(X1219,X1219,c_COMBI(X1219)),X1218)=X1218, inference(variable_rename,[status(thm)],[fact_vimage__ident])). 6.97/7.22 fof(c_0_5729, plain, ![X10567, X10568]:hAPP(c_Set_Ovimage(X10568,X10568,c_Fun_Oid(X10568)),X10567)=X10567, inference(variable_rename,[status(thm)],[fact_vimage__id])). 6.97/7.22 fof(c_0_5730, plain, ![X16718, X16719, X16720]:hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),X16720),c_List_Oupt(X16719,X16718))=c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16719),X16720),X16718), inference(variable_rename,[status(thm)],[fact_drop__upt])). 6.97/7.22 fof(c_0_5731, plain, ![X12614]: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),X12614)))=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),X12614)), inference(variable_rename,[status(thm)],[fact_one__div__nat__number__of])). 6.97/7.22 fof(c_0_5732, plain, ![X3138, X3139, X3140, X3141]:((hAPP(hAPP(c_Product__Type_OSigma(X3141,X3140),X3139),hAPP(c_COMBK(tc_fun(X3140,tc_HOL_Obool),X3141),X3138))!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3141,X3140),tc_HOL_Obool))|(X3139=c_Orderings_Obot__class_Obot(tc_fun(X3141,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X3140,tc_HOL_Obool))=X3138))&((X3139!=c_Orderings_Obot__class_Obot(tc_fun(X3141,tc_HOL_Obool))|hAPP(hAPP(c_Product__Type_OSigma(X3141,X3140),X3139),hAPP(c_COMBK(tc_fun(X3140,tc_HOL_Obool),X3141),X3138))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3141,X3140),tc_HOL_Obool)))&(c_Orderings_Obot__class_Obot(tc_fun(X3140,tc_HOL_Obool))!=X3138|hAPP(hAPP(c_Product__Type_OSigma(X3141,X3140),X3139),hAPP(c_COMBK(tc_fun(X3140,tc_HOL_Obool),X3141),X3138))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3141,X3140),tc_HOL_Obool))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Times__empty])])])). 6.97/7.22 fof(c_0_5733, plain, ![X14597, X14598, X14599, X14600]:X14598=c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X14600,X14599,X14598,X14597,c_Lazy__Sequence_Olazy__sequence_OEmpty(X14599)), inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osimps_I4_J])). 6.97/7.22 fof(c_0_5734, plain, ![X8876, X8877]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8876),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8877),X8876))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X8877,X8876))=X8877, inference(variable_rename,[status(thm)],[fact_zmod__zdiv__equality])). 6.97/7.22 fof(c_0_5735, plain, ![X16266, X16267, X16268, X16269, X16270]:((c_Orderings_Obot__class_Obot(tc_fun(X16269,tc_HOL_Obool))!=X16270|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16268,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16269,tc_fun(X16268,tc_HOL_Obool)),X16270),X16267)),X16266)=X16266)&(c_Orderings_Obot__class_Obot(tc_fun(X16269,tc_HOL_Obool))=X16270|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16268,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16269,tc_fun(X16268,tc_HOL_Obool)),X16270),X16267)),X16266)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16269,tc_fun(X16268,tc_HOL_Obool)),X16270),hAPP(hAPP(c_COMBC(X16269,tc_fun(X16268,tc_HOL_Obool),tc_fun(X16268,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16268,tc_HOL_Obool),tc_fun(tc_fun(X16268,tc_HOL_Obool),tc_fun(X16268,tc_HOL_Obool)),X16269),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16268,tc_HOL_Obool))),X16267)),X16266)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I2_J])])). 6.97/7.22 fof(c_0_5736, plain, ![X4395, X4396, X4397, X4398, X4399]:((c_Orderings_Obot__class_Obot(tc_fun(X4398,tc_HOL_Obool))!=X4399|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4397,tc_HOL_Obool)),X4396),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4398,tc_fun(X4397,tc_HOL_Obool)),X4399),X4395))=X4396)&(X4399=c_Orderings_Obot__class_Obot(tc_fun(X4398,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4397,tc_HOL_Obool)),X4396),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4398,tc_fun(X4397,tc_HOL_Obool)),X4399),X4395))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4398,tc_fun(X4397,tc_HOL_Obool)),X4399),hAPP(hAPP(c_COMBB(tc_fun(X4397,tc_HOL_Obool),tc_fun(X4397,tc_HOL_Obool),X4398),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4397,tc_HOL_Obool)),X4396)),X4395)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I3_J])])). 6.97/7.22 fof(c_0_5737, plain, ![X14919, X14920]:c_Relation_Oirrefl(X14920,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X14920,X14920),tc_HOL_Obool)),X14919),c_Relation_OId(X14920))), inference(variable_rename,[status(thm)],[fact_irrefl__diff__Id])). 6.97/7.22 fof(c_0_5738, plain, ![X4536, X4537, X4538, X4539, X4540]:((c_Orderings_Obot__class_Obot(tc_fun(X4539,tc_HOL_Obool))=X4540|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4539,tc_fun(X4538,tc_HOL_Obool)),X4540),hAPP(hAPP(c_COMBB(tc_fun(X4538,tc_HOL_Obool),tc_fun(X4538,tc_HOL_Obool),X4539),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4538,tc_HOL_Obool)),X4537)),X4536))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4538,tc_HOL_Obool)),X4537),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4539,tc_fun(X4538,tc_HOL_Obool)),X4540),X4536)))&(c_Orderings_Obot__class_Obot(tc_fun(X4539,tc_HOL_Obool))!=X4540|X4537=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4538,tc_HOL_Obool)),X4537),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4539,tc_fun(X4538,tc_HOL_Obool)),X4540),X4536)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INT__extend__simps_I4_J])])])). 6.97/7.22 fof(c_0_5739, plain, ![X5046, X5047, X5048]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5048)),X5046)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5048)),hAPP(c_List_Orotate(X5048,X5047),X5046)), inference(variable_rename,[status(thm)],[fact_length__rotate])). 6.97/7.22 cnf(c_0_5740, plain, (c_Int_OBit1(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)),X1)),X1)), inference(split_conjunct,[status(thm)],[c_0_4707])). 6.97/7.22 fof(c_0_5741, plain, ![X5352, X5353]: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),X5353)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X5352))))=hAPP(hAPP(c_Nitpick_Oint__gcd,X5353),X5352), inference(variable_rename,[status(thm)],[fact_Nitpick_Oint__gcd__def])). 6.97/7.22 fof(c_0_5742, plain, ![X5910, X5911, X5912]:((X5912!=c_Groups_Ozero__class_Ozero(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_Otimes__class_Otimes(tc_Nat_Onat),X5912),X5911)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5912),X5910)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X5912|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5912),X5911)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5912),X5910))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X5911),X5910))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__mult__div__cancel__disj])])])). 6.97/7.22 fof(c_0_5743, plain, ![X6149]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6149)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_mult__0])). 6.97/7.22 fof(c_0_5744, plain, ![X12354]: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),X12354)))=hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X12354)), inference(variable_rename,[status(thm)],[fact_lessThan__Suc__eq__insert__0])). 6.97/7.22 cnf(c_0_5745, 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_4708])). 6.97/7.22 cnf(c_0_5746, 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_4709]), ['final']). 6.97/7.22 fof(c_0_5747, plain, ![X11494, X11495]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11495),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X11495),X11494)),X11494))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X11495,X11494), inference(variable_rename,[status(thm)],[fact_Divides_Omod__div__equality_H])). 6.97/7.22 fof(c_0_5748, plain, ![X7487, X7488]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7487),X7488)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7488),X7487), inference(variable_rename,[status(thm)],[fact_nat__mult__commute])). 6.97/7.22 fof(c_0_5749, plain, ![X4256, X4257]:c_Divides_Odiv__class_Omod(tc_Int_Oint,X4257,X4256)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4257),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X4257),X4256)),X4256)), inference(variable_rename,[status(thm)],[fact_zmod__zdiv__equality_H])). 6.97/7.22 fof(c_0_5750, plain, ![X15002, X15003, X15004, X15005]:hAPP(hAPP(c_List_Otake(X15005),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X15004),X15003)),X15002)=hAPP(hAPP(c_List_Otake(X15005),X15004),hAPP(hAPP(c_List_Otake(X15005),X15003),X15002)), inference(variable_rename,[status(thm)],[fact_take__take])). 6.97/7.22 fof(c_0_5751, plain, ![X6815, X6816, X6817, X6818, X6819, X6821, X6822, X6823, X6824, X6825, X6826]:((((X6817=hAPP(hAPP(c_List_Oappend(X6819),esk222_5(X6815,X6816,X6817,X6818,X6819)),X6815)|c_List_Olist_ONil(X6819)=X6816|hAPP(hAPP(c_List_Olist_OCons(X6819),X6818),X6817)!=hAPP(hAPP(c_List_Oappend(X6819),X6816),X6815))&(X6816=hAPP(hAPP(c_List_Olist_OCons(X6819),X6818),esk222_5(X6815,X6816,X6817,X6818,X6819))|c_List_Olist_ONil(X6819)=X6816|hAPP(hAPP(c_List_Olist_OCons(X6819),X6818),X6817)!=hAPP(hAPP(c_List_Oappend(X6819),X6816),X6815)))&((X6817=hAPP(hAPP(c_List_Oappend(X6819),esk222_5(X6815,X6816,X6817,X6818,X6819)),X6815)|hAPP(hAPP(c_List_Olist_OCons(X6819),X6818),X6817)=X6815|hAPP(hAPP(c_List_Olist_OCons(X6819),X6818),X6817)!=hAPP(hAPP(c_List_Oappend(X6819),X6816),X6815))&(X6816=hAPP(hAPP(c_List_Olist_OCons(X6819),X6818),esk222_5(X6815,X6816,X6817,X6818,X6819))|hAPP(hAPP(c_List_Olist_OCons(X6819),X6818),X6817)=X6815|hAPP(hAPP(c_List_Olist_OCons(X6819),X6818),X6817)!=hAPP(hAPP(c_List_Oappend(X6819),X6816),X6815))))&((c_List_Olist_ONil(X6825)!=X6822|hAPP(hAPP(c_List_Olist_OCons(X6825),X6824),X6823)!=X6821|hAPP(hAPP(c_List_Olist_OCons(X6825),X6824),X6823)=hAPP(hAPP(c_List_Oappend(X6825),X6822),X6821))&(X6823!=hAPP(hAPP(c_List_Oappend(X6825),X6826),X6821)|X6822!=hAPP(hAPP(c_List_Olist_OCons(X6825),X6824),X6826)|hAPP(hAPP(c_List_Olist_OCons(X6825),X6824),X6823)=hAPP(hAPP(c_List_Oappend(X6825),X6822),X6821)))), 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])])])])])])). 6.97/7.22 fof(c_0_5752, plain, ![X15465, X15466, X15467, X15470, X15471, X15472, X15473, X15474]:((~hBOOL(hAPP(hAPP(c_member(X15467),X15466),hAPP(c_List_Oset(X15467),X15465)))|X15465=hAPP(hAPP(c_List_Oappend(X15467),esk522_3(X15465,X15466,X15467)),hAPP(hAPP(c_List_Olist_OCons(X15467),X15466),esk523_3(X15465,X15466,X15467))))&(X15470!=hAPP(hAPP(c_List_Oappend(X15472),X15473),hAPP(hAPP(c_List_Olist_OCons(X15472),X15471),X15474))|hBOOL(hAPP(hAPP(c_member(X15472),X15471),hAPP(c_List_Oset(X15472),X15470))))), 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])])])])])). 6.97/7.22 fof(c_0_5753, plain, ![X16794, X16795]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X16795))),c_Enum_Osublists(X16795,X16794))=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(X16795)),X16794)), inference(variable_rename,[status(thm)],[fact_length__sublists])). 6.97/7.22 cnf(c_0_5754, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X1))=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)))), inference(split_conjunct,[status(thm)],[c_0_4710])). 6.97/7.22 fof(c_0_5755, plain, ![X16766, X16767, X16768]:hAPP(c_List_Oset(X16768),X16766)=hAPP(c_List_Oset(X16768),hAPP(c_List_Orotate(X16768,X16767),X16766)), inference(variable_rename,[status(thm)],[fact_set__rotate])). 6.97/7.22 fof(c_0_5756, plain, ![X12648, X12649]:c_List_Oconcat(X12649,c_List_Oreplicate(tc_List_Olist(X12649),X12648,c_List_Olist_ONil(X12649)))=c_List_Olist_ONil(X12649), inference(variable_rename,[status(thm)],[fact_concat__replicate__trivial])). 6.97/7.22 fof(c_0_5757, plain, ![X13721, X13722]:hAPP(c_Relation_ODomain(X13722,X13722),X13721)=hAPP(c_Relation_ODomain(X13722,X13722),c_Transitive__Closure_Otrancl(X13722,X13721)), inference(variable_rename,[status(thm)],[fact_trancl__domain])). 6.97/7.22 fof(c_0_5758, plain, ![X3287, X3288]:hAPP(c_Relation_ORange(X3288,X3288),X3287)=hAPP(c_Relation_ORange(X3288,X3288),c_Transitive__Closure_Otrancl(X3288,X3287)), inference(variable_rename,[status(thm)],[fact_trancl__range])). 6.97/7.22 fof(c_0_5759, plain, ![X4798]:c_List_Olistset(X4798,c_List_Olist_ONil(tc_fun(X4798,tc_HOL_Obool)))=hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X4798)),c_List_Olist_ONil(X4798)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X4798),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_listset_Osimps_I1_J])). 6.97/7.22 fof(c_0_5760, plain, ![X7812]:c_Relation_OId(X7812)=hAPP(c_Relation_Oconverse(X7812,X7812),c_Relation_OId(X7812)), inference(variable_rename,[status(thm)],[fact_converse__Id])). 6.97/7.22 fof(c_0_5761, plain, ![X11707]:c_List_Olists(X11707,c_Orderings_Obot__class_Obot(tc_fun(X11707,tc_HOL_Obool)))=hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X11707)),c_List_Olist_ONil(X11707)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X11707),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_lists__empty])). 6.97/7.22 fof(c_0_5762, plain, ![X1191, X1192, X1193, X1194, X1195, X1196]:hAPP(hAPP(X1193,X1192),X1191)=hAPP(hAPP(c_Product__Type_Ointernal__split(X1196,X1195,X1194),X1193),hAPP(hAPP(c_Product__Type_OPair(X1196,X1195),X1192),X1191)), inference(variable_rename,[status(thm)],[fact_internal__split__conv])). 6.97/7.22 fof(c_0_5763, plain, ![X2115, X2116, X2117]:c_Product__Type_Ointernal__split(X2117,X2116,X2115)=c_Product__Type_Oprod_Oprod__case(X2117,X2116,X2115), inference(variable_rename,[status(thm)],[fact_internal__split__def])). 6.97/7.22 fof(c_0_5764, plain, ![X4584, X4585]:c_Hilbert__Choice_OEps(X4585,hAPP(hAPP(c_COMBC(X4585,X4585,tc_HOL_Obool),c_fequal),X4584))=X4584, inference(variable_rename,[status(thm)],[fact_some__eq__trivial])). 6.97/7.22 fof(c_0_5765, plain, ![X7776, X7777]:c_HOL_OThe(X7777,hAPP(hAPP(c_COMBC(X7777,X7777,tc_HOL_Obool),c_fequal),X7776))=X7776, inference(variable_rename,[status(thm)],[fact_the__eq__trivial])). 6.97/7.22 fof(c_0_5766, plain, ![X3222, X3223, X3224, X3225]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3224)),X3223)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X3225|c_List_Obutlast(X3224,hAPP(hAPP(c_List_Olist__update(X3224,X3223),X3225),X3222))=hAPP(hAPP(c_List_Olist__update(X3224,c_List_Obutlast(X3224,X3223)),X3225),X3222))&(X3225!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3224)),X3223)),c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_List_Obutlast(X3224,hAPP(hAPP(c_List_Olist__update(X3224,X3223),X3225),X3222))=c_List_Obutlast(X3224,X3223))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_butlast__list__update])])])). 6.97/7.22 fof(c_0_5767, plain, ![X5834, X5835, X5836]:hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X5836)),c_Lazy__Sequence_Olazy__sequence_OInsert(X5836,X5835,X5834))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X5836)),X5834)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osize_I4_J])). 6.97/7.22 fof(c_0_5768, plain, ![X11745]: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)),X11745)))), inference(variable_rename,[status(thm)],[fact_finite__Collect__less__nat])). 6.97/7.22 fof(c_0_5769, plain, ![X7821]: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)),X7821)))), inference(variable_rename,[status(thm)],[fact_finite__Collect__le__nat])). 6.97/7.22 fof(c_0_5770, plain, ![X7153, X7154, X7155, X7156]:((~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7156,X7155,hAPP(hAPP(c_Set_Oinsert(X7156),X7154),c_Orderings_Obot__class_Obot(tc_fun(X7156,tc_HOL_Obool)))),X7153))|X7153=X7154)&(X7153!=X7154|hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7156,X7155,hAPP(hAPP(c_Set_Oinsert(X7156),X7154),c_Orderings_Obot__class_Obot(tc_fun(X7156,tc_HOL_Obool)))),X7153)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1Set__sing])])). 6.97/7.22 cnf(c_0_5771, plain, (hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(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_4711])). 6.97/7.22 cnf(c_0_5772, 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_4712])). 6.97/7.22 cnf(c_0_5773, 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_4713])). 6.97/7.22 cnf(c_0_5774, 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_4714])). 6.97/7.22 fof(c_0_5775, plain, ![X14418, X14419]:hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X14419)),hAPP(c_Code__Numeral_Onat__of,X14418)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X14419),X14418), inference(variable_rename,[status(thm)],[fact_minus__code__numeral__def])). 6.97/7.22 fof(c_0_5776, plain, ![X9941, X9942]:hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X9942)),hAPP(c_Code__Numeral_Onat__of,X9941)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X9942),X9941), inference(variable_rename,[status(thm)],[fact_plus__code__numeral__def])). 6.97/7.22 fof(c_0_5777, plain, ![X5010, X5011]:hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X5011)),hAPP(c_Code__Numeral_Onat__of,X5010)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),X5011),X5010), inference(variable_rename,[status(thm)],[fact_times__code__numeral__def])). 6.97/7.22 fof(c_0_5778, plain, ![X468, X469]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X469),X468)=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X469)),hAPP(c_Code__Numeral_Onat__of,X468))), inference(variable_rename,[status(thm)],[fact_div__code__numeral__def])). 6.97/7.22 fof(c_0_5779, plain, ![X9851, X9852, X9853]:hAPP(hAPP(c_Relation_Orel__comp(X9853,X9853,X9852),c_Relation_OId(X9853)),X9851)=X9851, inference(variable_rename,[status(thm)],[fact_Id__O__R])). 6.97/7.22 fof(c_0_5780, plain, ![X12744, X12745, X12746]:X12744=hAPP(hAPP(c_Relation_Orel__comp(X12746,X12745,X12745),X12744),c_Relation_OId(X12745)), inference(variable_rename,[status(thm)],[fact_R__O__Id])). 6.97/7.22 fof(c_0_5781, plain, ![X8197, X8198, X8199, X8200]:((c_Orderings_Obot__class_Obot(tc_fun(X8200,tc_HOL_Obool))!=X8198|X8197!=c_Orderings_Obot__class_Obot(tc_fun(X8199,tc_HOL_Obool))|c_Sum__Type_OPlus(X8200,X8199,X8198,X8197)=c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X8200,X8199),tc_HOL_Obool)))&((c_Orderings_Obot__class_Obot(tc_fun(X8200,tc_HOL_Obool))=X8198|c_Sum__Type_OPlus(X8200,X8199,X8198,X8197)!=c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X8200,X8199),tc_HOL_Obool)))&(X8197=c_Orderings_Obot__class_Obot(tc_fun(X8199,tc_HOL_Obool))|c_Sum__Type_OPlus(X8200,X8199,X8198,X8197)!=c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X8200,X8199),tc_HOL_Obool))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Plus__eq__empty__conv])])])). 6.97/7.22 fof(c_0_5782, plain, ![X5378]: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),X5378)))=hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X5378), inference(variable_rename,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__functions_I1_J])). 6.97/7.22 cnf(c_0_5783, 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])). 6.97/7.22 fof(c_0_5784, plain, ![X481, X482]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X482),X481)=hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X482,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X481),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(variable_rename,[status(thm)],[fact_atLeastLessThan__upto])). 6.97/7.22 fof(c_0_5785, plain, ![X17667, X17668]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17668)),hAPP(c_Nat_OSuc,X17667))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X17668),X17667)), inference(variable_rename,[status(thm)],[fact_min__Suc__Suc])). 6.97/7.22 fof(c_0_5786, plain, ![X6618, X6619]:hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X6619),X6618))=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X6619)),hAPP(c_Nat_OSuc,X6618)), inference(variable_rename,[status(thm)],[fact_max__Suc__Suc])). 6.97/7.22 fof(c_0_5787, plain, ![X426, X427, X428, X429, X430]:((X426!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X427),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X428)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X427),X426)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X430),X429))|X429=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X430),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,esk7_2(X429,X430)))))), 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])])])])])). 6.97/7.22 fof(c_0_5788, plain, ![X9154, X9155]:hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9155),X9154))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X9155)),hAPP(c_Code__Numeral_Oof__nat,X9154)), inference(variable_rename,[status(thm)],[fact_plus__code__numeral__code])). 6.97/7.22 fof(c_0_5789, plain, ![X10444, X10445]:hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10445),X10444))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X10445)),hAPP(c_Code__Numeral_Oof__nat,X10444)), inference(variable_rename,[status(thm)],[fact_times__code__numeral__code])). 6.97/7.22 fof(c_0_5790, plain, ![X13266, X13267, X13268]:((hAPP(hAPP(c_List_Olist_OCons(X13268),X13267),c_List_Olist_ONil(X13268))!=hAPP(c_List_Orev(X13268),X13266)|X13266=hAPP(hAPP(c_List_Olist_OCons(X13268),X13267),c_List_Olist_ONil(X13268)))&(X13266!=hAPP(hAPP(c_List_Olist_OCons(X13268),X13267),c_List_Olist_ONil(X13268))|hAPP(hAPP(c_List_Olist_OCons(X13268),X13267),c_List_Olist_ONil(X13268))=hAPP(c_List_Orev(X13268),X13266))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__rev__conv])])). 6.97/7.22 fof(c_0_5791, plain, ![X3401, X3402, X3403, X3404]:c_List_Oreplicate(X3404,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X3403),X3402),X3401)=hAPP(hAPP(c_List_Otake(X3404),X3403),c_List_Oreplicate(X3404,X3402,X3401)), inference(variable_rename,[status(thm)],[fact_take__replicate])). 6.97/7.22 fof(c_0_5792, plain, ![X2061, X2062]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2061),X2062)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(X2062,X2061)), inference(variable_rename,[status(thm)],[fact_length__upt])). 6.97/7.22 cnf(c_0_5793, 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_4715])). 6.97/7.22 cnf(c_0_5794, 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_4716])). 6.97/7.22 fof(c_0_5795, plain, ![X1490, X1491]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1491),X1490)=hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X1491,X1490)), inference(variable_rename,[status(thm)],[fact_div__nat__def])). 6.97/7.22 fof(c_0_5796, plain, ![X3822]:hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3822))=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3822)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X3822)), inference(variable_rename,[status(thm)],[fact_atMost__Suc])). 6.97/7.22 cnf(c_0_5797, plain, (hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X1,hAPP(c_Nat_OSuc,X2)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_4717])). 6.97/7.22 cnf(c_0_5798, plain, (c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(X1))=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)))), inference(split_conjunct,[status(thm)],[c_0_4718])). 6.97/7.22 fof(c_0_5799, plain, ![X8303, X8304, X8306, X8307, X8308]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X8304),X8303))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X8304),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk271_2(X8303,X8304)))=X8303)&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X8307),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X8308))!=X8306|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X8307),X8306)))), 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])])])])])). 6.97/7.22 fof(c_0_5800, plain, ![X13908, X13909]:hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X13909),X13908))=hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,X13909)),hAPP(c_Code__Numeral_Oof__nat,X13908)), inference(variable_rename,[status(thm)],[fact_subtract__code__numeral__code])). 6.97/7.22 fof(c_0_5801, plain, ![X8821, X8822]:c_Transitive__Closure_Ortrancl(X8822,X8821)=c_Transitive__Closure_Ortrancl(X8822,c_Transitive__Closure_Otrancl(X8822,X8821)), inference(variable_rename,[status(thm)],[fact_trancl__rtrancl__absorb])). 6.97/7.22 fof(c_0_5802, plain, ![X13672]:c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13672,X13672)=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X13672),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_dvd_OatLeastAtMost__singleton])). 6.97/7.22 cnf(c_0_5803, 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_4719])). 6.97/7.22 fof(c_0_5804, plain, ![X11932, X11933]:hAPP(c_Relation_OImage(X11933,X11933,c_Relation_OId(X11933)),X11932)=X11932, inference(variable_rename,[status(thm)],[fact_Image__Id])). 6.97/7.22 cnf(c_0_5805, plain, (X1=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))), inference(split_conjunct,[status(thm)],[c_0_4720])). 6.97/7.22 fof(c_0_5806, plain, ![X9148, X9149, X9151, X9152, X9153]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9149),X9148))|hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9149),esk301_2(X9148,X9149)))=X9148)&(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9152),X9153))!=X9151|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9152),X9151)))), 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])])])])])). 6.97/7.22 fof(c_0_5807, plain, ![X14516, X14517]:hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X14517,X14516))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X14517,X14516), inference(variable_rename,[status(thm)],[fact_mod__nat__def])). 6.97/7.22 fof(c_0_5808, plain, ![X10076, X10077]:c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X10077,X10076)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X10077),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X10076),c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(variable_rename,[status(thm)],[fact_atLeastLessThanPlusOne__atLeastAtMost__int])). 6.97/7.22 fof(c_0_5809, plain, ![X4792]:c_Wellfounded_OwfP(X4792,hAPP(c_COMBK(tc_fun(X4792,tc_HOL_Obool),X4792),hAPP(c_COMBK(tc_HOL_Obool,X4792),c_fFalse))), inference(variable_rename,[status(thm)],[fact_wfP__empty])). 6.97/7.22 cnf(c_0_5810, plain, (hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_4721])). 6.97/7.22 fof(c_0_5811, plain, ![X477, X478]:hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X478),X477))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X477),X478)), inference(variable_rename,[status(thm)],[fact_card__atLeastLessThan__int])). 6.97/7.22 fof(c_0_5812, plain, ![X6637]:c_Divides_Odivmod__nat(X6637,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)),X6637), inference(variable_rename,[status(thm)],[fact_divmod__nat__zero])). 6.97/7.22 cnf(c_0_5813, plain, (c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X1,X2,X3,c_Code__Numeral_OSuc__code__numeral(X4))=hAPP(X3,X4)), inference(split_conjunct,[status(thm)],[c_0_4722])). 6.97/7.22 cnf(c_0_5814, 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_4723])). 6.97/7.22 cnf(c_0_5815, 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_4724]), ['final']). 6.97/7.22 fof(c_0_5816, plain, ![X4605]:hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X4605),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X4605))=hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X4605)), inference(variable_rename,[status(thm)],[fact_lessThan__Suc])). 6.97/7.22 fof(c_0_5817, plain, ![X13725]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X13725|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X13725)),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),X13725)),c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X13725)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zabs__less__one__iff])])). 6.97/7.22 fof(c_0_5818, plain, ![X1824, X1825]:hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,X1825),hAPP(c_Code__Numeral_Onat__of,X1824)))=c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1825,X1824), inference(variable_rename,[status(thm)],[fact_mod__code__numeral__def])). 6.97/7.22 fof(c_0_5819, plain, ![X11913, X11914, X11915]:((X11914!=c_Orderings_Obot__class_Obot(tc_fun(X11915,tc_HOL_Obool))|hAPP(hAPP(c_Equiv__Relations_Oquotient(X11915),X11914),X11913)=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X11915,tc_HOL_Obool),tc_HOL_Obool)))&(hAPP(hAPP(c_Equiv__Relations_Oquotient(X11915),X11914),X11913)!=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X11915,tc_HOL_Obool),tc_HOL_Obool))|X11914=c_Orderings_Obot__class_Obot(tc_fun(X11915,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__is__empty2])])). 6.97/7.22 fof(c_0_5820, plain, ![X13080]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X13080)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X13080)), inference(variable_rename,[status(thm)],[fact_nat_Osize_I2_J])). 6.97/7.22 fof(c_0_5821, plain, ![X5363, X5364]:c_Relation_Otrans(X5364,c_Transitive__Closure_Otrancl(X5364,X5363)), inference(variable_rename,[status(thm)],[fact_trans__trancl])). 6.97/7.22 fof(c_0_5822, plain, ![X14473, X14474]:hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X14474,X14473),c_Divides_Odivmod__nat(X14474,X14473))), inference(variable_rename,[status(thm)],[fact_divmod__nat__rel__divmod__nat])). 6.97/7.22 cnf(c_0_5823, 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_4725])). 6.97/7.22 cnf(c_0_5824, 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_4726]), ['final']). 6.97/7.22 fof(c_0_5825, plain, ![X6040, X6041]:hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X6041,X6040))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X6040)),X6041), inference(variable_rename,[status(thm)],[fact_card__atLeastAtMost])). 6.97/7.22 fof(c_0_5826, plain, ![X3384, X3385, X3387, X3388, X3389]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3385),X3384))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3385),esk109_2(X3384,X3385))=X3384)&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3388),X3389)!=X3387|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3388),X3387)))), 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])])])])])). 6.97/7.22 fof(c_0_5827, plain, ![X5713, X5714]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X5714|c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X5713),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X5714))=c_Divides_Opdivmod(X5713,X5714))&(X5714!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Opdivmod(X5713,X5714)=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),X5713)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pdivmod__posDivAlg])])])). 6.97/7.22 fof(c_0_5828, plain, ![X11236, X11237, X11238, X11239, X11240]:((c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X11240|hAPP(c_Random_Oiterate(X11239,X11238,X11240,X11237),X11236)=hAPP(c_Product__Type_OPair(X11239,X11238),X11236))&(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X11240|hAPP(c_Random_Oiterate(X11239,X11238,X11240,X11237),X11236)=hAPP(hAPP(c_Product__Type_Oscomp(X11238,X11239,X11238,tc_prod(X11239,X11238)),hAPP(X11237,X11236)),c_Random_Oiterate(X11239,X11238,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X11240),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X11237)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iterate_Osimps])])). 6.97/7.22 fof(c_0_5829, plain, ![X12229]:c_Int_Osucc(c_Int_Opred(X12229))=X12229, inference(variable_rename,[status(thm)],[fact_succ__pred])). 6.97/7.22 fof(c_0_5830, plain, ![X9106, X9107, X9108, X9109]:((c_Orderings_Obot__class_Obot(tc_fun(X9108,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X9109,X9108,X9107),X9106)|c_Orderings_Obot__class_Obot(tc_fun(X9109,tc_HOL_Obool))=X9106)&(c_Orderings_Obot__class_Obot(tc_fun(X9109,tc_HOL_Obool))!=X9106|c_Orderings_Obot__class_Obot(tc_fun(X9108,tc_HOL_Obool))=hAPP(c_Set_Oimage(X9109,X9108,X9107),X9106))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__is__empty])])). 6.97/7.22 fof(c_0_5831, plain, ![X5003]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X5003),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X5003), inference(variable_rename,[status(thm)],[fact_zdiv__minus1__right])). 6.97/7.22 fof(c_0_5832, plain, ![X4328, X4329, X4330]:((c_Orderings_Obot__class_Obot(tc_fun(X4330,tc_HOL_Obool))!=hAPP(c_Relation_ODomain(X4330,X4329),X4328)|c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4330,X4329),tc_HOL_Obool))=X4328)&(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4330,X4329),tc_HOL_Obool))!=X4328|c_Orderings_Obot__class_Obot(tc_fun(X4330,tc_HOL_Obool))=hAPP(c_Relation_ODomain(X4330,X4329),X4328))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Domain__empty__iff])])). 6.97/7.22 fof(c_0_5833, plain, ![X924, X925, X926]:((c_Orderings_Obot__class_Obot(tc_fun(X925,tc_HOL_Obool))!=hAPP(c_Relation_ORange(X926,X925),X924)|X924=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X926,X925),tc_HOL_Obool)))&(X924!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X926,X925),tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X925,tc_HOL_Obool))=hAPP(c_Relation_ORange(X926,X925),X924))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Range__empty__iff])])). 6.97/7.22 fof(c_0_5834, plain, ![X11390]:c_Relation_Osingle__valued(X11390,X11390,c_Relation_OId(X11390)), inference(variable_rename,[status(thm)],[fact_single__valued__Id])). 6.97/7.22 fof(c_0_5835, plain, ![X15789, X15790]:hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X15790,X15789))), inference(variable_rename,[status(thm)],[fact_distinct__upt])). 6.97/7.22 fof(c_0_5836, plain, ![X7933, X7934]:c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X7934,X7933)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7934),c_Groups_Oone__class_Oone(tc_Int_Oint))),X7933), inference(variable_rename,[status(thm)],[fact_atLeastPlusOneLessThan__greaterThanLessThan__int])). 6.97/7.22 fof(c_0_5837, plain, ![X4850, X4851, X4852]:((c_List_Olist_ONil(X4851)=X4852|hAPP(hAPP(c_List_Olist_OCons(X4851),X4850),c_List_Obutlast(X4851,X4852))=c_List_Obutlast(X4851,hAPP(hAPP(c_List_Olist_OCons(X4851),X4850),X4852)))&(c_List_Olist_ONil(X4851)!=X4852|c_List_Obutlast(X4851,hAPP(hAPP(c_List_Olist_OCons(X4851),X4850),X4852))=c_List_Olist_ONil(X4851))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_butlast_Osimps_I2_J])])])). 6.97/7.22 fof(c_0_5838, plain, ![X16051, X16052, X16053, X16054]:((X16053=X16054|c_List_Oremove1(X16052,X16054,hAPP(hAPP(c_List_Olist_OCons(X16052),X16053),X16051))=hAPP(hAPP(c_List_Olist_OCons(X16052),X16053),c_List_Oremove1(X16052,X16054,X16051)))&(X16054!=X16053|X16051=c_List_Oremove1(X16052,X16054,hAPP(hAPP(c_List_Olist_OCons(X16052),X16053),X16051)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_remove1_Osimps_I2_J])])])). 6.97/7.22 fof(c_0_5839, plain, ![X4581, X4582, X4583]:c_List_Osublist(X4583,X4582,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X4581))=hAPP(hAPP(c_List_Otake(X4583),X4581),X4582), inference(variable_rename,[status(thm)],[fact_sublist__upt__eq__take])). 6.97/7.22 cnf(c_0_5840, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))=hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fTrue))), inference(split_conjunct,[status(thm)],[c_0_4727])). 6.97/7.22 fof(c_0_5841, plain, ![X8788, X8789, X8790, X8791, X8792]:((X8789!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8788),X8790)|c_Divides_Odiv__class_Omod(tc_Int_Oint,X8789,X8788)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(c_Divides_Odiv__class_Omod(tc_Int_Oint,X8792,X8791)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X8792=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8791),esk284_2(X8791,X8792)))), 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])])])])])). 6.97/7.22 fof(c_0_5842, plain, ![X3245, X3246, X3247, X3248, X3249]:((X3246!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3245),X3247)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3246,X3245))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3249,X3248)|X3249=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3248),esk103_2(X3248,X3249)))), 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])])])])])). 6.97/7.22 fof(c_0_5843, plain, ![X5379, X5380, X5381]:(c_List_Olist_ONil(X5380)!=X5381|X5379=c_List_Olast(X5380,hAPP(hAPP(c_List_Olist_OCons(X5380),X5379),X5381))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__ConsL])])). 6.97/7.22 cnf(c_0_5844, plain, (X2=c_Code__Numeral_Onat__of__aux(X1,X2)|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X1), inference(split_conjunct,[status(thm)],[c_0_4594])). 6.97/7.22 fof(c_0_5845, plain, ![X1144]:c_Relation_Oantisym(X1144,c_Relation_OId(X1144)), inference(variable_rename,[status(thm)],[fact_antisym__Id])). 6.97/7.22 fof(c_0_5846, plain, ![X572]:c_Relation_Osym(X572,c_Relation_OId(X572)), inference(variable_rename,[status(thm)],[fact_sym__Id])). 6.97/7.22 fof(c_0_5847, plain, ![X16004, X16005, X16006, X16007]:((~hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X16007),X16006),X16005),X16004))|(X16004=X16006|hBOOL(hAPP(X16005,X16004))))&((X16004!=X16006|hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X16007),X16006),X16005),X16004)))&(~hBOOL(hAPP(X16005,X16004))|hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X16007),X16006),X16005),X16004))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])])). 6.97/7.22 fof(c_0_5848, plain, ![X4151, X4152, X4153]:((~hBOOL(hAPP(hAPP(c_member(X4153),X4152),hAPP(c_fequal,X4151)))|X4151=X4152)&(X4151!=X4152|hBOOL(hAPP(hAPP(c_member(X4153),X4152),hAPP(c_fequal,X4151))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__mem])])). 6.97/7.22 fof(c_0_5849, plain, ![X4233]:hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X4233)), inference(variable_rename,[status(thm)],[fact_dvd__1__left])). 6.97/7.22 fof(c_0_5850, plain, ![X13252]:(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X13252),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))|X13252=hAPP(c_Code__Numeral_Onat__of,esk433_1(X13252))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__of__cases])])])). 6.97/7.22 fof(c_0_5851, plain, ![X16662]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X16662))), inference(variable_rename,[status(thm)],[fact_nat__zminus__int])). 6.97/7.22 fof(c_0_5852, plain, ![X6328, X6329, X6330, X6331, X6332]:((c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X6332|hAPP(c_New__DSequence_Opos__decr__bind(X6331,X6330,X6329,X6328),X6332)=c_Lazy__Sequence_Oempty(X6330))&(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X6332|hAPP(c_Lazy__Sequence_Obind(X6331,X6330,hAPP(X6329,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X6332),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(X6331,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X6330)),X6328),X6332))=hAPP(c_New__DSequence_Opos__decr__bind(X6331,X6330,X6329,X6328),X6332))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_New__DSequence_Opos__decr__bind__def])])). 6.97/7.22 fof(c_0_5853, plain, ![X8924, X8925, X8926, X8927, X8928]:((c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X8928|c_Lazy__Sequence_Ohit__bound(X8926)=hAPP(c_New__DSequence_Oneg__decr__bind(X8927,X8926,X8925,X8924),X8928))&(X8928=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|hAPP(c_New__DSequence_Oneg__decr__bind(X8927,X8926,X8925,X8924),X8928)=c_Lazy__Sequence_Ohb__bind(X8927,X8926,hAPP(X8925,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X8928),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X8927,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X8926))),X8924),X8928)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_New__DSequence_Oneg__decr__bind__def])])])). 6.97/7.22 fof(c_0_5854, plain, ![X12702]:X12702=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X12702),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_div__1])). 6.97/7.22 fof(c_0_5855, plain, ![X11310, X11311]:c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X11311,X11310)), inference(variable_rename,[status(thm)],[fact_sorted__upt])). 6.97/7.22 fof(c_0_5856, plain, ![X8504, X8505]:c_Wellfounded_Owf(X8505,hAPP(c_Wellfounded_Omeasure(X8505),X8504)), inference(variable_rename,[status(thm)],[fact_wf__measure])). 6.97/7.22 fof(c_0_5857, plain, ![X17259, X17260, X17261, X17262, X17263]:((X17261!=c_Fun_Ofun__upd(X17263,X17262,X17261,X17260,X17259)|X17259=hAPP(X17261,X17260))&(X17259!=hAPP(X17261,X17260)|X17261=c_Fun_Ofun__upd(X17263,X17262,X17261,X17260,X17259))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__idem__iff])])). 6.97/7.22 fof(c_0_5858, plain, ![X7927]:X7927=hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X7927)), inference(variable_rename,[status(thm)],[fact_nat__int])). 6.97/7.22 fof(c_0_5859, plain, ![X2540, X2541, X2542, X2543]:((c_List_Olist_ONil(X2543)!=X2540|c_List_Olist__all2(X2543,X2542,X2541,X2540,c_List_Olist_ONil(X2542)))&(~c_List_Olist__all2(X2543,X2542,X2541,X2540,c_List_Olist_ONil(X2542))|c_List_Olist_ONil(X2543)=X2540)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__Nil2])])). 6.97/7.22 fof(c_0_5860, plain, ![X1466, X1467]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1467|c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1466),X1467))&(X1467=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1466),X1467)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1466),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1466),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1467),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__eq__if])])])). 6.97/7.22 fof(c_0_5861, plain, ![X14479]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X14479,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)), inference(variable_rename,[status(thm)],[fact_zmod__minus1__right])). 6.97/7.22 fof(c_0_5862, plain, ![X8710]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X8710,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_mod__1])). 6.97/7.22 fof(c_0_5863, plain, ![X3091]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3091)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_min__0L])). 6.97/7.22 fof(c_0_5864, plain, ![X7358]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X7358),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_min__0R])). 6.97/7.22 fof(c_0_5865, plain, ![X17425]:hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17425)=X17425, inference(variable_rename,[status(thm)],[fact_max__0L])). 6.97/7.22 fof(c_0_5866, plain, ![X12279]:X12279=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X12279),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_max__0R])). 6.97/7.22 fof(c_0_5867, plain, ![X4958, X4959, X4960]:((~c_List_Olist__all2(X4958,X4958,c_fequal,X4960,X4959)|X4960=X4959)&(X4960!=X4959|c_List_Olist__all2(X4958,X4958,c_fequal,X4960,X4959))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__eq])])). 6.97/7.22 fof(c_0_5868, plain, ![X7913, X7914]:(X7914!=X7913|hBOOL(hAPP(hAPP(c_fequal,X7914),X7913))), inference(variable_rename,[status(thm)],[help_c__fequal__2])). 6.97/7.22 fof(c_0_5869, plain, ![X3344]:X3344=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3344),c_Int_OPls), inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I1_J])). 6.97/7.22 fof(c_0_5870, plain, ![X1826]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X1826)=c_Int_OPls, inference(variable_rename,[status(thm)],[fact_mult__Pls])). 6.97/7.22 fof(c_0_5871, plain, ![X13272]:hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X13272))=X13272, inference(variable_rename,[status(thm)],[fact_of__nat__nat__of])). 6.97/7.22 fof(c_0_5872, plain, ![X10833]:X10833=hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X10833)), inference(variable_rename,[status(thm)],[fact_nat__of__of__nat])). 6.97/7.22 fof(c_0_5873, plain, ![X6559, X6560]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X6560|X6559=c_Nitpick_Onat__gcd(X6559,X6560))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X6560|c_Nitpick_Onat__gcd(X6559,X6560)=c_Nitpick_Onat__gcd(X6560,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X6559,X6560)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__gcd_Osimps])])])). 6.97/7.22 fof(c_0_5874, plain, ![X10979, X10980]:((X10979!=X10980|c_Random_Oinc__shift(X10980,X10979)=c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))&(X10980=X10979|c_Random_Oinc__shift(X10980,X10979)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X10979),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inc__shift__def])])])). 6.97/7.22 fof(c_0_5875, plain, ![X16981]:(X16981=hAPP(c_Code__Numeral_Oof__nat,esk571_1(X16981))&hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk571_1(X16981)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__cases])])])])). 6.97/7.22 cnf(c_0_5876, plain, (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))=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)))))))|~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_4728])). 6.97/7.22 cnf(c_0_5877, 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))|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_4729])). 6.97/7.22 cnf(c_0_5878, 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_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_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)))))))|~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_4730])). 6.97/7.22 cnf(c_0_5879, 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__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_4731])). 6.97/7.22 cnf(c_0_5880, 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))|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)))))))=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))|~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_4732])). 6.97/7.22 cnf(c_0_5881, 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_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_4733, c_0_4734])). 6.97/7.22 cnf(c_0_5882, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|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_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_4735, c_0_4734])). 6.97/7.22 cnf(c_0_5883, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[c_0_4736, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 fof(c_0_5884, plain, ![X13258, X13259, X13260]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13260,tc_HOL_Obool)),X13259),hAPP(X13258,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X13260,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X13260,tc_HOL_Obool),tc_fun(X13260,tc_HOL_Obool),tc_fun(X13260,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13260,tc_HOL_Obool),tc_fun(tc_fun(X13260,tc_HOL_Obool),tc_fun(X13260,tc_HOL_Obool)),tc_fun(X13260,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13260,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X13260,tc_HOL_Obool),tc_fun(X13260,tc_HOL_Obool),tc_fun(X13260,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13260,tc_HOL_Obool),tc_fun(tc_fun(X13260,tc_HOL_Obool),tc_fun(X13260,tc_HOL_Obool)),tc_fun(X13260,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13260,tc_HOL_Obool))),X13258)),X13259))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X13260,tc_HOL_Obool),X13258))))))|(~c_Orderings_Oorder__class_Omono(tc_fun(X13260,tc_HOL_Obool),tc_fun(X13260,tc_HOL_Obool),X13258)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13260,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X13260,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X13260,tc_HOL_Obool),tc_fun(X13260,tc_HOL_Obool),tc_fun(X13260,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13260,tc_HOL_Obool),tc_fun(tc_fun(X13260,tc_HOL_Obool),tc_fun(X13260,tc_HOL_Obool)),tc_fun(X13260,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13260,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X13260,tc_HOL_Obool),tc_fun(X13260,tc_HOL_Obool),tc_fun(X13260,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13260,tc_HOL_Obool),tc_fun(tc_fun(X13260,tc_HOL_Obool),tc_fun(X13260,tc_HOL_Obool)),tc_fun(X13260,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13260,tc_HOL_Obool))),X13258)),X13259))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X13260,tc_HOL_Obool),X13258)))),hAPP(X13258,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X13260,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X13260,tc_HOL_Obool),tc_fun(X13260,tc_HOL_Obool),tc_fun(X13260,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13260,tc_HOL_Obool),tc_fun(tc_fun(X13260,tc_HOL_Obool),tc_fun(X13260,tc_HOL_Obool)),tc_fun(X13260,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13260,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X13260,tc_HOL_Obool),tc_fun(X13260,tc_HOL_Obool),tc_fun(X13260,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13260,tc_HOL_Obool),tc_fun(tc_fun(X13260,tc_HOL_Obool),tc_fun(X13260,tc_HOL_Obool)),tc_fun(X13260,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13260,tc_HOL_Obool))),X13258)),X13259))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X13260,tc_HOL_Obool),X13258)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coinduct3__lemma])])). 6.97/7.22 fof(c_0_5885, plain, ![X16344, X16345, X16346, X16347, X16348, X16349]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X16349,X16348)),hAPP(hAPP(c_Product__Type_OPair(X16349,X16348),X16345),X16344)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X16349,X16348),tc_HOL_Obool)),X16347),X16346)))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16349,tc_fun(X16348,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X16349,tc_fun(tc_prod(X16349,X16348),tc_HOL_Obool),tc_fun(X16348,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16348,tc_fun(tc_fun(tc_prod(X16349,X16348),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X16349,X16348),tc_HOL_Obool),tc_fun(X16348,tc_HOL_Obool)),X16349),c_COMBC(X16348,tc_fun(tc_prod(X16349,X16348),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16348,tc_prod(X16349,X16348)),tc_fun(X16348,tc_fun(tc_fun(tc_prod(X16349,X16348),tc_HOL_Obool),tc_HOL_Obool)),X16349),hAPP(c_COMBB(tc_prod(X16349,X16348),tc_fun(tc_fun(tc_prod(X16349,X16348),tc_HOL_Obool),tc_HOL_Obool),X16348),c_member(tc_prod(X16349,X16348)))),c_Product__Type_OPair(X16349,X16348)))),X16347)),hAPP(hAPP(c_COMBC(X16349,tc_fun(tc_prod(X16349,X16348),tc_HOL_Obool),tc_fun(X16348,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16348,tc_fun(tc_fun(tc_prod(X16349,X16348),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X16349,X16348),tc_HOL_Obool),tc_fun(X16348,tc_HOL_Obool)),X16349),c_COMBC(X16348,tc_fun(tc_prod(X16349,X16348),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16348,tc_prod(X16349,X16348)),tc_fun(X16348,tc_fun(tc_fun(tc_prod(X16349,X16348),tc_HOL_Obool),tc_HOL_Obool)),X16349),hAPP(c_COMBB(tc_prod(X16349,X16348),tc_fun(tc_fun(tc_prod(X16349,X16348),tc_HOL_Obool),tc_HOL_Obool),X16348),c_member(tc_prod(X16349,X16348)))),c_Product__Type_OPair(X16349,X16348)))),X16346)),X16345),X16344)))&(~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16349,tc_fun(X16348,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X16349,tc_fun(tc_prod(X16349,X16348),tc_HOL_Obool),tc_fun(X16348,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16348,tc_fun(tc_fun(tc_prod(X16349,X16348),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X16349,X16348),tc_HOL_Obool),tc_fun(X16348,tc_HOL_Obool)),X16349),c_COMBC(X16348,tc_fun(tc_prod(X16349,X16348),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16348,tc_prod(X16349,X16348)),tc_fun(X16348,tc_fun(tc_fun(tc_prod(X16349,X16348),tc_HOL_Obool),tc_HOL_Obool)),X16349),hAPP(c_COMBB(tc_prod(X16349,X16348),tc_fun(tc_fun(tc_prod(X16349,X16348),tc_HOL_Obool),tc_HOL_Obool),X16348),c_member(tc_prod(X16349,X16348)))),c_Product__Type_OPair(X16349,X16348)))),X16347)),hAPP(hAPP(c_COMBC(X16349,tc_fun(tc_prod(X16349,X16348),tc_HOL_Obool),tc_fun(X16348,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16348,tc_fun(tc_fun(tc_prod(X16349,X16348),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X16349,X16348),tc_HOL_Obool),tc_fun(X16348,tc_HOL_Obool)),X16349),c_COMBC(X16348,tc_fun(tc_prod(X16349,X16348),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16348,tc_prod(X16349,X16348)),tc_fun(X16348,tc_fun(tc_fun(tc_prod(X16349,X16348),tc_HOL_Obool),tc_HOL_Obool)),X16349),hAPP(c_COMBB(tc_prod(X16349,X16348),tc_fun(tc_fun(tc_prod(X16349,X16348),tc_HOL_Obool),tc_HOL_Obool),X16348),c_member(tc_prod(X16349,X16348)))),c_Product__Type_OPair(X16349,X16348)))),X16346)),X16345),X16344))|hBOOL(hAPP(hAPP(c_member(tc_prod(X16349,X16348)),hAPP(hAPP(c_Product__Type_OPair(X16349,X16348),X16345),X16344)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X16349,X16348),tc_HOL_Obool)),X16347),X16346))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Int__eq2])])). 6.97/7.22 fof(c_0_5886, plain, ![X14319, X14320, X14321, X14322, X14323, X14324]:((~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14324,tc_fun(X14323,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X14324,tc_fun(tc_prod(X14324,X14323),tc_HOL_Obool),tc_fun(X14323,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14323,tc_fun(tc_fun(tc_prod(X14324,X14323),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X14324,X14323),tc_HOL_Obool),tc_fun(X14323,tc_HOL_Obool)),X14324),c_COMBC(X14323,tc_fun(tc_prod(X14324,X14323),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14323,tc_prod(X14324,X14323)),tc_fun(X14323,tc_fun(tc_fun(tc_prod(X14324,X14323),tc_HOL_Obool),tc_HOL_Obool)),X14324),hAPP(c_COMBB(tc_prod(X14324,X14323),tc_fun(tc_fun(tc_prod(X14324,X14323),tc_HOL_Obool),tc_HOL_Obool),X14323),c_member(tc_prod(X14324,X14323)))),c_Product__Type_OPair(X14324,X14323)))),X14322)),hAPP(hAPP(c_COMBC(X14324,tc_fun(tc_prod(X14324,X14323),tc_HOL_Obool),tc_fun(X14323,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14323,tc_fun(tc_fun(tc_prod(X14324,X14323),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X14324,X14323),tc_HOL_Obool),tc_fun(X14323,tc_HOL_Obool)),X14324),c_COMBC(X14323,tc_fun(tc_prod(X14324,X14323),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14323,tc_prod(X14324,X14323)),tc_fun(X14323,tc_fun(tc_fun(tc_prod(X14324,X14323),tc_HOL_Obool),tc_HOL_Obool)),X14324),hAPP(c_COMBB(tc_prod(X14324,X14323),tc_fun(tc_fun(tc_prod(X14324,X14323),tc_HOL_Obool),tc_HOL_Obool),X14323),c_member(tc_prod(X14324,X14323)))),c_Product__Type_OPair(X14324,X14323)))),X14321)),X14320),X14319))|hBOOL(hAPP(hAPP(c_member(tc_prod(X14324,X14323)),hAPP(hAPP(c_Product__Type_OPair(X14324,X14323),X14320),X14319)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X14324,X14323),tc_HOL_Obool)),X14322),X14321))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X14324,X14323)),hAPP(hAPP(c_Product__Type_OPair(X14324,X14323),X14320),X14319)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X14324,X14323),tc_HOL_Obool)),X14322),X14321)))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14324,tc_fun(X14323,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X14324,tc_fun(tc_prod(X14324,X14323),tc_HOL_Obool),tc_fun(X14323,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14323,tc_fun(tc_fun(tc_prod(X14324,X14323),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X14324,X14323),tc_HOL_Obool),tc_fun(X14323,tc_HOL_Obool)),X14324),c_COMBC(X14323,tc_fun(tc_prod(X14324,X14323),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14323,tc_prod(X14324,X14323)),tc_fun(X14323,tc_fun(tc_fun(tc_prod(X14324,X14323),tc_HOL_Obool),tc_HOL_Obool)),X14324),hAPP(c_COMBB(tc_prod(X14324,X14323),tc_fun(tc_fun(tc_prod(X14324,X14323),tc_HOL_Obool),tc_HOL_Obool),X14323),c_member(tc_prod(X14324,X14323)))),c_Product__Type_OPair(X14324,X14323)))),X14322)),hAPP(hAPP(c_COMBC(X14324,tc_fun(tc_prod(X14324,X14323),tc_HOL_Obool),tc_fun(X14323,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14323,tc_fun(tc_fun(tc_prod(X14324,X14323),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X14324,X14323),tc_HOL_Obool),tc_fun(X14323,tc_HOL_Obool)),X14324),c_COMBC(X14323,tc_fun(tc_prod(X14324,X14323),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14323,tc_prod(X14324,X14323)),tc_fun(X14323,tc_fun(tc_fun(tc_prod(X14324,X14323),tc_HOL_Obool),tc_HOL_Obool)),X14324),hAPP(c_COMBB(tc_prod(X14324,X14323),tc_fun(tc_fun(tc_prod(X14324,X14323),tc_HOL_Obool),tc_HOL_Obool),X14323),c_member(tc_prod(X14324,X14323)))),c_Product__Type_OPair(X14324,X14323)))),X14321)),X14320),X14319)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Un__eq2])])). 6.97/7.22 fof(c_0_5887, plain, ![X9791, X9792, X9793, X9794, X9795, X9796, X9797]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X9797,X9795)),hAPP(hAPP(c_Product__Type_OPair(X9797,X9795),X9792),X9791)),hAPP(hAPP(c_Relation_Orel__comp(X9797,X9796,X9795),X9794),X9793)))|hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X9797,X9796,X9795,hAPP(hAPP(c_COMBC(X9797,tc_fun(tc_prod(X9797,X9796),tc_HOL_Obool),tc_fun(X9796,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9796,tc_fun(tc_fun(tc_prod(X9797,X9796),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X9797,X9796),tc_HOL_Obool),tc_fun(X9796,tc_HOL_Obool)),X9797),c_COMBC(X9796,tc_fun(tc_prod(X9797,X9796),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9796,tc_prod(X9797,X9796)),tc_fun(X9796,tc_fun(tc_fun(tc_prod(X9797,X9796),tc_HOL_Obool),tc_HOL_Obool)),X9797),hAPP(c_COMBB(tc_prod(X9797,X9796),tc_fun(tc_fun(tc_prod(X9797,X9796),tc_HOL_Obool),tc_HOL_Obool),X9796),c_member(tc_prod(X9797,X9796)))),c_Product__Type_OPair(X9797,X9796)))),X9794),hAPP(hAPP(c_COMBC(X9796,tc_fun(tc_prod(X9796,X9795),tc_HOL_Obool),tc_fun(X9795,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9795,tc_fun(tc_fun(tc_prod(X9796,X9795),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X9796,X9795),tc_HOL_Obool),tc_fun(X9795,tc_HOL_Obool)),X9796),c_COMBC(X9795,tc_fun(tc_prod(X9796,X9795),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9795,tc_prod(X9796,X9795)),tc_fun(X9795,tc_fun(tc_fun(tc_prod(X9796,X9795),tc_HOL_Obool),tc_HOL_Obool)),X9796),hAPP(c_COMBB(tc_prod(X9796,X9795),tc_fun(tc_fun(tc_prod(X9796,X9795),tc_HOL_Obool),tc_HOL_Obool),X9795),c_member(tc_prod(X9796,X9795)))),c_Product__Type_OPair(X9796,X9795)))),X9793)),X9792),X9791)))&(~hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X9797,X9796,X9795,hAPP(hAPP(c_COMBC(X9797,tc_fun(tc_prod(X9797,X9796),tc_HOL_Obool),tc_fun(X9796,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9796,tc_fun(tc_fun(tc_prod(X9797,X9796),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X9797,X9796),tc_HOL_Obool),tc_fun(X9796,tc_HOL_Obool)),X9797),c_COMBC(X9796,tc_fun(tc_prod(X9797,X9796),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9796,tc_prod(X9797,X9796)),tc_fun(X9796,tc_fun(tc_fun(tc_prod(X9797,X9796),tc_HOL_Obool),tc_HOL_Obool)),X9797),hAPP(c_COMBB(tc_prod(X9797,X9796),tc_fun(tc_fun(tc_prod(X9797,X9796),tc_HOL_Obool),tc_HOL_Obool),X9796),c_member(tc_prod(X9797,X9796)))),c_Product__Type_OPair(X9797,X9796)))),X9794),hAPP(hAPP(c_COMBC(X9796,tc_fun(tc_prod(X9796,X9795),tc_HOL_Obool),tc_fun(X9795,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9795,tc_fun(tc_fun(tc_prod(X9796,X9795),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X9796,X9795),tc_HOL_Obool),tc_fun(X9795,tc_HOL_Obool)),X9796),c_COMBC(X9795,tc_fun(tc_prod(X9796,X9795),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9795,tc_prod(X9796,X9795)),tc_fun(X9795,tc_fun(tc_fun(tc_prod(X9796,X9795),tc_HOL_Obool),tc_HOL_Obool)),X9796),hAPP(c_COMBB(tc_prod(X9796,X9795),tc_fun(tc_fun(tc_prod(X9796,X9795),tc_HOL_Obool),tc_HOL_Obool),X9795),c_member(tc_prod(X9796,X9795)))),c_Product__Type_OPair(X9796,X9795)))),X9793)),X9792),X9791))|hBOOL(hAPP(hAPP(c_member(tc_prod(X9797,X9795)),hAPP(hAPP(c_Product__Type_OPair(X9797,X9795),X9792),X9791)),hAPP(hAPP(c_Relation_Orel__comp(X9797,X9796,X9795),X9794),X9793))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__comp__rel__comp__eq])])). 6.97/7.22 fof(c_0_5888, plain, ![X6080, X6081, X6082, X6083]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6083,tc_fun(X6082,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X6083,tc_fun(tc_prod(X6083,X6082),tc_HOL_Obool),tc_fun(X6082,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6082,tc_fun(tc_fun(tc_prod(X6083,X6082),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6083,X6082),tc_HOL_Obool),tc_fun(X6082,tc_HOL_Obool)),X6083),c_COMBC(X6082,tc_fun(tc_prod(X6083,X6082),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6082,tc_prod(X6083,X6082)),tc_fun(X6082,tc_fun(tc_fun(tc_prod(X6083,X6082),tc_HOL_Obool),tc_HOL_Obool)),X6083),hAPP(c_COMBB(tc_prod(X6083,X6082),tc_fun(tc_fun(tc_prod(X6083,X6082),tc_HOL_Obool),tc_HOL_Obool),X6082),c_member(tc_prod(X6083,X6082)))),c_Product__Type_OPair(X6083,X6082)))),X6081)),hAPP(hAPP(c_COMBC(X6083,tc_fun(tc_prod(X6083,X6082),tc_HOL_Obool),tc_fun(X6082,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6082,tc_fun(tc_fun(tc_prod(X6083,X6082),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6083,X6082),tc_HOL_Obool),tc_fun(X6082,tc_HOL_Obool)),X6083),c_COMBC(X6082,tc_fun(tc_prod(X6083,X6082),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6082,tc_prod(X6083,X6082)),tc_fun(X6082,tc_fun(tc_fun(tc_prod(X6083,X6082),tc_HOL_Obool),tc_HOL_Obool)),X6083),hAPP(c_COMBB(tc_prod(X6083,X6082),tc_fun(tc_fun(tc_prod(X6083,X6082),tc_HOL_Obool),tc_HOL_Obool),X6082),c_member(tc_prod(X6083,X6082)))),c_Product__Type_OPair(X6083,X6082)))),X6080)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6083,X6082),tc_HOL_Obool)),X6081),X6080)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6083,X6082),tc_HOL_Obool)),X6081),X6080))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6083,tc_fun(X6082,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X6083,tc_fun(tc_prod(X6083,X6082),tc_HOL_Obool),tc_fun(X6082,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6082,tc_fun(tc_fun(tc_prod(X6083,X6082),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6083,X6082),tc_HOL_Obool),tc_fun(X6082,tc_HOL_Obool)),X6083),c_COMBC(X6082,tc_fun(tc_prod(X6083,X6082),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6082,tc_prod(X6083,X6082)),tc_fun(X6082,tc_fun(tc_fun(tc_prod(X6083,X6082),tc_HOL_Obool),tc_HOL_Obool)),X6083),hAPP(c_COMBB(tc_prod(X6083,X6082),tc_fun(tc_fun(tc_prod(X6083,X6082),tc_HOL_Obool),tc_HOL_Obool),X6082),c_member(tc_prod(X6083,X6082)))),c_Product__Type_OPair(X6083,X6082)))),X6081)),hAPP(hAPP(c_COMBC(X6083,tc_fun(tc_prod(X6083,X6082),tc_HOL_Obool),tc_fun(X6082,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6082,tc_fun(tc_fun(tc_prod(X6083,X6082),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6083,X6082),tc_HOL_Obool),tc_fun(X6082,tc_HOL_Obool)),X6083),c_COMBC(X6082,tc_fun(tc_prod(X6083,X6082),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6082,tc_prod(X6083,X6082)),tc_fun(X6082,tc_fun(tc_fun(tc_prod(X6083,X6082),tc_HOL_Obool),tc_HOL_Obool)),X6083),hAPP(c_COMBB(tc_prod(X6083,X6082),tc_fun(tc_fun(tc_prod(X6083,X6082),tc_HOL_Obool),tc_HOL_Obool),X6082),c_member(tc_prod(X6083,X6082)))),c_Product__Type_OPair(X6083,X6082)))),X6080))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2])])). 6.97/7.22 cnf(c_0_5889, plain, (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)=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)|~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_4737])). 6.97/7.22 cnf(c_0_5890, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4738, c_0_4409]), c_0_4409]), c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_5891, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))=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_4739, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4742]), ['final']). 6.97/7.22 cnf(c_0_5892, 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_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4743, c_0_4409]), c_0_4409]), c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 fof(c_0_5893, plain, ![X9337, X9338, X9339, X9340]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X9340),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))|hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X9339)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X9339))=c_Random__Sequence_ORandom(X9339,X9338,X9340,X9337))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X9340),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))|c_Random__Sequence_ORandom(X9339,X9338,X9340,X9337)=hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X9339,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X9339)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(X9338,X9337)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X9339)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X9339)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X9339)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(X9339,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X9339)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X9339)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(X9339,X9338,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X9340),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X9337))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X9339)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X9339))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X9339)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X9339)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(X9339,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X9339)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X9339)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X9339))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X9339)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X9339)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X9339)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X9339))))),tc_prod(X9339,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(X9339)),hAPP(hAPP(c_COMBB(X9339,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X9339)))),tc_prod(X9339,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(X9339)),c_Product__Type_Ofst(X9339,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Random_Osimps])])])). 6.97/7.22 cnf(c_0_5894, plain, (hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,X1),X3),X4)=c_Complete__Lattice_OSup__class_OSup(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_fun(X2,X1))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_HOL_Obool),X1),hAPP(c_COMBS(tc_fun(X2,X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X2,X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X2,X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X2,X1))),X3)))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_fun(X2,X1),X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X2,X1),X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_fun(X2,X1))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X2,X1),X2,X1),c_COMBI(tc_fun(X2,X1))),X4))))))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_4744])). 6.97/7.22 cnf(c_0_5895, plain, (hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,X1),X3),X4)=c_Complete__Lattice_OInf__class_OInf(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_fun(X2,X1))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_HOL_Obool),X1),hAPP(c_COMBS(tc_fun(X2,X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X2,X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X2,X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X2,X1))),X3)))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_fun(X2,X1),X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X2,X1),X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_fun(X2,X1))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X2,X1),X2,X1),c_COMBI(tc_fun(X2,X1))),X4))))))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_4745])). 6.97/7.22 cnf(c_0_5896, 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(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)))))=hAPP(hAPP(c_Orderings_Oord__class_Omax(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_4746])). 6.97/7.22 cnf(c_0_5897, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Orderings_Oord__class_Omin(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),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)))))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4747])). 6.97/7.22 cnf(c_0_5898, 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_4748])). 6.97/7.22 fof(c_0_5899, plain, ![X640, X641, X642, X643, X644, X645]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X644,X643)),hAPP(hAPP(c_Product__Type_OPair(X644,X643),X641),X640)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X645,tc_fun(tc_prod(X644,X643),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X645,tc_HOL_Obool))),X642)))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X645,tc_fun(X644,tc_fun(X643,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X645,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X644,X643),tc_HOL_Obool),tc_fun(X644,tc_fun(X643,tc_HOL_Obool)),X645),hAPP(c_COMBC(X644,tc_fun(tc_prod(X644,X643),tc_HOL_Obool),tc_fun(X643,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X643,tc_fun(tc_fun(tc_prod(X644,X643),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X644,X643),tc_HOL_Obool),tc_fun(X643,tc_HOL_Obool)),X644),c_COMBC(X643,tc_fun(tc_prod(X644,X643),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X643,tc_prod(X644,X643)),tc_fun(X643,tc_fun(tc_fun(tc_prod(X644,X643),tc_HOL_Obool),tc_HOL_Obool)),X644),hAPP(c_COMBB(tc_prod(X644,X643),tc_fun(tc_fun(tc_prod(X644,X643),tc_HOL_Obool),tc_HOL_Obool),X643),c_member(tc_prod(X644,X643)))),c_Product__Type_OPair(X644,X643))))),X642)),X641),X640)))&(~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X645,tc_fun(X644,tc_fun(X643,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X645,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X644,X643),tc_HOL_Obool),tc_fun(X644,tc_fun(X643,tc_HOL_Obool)),X645),hAPP(c_COMBC(X644,tc_fun(tc_prod(X644,X643),tc_HOL_Obool),tc_fun(X643,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X643,tc_fun(tc_fun(tc_prod(X644,X643),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X644,X643),tc_HOL_Obool),tc_fun(X643,tc_HOL_Obool)),X644),c_COMBC(X643,tc_fun(tc_prod(X644,X643),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X643,tc_prod(X644,X643)),tc_fun(X643,tc_fun(tc_fun(tc_prod(X644,X643),tc_HOL_Obool),tc_HOL_Obool)),X644),hAPP(c_COMBB(tc_prod(X644,X643),tc_fun(tc_fun(tc_prod(X644,X643),tc_HOL_Obool),tc_HOL_Obool),X643),c_member(tc_prod(X644,X643)))),c_Product__Type_OPair(X644,X643))))),X642)),X641),X640))|hBOOL(hAPP(hAPP(c_member(tc_prod(X644,X643)),hAPP(hAPP(c_Product__Type_OPair(X644,X643),X641),X640)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X645,tc_fun(tc_prod(X644,X643),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X645,tc_HOL_Obool))),X642))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__INT__eq2])])). 6.97/7.22 fof(c_0_5900, plain, ![X780, X781, X782, X783, X784, X785]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X784,X783)),hAPP(hAPP(c_Product__Type_OPair(X784,X783),X781),X780)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X785,tc_fun(tc_prod(X784,X783),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X785,tc_HOL_Obool))),X782)))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X785,tc_fun(X784,tc_fun(X783,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X785,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X784,X783),tc_HOL_Obool),tc_fun(X784,tc_fun(X783,tc_HOL_Obool)),X785),hAPP(c_COMBC(X784,tc_fun(tc_prod(X784,X783),tc_HOL_Obool),tc_fun(X783,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X783,tc_fun(tc_fun(tc_prod(X784,X783),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X784,X783),tc_HOL_Obool),tc_fun(X783,tc_HOL_Obool)),X784),c_COMBC(X783,tc_fun(tc_prod(X784,X783),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X783,tc_prod(X784,X783)),tc_fun(X783,tc_fun(tc_fun(tc_prod(X784,X783),tc_HOL_Obool),tc_HOL_Obool)),X784),hAPP(c_COMBB(tc_prod(X784,X783),tc_fun(tc_fun(tc_prod(X784,X783),tc_HOL_Obool),tc_HOL_Obool),X783),c_member(tc_prod(X784,X783)))),c_Product__Type_OPair(X784,X783))))),X782)),X781),X780)))&(~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X785,tc_fun(X784,tc_fun(X783,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X785,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X784,X783),tc_HOL_Obool),tc_fun(X784,tc_fun(X783,tc_HOL_Obool)),X785),hAPP(c_COMBC(X784,tc_fun(tc_prod(X784,X783),tc_HOL_Obool),tc_fun(X783,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X783,tc_fun(tc_fun(tc_prod(X784,X783),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X784,X783),tc_HOL_Obool),tc_fun(X783,tc_HOL_Obool)),X784),c_COMBC(X783,tc_fun(tc_prod(X784,X783),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X783,tc_prod(X784,X783)),tc_fun(X783,tc_fun(tc_fun(tc_prod(X784,X783),tc_HOL_Obool),tc_HOL_Obool)),X784),hAPP(c_COMBB(tc_prod(X784,X783),tc_fun(tc_fun(tc_prod(X784,X783),tc_HOL_Obool),tc_HOL_Obool),X783),c_member(tc_prod(X784,X783)))),c_Product__Type_OPair(X784,X783))))),X782)),X781),X780))|hBOOL(hAPP(hAPP(c_member(tc_prod(X784,X783)),hAPP(hAPP(c_Product__Type_OPair(X784,X783),X781),X780)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X785,tc_fun(tc_prod(X784,X783),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X785,tc_HOL_Obool))),X782))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__UN__eq2])])). 6.97/7.22 cnf(c_0_5901, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Big__Operators_Olattice__class_OInf__fin(X1,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)))))|~class_Lattices_Odistrib__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4749])). 6.97/7.22 cnf(c_0_5902, 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_4750])). 6.97/7.22 cnf(c_0_5903, 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_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_4751])). 6.97/7.22 cnf(c_0_5904, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4752, c_0_4409]), c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 fof(c_0_5905, plain, ![X17030, X17031, X17032, X17033, X17034, X17035, X17036, X17037, X17038]:(((~hBOOL(hAPP(hAPP(c_member(tc_prod(X17033,X17033)),X17034),hAPP(c_List_Oset(tc_prod(X17033,X17033)),hAPP(hAPP(c_List_Ozip(X17033,X17033),X17032),X17031))))|hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X17033,X17033,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X17033,tc_fun(tc_prod(X17033,X17033),tc_HOL_Obool),tc_fun(X17033,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17033,tc_fun(tc_fun(tc_prod(X17033,X17033),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X17033,X17033),tc_HOL_Obool),tc_fun(X17033,tc_HOL_Obool)),X17033),c_COMBC(X17033,tc_fun(tc_prod(X17033,X17033),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17033,tc_prod(X17033,X17033)),tc_fun(X17033,tc_fun(tc_fun(tc_prod(X17033,X17033),tc_HOL_Obool),tc_HOL_Obool)),X17033),hAPP(c_COMBB(tc_prod(X17033,X17033),tc_fun(tc_fun(tc_prod(X17033,X17033),tc_HOL_Obool),tc_HOL_Obool),X17033),c_member(tc_prod(X17033,X17033)))),c_Product__Type_OPair(X17033,X17033)))),X17030)),X17034))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17033),tc_List_Olist(X17033))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17033),tc_List_Olist(X17033)),X17032),X17031)),c_List_Olistrel(X17033,X17030))))&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17033)),X17032)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17033)),X17031)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17033),tc_List_Olist(X17033))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17033),tc_List_Olist(X17033)),X17032),X17031)),c_List_Olistrel(X17033,X17030)))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X17038,X17038)),esk575_4(X17035,X17036,X17037,X17038)),hAPP(c_List_Oset(tc_prod(X17038,X17038)),hAPP(hAPP(c_List_Ozip(X17038,X17038),X17037),X17036))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17038)),X17037)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17038)),X17036)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17038),tc_List_Olist(X17038))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17038),tc_List_Olist(X17038)),X17037),X17036)),c_List_Olistrel(X17038,X17035))))&(~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X17038,X17038,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X17038,tc_fun(tc_prod(X17038,X17038),tc_HOL_Obool),tc_fun(X17038,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17038,tc_fun(tc_fun(tc_prod(X17038,X17038),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X17038,X17038),tc_HOL_Obool),tc_fun(X17038,tc_HOL_Obool)),X17038),c_COMBC(X17038,tc_fun(tc_prod(X17038,X17038),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X17038,tc_prod(X17038,X17038)),tc_fun(X17038,tc_fun(tc_fun(tc_prod(X17038,X17038),tc_HOL_Obool),tc_HOL_Obool)),X17038),hAPP(c_COMBB(tc_prod(X17038,X17038),tc_fun(tc_fun(tc_prod(X17038,X17038),tc_HOL_Obool),tc_HOL_Obool),X17038),c_member(tc_prod(X17038,X17038)))),c_Product__Type_OPair(X17038,X17038)))),X17035)),esk575_4(X17035,X17036,X17037,X17038)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17038)),X17037)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17038)),X17036)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17038),tc_List_Olist(X17038))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17038),tc_List_Olist(X17038)),X17037),X17036)),c_List_Olistrel(X17038,X17035)))))), 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])])])])])])). 6.97/7.22 cnf(c_0_5906, 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_4753])). 6.97/7.22 cnf(c_0_5907, 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),esk25_6(X5,X4,X6,X3,X2,X1)))))!=hAPP(X5,esk25_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_4754])). 6.97/7.22 cnf(c_0_5908, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4755, c_0_4409]), c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_5909, 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_4756])). 6.97/7.22 cnf(c_0_5910, 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),esk47_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_4757])). 6.97/7.22 cnf(c_0_5911, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4758, c_0_4409]), c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 fof(c_0_5912, plain, ![X15069, X15070]:(~c_Equiv__Relations_Opart__equivp(X15070,X15069)|hBOOL(hAPP(hAPP(c_member(tc_fun(X15070,tc_HOL_Obool)),esk508_2(X15069,X15070)),hAPP(hAPP(c_COMBB(tc_fun(X15070,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X15070,tc_HOL_Obool)),c_HOL_OEx(X15070)),hAPP(hAPP(c_COMBB(tc_fun(X15070,tc_HOL_Obool),tc_fun(X15070,tc_HOL_Obool),tc_fun(X15070,tc_HOL_Obool)),hAPP(c_COMBS(X15070,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X15070),c_fconj),hAPP(hAPP(c_COMBS(X15070,X15070,tc_HOL_Obool),X15069),c_COMBI(X15070))))),hAPP(hAPP(c_COMBC(tc_fun(X15070,tc_HOL_Obool),tc_fun(X15070,tc_fun(X15070,tc_HOL_Obool)),tc_fun(X15070,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X15070,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X15070,tc_fun(X15070,tc_HOL_Obool)),tc_fun(X15070,tc_HOL_Obool)),tc_fun(X15070,tc_HOL_Obool)),c_COMBB(tc_fun(X15070,tc_HOL_Obool),tc_HOL_Obool,X15070)),c_fequal)),X15069)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_part__equivp__typedef])])])). 6.97/7.22 cnf(c_0_5913, 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_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))))=c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X1),X2)|~class_Lazy__Sequence_Osmall__lazy(X1)), inference(split_conjunct,[status(thm)],[c_0_4759])). 6.97/7.22 fof(c_0_5914, plain, ![X5586, X5587, X5588, X5589, X5590]:((~hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X5590,X5589,hAPP(hAPP(c_COMBC(X5590,tc_fun(tc_prod(X5590,X5589),tc_HOL_Obool),tc_fun(X5589,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5589,tc_fun(tc_fun(tc_prod(X5590,X5589),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5590,X5589),tc_HOL_Obool),tc_fun(X5589,tc_HOL_Obool)),X5590),c_COMBC(X5589,tc_fun(tc_prod(X5590,X5589),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5589,tc_prod(X5590,X5589)),tc_fun(X5589,tc_fun(tc_fun(tc_prod(X5590,X5589),tc_HOL_Obool),tc_HOL_Obool)),X5590),hAPP(c_COMBB(tc_prod(X5590,X5589),tc_fun(tc_fun(tc_prod(X5590,X5589),tc_HOL_Obool),tc_HOL_Obool),X5589),c_member(tc_prod(X5590,X5589)))),c_Product__Type_OPair(X5590,X5589)))),X5588)),X5587),X5586))|hBOOL(hAPP(hAPP(c_member(tc_prod(X5589,X5590)),hAPP(hAPP(c_Product__Type_OPair(X5589,X5590),X5587),X5586)),hAPP(c_Relation_Oconverse(X5590,X5589),X5588))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X5589,X5590)),hAPP(hAPP(c_Product__Type_OPair(X5589,X5590),X5587),X5586)),hAPP(c_Relation_Oconverse(X5590,X5589),X5588)))|hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X5590,X5589,hAPP(hAPP(c_COMBC(X5590,tc_fun(tc_prod(X5590,X5589),tc_HOL_Obool),tc_fun(X5589,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5589,tc_fun(tc_fun(tc_prod(X5590,X5589),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5590,X5589),tc_HOL_Obool),tc_fun(X5589,tc_HOL_Obool)),X5590),c_COMBC(X5589,tc_fun(tc_prod(X5590,X5589),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5589,tc_prod(X5590,X5589)),tc_fun(X5589,tc_fun(tc_fun(tc_prod(X5590,X5589),tc_HOL_Obool),tc_HOL_Obool)),X5590),hAPP(c_COMBB(tc_prod(X5590,X5589),tc_fun(tc_fun(tc_prod(X5590,X5589),tc_HOL_Obool),tc_HOL_Obool),X5589),c_member(tc_prod(X5590,X5589)))),c_Product__Type_OPair(X5590,X5589)))),X5588)),X5587),X5586)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep__converse__eq])])). 6.97/7.22 fof(c_0_5915, plain, ![X12240, X12241, X12242, X12243]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X12243,tc_HOL_Obool),tc_fun(X12243,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X12243,tc_HOL_Obool),tc_fun(X12243,tc_HOL_Obool)),X12241),X12240)),c_Wellfounded_Omax__ext(X12243,X12242)))|c_Wellfounded_Omax__extp(X12243,hAPP(hAPP(c_COMBC(X12243,tc_fun(tc_prod(X12243,X12243),tc_HOL_Obool),tc_fun(X12243,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12243,tc_fun(tc_fun(tc_prod(X12243,X12243),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X12243,X12243),tc_HOL_Obool),tc_fun(X12243,tc_HOL_Obool)),X12243),c_COMBC(X12243,tc_fun(tc_prod(X12243,X12243),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12243,tc_prod(X12243,X12243)),tc_fun(X12243,tc_fun(tc_fun(tc_prod(X12243,X12243),tc_HOL_Obool),tc_HOL_Obool)),X12243),hAPP(c_COMBB(tc_prod(X12243,X12243),tc_fun(tc_fun(tc_prod(X12243,X12243),tc_HOL_Obool),tc_HOL_Obool),X12243),c_member(tc_prod(X12243,X12243)))),c_Product__Type_OPair(X12243,X12243)))),X12242),X12241,X12240))&(~c_Wellfounded_Omax__extp(X12243,hAPP(hAPP(c_COMBC(X12243,tc_fun(tc_prod(X12243,X12243),tc_HOL_Obool),tc_fun(X12243,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12243,tc_fun(tc_fun(tc_prod(X12243,X12243),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X12243,X12243),tc_HOL_Obool),tc_fun(X12243,tc_HOL_Obool)),X12243),c_COMBC(X12243,tc_fun(tc_prod(X12243,X12243),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12243,tc_prod(X12243,X12243)),tc_fun(X12243,tc_fun(tc_fun(tc_prod(X12243,X12243),tc_HOL_Obool),tc_HOL_Obool)),X12243),hAPP(c_COMBB(tc_prod(X12243,X12243),tc_fun(tc_fun(tc_prod(X12243,X12243),tc_HOL_Obool),tc_HOL_Obool),X12243),c_member(tc_prod(X12243,X12243)))),c_Product__Type_OPair(X12243,X12243)))),X12242),X12241,X12240)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X12243,tc_HOL_Obool),tc_fun(X12243,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X12243,tc_HOL_Obool),tc_fun(X12243,tc_HOL_Obool)),X12241),X12240)),c_Wellfounded_Omax__ext(X12243,X12242))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__extp__max__ext__eq])])). 6.97/7.22 cnf(c_0_5916, 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_4760])). 6.97/7.22 cnf(c_0_5917, 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_4761])). 6.97/7.22 cnf(c_0_5918, 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_4762])). 6.97/7.22 cnf(c_0_5919, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4763, c_0_4409]), c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 fof(c_0_5920, plain, ![X1605, X1606, X1607, X1608]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1608),tc_List_Olist(X1608))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1608),tc_List_Olist(X1608)),X1606),X1605)),c_List_Olistrel(X1608,X1607)))|c_List_Olistrelp(X1608,hAPP(hAPP(c_COMBC(X1608,tc_fun(tc_prod(X1608,X1608),tc_HOL_Obool),tc_fun(X1608,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1608,tc_fun(tc_fun(tc_prod(X1608,X1608),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1608,X1608),tc_HOL_Obool),tc_fun(X1608,tc_HOL_Obool)),X1608),c_COMBC(X1608,tc_fun(tc_prod(X1608,X1608),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1608,tc_prod(X1608,X1608)),tc_fun(X1608,tc_fun(tc_fun(tc_prod(X1608,X1608),tc_HOL_Obool),tc_HOL_Obool)),X1608),hAPP(c_COMBB(tc_prod(X1608,X1608),tc_fun(tc_fun(tc_prod(X1608,X1608),tc_HOL_Obool),tc_HOL_Obool),X1608),c_member(tc_prod(X1608,X1608)))),c_Product__Type_OPair(X1608,X1608)))),X1607),X1606,X1605))&(~c_List_Olistrelp(X1608,hAPP(hAPP(c_COMBC(X1608,tc_fun(tc_prod(X1608,X1608),tc_HOL_Obool),tc_fun(X1608,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1608,tc_fun(tc_fun(tc_prod(X1608,X1608),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1608,X1608),tc_HOL_Obool),tc_fun(X1608,tc_HOL_Obool)),X1608),c_COMBC(X1608,tc_fun(tc_prod(X1608,X1608),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1608,tc_prod(X1608,X1608)),tc_fun(X1608,tc_fun(tc_fun(tc_prod(X1608,X1608),tc_HOL_Obool),tc_HOL_Obool)),X1608),hAPP(c_COMBB(tc_prod(X1608,X1608),tc_fun(tc_fun(tc_prod(X1608,X1608),tc_HOL_Obool),tc_HOL_Obool),X1608),c_member(tc_prod(X1608,X1608)))),c_Product__Type_OPair(X1608,X1608)))),X1607),X1606,X1605)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1608),tc_List_Olist(X1608))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1608),tc_List_Olist(X1608)),X1606),X1605)),c_List_Olistrel(X1608,X1607))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp__listrel__eq])])). 6.97/7.22 cnf(c_0_5921, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk47_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_4757])). 6.97/7.22 fof(c_0_5922, plain, ![X10229, X10230, X10231, X10232]:((~hBOOL(hAPP(hAPP(c_member(X10231),X10229),hAPP(c_Relation_ORange(X10232,X10231),X10230)))|hBOOL(hAPP(c_Predicate_ORangeP(X10232,X10231,hAPP(hAPP(c_COMBC(X10232,tc_fun(tc_prod(X10232,X10231),tc_HOL_Obool),tc_fun(X10231,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10231,tc_fun(tc_fun(tc_prod(X10232,X10231),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10232,X10231),tc_HOL_Obool),tc_fun(X10231,tc_HOL_Obool)),X10232),c_COMBC(X10231,tc_fun(tc_prod(X10232,X10231),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10231,tc_prod(X10232,X10231)),tc_fun(X10231,tc_fun(tc_fun(tc_prod(X10232,X10231),tc_HOL_Obool),tc_HOL_Obool)),X10232),hAPP(c_COMBB(tc_prod(X10232,X10231),tc_fun(tc_fun(tc_prod(X10232,X10231),tc_HOL_Obool),tc_HOL_Obool),X10231),c_member(tc_prod(X10232,X10231)))),c_Product__Type_OPair(X10232,X10231)))),X10230)),X10229)))&(~hBOOL(hAPP(c_Predicate_ORangeP(X10232,X10231,hAPP(hAPP(c_COMBC(X10232,tc_fun(tc_prod(X10232,X10231),tc_HOL_Obool),tc_fun(X10231,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10231,tc_fun(tc_fun(tc_prod(X10232,X10231),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10232,X10231),tc_HOL_Obool),tc_fun(X10231,tc_HOL_Obool)),X10232),c_COMBC(X10231,tc_fun(tc_prod(X10232,X10231),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10231,tc_prod(X10232,X10231)),tc_fun(X10231,tc_fun(tc_fun(tc_prod(X10232,X10231),tc_HOL_Obool),tc_HOL_Obool)),X10232),hAPP(c_COMBB(tc_prod(X10232,X10231),tc_fun(tc_fun(tc_prod(X10232,X10231),tc_HOL_Obool),tc_HOL_Obool),X10231),c_member(tc_prod(X10232,X10231)))),c_Product__Type_OPair(X10232,X10231)))),X10230)),X10229))|hBOOL(hAPP(hAPP(c_member(X10231),X10229),hAPP(c_Relation_ORange(X10232,X10231),X10230))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP__Range__eq])])). 6.97/7.22 fof(c_0_5923, plain, ![X13746, X13747, X13748, X13749]:((~hBOOL(hAPP(hAPP(c_member(X13749),X13746),hAPP(c_Relation_ODomain(X13749,X13748),X13747)))|hBOOL(hAPP(c_Predicate_ODomainP(X13749,X13748,hAPP(hAPP(c_COMBC(X13749,tc_fun(tc_prod(X13749,X13748),tc_HOL_Obool),tc_fun(X13748,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13748,tc_fun(tc_fun(tc_prod(X13749,X13748),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X13749,X13748),tc_HOL_Obool),tc_fun(X13748,tc_HOL_Obool)),X13749),c_COMBC(X13748,tc_fun(tc_prod(X13749,X13748),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13748,tc_prod(X13749,X13748)),tc_fun(X13748,tc_fun(tc_fun(tc_prod(X13749,X13748),tc_HOL_Obool),tc_HOL_Obool)),X13749),hAPP(c_COMBB(tc_prod(X13749,X13748),tc_fun(tc_fun(tc_prod(X13749,X13748),tc_HOL_Obool),tc_HOL_Obool),X13748),c_member(tc_prod(X13749,X13748)))),c_Product__Type_OPair(X13749,X13748)))),X13747)),X13746)))&(~hBOOL(hAPP(c_Predicate_ODomainP(X13749,X13748,hAPP(hAPP(c_COMBC(X13749,tc_fun(tc_prod(X13749,X13748),tc_HOL_Obool),tc_fun(X13748,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13748,tc_fun(tc_fun(tc_prod(X13749,X13748),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X13749,X13748),tc_HOL_Obool),tc_fun(X13748,tc_HOL_Obool)),X13749),c_COMBC(X13748,tc_fun(tc_prod(X13749,X13748),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13748,tc_prod(X13749,X13748)),tc_fun(X13748,tc_fun(tc_fun(tc_prod(X13749,X13748),tc_HOL_Obool),tc_HOL_Obool)),X13749),hAPP(c_COMBB(tc_prod(X13749,X13748),tc_fun(tc_fun(tc_prod(X13749,X13748),tc_HOL_Obool),tc_HOL_Obool),X13748),c_member(tc_prod(X13749,X13748)))),c_Product__Type_OPair(X13749,X13748)))),X13747)),X13746))|hBOOL(hAPP(hAPP(c_member(X13749),X13746),hAPP(c_Relation_ODomain(X13749,X13748),X13747))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainP__Domain__eq])])). 6.97/7.22 cnf(c_0_5924, plain, (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)=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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[c_0_4764, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 fof(c_0_5925, plain, ![X486, X487]:(~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X487),X486))|c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X486,X487)=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dvd_OgreaterThanAtMost__empty])])])). 6.97/7.22 fof(c_0_5926, plain, ![X7584, X7585]:((c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))!=c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X7585,X7584)|(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X7584),X7585))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X7585),X7584))))&((~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X7584),X7585))|c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X7585,X7584))&(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X7585),X7584))|c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X7585,X7584)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dvd_OatLeastLessThan__empty__iff])])])])). 6.97/7.22 cnf(c_0_5927, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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))|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)],[inference(rw,[status(thm)],[c_0_4765, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_5928, 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_4766])). 6.97/7.22 cnf(c_0_5929, 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_4767, c_0_4467]), c_0_4768]), ['final']). 6.97/7.22 fof(c_0_5930, plain, ![X727, X728, X729]:((~hBOOL(hAPP(hAPP(c_member(X729),X727),c_Wellfounded_Oacc(X729,X728)))|hBOOL(hAPP(c_Wellfounded_Oaccp(X729,hAPP(hAPP(c_COMBC(X729,tc_fun(tc_prod(X729,X729),tc_HOL_Obool),tc_fun(X729,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X729,tc_fun(tc_fun(tc_prod(X729,X729),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X729,X729),tc_HOL_Obool),tc_fun(X729,tc_HOL_Obool)),X729),c_COMBC(X729,tc_fun(tc_prod(X729,X729),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X729,tc_prod(X729,X729)),tc_fun(X729,tc_fun(tc_fun(tc_prod(X729,X729),tc_HOL_Obool),tc_HOL_Obool)),X729),hAPP(c_COMBB(tc_prod(X729,X729),tc_fun(tc_fun(tc_prod(X729,X729),tc_HOL_Obool),tc_HOL_Obool),X729),c_member(tc_prod(X729,X729)))),c_Product__Type_OPair(X729,X729)))),X728)),X727)))&(~hBOOL(hAPP(c_Wellfounded_Oaccp(X729,hAPP(hAPP(c_COMBC(X729,tc_fun(tc_prod(X729,X729),tc_HOL_Obool),tc_fun(X729,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X729,tc_fun(tc_fun(tc_prod(X729,X729),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X729,X729),tc_HOL_Obool),tc_fun(X729,tc_HOL_Obool)),X729),c_COMBC(X729,tc_fun(tc_prod(X729,X729),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X729,tc_prod(X729,X729)),tc_fun(X729,tc_fun(tc_fun(tc_prod(X729,X729),tc_HOL_Obool),tc_HOL_Obool)),X729),hAPP(c_COMBB(tc_prod(X729,X729),tc_fun(tc_fun(tc_prod(X729,X729),tc_HOL_Obool),tc_HOL_Obool),X729),c_member(tc_prod(X729,X729)))),c_Product__Type_OPair(X729,X729)))),X728)),X727))|hBOOL(hAPP(hAPP(c_member(X729),X727),c_Wellfounded_Oacc(X729,X728))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__acc__eq])])). 6.97/7.22 cnf(c_0_5931, plain, (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)))))=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)))))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_4769])). 6.97/7.22 cnf(c_0_5932, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk25_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_4754])). 6.97/7.22 cnf(c_0_5933, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk171_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3)))|c_List_Otranspose(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_Olist_ONil(tc_List_Olist(X2))=X3), inference(split_conjunct,[status(thm)],[c_0_4469])). 6.97/7.22 cnf(c_0_5934, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4770, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_5935, plain, (c_List_Otranspose(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)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk171_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4771, c_0_4471]), c_0_4471])). 6.97/7.22 cnf(c_0_5936, 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_4772, c_0_4773]), ['final']). 6.97/7.22 cnf(c_0_5937, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X2)), inference(split_conjunct,[status(thm)],[c_0_4774]), ['final']). 6.97/7.22 cnf(c_0_5938, 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),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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4775, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_5939, plain, (c_List_Otranspose(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_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_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),esk171_3(X3,X1,X2)))!=X3), inference(split_conjunct,[status(thm)],[c_0_4469])). 6.97/7.22 cnf(c_0_5940, 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_4776])). 6.97/7.22 cnf(c_0_5941, 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)), inference(split_conjunct,[status(thm)],[c_0_4777]), ['final']). 6.97/7.22 fof(c_0_5942, plain, ![X2759, X2760]:((~c_Equiv__Relations_Oequiv(X2760,c_Orderings_Otop__class_Otop(tc_fun(X2760,tc_HOL_Obool)),X2759)|c_Equiv__Relations_Oequivp(X2760,hAPP(hAPP(c_COMBC(X2760,tc_fun(tc_prod(X2760,X2760),tc_HOL_Obool),tc_fun(X2760,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2760,tc_fun(tc_fun(tc_prod(X2760,X2760),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2760,X2760),tc_HOL_Obool),tc_fun(X2760,tc_HOL_Obool)),X2760),c_COMBC(X2760,tc_fun(tc_prod(X2760,X2760),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2760,tc_prod(X2760,X2760)),tc_fun(X2760,tc_fun(tc_fun(tc_prod(X2760,X2760),tc_HOL_Obool),tc_HOL_Obool)),X2760),hAPP(c_COMBB(tc_prod(X2760,X2760),tc_fun(tc_fun(tc_prod(X2760,X2760),tc_HOL_Obool),tc_HOL_Obool),X2760),c_member(tc_prod(X2760,X2760)))),c_Product__Type_OPair(X2760,X2760)))),X2759)))&(~c_Equiv__Relations_Oequivp(X2760,hAPP(hAPP(c_COMBC(X2760,tc_fun(tc_prod(X2760,X2760),tc_HOL_Obool),tc_fun(X2760,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2760,tc_fun(tc_fun(tc_prod(X2760,X2760),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2760,X2760),tc_HOL_Obool),tc_fun(X2760,tc_HOL_Obool)),X2760),c_COMBC(X2760,tc_fun(tc_prod(X2760,X2760),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2760,tc_prod(X2760,X2760)),tc_fun(X2760,tc_fun(tc_fun(tc_prod(X2760,X2760),tc_HOL_Obool),tc_HOL_Obool)),X2760),hAPP(c_COMBB(tc_prod(X2760,X2760),tc_fun(tc_fun(tc_prod(X2760,X2760),tc_HOL_Obool),tc_HOL_Obool),X2760),c_member(tc_prod(X2760,X2760)))),c_Product__Type_OPair(X2760,X2760)))),X2759))|c_Equiv__Relations_Oequiv(X2760,c_Orderings_Otop__class_Otop(tc_fun(X2760,tc_HOL_Obool)),X2759))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__equiv])])). 6.97/7.22 fof(c_0_5943, plain, ![X1527, X1528]:(((hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1528),X1527))|c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1528,X1527)=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))&(~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1527),X1528))|c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1528,X1527)=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))&(c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1528,X1527)!=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1528),X1527))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1527),X1528))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dvd_OgreaterThanAtMost__empty__iff2])])])])). 6.97/7.22 cnf(c_0_5944, 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),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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4778, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_5945, 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_4779, c_0_4565])). 6.97/7.22 cnf(c_0_5946, 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_4780, c_0_4467]), c_0_4467]), c_0_4467]), c_0_4781]), ['final']). 6.97/7.22 cnf(c_0_5947, 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)), inference(split_conjunct,[status(thm)],[c_0_4782]), ['final']). 6.97/7.22 cnf(c_0_5948, plain, (c_List_Otranspose(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_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X3|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),esk171_3(X3,X1,X2)))!=X3), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4783, c_0_4471]), c_0_4471])). 6.97/7.22 cnf(c_0_5949, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4784, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 fof(c_0_5950, plain, ![X13723, X13724]:((~c_Wellfounded_Owf(X13724,X13723)|c_Wellfounded_OwfP(X13724,hAPP(hAPP(c_COMBC(X13724,tc_fun(tc_prod(X13724,X13724),tc_HOL_Obool),tc_fun(X13724,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13724,tc_fun(tc_fun(tc_prod(X13724,X13724),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X13724,X13724),tc_HOL_Obool),tc_fun(X13724,tc_HOL_Obool)),X13724),c_COMBC(X13724,tc_fun(tc_prod(X13724,X13724),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13724,tc_prod(X13724,X13724)),tc_fun(X13724,tc_fun(tc_fun(tc_prod(X13724,X13724),tc_HOL_Obool),tc_HOL_Obool)),X13724),hAPP(c_COMBB(tc_prod(X13724,X13724),tc_fun(tc_fun(tc_prod(X13724,X13724),tc_HOL_Obool),tc_HOL_Obool),X13724),c_member(tc_prod(X13724,X13724)))),c_Product__Type_OPair(X13724,X13724)))),X13723)))&(~c_Wellfounded_OwfP(X13724,hAPP(hAPP(c_COMBC(X13724,tc_fun(tc_prod(X13724,X13724),tc_HOL_Obool),tc_fun(X13724,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13724,tc_fun(tc_fun(tc_prod(X13724,X13724),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X13724,X13724),tc_HOL_Obool),tc_fun(X13724,tc_HOL_Obool)),X13724),c_COMBC(X13724,tc_fun(tc_prod(X13724,X13724),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13724,tc_prod(X13724,X13724)),tc_fun(X13724,tc_fun(tc_fun(tc_prod(X13724,X13724),tc_HOL_Obool),tc_HOL_Obool)),X13724),hAPP(c_COMBB(tc_prod(X13724,X13724),tc_fun(tc_fun(tc_prod(X13724,X13724),tc_HOL_Obool),tc_HOL_Obool),X13724),c_member(tc_prod(X13724,X13724)))),c_Product__Type_OPair(X13724,X13724)))),X13723))|c_Wellfounded_Owf(X13724,X13723))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__wf__eq])])). 6.97/7.22 fof(c_0_5951, plain, ![X9740, X9741, X9742, X9743]:((X9740!=X9741|hAPP(hAPP(c_COMBC(X9743,tc_fun(tc_prod(X9743,X9742),tc_HOL_Obool),tc_fun(X9742,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9742,tc_fun(tc_fun(tc_prod(X9743,X9742),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X9743,X9742),tc_HOL_Obool),tc_fun(X9742,tc_HOL_Obool)),X9743),c_COMBC(X9742,tc_fun(tc_prod(X9743,X9742),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9742,tc_prod(X9743,X9742)),tc_fun(X9742,tc_fun(tc_fun(tc_prod(X9743,X9742),tc_HOL_Obool),tc_HOL_Obool)),X9743),hAPP(c_COMBB(tc_prod(X9743,X9742),tc_fun(tc_fun(tc_prod(X9743,X9742),tc_HOL_Obool),tc_HOL_Obool),X9742),c_member(tc_prod(X9743,X9742)))),c_Product__Type_OPair(X9743,X9742)))),X9740)=hAPP(hAPP(c_COMBC(X9743,tc_fun(tc_prod(X9743,X9742),tc_HOL_Obool),tc_fun(X9742,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9742,tc_fun(tc_fun(tc_prod(X9743,X9742),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X9743,X9742),tc_HOL_Obool),tc_fun(X9742,tc_HOL_Obool)),X9743),c_COMBC(X9742,tc_fun(tc_prod(X9743,X9742),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9742,tc_prod(X9743,X9742)),tc_fun(X9742,tc_fun(tc_fun(tc_prod(X9743,X9742),tc_HOL_Obool),tc_HOL_Obool)),X9743),hAPP(c_COMBB(tc_prod(X9743,X9742),tc_fun(tc_fun(tc_prod(X9743,X9742),tc_HOL_Obool),tc_HOL_Obool),X9742),c_member(tc_prod(X9743,X9742)))),c_Product__Type_OPair(X9743,X9742)))),X9741))&(hAPP(hAPP(c_COMBC(X9743,tc_fun(tc_prod(X9743,X9742),tc_HOL_Obool),tc_fun(X9742,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9742,tc_fun(tc_fun(tc_prod(X9743,X9742),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X9743,X9742),tc_HOL_Obool),tc_fun(X9742,tc_HOL_Obool)),X9743),c_COMBC(X9742,tc_fun(tc_prod(X9743,X9742),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9742,tc_prod(X9743,X9742)),tc_fun(X9742,tc_fun(tc_fun(tc_prod(X9743,X9742),tc_HOL_Obool),tc_HOL_Obool)),X9743),hAPP(c_COMBB(tc_prod(X9743,X9742),tc_fun(tc_fun(tc_prod(X9743,X9742),tc_HOL_Obool),tc_HOL_Obool),X9742),c_member(tc_prod(X9743,X9742)))),c_Product__Type_OPair(X9743,X9742)))),X9740)!=hAPP(hAPP(c_COMBC(X9743,tc_fun(tc_prod(X9743,X9742),tc_HOL_Obool),tc_fun(X9742,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9742,tc_fun(tc_fun(tc_prod(X9743,X9742),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X9743,X9742),tc_HOL_Obool),tc_fun(X9742,tc_HOL_Obool)),X9743),c_COMBC(X9742,tc_fun(tc_prod(X9743,X9742),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9742,tc_prod(X9743,X9742)),tc_fun(X9742,tc_fun(tc_fun(tc_prod(X9743,X9742),tc_HOL_Obool),tc_HOL_Obool)),X9743),hAPP(c_COMBB(tc_prod(X9743,X9742),tc_fun(tc_fun(tc_prod(X9743,X9742),tc_HOL_Obool),tc_HOL_Obool),X9742),c_member(tc_prod(X9743,X9742)))),c_Product__Type_OPair(X9743,X9742)))),X9741)|X9740=X9741)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2])])). 6.97/7.22 cnf(c_0_5952, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4785, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_5953, 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_4786])). 6.97/7.22 cnf(c_0_5954, 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_4787, c_0_4467]), ['final']). 6.97/7.22 cnf(c_0_5955, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)),hAPP(c_Int_Onumber__class_Onumber__of(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)),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)],[inference(rw,[status(thm)],[c_0_4788, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_5956, 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_4789])). 6.97/7.22 cnf(c_0_5957, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(c_Set_OCollect(X2),X5)))),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),X5)))))=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)),X5)),X4)),X6)),X3)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_4790])). 6.97/7.22 cnf(c_0_5958, 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,esk565_4(X3,X2,X1,X4)))),hAPP(X1,esk565_4(X3,X2,X1,X4))))), inference(split_conjunct,[status(thm)],[c_0_4791])). 6.97/7.22 fof(c_0_5959, plain, ![X5447, X5448, X5449, X5450, X5451, X5452, X5453, X5454]:((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5454,X5453),tc_prod(X5454,X5453))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5454,X5453),tc_prod(X5454,X5453)),hAPP(hAPP(c_Product__Type_OPair(X5454,X5453),X5452),X5451)),hAPP(hAPP(c_Product__Type_OPair(X5454,X5453),esk173_8(X5447,X5448,X5449,X5450,X5451,X5452,X5453,X5454)),esk174_8(X5447,X5448,X5449,X5450,X5451,X5452,X5453,X5454)))),c_Transitive__Closure_Ortrancl(tc_prod(X5454,X5453),X5448)))|hBOOL(hAPP(hAPP(X5447,X5450),X5449))|~hBOOL(hAPP(hAPP(X5447,X5452),X5451))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5454,X5453),tc_prod(X5454,X5453))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5454,X5453),tc_prod(X5454,X5453)),hAPP(hAPP(c_Product__Type_OPair(X5454,X5453),X5452),X5451)),hAPP(hAPP(c_Product__Type_OPair(X5454,X5453),X5450),X5449))),c_Transitive__Closure_Ortrancl(tc_prod(X5454,X5453),X5448))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5454,X5453),tc_prod(X5454,X5453))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5454,X5453),tc_prod(X5454,X5453)),hAPP(hAPP(c_Product__Type_OPair(X5454,X5453),esk173_8(X5447,X5448,X5449,X5450,X5451,X5452,X5453,X5454)),esk174_8(X5447,X5448,X5449,X5450,X5451,X5452,X5453,X5454))),hAPP(hAPP(c_Product__Type_OPair(X5454,X5453),esk175_8(X5447,X5448,X5449,X5450,X5451,X5452,X5453,X5454)),esk176_8(X5447,X5448,X5449,X5450,X5451,X5452,X5453,X5454)))),X5448))|hBOOL(hAPP(hAPP(X5447,X5450),X5449))|~hBOOL(hAPP(hAPP(X5447,X5452),X5451))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5454,X5453),tc_prod(X5454,X5453))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5454,X5453),tc_prod(X5454,X5453)),hAPP(hAPP(c_Product__Type_OPair(X5454,X5453),X5452),X5451)),hAPP(hAPP(c_Product__Type_OPair(X5454,X5453),X5450),X5449))),c_Transitive__Closure_Ortrancl(tc_prod(X5454,X5453),X5448))))&((hBOOL(hAPP(hAPP(X5447,esk173_8(X5447,X5448,X5449,X5450,X5451,X5452,X5453,X5454)),esk174_8(X5447,X5448,X5449,X5450,X5451,X5452,X5453,X5454)))|hBOOL(hAPP(hAPP(X5447,X5450),X5449))|~hBOOL(hAPP(hAPP(X5447,X5452),X5451))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5454,X5453),tc_prod(X5454,X5453))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5454,X5453),tc_prod(X5454,X5453)),hAPP(hAPP(c_Product__Type_OPair(X5454,X5453),X5452),X5451)),hAPP(hAPP(c_Product__Type_OPair(X5454,X5453),X5450),X5449))),c_Transitive__Closure_Ortrancl(tc_prod(X5454,X5453),X5448))))&(~hBOOL(hAPP(hAPP(X5447,esk175_8(X5447,X5448,X5449,X5450,X5451,X5452,X5453,X5454)),esk176_8(X5447,X5448,X5449,X5450,X5451,X5452,X5453,X5454)))|hBOOL(hAPP(hAPP(X5447,X5450),X5449))|~hBOOL(hAPP(hAPP(X5447,X5452),X5451))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5454,X5453),tc_prod(X5454,X5453))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5454,X5453),tc_prod(X5454,X5453)),hAPP(hAPP(c_Product__Type_OPair(X5454,X5453),X5452),X5451)),hAPP(hAPP(c_Product__Type_OPair(X5454,X5453),X5450),X5449))),c_Transitive__Closure_Ortrancl(tc_prod(X5454,X5453),X5448))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rtrancl__induct2])])])])])). 6.97/7.22 fof(c_0_5960, plain, ![X10716, X10717]:(~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X10717),X10716))|c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X10716,X10717)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_OgreaterThanLessThan__empty])])). 6.97/7.22 cnf(c_0_5961, 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_4792, c_0_4565])). 6.97/7.22 cnf(c_0_5962, 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_4793, c_0_4565])). 6.97/7.22 cnf(c_0_5963, 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_4794]), ['final']). 6.97/7.22 cnf(c_0_5964, plain, (hBOOL(hAPP(hAPP(X1,X3),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk439_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),esk438_3(X1,X2,X3)),esk439_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,esk438_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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),esk439_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)],[inference(rw,[status(thm)],[c_0_4795, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_5965, plain, (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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))|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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4796, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 fof(c_0_5966, plain, ![X17135, X17136, X17137, X17138, X17139, X17140, X17141, X17142]:((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X17142,X17141),tc_prod(X17142,X17141))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X17142,X17141),tc_prod(X17142,X17141)),hAPP(hAPP(c_Product__Type_OPair(X17142,X17141),esk579_8(X17135,X17136,X17137,X17138,X17139,X17140,X17141,X17142)),esk580_8(X17135,X17136,X17137,X17138,X17139,X17140,X17141,X17142))),hAPP(hAPP(c_Product__Type_OPair(X17142,X17141),esk581_8(X17135,X17136,X17137,X17138,X17139,X17140,X17141,X17142)),esk582_8(X17135,X17136,X17137,X17138,X17139,X17140,X17141,X17142)))),X17136))|hBOOL(hAPP(hAPP(X17135,X17140),X17139))|~hBOOL(hAPP(hAPP(X17135,X17138),X17137))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X17142,X17141),tc_prod(X17142,X17141))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X17142,X17141),tc_prod(X17142,X17141)),hAPP(hAPP(c_Product__Type_OPair(X17142,X17141),X17140),X17139)),hAPP(hAPP(c_Product__Type_OPair(X17142,X17141),X17138),X17137))),c_Transitive__Closure_Ortrancl(tc_prod(X17142,X17141),X17136))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X17142,X17141),tc_prod(X17142,X17141))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X17142,X17141),tc_prod(X17142,X17141)),hAPP(hAPP(c_Product__Type_OPair(X17142,X17141),esk581_8(X17135,X17136,X17137,X17138,X17139,X17140,X17141,X17142)),esk582_8(X17135,X17136,X17137,X17138,X17139,X17140,X17141,X17142))),hAPP(hAPP(c_Product__Type_OPair(X17142,X17141),X17138),X17137))),c_Transitive__Closure_Ortrancl(tc_prod(X17142,X17141),X17136)))|hBOOL(hAPP(hAPP(X17135,X17140),X17139))|~hBOOL(hAPP(hAPP(X17135,X17138),X17137))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X17142,X17141),tc_prod(X17142,X17141))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X17142,X17141),tc_prod(X17142,X17141)),hAPP(hAPP(c_Product__Type_OPair(X17142,X17141),X17140),X17139)),hAPP(hAPP(c_Product__Type_OPair(X17142,X17141),X17138),X17137))),c_Transitive__Closure_Ortrancl(tc_prod(X17142,X17141),X17136))))&((hBOOL(hAPP(hAPP(X17135,esk581_8(X17135,X17136,X17137,X17138,X17139,X17140,X17141,X17142)),esk582_8(X17135,X17136,X17137,X17138,X17139,X17140,X17141,X17142)))|hBOOL(hAPP(hAPP(X17135,X17140),X17139))|~hBOOL(hAPP(hAPP(X17135,X17138),X17137))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X17142,X17141),tc_prod(X17142,X17141))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X17142,X17141),tc_prod(X17142,X17141)),hAPP(hAPP(c_Product__Type_OPair(X17142,X17141),X17140),X17139)),hAPP(hAPP(c_Product__Type_OPair(X17142,X17141),X17138),X17137))),c_Transitive__Closure_Ortrancl(tc_prod(X17142,X17141),X17136))))&(~hBOOL(hAPP(hAPP(X17135,esk579_8(X17135,X17136,X17137,X17138,X17139,X17140,X17141,X17142)),esk580_8(X17135,X17136,X17137,X17138,X17139,X17140,X17141,X17142)))|hBOOL(hAPP(hAPP(X17135,X17140),X17139))|~hBOOL(hAPP(hAPP(X17135,X17138),X17137))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X17142,X17141),tc_prod(X17142,X17141))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X17142,X17141),tc_prod(X17142,X17141)),hAPP(hAPP(c_Product__Type_OPair(X17142,X17141),X17140),X17139)),hAPP(hAPP(c_Product__Type_OPair(X17142,X17141),X17138),X17137))),c_Transitive__Closure_Ortrancl(tc_prod(X17142,X17141),X17136))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_converse__rtrancl__induct2])])])])])). 6.97/7.22 fof(c_0_5967, plain, ![X533, X534, X535, X536, X537, X538]:((hBOOL(hAPP(hAPP(c_member(X537),esk9_6(X533,X534,X535,X536,X537,X538)),X536))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X538,tc_prod(X537,X535),c_Groups_Otimes__class_Otimes(X538)),hAPP(c_Product__Type_Oprod_Oprod__case(X537,X535,X538),X533)),c_Groups_Oone__class_Oone(X538)),hAPP(hAPP(c_Product__Type_OSigma(X537,X535),X536),X534))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X538,X537,c_Groups_Otimes__class_Otimes(X538)),hAPP(hAPP(c_COMBS(X537,tc_fun(X535,tc_HOL_Obool),X538),hAPP(hAPP(c_COMBC(X537,X538,tc_fun(tc_fun(X535,tc_HOL_Obool),X538)),hAPP(hAPP(c_COMBB(tc_fun(X535,X538),tc_fun(X538,tc_fun(tc_fun(X535,tc_HOL_Obool),X538)),X537),c_Finite__Set_Ofold__image(X538,X535,c_Groups_Otimes__class_Otimes(X538))),X533)),c_Groups_Oone__class_Oone(X538))),X534)),c_Groups_Oone__class_Oone(X538)),X536)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X537),X536))|~class_Groups_Ocomm__monoid__mult(X538))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X535),hAPP(X534,esk9_6(X533,X534,X535,X536,X537,X538))))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X538,tc_prod(X537,X535),c_Groups_Otimes__class_Otimes(X538)),hAPP(c_Product__Type_Oprod_Oprod__case(X537,X535,X538),X533)),c_Groups_Oone__class_Oone(X538)),hAPP(hAPP(c_Product__Type_OSigma(X537,X535),X536),X534))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X538,X537,c_Groups_Otimes__class_Otimes(X538)),hAPP(hAPP(c_COMBS(X537,tc_fun(X535,tc_HOL_Obool),X538),hAPP(hAPP(c_COMBC(X537,X538,tc_fun(tc_fun(X535,tc_HOL_Obool),X538)),hAPP(hAPP(c_COMBB(tc_fun(X535,X538),tc_fun(X538,tc_fun(tc_fun(X535,tc_HOL_Obool),X538)),X537),c_Finite__Set_Ofold__image(X538,X535,c_Groups_Otimes__class_Otimes(X538))),X533)),c_Groups_Oone__class_Oone(X538))),X534)),c_Groups_Oone__class_Oone(X538)),X536)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X537),X536))|~class_Groups_Ocomm__monoid__mult(X538))), 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])])])])])). 6.97/7.22 fof(c_0_5968, plain, ![X10546, X10547, X10548, X10549, X10550, X10551, X10552]:(~class_Rings_Osemiring__0(X10552)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10552),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10551,X10552),X10550),X10549)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10548,X10552),X10547),X10546))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10551,X10552),hAPP(hAPP(c_COMBC(X10551,tc_fun(X10548,tc_HOL_Obool),X10552),hAPP(hAPP(c_COMBB(tc_fun(X10548,X10552),tc_fun(tc_fun(X10548,tc_HOL_Obool),X10552),X10551),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10548,X10552)),hAPP(hAPP(c_COMBC(X10551,tc_fun(X10548,X10552),tc_fun(X10548,X10552)),hAPP(hAPP(c_COMBB(tc_fun(X10552,X10552),tc_fun(tc_fun(X10548,X10552),tc_fun(X10548,X10552)),X10551),c_COMBB(X10552,X10552,X10548)),hAPP(hAPP(c_COMBB(X10552,tc_fun(X10552,X10552),X10551),c_Groups_Otimes__class_Otimes(X10552)),X10550))),X10547))),X10546)),X10549)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__product])])])). 6.97/7.22 cnf(c_0_5969, 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_4503])). 6.97/7.22 cnf(c_0_5970, plain, (hBOOL(hAPP(X1,esk565_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_4791])). 6.97/7.22 cnf(c_0_5971, 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_4797, c_0_4798]), c_0_4467])). 6.97/7.22 cnf(c_0_5972, 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))),X4))=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)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4799, c_0_4798]), c_0_4467]), ['final']). 6.97/7.22 cnf(c_0_5973, 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_4800, c_0_4798]), c_0_4467])). 6.97/7.22 fof(c_0_5974, plain, ![X4465, X4466, X4467, X4468]:(~c_Fun_Oinj__on(X4468,tc_fun(tc_fun(X4468,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4468,tc_fun(tc_prod(X4468,X4468),tc_HOL_Obool),tc_fun(tc_fun(X4468,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4468,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X4468,X4468),tc_HOL_Obool),tc_fun(tc_fun(X4468,tc_HOL_Obool),tc_HOL_Obool)),X4468),c_Equiv__Relations_Oquotient(X4468)),hAPP(hAPP(c_COMBC(X4468,tc_fun(X4468,tc_HOL_Obool),tc_fun(X4468,tc_HOL_Obool)),c_Set_Oinsert(X4468)),c_Orderings_Obot__class_Obot(tc_fun(X4468,tc_HOL_Obool))))),X4467),X4466)|(~hBOOL(hAPP(hAPP(c_member(X4468),X4465),X4466))|hAPP(hAPP(c_Equiv__Relations_Oquotient(X4468),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4468,tc_HOL_Obool)),X4466),hAPP(hAPP(c_Set_Oinsert(X4468),X4465),c_Orderings_Obot__class_Obot(tc_fun(X4468,tc_HOL_Obool))))),X4467)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(X4468,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4468),X4466),X4467)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4468),hAPP(hAPP(c_Set_Oinsert(X4468),X4465),c_Orderings_Obot__class_Obot(tc_fun(X4468,tc_HOL_Obool)))),X4467)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_quotient__diff1])])])). 6.97/7.22 fof(c_0_5975, plain, ![X6405, X6406, X6407, X6408]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X6408),X6407))|(~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)),X6406),X6408)),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)),X6405),X6407)),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)),X6406),X6405)),X6407)),c_FunDef_Omax__strict))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_smax__insertI])])])). 6.97/7.22 fof(c_0_5976, plain, ![X2825, X2826, X2827, X2828]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X2828),X2827))|(~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)),X2826),X2828)),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)),X2825),X2827)),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)),X2826),X2825)),X2827)),c_FunDef_Omax__weak))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wmax__insertI])])])). 6.97/7.22 fof(c_0_5977, plain, ![X5742, X5743, X5744, X5745]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X5745),X5744))|(~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)),X5745),X5743)),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)),X5744),X5742)),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)),X5744),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X5743),X5742))),c_FunDef_Omin__strict))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_smin__insertI])])])). 6.97/7.22 cnf(c_0_5978, 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_4801])). 6.97/7.22 fof(c_0_5979, plain, ![X17356, X17357, X17358, X17359]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X17359),X17358))|(~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)),X17359),X17357)),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)),X17358),X17356)),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)),X17358),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X17357),X17356))),c_FunDef_Omin__weak))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wmin__insertI])])])). 6.97/7.22 fof(c_0_5980, plain, ![X11592, X11593, X11594, X11595, X11596, X11597, X11598]:((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X11598,X11597),tc_prod(X11598,X11597))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X11598,X11597),tc_prod(X11598,X11597)),hAPP(hAPP(c_Product__Type_OPair(X11598,X11597),X11596),X11595)),hAPP(hAPP(c_Product__Type_OPair(X11598,X11597),esk387_7(X11592,X11593,X11594,X11595,X11596,X11597,X11598)),esk388_7(X11592,X11593,X11594,X11595,X11596,X11597,X11598)))),X11592))|hAPP(hAPP(c_Product__Type_OPair(X11598,X11597),X11596),X11595)=hAPP(hAPP(c_Product__Type_OPair(X11598,X11597),X11594),X11593)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X11598,X11597),tc_prod(X11598,X11597))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X11598,X11597),tc_prod(X11598,X11597)),hAPP(hAPP(c_Product__Type_OPair(X11598,X11597),X11596),X11595)),hAPP(hAPP(c_Product__Type_OPair(X11598,X11597),X11594),X11593))),c_Transitive__Closure_Ortrancl(tc_prod(X11598,X11597),X11592))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X11598,X11597),tc_prod(X11598,X11597))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X11598,X11597),tc_prod(X11598,X11597)),hAPP(hAPP(c_Product__Type_OPair(X11598,X11597),esk387_7(X11592,X11593,X11594,X11595,X11596,X11597,X11598)),esk388_7(X11592,X11593,X11594,X11595,X11596,X11597,X11598))),hAPP(hAPP(c_Product__Type_OPair(X11598,X11597),X11594),X11593))),c_Transitive__Closure_Ortrancl(tc_prod(X11598,X11597),X11592)))|hAPP(hAPP(c_Product__Type_OPair(X11598,X11597),X11596),X11595)=hAPP(hAPP(c_Product__Type_OPair(X11598,X11597),X11594),X11593)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X11598,X11597),tc_prod(X11598,X11597))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X11598,X11597),tc_prod(X11598,X11597)),hAPP(hAPP(c_Product__Type_OPair(X11598,X11597),X11596),X11595)),hAPP(hAPP(c_Product__Type_OPair(X11598,X11597),X11594),X11593))),c_Transitive__Closure_Ortrancl(tc_prod(X11598,X11597),X11592))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_converse__rtranclE2])])])])])). 6.97/7.22 fof(c_0_5981, plain, ![X3349, X3350, X3351, X3352, X3353, X3354, X3355, X3356, X3357, X3358]:(~c_Equiv__Relations_Oequiv(X3358,X3357,X3356)|(~c_Equiv__Relations_Oequiv(X3355,X3354,X3353)|(~c_Equiv__Relations_Ocongruent2(X3358,X3355,tc_fun(X3352,tc_HOL_Obool),X3356,X3353,X3351)|(~hBOOL(hAPP(hAPP(c_member(X3358),X3350),X3357))|(~hBOOL(hAPP(hAPP(c_member(X3355),X3349),X3354))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3358,tc_fun(X3352,tc_HOL_Obool)),hAPP(c_Relation_OImage(X3358,X3358,X3356),hAPP(hAPP(c_Set_Oinsert(X3358),X3350),c_Orderings_Obot__class_Obot(tc_fun(X3358,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(X3355,tc_fun(X3352,tc_HOL_Obool)),tc_fun(X3352,tc_HOL_Obool),X3358),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3355,tc_fun(X3352,tc_HOL_Obool)),hAPP(c_Relation_OImage(X3355,X3355,X3353),hAPP(hAPP(c_Set_Oinsert(X3355),X3349),c_Orderings_Obot__class_Obot(tc_fun(X3355,tc_HOL_Obool)))))),X3351))=hAPP(hAPP(X3351,X3350),X3349)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__equiv__class2])])])). 6.97/7.22 cnf(c_0_5982, 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_4802])). 6.97/7.22 cnf(c_0_5983, plain, (hBOOL(hAPP(hAPP(X1,X3),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk291_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk290_3(X1,X2,X3)),esk291_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(X1,esk290_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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),esk291_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)],[inference(rw,[status(thm)],[c_0_4803, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_5984, 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_4804])). 6.97/7.22 cnf(c_0_5985, 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_4805, c_0_4798]), c_0_4798]), c_0_4806]), c_0_4467]), ['final']). 6.97/7.22 cnf(c_0_5986, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4807, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 fof(c_0_5987, plain, ![X5837, X5838, X5839, X5840, X5841, X5842, X5843, X5844, X5845, X5846, X5847]:((hBOOL(hAPP(hAPP(c_member(X5847),esk190_11(X5837,X5838,X5839,X5840,X5841,X5842,X5843,X5844,X5845,X5846,X5847)),X5846))|hBOOL(hAPP(hAPP(c_member(tc_fun(X5841,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5847,tc_fun(X5841,tc_HOL_Obool)),X5839),hAPP(hAPP(c_COMBB(tc_fun(X5844,tc_fun(X5841,tc_HOL_Obool)),tc_fun(X5841,tc_HOL_Obool),X5847),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5844,tc_fun(X5841,tc_HOL_Obool)),X5838)),X5840))),X5837))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X5844,tc_HOL_Obool)),X5838),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5844),X5843),X5842)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X5847,tc_HOL_Obool)),X5839),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5847),X5846),X5845)))|~c_Equiv__Relations_Ocongruent2(X5847,X5844,tc_fun(X5841,tc_HOL_Obool),X5845,X5842,X5840)|~c_Equiv__Relations_Oequiv(X5844,X5843,X5842)|~c_Equiv__Relations_Oequiv(X5847,X5846,X5845))&((hBOOL(hAPP(hAPP(c_member(X5844),esk191_11(X5837,X5838,X5839,X5840,X5841,X5842,X5843,X5844,X5845,X5846,X5847)),X5843))|hBOOL(hAPP(hAPP(c_member(tc_fun(X5841,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5847,tc_fun(X5841,tc_HOL_Obool)),X5839),hAPP(hAPP(c_COMBB(tc_fun(X5844,tc_fun(X5841,tc_HOL_Obool)),tc_fun(X5841,tc_HOL_Obool),X5847),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5844,tc_fun(X5841,tc_HOL_Obool)),X5838)),X5840))),X5837))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X5844,tc_HOL_Obool)),X5838),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5844),X5843),X5842)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X5847,tc_HOL_Obool)),X5839),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5847),X5846),X5845)))|~c_Equiv__Relations_Ocongruent2(X5847,X5844,tc_fun(X5841,tc_HOL_Obool),X5845,X5842,X5840)|~c_Equiv__Relations_Oequiv(X5844,X5843,X5842)|~c_Equiv__Relations_Oequiv(X5847,X5846,X5845))&(~hBOOL(hAPP(hAPP(c_member(tc_fun(X5841,tc_HOL_Obool)),hAPP(hAPP(X5840,esk190_11(X5837,X5838,X5839,X5840,X5841,X5842,X5843,X5844,X5845,X5846,X5847)),esk191_11(X5837,X5838,X5839,X5840,X5841,X5842,X5843,X5844,X5845,X5846,X5847))),X5837))|hBOOL(hAPP(hAPP(c_member(tc_fun(X5841,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5847,tc_fun(X5841,tc_HOL_Obool)),X5839),hAPP(hAPP(c_COMBB(tc_fun(X5844,tc_fun(X5841,tc_HOL_Obool)),tc_fun(X5841,tc_HOL_Obool),X5847),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5844,tc_fun(X5841,tc_HOL_Obool)),X5838)),X5840))),X5837))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X5844,tc_HOL_Obool)),X5838),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5844),X5843),X5842)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X5847,tc_HOL_Obool)),X5839),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5847),X5846),X5845)))|~c_Equiv__Relations_Ocongruent2(X5847,X5844,tc_fun(X5841,tc_HOL_Obool),X5845,X5842,X5840)|~c_Equiv__Relations_Oequiv(X5844,X5843,X5842)|~c_Equiv__Relations_Oequiv(X5847,X5846,X5845)))), 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])])])])])). 6.97/7.22 cnf(c_0_5988, 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_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X3))=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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4808, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_5989, 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_4753])). 6.97/7.22 cnf(c_0_5990, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk336_6(X3,X4,X5,X6,X2,X1)),esk337_6(X3,X4,X5,X6,X2,X1))),hAPP(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X4)),hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3))))))|hBOOL(hAPP(hAPP(X3,X6),X5))|~c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X5)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X4)))), inference(split_conjunct,[status(thm)],[c_0_4809])). 6.97/7.22 fof(c_0_5991, plain, ![X519, X520, X521, X522, X523]:(~class_Orderings_Oorder(X523)|(~c_Orderings_Oorder__class_Omono(X523,tc_fun(X522,tc_HOL_Obool),X521)|c_Orderings_Oorder__class_Omono(X523,tc_fun(X522,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X523,tc_fun(X522,tc_HOL_Obool),tc_fun(X522,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X522,tc_HOL_Obool),tc_fun(tc_fun(X522,tc_HOL_Obool),tc_fun(X522,tc_HOL_Obool)),X523),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X522,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X523,tc_fun(X522,tc_HOL_Obool),tc_fun(X522,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X522,tc_HOL_Obool),tc_fun(tc_fun(X522,tc_HOL_Obool),tc_fun(X522,tc_HOL_Obool)),X523),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X522,tc_HOL_Obool))),X521)),X520))),X519)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coinduct3__mono__lemma])])). 6.97/7.22 cnf(c_0_5992, 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),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X4)))),X3)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X3),esk62_4(X3,X1,X4,X2)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))), inference(split_conjunct,[status(thm)],[c_0_4810])). 6.97/7.22 fof(c_0_5993, plain, ![X2130, X2131, X2132, X2133, X2134, X2135]:((hBOOL(hAPP(hAPP(c_member(X2134),esk65_6(X2130,X2131,X2132,X2133,X2134,X2135)),X2133))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X2134,X2132),X2135),hAPP(c_Product__Type_Oprod_Oprod__case(X2134,X2132,X2135),X2130)),hAPP(hAPP(c_Product__Type_OSigma(X2134,X2132),X2133),X2131))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2134,X2135),hAPP(hAPP(c_COMBS(X2134,tc_fun(X2132,tc_HOL_Obool),X2135),hAPP(hAPP(c_COMBB(tc_fun(X2132,X2135),tc_fun(tc_fun(X2132,tc_HOL_Obool),X2135),X2134),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2132,X2135)),X2130)),X2131)),X2133)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2134),X2133))|~class_Groups_Ocomm__monoid__add(X2135))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2132),hAPP(X2131,esk65_6(X2130,X2131,X2132,X2133,X2134,X2135))))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X2134,X2132),X2135),hAPP(c_Product__Type_Oprod_Oprod__case(X2134,X2132,X2135),X2130)),hAPP(hAPP(c_Product__Type_OSigma(X2134,X2132),X2133),X2131))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2134,X2135),hAPP(hAPP(c_COMBS(X2134,tc_fun(X2132,tc_HOL_Obool),X2135),hAPP(hAPP(c_COMBB(tc_fun(X2132,X2135),tc_fun(tc_fun(X2132,tc_HOL_Obool),X2135),X2134),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2132,X2135)),X2130)),X2131)),X2133)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2134),X2133))|~class_Groups_Ocomm__monoid__add(X2135))), 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])])])])])). 6.97/7.22 cnf(c_0_5994, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk62_4(X2,X3,X4,X1)),X4))|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_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),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4)))),X2)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_4810])). 6.97/7.22 cnf(c_0_5995, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4811, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_5996, 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_4812, c_0_4813])). 6.97/7.22 fof(c_0_5997, plain, ![X5972, X5973, X5974, X5975, X5976, X5977]:(((hBOOL(hAPP(hAPP(c_member(X5976),esk198_6(X5972,X5973,X5974,X5975,X5976,X5977)),X5975))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5977,X5974,c_Groups_Otimes__class_Otimes(X5977)),X5972),c_Groups_Oone__class_Oone(X5977)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5976,tc_fun(X5974,tc_HOL_Obool)),X5975),X5973))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5977,X5976,c_Groups_Otimes__class_Otimes(X5977)),hAPP(hAPP(c_COMBB(tc_fun(X5974,tc_HOL_Obool),X5977,X5976),hAPP(hAPP(c_Finite__Set_Ofold__image(X5977,X5974,c_Groups_Otimes__class_Otimes(X5977)),X5972),c_Groups_Oone__class_Oone(X5977))),X5973)),c_Groups_Oone__class_Oone(X5977)),X5975)|hBOOL(hAPP(hAPP(c_member(X5976),esk197_6(X5972,X5973,X5974,X5975,X5976,X5977)),X5975))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5976),X5975))|~class_Groups_Ocomm__monoid__mult(X5977))&((hBOOL(hAPP(hAPP(c_member(X5976),esk199_6(X5972,X5973,X5974,X5975,X5976,X5977)),X5975))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5977,X5974,c_Groups_Otimes__class_Otimes(X5977)),X5972),c_Groups_Oone__class_Oone(X5977)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5976,tc_fun(X5974,tc_HOL_Obool)),X5975),X5973))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5977,X5976,c_Groups_Otimes__class_Otimes(X5977)),hAPP(hAPP(c_COMBB(tc_fun(X5974,tc_HOL_Obool),X5977,X5976),hAPP(hAPP(c_Finite__Set_Ofold__image(X5977,X5974,c_Groups_Otimes__class_Otimes(X5977)),X5972),c_Groups_Oone__class_Oone(X5977))),X5973)),c_Groups_Oone__class_Oone(X5977)),X5975)|hBOOL(hAPP(hAPP(c_member(X5976),esk197_6(X5972,X5973,X5974,X5975,X5976,X5977)),X5975))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5976),X5975))|~class_Groups_Ocomm__monoid__mult(X5977))&((esk198_6(X5972,X5973,X5974,X5975,X5976,X5977)!=esk199_6(X5972,X5973,X5974,X5975,X5976,X5977)|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5977,X5974,c_Groups_Otimes__class_Otimes(X5977)),X5972),c_Groups_Oone__class_Oone(X5977)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5976,tc_fun(X5974,tc_HOL_Obool)),X5975),X5973))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5977,X5976,c_Groups_Otimes__class_Otimes(X5977)),hAPP(hAPP(c_COMBB(tc_fun(X5974,tc_HOL_Obool),X5977,X5976),hAPP(hAPP(c_Finite__Set_Ofold__image(X5977,X5974,c_Groups_Otimes__class_Otimes(X5977)),X5972),c_Groups_Oone__class_Oone(X5977))),X5973)),c_Groups_Oone__class_Oone(X5977)),X5975)|hBOOL(hAPP(hAPP(c_member(X5976),esk197_6(X5972,X5973,X5974,X5975,X5976,X5977)),X5975))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5976),X5975))|~class_Groups_Ocomm__monoid__mult(X5977))&(c_Orderings_Obot__class_Obot(tc_fun(X5974,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5974,tc_HOL_Obool)),hAPP(X5973,esk198_6(X5972,X5973,X5974,X5975,X5976,X5977))),hAPP(X5973,esk199_6(X5972,X5973,X5974,X5975,X5976,X5977)))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5977,X5974,c_Groups_Otimes__class_Otimes(X5977)),X5972),c_Groups_Oone__class_Oone(X5977)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5976,tc_fun(X5974,tc_HOL_Obool)),X5975),X5973))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5977,X5976,c_Groups_Otimes__class_Otimes(X5977)),hAPP(hAPP(c_COMBB(tc_fun(X5974,tc_HOL_Obool),X5977,X5976),hAPP(hAPP(c_Finite__Set_Ofold__image(X5977,X5974,c_Groups_Otimes__class_Otimes(X5977)),X5972),c_Groups_Oone__class_Oone(X5977))),X5973)),c_Groups_Oone__class_Oone(X5977)),X5975)|hBOOL(hAPP(hAPP(c_member(X5976),esk197_6(X5972,X5973,X5974,X5975,X5976,X5977)),X5975))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5976),X5975))|~class_Groups_Ocomm__monoid__mult(X5977)))))&((hBOOL(hAPP(hAPP(c_member(X5976),esk198_6(X5972,X5973,X5974,X5975,X5976,X5977)),X5975))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5977,X5974,c_Groups_Otimes__class_Otimes(X5977)),X5972),c_Groups_Oone__class_Oone(X5977)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5976,tc_fun(X5974,tc_HOL_Obool)),X5975),X5973))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5977,X5976,c_Groups_Otimes__class_Otimes(X5977)),hAPP(hAPP(c_COMBB(tc_fun(X5974,tc_HOL_Obool),X5977,X5976),hAPP(hAPP(c_Finite__Set_Ofold__image(X5977,X5974,c_Groups_Otimes__class_Otimes(X5977)),X5972),c_Groups_Oone__class_Oone(X5977))),X5973)),c_Groups_Oone__class_Oone(X5977)),X5975)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5974),hAPP(X5973,esk197_6(X5972,X5973,X5974,X5975,X5976,X5977))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5976),X5975))|~class_Groups_Ocomm__monoid__mult(X5977))&((hBOOL(hAPP(hAPP(c_member(X5976),esk199_6(X5972,X5973,X5974,X5975,X5976,X5977)),X5975))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5977,X5974,c_Groups_Otimes__class_Otimes(X5977)),X5972),c_Groups_Oone__class_Oone(X5977)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5976,tc_fun(X5974,tc_HOL_Obool)),X5975),X5973))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5977,X5976,c_Groups_Otimes__class_Otimes(X5977)),hAPP(hAPP(c_COMBB(tc_fun(X5974,tc_HOL_Obool),X5977,X5976),hAPP(hAPP(c_Finite__Set_Ofold__image(X5977,X5974,c_Groups_Otimes__class_Otimes(X5977)),X5972),c_Groups_Oone__class_Oone(X5977))),X5973)),c_Groups_Oone__class_Oone(X5977)),X5975)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5974),hAPP(X5973,esk197_6(X5972,X5973,X5974,X5975,X5976,X5977))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5976),X5975))|~class_Groups_Ocomm__monoid__mult(X5977))&((esk198_6(X5972,X5973,X5974,X5975,X5976,X5977)!=esk199_6(X5972,X5973,X5974,X5975,X5976,X5977)|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5977,X5974,c_Groups_Otimes__class_Otimes(X5977)),X5972),c_Groups_Oone__class_Oone(X5977)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5976,tc_fun(X5974,tc_HOL_Obool)),X5975),X5973))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5977,X5976,c_Groups_Otimes__class_Otimes(X5977)),hAPP(hAPP(c_COMBB(tc_fun(X5974,tc_HOL_Obool),X5977,X5976),hAPP(hAPP(c_Finite__Set_Ofold__image(X5977,X5974,c_Groups_Otimes__class_Otimes(X5977)),X5972),c_Groups_Oone__class_Oone(X5977))),X5973)),c_Groups_Oone__class_Oone(X5977)),X5975)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5974),hAPP(X5973,esk197_6(X5972,X5973,X5974,X5975,X5976,X5977))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5976),X5975))|~class_Groups_Ocomm__monoid__mult(X5977))&(c_Orderings_Obot__class_Obot(tc_fun(X5974,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5974,tc_HOL_Obool)),hAPP(X5973,esk198_6(X5972,X5973,X5974,X5975,X5976,X5977))),hAPP(X5973,esk199_6(X5972,X5973,X5974,X5975,X5976,X5977)))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5977,X5974,c_Groups_Otimes__class_Otimes(X5977)),X5972),c_Groups_Oone__class_Oone(X5977)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5976,tc_fun(X5974,tc_HOL_Obool)),X5975),X5973))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5977,X5976,c_Groups_Otimes__class_Otimes(X5977)),hAPP(hAPP(c_COMBB(tc_fun(X5974,tc_HOL_Obool),X5977,X5976),hAPP(hAPP(c_Finite__Set_Ofold__image(X5977,X5974,c_Groups_Otimes__class_Otimes(X5977)),X5972),c_Groups_Oone__class_Oone(X5977))),X5973)),c_Groups_Oone__class_Oone(X5977)),X5975)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5974),hAPP(X5973,esk197_6(X5972,X5973,X5974,X5975,X5976,X5977))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5976),X5975))|~class_Groups_Ocomm__monoid__mult(X5977)))))), 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__disjoint])])])])])). 6.97/7.22 cnf(c_0_5998, plain, (c_Nitpick_Osetsum_H(X1,X3,X4,X2)=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)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Groups_Ocomm__monoid__add(X3)), inference(split_conjunct,[status(thm)],[c_0_4814])). 6.97/7.22 cnf(c_0_5999, 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_4815]), ['final']). 6.97/7.22 cnf(c_0_6000, plain, (c_Hilbert__Choice_OEps(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_Hilbert__Choice_Oinv__into(X1,X3,X2,X4),X5)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4816, c_0_4798]), c_0_4817]), ['final']). 6.97/7.22 cnf(c_0_6001, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_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)],[c_0_4818, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_6002, 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_4819])). 6.97/7.22 cnf(c_0_6003, 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_4820, c_0_4821]), ['final']). 6.97/7.22 fof(c_0_6004, plain, ![X1409, X1410, X1411, X1412, X1413]:(~class_Groups_Ocomm__monoid__mult(X1413)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1412),X1411))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1412),X1410))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1413),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1413,X1412,c_Groups_Otimes__class_Otimes(X1413)),X1409),c_Groups_Oone__class_Oone(X1413)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1412,tc_HOL_Obool)),X1411),X1410))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1413,X1412,c_Groups_Otimes__class_Otimes(X1413)),X1409),c_Groups_Oone__class_Oone(X1413)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1412,tc_HOL_Obool)),X1411),X1410)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1413),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1413,X1412,c_Groups_Otimes__class_Otimes(X1413)),X1409),c_Groups_Oone__class_Oone(X1413)),X1411)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1413,X1412,c_Groups_Otimes__class_Otimes(X1413)),X1409),c_Groups_Oone__class_Oone(X1413)),X1410))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__image__Un__Int])])])). 6.97/7.22 cnf(c_0_6005, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2)=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)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4822])). 6.97/7.22 cnf(c_0_6006, 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)), inference(split_conjunct,[status(thm)],[c_0_4823]), ['final']). 6.97/7.22 cnf(c_0_6007, 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_4824, c_0_4565])). 6.97/7.22 cnf(c_0_6008, 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_4825, c_0_4565])). 6.97/7.22 fof(c_0_6009, plain, ![X4271, X4272, X4273, X4274, X4275]:((hBOOL(hAPP(hAPP(c_member(X4274),esk147_5(X4271,X4272,X4273,X4274,X4275)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4274,tc_HOL_Obool)),X4273),X4272)))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4275),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X4275,X4274,c_Groups_Otimes__class_Otimes(X4275)),X4271),c_Groups_Oone__class_Oone(X4275)),X4273)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X4275,X4274,c_Groups_Otimes__class_Otimes(X4275)),X4271),c_Groups_Oone__class_Oone(X4275)),X4272))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X4275,X4274,c_Groups_Otimes__class_Otimes(X4275)),X4271),c_Groups_Oone__class_Oone(X4275)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4274,tc_HOL_Obool)),X4273),X4272))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4274),X4272))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4274),X4273))|~class_Groups_Ocomm__monoid__mult(X4275))&(hAPP(X4271,esk147_5(X4271,X4272,X4273,X4274,X4275))!=c_Groups_Oone__class_Oone(X4275)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4275),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X4275,X4274,c_Groups_Otimes__class_Otimes(X4275)),X4271),c_Groups_Oone__class_Oone(X4275)),X4273)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X4275,X4274,c_Groups_Otimes__class_Otimes(X4275)),X4271),c_Groups_Oone__class_Oone(X4275)),X4272))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X4275,X4274,c_Groups_Otimes__class_Otimes(X4275)),X4271),c_Groups_Oone__class_Oone(X4275)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4274,tc_HOL_Obool)),X4273),X4272))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4274),X4272))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4274),X4273))|~class_Groups_Ocomm__monoid__mult(X4275))), 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])])])])])). 6.97/7.22 cnf(c_0_6010, 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),X2))),X2)),esk216_3(X3,X2,X1)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk217_3(X3,X2,X1)),esk217_3(X3,X2,X1))),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4826, c_0_4798]), c_0_4798])). 6.97/7.22 cnf(c_0_6011, plain, (c_Relation_Orefl__on(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk217_3(X3,X2,X1)),X2))|~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),X2))),X2)),esk216_3(X3,X2,X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4827, c_0_4798]), c_0_4798])). 6.97/7.22 fof(c_0_6012, plain, ![X8119, X8120, X8121, X8122, X8123]:((hBOOL(hAPP(hAPP(c_member(X8122),esk266_5(X8119,X8120,X8121,X8122,X8123)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8122,tc_HOL_Obool)),X8121),X8120)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8122,X8123),X8119),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8122,tc_HOL_Obool)),X8121),X8120))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8123),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8123),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8122,X8123),X8119),X8121)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8122,X8123),X8119),X8120))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8122,X8123),X8119),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8122,tc_HOL_Obool)),X8121),X8120)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8122),X8120))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8122),X8121))|~class_Fields_Ofield(X8123))&(hAPP(X8119,esk266_5(X8119,X8120,X8121,X8122,X8123))=c_Groups_Ozero__class_Ozero(X8123)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8122,X8123),X8119),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8122,tc_HOL_Obool)),X8121),X8120))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8123),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8123),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8122,X8123),X8119),X8121)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8122,X8123),X8119),X8120))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8122,X8123),X8119),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8122,tc_HOL_Obool)),X8121),X8120)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8122),X8120))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8122),X8121))|~class_Fields_Ofield(X8123))), 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])])])])])). 6.97/7.22 cnf(c_0_6013, plain, (hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X2)!=X3|~c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(X2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),X2)),X5))),X3)))))), inference(split_conjunct,[status(thm)],[c_0_4828])). 6.97/7.22 cnf(c_0_6014, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4829, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_6015, plain, (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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4830, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_6016, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4831, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 fof(c_0_6017, plain, ![X1370, X1371, X1372, X1373, X1374]:(~class_Groups_Ocomm__monoid__mult(X1374)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1373),X1372))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1374,X1373,c_Groups_Otimes__class_Otimes(X1374)),hAPP(hAPP(c_COMBS(X1373,X1374,X1374),hAPP(hAPP(c_COMBB(X1374,tc_fun(X1374,X1374),X1373),c_Groups_Otimes__class_Otimes(X1374)),X1371)),X1370)),c_Groups_Oone__class_Oone(X1374)),X1372)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1374),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1374,X1373,c_Groups_Otimes__class_Otimes(X1374)),X1371),c_Groups_Oone__class_Oone(X1374)),X1372)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1374,X1373,c_Groups_Otimes__class_Otimes(X1374)),X1370),c_Groups_Oone__class_Oone(X1374)),X1372)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__image__distrib])])])). 6.97/7.22 fof(c_0_6018, plain, ![X3305, X3306, X3307, X3308, X3309, X3310]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X3310,tc_HOL_Obool),tc_fun(X3310,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X3310,tc_HOL_Obool),tc_fun(X3310,tc_HOL_Obool)),X3309),X3308)),c_Wellfounded_Omax__ext(X3310,X3307)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X3310,tc_HOL_Obool),tc_fun(X3310,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X3310,tc_HOL_Obool),tc_fun(X3310,tc_HOL_Obool)),X3306),X3305)),c_Wellfounded_Omax__ext(X3310,X3307)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X3310,tc_HOL_Obool),tc_fun(X3310,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X3310,tc_HOL_Obool),tc_fun(X3310,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3310,tc_HOL_Obool)),X3309),X3306)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3310,tc_HOL_Obool)),X3308),X3305))),c_Wellfounded_Omax__ext(X3310,X3307))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_max__ext__additive])])])). 6.97/7.22 cnf(c_0_6019, plain, (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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X2)))=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)))|~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)],[c_0_4832, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_6020, 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_4833])). 6.97/7.22 cnf(c_0_6021, 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))), inference(split_conjunct,[status(thm)],[c_0_4834]), ['final']). 6.97/7.22 cnf(c_0_6022, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(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),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=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))), inference(split_conjunct,[status(thm)],[c_0_4835])). 6.97/7.22 cnf(c_0_6023, 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_4836])). 6.97/7.22 cnf(c_0_6024, 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),esk110_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_4837])). 6.97/7.22 cnf(c_0_6025, plain, (hBOOL(hAPP(X1,esk311_2(X2,X1)))|hBOOL(hAPP(X2,esk311_2(X2,X1)))|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_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))), inference(split_conjunct,[status(thm)],[c_0_4838])). 6.97/7.22 cnf(c_0_6026, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|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_4839])). 6.97/7.22 fof(c_0_6027, plain, ![X10553, X10554, X10555, X10556, X10557, X10558]:(~class_Groups_Ocomm__monoid__mult(X10558)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10557,X10558),hAPP(hAPP(c_COMBC(X10557,tc_fun(X10556,tc_HOL_Obool),X10558),hAPP(hAPP(c_COMBB(tc_fun(X10556,X10558),tc_fun(tc_fun(X10556,tc_HOL_Obool),X10558),X10557),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10556,X10558)),X10555)),X10554)),X10553)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X10557,X10556),X10558),hAPP(c_Product__Type_Oprod_Oprod__case(X10557,X10556,X10558),X10555)),hAPP(hAPP(c_Product__Type_OSigma(X10557,X10556),X10553),hAPP(c_COMBK(tc_fun(X10556,tc_HOL_Obool),X10557),X10554)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__cartesian__product])])). 6.97/7.22 cnf(c_0_6028, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk311_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_4838])). 6.97/7.22 cnf(c_0_6029, plain, (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))))=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))|~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_4840])). 6.97/7.22 cnf(c_0_6030, 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_4841]), ['final']). 6.97/7.22 fof(c_0_6031, plain, ![X7945, X7946, X7947, X7948, X7949, X7950]:(~class_Groups_Ocomm__monoid__add(X7950)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X7949,X7948),X7950),hAPP(c_Product__Type_Oprod_Oprod__case(X7949,X7948,X7950),X7947)),hAPP(hAPP(c_Product__Type_OSigma(X7949,X7948),X7945),hAPP(c_COMBK(tc_fun(X7948,tc_HOL_Obool),X7949),X7946)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7949,X7950),hAPP(hAPP(c_COMBC(X7949,tc_fun(X7948,tc_HOL_Obool),X7950),hAPP(hAPP(c_COMBB(tc_fun(X7948,X7950),tc_fun(tc_fun(X7948,tc_HOL_Obool),X7950),X7949),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7948,X7950)),X7947)),X7946)),X7945)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__cartesian__product])])])). 6.97/7.22 cnf(c_0_6032, plain, (c_Nitpick_Ocard_H(X1,X2)=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))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4842])). 6.97/7.22 cnf(c_0_6033, 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_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))|~hBOOL(hAPP(X1,esk311_2(X2,X1)))|~hBOOL(hAPP(X2,esk311_2(X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_4838])). 6.97/7.22 cnf(c_0_6034, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[c_0_4843, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 fof(c_0_6035, plain, ![X2052, X2053]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2053,X2053),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X2053,X2053,X2053),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X2053,X2053),tc_HOL_Obool),tc_fun(tc_prod(X2053,X2053),tc_HOL_Obool)),X2052)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X2053,X2053),tc_HOL_Obool),tc_fun(tc_prod(X2053,X2053),tc_HOL_Obool)),X2052))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X2053,X2053),tc_HOL_Obool),tc_fun(tc_prod(X2053,X2053),tc_HOL_Obool)),X2052)))|~c_FunDef_Oreduction__pair(X2053,X2052))&(c_Wellfounded_Owf(X2053,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X2053,X2053),tc_HOL_Obool),tc_fun(tc_prod(X2053,X2053),tc_HOL_Obool)),X2052))|~c_FunDef_Oreduction__pair(X2053,X2052)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2053,X2053),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X2053,X2053,X2053),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X2053,X2053),tc_HOL_Obool),tc_fun(tc_prod(X2053,X2053),tc_HOL_Obool)),X2052)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X2053,X2053),tc_HOL_Obool),tc_fun(tc_prod(X2053,X2053),tc_HOL_Obool)),X2052))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X2053,X2053),tc_HOL_Obool),tc_fun(tc_prod(X2053,X2053),tc_HOL_Obool)),X2052)))|~c_Wellfounded_Owf(X2053,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X2053,X2053),tc_HOL_Obool),tc_fun(tc_prod(X2053,X2053),tc_HOL_Obool)),X2052))|c_FunDef_Oreduction__pair(X2053,X2052))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reduction__pair__def])])])). 6.97/7.22 cnf(c_0_6036, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X5))=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)),X5))),X4)),c_Groups_Ozero__class_Ozero(X1))),X3)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_4844])). 6.97/7.22 cnf(c_0_6037, 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_4845])). 6.97/7.22 fof(c_0_6038, plain, ![X8318, X8319, X8320, X8321, X8322, X8323]:((hBOOL(hAPP(hAPP(c_member(X8322),esk272_6(X8318,X8319,X8320,X8321,X8322,X8323)),X8321))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X8322,X8320),X8323),hAPP(c_Product__Type_Oprod_Oprod__case(X8322,X8320,X8323),X8318)),hAPP(hAPP(c_Product__Type_OSigma(X8322,X8320),X8321),X8319))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8322,X8323),hAPP(hAPP(c_COMBS(X8322,tc_fun(X8320,tc_HOL_Obool),X8323),hAPP(hAPP(c_COMBB(tc_fun(X8320,X8323),tc_fun(tc_fun(X8320,tc_HOL_Obool),X8323),X8322),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8320,X8323)),X8318)),X8319)),X8321)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8322),X8321))|~class_Groups_Ocomm__monoid__mult(X8323))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8320),hAPP(X8319,esk272_6(X8318,X8319,X8320,X8321,X8322,X8323))))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X8322,X8320),X8323),hAPP(c_Product__Type_Oprod_Oprod__case(X8322,X8320,X8323),X8318)),hAPP(hAPP(c_Product__Type_OSigma(X8322,X8320),X8321),X8319))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8322,X8323),hAPP(hAPP(c_COMBS(X8322,tc_fun(X8320,tc_HOL_Obool),X8323),hAPP(hAPP(c_COMBB(tc_fun(X8320,X8323),tc_fun(tc_fun(X8320,tc_HOL_Obool),X8323),X8322),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8320,X8323)),X8318)),X8319)),X8321)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8322),X8321))|~class_Groups_Ocomm__monoid__mult(X8323))), 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])])])])])). 6.97/7.22 fof(c_0_6039, plain, ![X11052, X11053, X11054, X11055, X11057, X11058, X11059, X11060, X11061]:(((hBOOL(hAPP(hAPP(c_member(tc_prod(X11055,X11055)),esk368_4(X11052,X11053,X11054,X11055)),X11053))|c_Equiv__Relations_Ocongruent(X11055,X11054,X11053,X11052))&(~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X11055,X11055,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X11055,tc_fun(X11055,X11054),tc_fun(X11055,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X11054,tc_HOL_Obool),tc_fun(tc_fun(X11055,X11054),tc_fun(X11055,tc_HOL_Obool)),X11055),c_COMBB(X11054,tc_HOL_Obool,X11055)),hAPP(hAPP(c_COMBB(X11054,tc_fun(X11054,tc_HOL_Obool),X11055),c_fequal),X11052))),X11052)),esk368_4(X11052,X11053,X11054,X11055)))|c_Equiv__Relations_Ocongruent(X11055,X11054,X11053,X11052)))&(~c_Equiv__Relations_Ocongruent(X11060,X11059,X11058,X11057)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X11060,X11060)),X11061),X11058))|hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X11060,X11060,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X11060,tc_fun(X11060,X11059),tc_fun(X11060,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X11059,tc_HOL_Obool),tc_fun(tc_fun(X11060,X11059),tc_fun(X11060,tc_HOL_Obool)),X11060),c_COMBB(X11059,tc_HOL_Obool,X11060)),hAPP(hAPP(c_COMBB(X11059,tc_fun(X11059,tc_HOL_Obool),X11060),c_fequal),X11057))),X11057)),X11061))))), 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])])])])])])). 6.97/7.22 cnf(c_0_6040, plain, (c_Divides_OnegDivAlg(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)))|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)],[inference(rw,[status(thm)],[c_0_4846, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_6041, plain, (hBOOL(hAPP(X1,esk110_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_4837])). 6.97/7.22 cnf(c_0_6042, 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_4845])). 6.97/7.22 fof(c_0_6043, plain, ![X7039, X7040, X7041, X7042, X7043]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7043),tc_List_Olist(X7043))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7043),tc_List_Olist(X7043)),hAPP(hAPP(c_List_Oappend(X7043),X7042),X7041)),hAPP(hAPP(c_List_Oappend(X7043),X7042),X7040))),c_List_Olexord(X7043,X7039)))|(hBOOL(hAPP(hAPP(c_member(tc_prod(X7043,X7043)),hAPP(hAPP(c_Product__Type_OPair(X7043,X7043),esk226_5(X7039,X7040,X7041,X7042,X7043)),esk226_5(X7039,X7040,X7041,X7042,X7043))),X7039))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7043),tc_List_Olist(X7043))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7043),tc_List_Olist(X7043)),X7041),X7040)),c_List_Olexord(X7043,X7039))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lexord__append__leftD])])])])). 6.97/7.22 cnf(c_0_6044, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(hAPP(c_Power_Opower__class_Opower(X4),X5),hAPP(c_Finite__Set_Ocard(X1),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))),X6)),X5)),X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Groups_Ocomm__monoid__mult(X4)), inference(split_conjunct,[status(thm)],[c_0_4836])). 6.97/7.22 fof(c_0_6045, plain, ![X557, X558, X559, X560, X561, X562, X563, X564]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X564,X563),tc_HOL_Obool)),X562),hAPP(hAPP(c_Product__Type_OSigma(X564,X563),X561),hAPP(c_COMBK(tc_fun(X563,tc_HOL_Obool),X564),X560))))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X563,X559),tc_HOL_Obool)),X558),hAPP(hAPP(c_Product__Type_OSigma(X563,X559),X560),hAPP(c_COMBK(tc_fun(X559,tc_HOL_Obool),X563),X557))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X564,X559),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X564,X563,X559),X562),X558)),hAPP(hAPP(c_Product__Type_OSigma(X564,X559),X561),hAPP(c_COMBK(tc_fun(X559,tc_HOL_Obool),X564),X557)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rel__comp__subset__Sigma])])])). 6.97/7.22 fof(c_0_6046, plain, ![X2792, X2793, X2794, X2795, X2796]:(~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2796,X2795),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2794),X2793)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2795))|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2792),X2796),X2795),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),X2792),X2794)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2792),X2793)),X2795))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2792),X2793),X2795)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__nat__rel__mult1__eq])])])). 6.97/7.22 fof(c_0_6047, plain, ![X14699, X14700, X14701, X14702, X14703, X14704]:(~class_Groups_Ocomm__monoid__add(X14704)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14702,X14704),hAPP(hAPP(c_COMBC(X14702,tc_fun(X14703,tc_HOL_Obool),X14704),hAPP(hAPP(c_COMBB(tc_fun(X14703,X14704),tc_fun(tc_fun(X14703,tc_HOL_Obool),X14704),X14702),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14703,X14704)),hAPP(c_COMBC(X14703,X14702,X14704),X14701))),X14699)),X14700)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14703,X14704),hAPP(hAPP(c_COMBC(X14703,tc_fun(X14702,tc_HOL_Obool),X14704),hAPP(hAPP(c_COMBB(tc_fun(X14702,X14704),tc_fun(tc_fun(X14702,tc_HOL_Obool),X14704),X14703),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14702,X14704)),X14701)),X14700)),X14699)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__commute])])])). 6.97/7.22 cnf(c_0_6048, 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_4847])). 6.97/7.22 cnf(c_0_6049, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[c_0_4848, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_6050, plain, (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)))=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))|~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_4849, c_0_4813])). 6.97/7.22 cnf(c_0_6051, 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_4850, c_0_4851]), ['final']). 6.97/7.22 fof(c_0_6052, plain, ![X17185, X17186, X17187]:(~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X17187),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X17187))),X17186)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17185),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X17187))),X17186)))|hAPP(hAPP(c_List_Onth(tc_List_Olist(X17187)),X17186),X17185)=hAPP(hAPP(c_List_Omap(tc_List_Olist(X17187),X17187),hAPP(hAPP(c_COMBC(tc_List_Olist(X17187),tc_Nat_Onat,X17187),c_List_Onth(X17187)),X17185)),hAPP(c_List_Ofilter(tc_List_Olist(X17187),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X17187)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17185)),c_Nat_Osize__class_Osize(tc_List_Olist(X17187)))),c_List_Otranspose(X17187,X17186))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transpose__column])])])). 6.97/7.22 cnf(c_0_6053, 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,esk124_3(X2,X3,X1))),hAPP(X3,esk124_3(X2,X3,X1))))), inference(split_conjunct,[status(thm)],[c_0_4852])). 6.97/7.22 cnf(c_0_6054, 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_4853, c_0_4565])). 6.97/7.22 cnf(c_0_6055, 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_4854, c_0_4565])). 6.97/7.22 fof(c_0_6056, plain, ![X11123, X11124, X11125, X11126, X11127]:(~c_Relation_Osingle__valued(X11127,X11127,X11126)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X11127,X11127)),hAPP(hAPP(c_Product__Type_OPair(X11127,X11127),X11125),X11124)),c_Transitive__Closure_Ortrancl(X11127,X11126)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X11127,X11127)),hAPP(hAPP(c_Product__Type_OPair(X11127,X11127),X11125),X11123)),c_Transitive__Closure_Ortrancl(X11127,X11126)))|(hBOOL(hAPP(hAPP(c_member(tc_prod(X11127,X11127)),hAPP(hAPP(c_Product__Type_OPair(X11127,X11127),X11124),X11123)),c_Transitive__Closure_Ortrancl(X11127,X11126)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X11127,X11127)),hAPP(hAPP(c_Product__Type_OPair(X11127,X11127),X11123),X11124)),c_Transitive__Closure_Ortrancl(X11127,X11126))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_single__valued__confluent])])])). 6.97/7.22 cnf(c_0_6057, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[c_0_4855, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_6058, 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_4856, c_0_4565])). 6.97/7.22 fof(c_0_6059, plain, ![X1867, X1868, X1869, X1870]:(~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1870),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1870))),X1869)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1868),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1870))),c_List_Otranspose(X1870,X1869))))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1867),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1870))),hAPP(c_List_Ofilter(tc_List_Olist(X1870),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1870)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1868)),c_Nat_Osize__class_Osize(tc_List_Olist(X1870)))),X1869))))|hAPP(hAPP(c_List_Onth(X1870),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1870)),X1869),X1867)),X1868)=hAPP(hAPP(c_List_Onth(X1870),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1870)),c_List_Otranspose(X1870,X1869)),X1868)),X1867)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__nth__transpose__sorted])])])). 6.97/7.22 cnf(c_0_6060, plain, (c_Orderings_Otop__class_Otop(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),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X6),X3))), inference(split_conjunct,[status(thm)],[c_0_4845])). 6.97/7.22 cnf(c_0_6061, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[c_0_4857, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_6062, 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_4845])). 6.97/7.22 fof(c_0_6063, plain, ![X11532, X11533, X11534, X11535, X11536]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X11536,X11535),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X11534),X11533)))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X11535|hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11532),X11536),X11535),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),X11532),X11534)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11532),X11533)),X11535))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11532),X11533),X11535)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult1__lemma])])). 6.97/7.22 cnf(c_0_6064, 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_4801])). 6.97/7.22 fof(c_0_6065, plain, ![X16285, X16286, X16287, X16288]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16288),X16287))|hAPP(c_Set_Oimage(X16288,X16286,X16285),X16287)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(X16286,tc_HOL_Obool),X16288,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16286,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X16288,tc_fun(X16286,tc_HOL_Obool),tc_fun(X16286,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X16286,tc_fun(tc_fun(X16286,tc_HOL_Obool),tc_fun(X16286,tc_HOL_Obool)),X16288),c_Set_Oinsert(X16286)),X16285)),c_Orderings_Obot__class_Obot(tc_fun(X16286,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(X16286,tc_HOL_Obool))),X16287)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__eq__fold__image])])). 6.97/7.22 cnf(c_0_6066, 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_4858])). 6.97/7.22 cnf(c_0_6067, 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_4859]), ['final']). 6.97/7.22 cnf(c_0_6068, 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_4860])). 6.97/7.22 cnf(c_0_6069, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|c_Groups_Ozero__class_Ozero(X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X3),X4),X2)|~class_Groups_Ocomm__monoid__add(X3)), inference(split_conjunct,[status(thm)],[c_0_4861]), ['final']). 6.97/7.22 cnf(c_0_6070, 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_4802])). 6.97/7.22 fof(c_0_6071, plain, ![X6899, X6900, X6901, X6902, X6903, X6904, X6905, X6906, X6907]:(~c_Equiv__Relations_Oequiv(X6907,X6906,X6905)|(~c_Equiv__Relations_Oequiv(X6904,X6903,X6902)|(~c_Equiv__Relations_Ocongruent2(X6907,X6904,tc_fun(X6901,tc_HOL_Obool),X6905,X6902,X6900)|(~hBOOL(hAPP(hAPP(c_member(X6904),X6899),X6903))|c_Equiv__Relations_Ocongruent(X6907,tc_fun(X6901,tc_HOL_Obool),X6905,hAPP(hAPP(c_COMBB(tc_fun(X6904,tc_fun(X6901,tc_HOL_Obool)),tc_fun(X6901,tc_HOL_Obool),X6907),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6904,tc_fun(X6901,tc_HOL_Obool)),hAPP(c_Relation_OImage(X6904,X6904,X6902),hAPP(hAPP(c_Set_Oinsert(X6904),X6899),c_Orderings_Obot__class_Obot(tc_fun(X6904,tc_HOL_Obool)))))),X6900)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_congruent2__implies__congruent__UN])])])). 6.97/7.22 cnf(c_0_6072, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)))|~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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4862, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.22 fof(c_0_6073, plain, ![X1987, X1988, X1989, X1990, X1991]:(~class_Groups_Oab__group__add(X1991)|hAPP(c_List_Omonoid__add__class_Olistsum(X1991),hAPP(hAPP(c_List_Omap(X1990,X1991),hAPP(hAPP(c_COMBS(X1990,X1991,X1991),hAPP(hAPP(c_COMBB(X1991,tc_fun(X1991,X1991),X1990),c_Groups_Ominus__class_Ominus(X1991)),X1989)),X1988)),X1987))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1991),hAPP(c_List_Omonoid__add__class_Olistsum(X1991),hAPP(hAPP(c_List_Omap(X1990,X1991),X1989),X1987))),hAPP(c_List_Omonoid__add__class_Olistsum(X1991),hAPP(hAPP(c_List_Omap(X1990,X1991),X1988),X1987)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__subtractf])])])). 6.97/7.22 fof(c_0_6074, plain, ![X4180, X4181, X4182, X4183, X4184]:(~class_Groups_Ocomm__monoid__add(X4184)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4184),hAPP(c_List_Omonoid__add__class_Olistsum(X4184),hAPP(hAPP(c_List_Omap(X4183,X4184),X4182),X4180))),hAPP(c_List_Omonoid__add__class_Olistsum(X4184),hAPP(hAPP(c_List_Omap(X4183,X4184),X4181),X4180)))=hAPP(c_List_Omonoid__add__class_Olistsum(X4184),hAPP(hAPP(c_List_Omap(X4183,X4184),hAPP(hAPP(c_COMBS(X4183,X4184,X4184),hAPP(hAPP(c_COMBB(X4184,tc_fun(X4184,X4184),X4183),c_Groups_Oplus__class_Oplus(X4184)),X4182)),X4181)),X4180))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__addf])])])). 6.97/7.22 cnf(c_0_6075, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk554_5(X2,X3,X1,X4,X5)),X2))|c_Orderings_Oord__class_OLeast(X4,hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),hAPP(c_Set_Oimage(X1,X4,X3),X2)))=hAPP(X3,c_Orderings_Oord__class_OLeast(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X2))|~c_Orderings_Oorder__class_Omono(X1,X4,X3)|~class_Orderings_Oorder(X1)|~class_Orderings_Oorder(X4)), inference(split_conjunct,[status(thm)],[c_0_4863])). 6.97/7.22 cnf(c_0_6076, 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),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),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_4810])). 6.97/7.22 fof(c_0_6077, plain, ![X12086, X12087, X12088, X12089, X12090, X12091]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X12091,X12091)),hAPP(hAPP(c_Product__Type_OPair(X12091,X12091),X12090),X12089)),c_Transitive__Closure_Ortrancl(X12091,X12088)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X12091),tc_List_Olist(X12091))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X12091),tc_List_Olist(X12091)),X12087),X12086)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X12091),c_List_Olistrel1(X12091,X12088))))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X12091),tc_List_Olist(X12091))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X12091),tc_List_Olist(X12091)),hAPP(hAPP(c_List_Olist_OCons(X12091),X12090),X12087)),hAPP(hAPP(c_List_Olist_OCons(X12091),X12089),X12086))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X12091),c_List_Olistrel1(X12091,X12088)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__ConsI2])])). 6.97/7.22 cnf(c_0_6078, 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)),esk539_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),esk539_4(X2,X3,X4,X1)),X3))),X2)))), inference(split_conjunct,[status(thm)],[c_0_4864])). 6.97/7.22 fof(c_0_6079, plain, ![X16397, X16398, X16399, X16400, X16401]:((hBOOL(hAPP(hAPP(c_member(X16400),esk547_5(X16397,X16398,X16399,X16400,X16401)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16400,tc_HOL_Obool)),X16399),X16398)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16401),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16400,X16401),X16397),X16399)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16400,X16401),X16397),X16398))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16400,X16401),X16397),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16400,tc_HOL_Obool)),X16399),X16398))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16400),X16398))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16400),X16399))|~class_Groups_Ocomm__monoid__add(X16401))&(c_Groups_Ozero__class_Ozero(X16401)!=hAPP(X16397,esk547_5(X16397,X16398,X16399,X16400,X16401))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16401),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16400,X16401),X16397),X16399)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16400,X16401),X16397),X16398))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16400,X16401),X16397),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16400,tc_HOL_Obool)),X16399),X16398))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16400),X16398))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16400),X16399))|~class_Groups_Ocomm__monoid__add(X16401))), 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])])])])])). 6.97/7.22 fof(c_0_6080, plain, ![X3339, X3340, X3341, X3342, X3343]:((X3343!=c_Orderings_Obot__class_Obot(tc_fun(X3342,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3342,tc_fun(X3341,tc_HOL_Obool)),X3343),hAPP(hAPP(c_COMBC(X3342,tc_fun(X3341,tc_HOL_Obool),tc_fun(X3341,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3341,tc_HOL_Obool),tc_fun(tc_fun(X3341,tc_HOL_Obool),tc_fun(X3341,tc_HOL_Obool)),X3342),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3341,tc_HOL_Obool))),X3340)),X3339))=c_Orderings_Otop__class_Otop(tc_fun(X3341,tc_HOL_Obool)))&(X3343=c_Orderings_Obot__class_Obot(tc_fun(X3342,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3342,tc_fun(X3341,tc_HOL_Obool)),X3343),hAPP(hAPP(c_COMBC(X3342,tc_fun(X3341,tc_HOL_Obool),tc_fun(X3341,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3341,tc_HOL_Obool),tc_fun(tc_fun(X3341,tc_HOL_Obool),tc_fun(X3341,tc_HOL_Obool)),X3342),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3341,tc_HOL_Obool))),X3340)),X3339))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3341,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3342,tc_fun(X3341,tc_HOL_Obool)),X3343),X3340)),X3339))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__simps_I1_J])])). 6.97/7.22 cnf(c_0_6081, 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_4847])). 6.97/7.22 fof(c_0_6082, plain, ![X5129, X5130, X5131, X5132, X5133]:((hBOOL(hAPP(hAPP(c_member(X5132),esk166_5(X5129,X5130,X5131,X5132,X5133)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5132,tc_HOL_Obool)),X5131),X5130)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5132,X5133),X5129),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5132,tc_HOL_Obool)),X5131),X5130))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5133),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5132,X5133),X5129),X5131)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5132,X5133),X5129),X5130))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5132),X5130))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5132),X5131))|~class_Groups_Ocomm__monoid__mult(X5133))&(c_Groups_Oone__class_Oone(X5133)!=hAPP(X5129,esk166_5(X5129,X5130,X5131,X5132,X5133))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5132,X5133),X5129),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5132,tc_HOL_Obool)),X5131),X5130))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5133),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5132,X5133),X5129),X5131)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5132,X5133),X5129),X5130))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5132),X5130))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5132),X5131))|~class_Groups_Ocomm__monoid__mult(X5133))), 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])])])])])). 6.97/7.22 fof(c_0_6083, plain, ![X5031, X5032, X5033, X5034, X5035]:((hBOOL(hAPP(hAPP(c_member(X5034),esk161_5(X5031,X5032,X5033,X5034,X5035)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5034,tc_HOL_Obool)),X5033),X5032)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5034,X5035),X5031),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5034,tc_HOL_Obool)),X5033),X5032))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5035),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5034,X5035),X5031),X5033)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5034,X5035),X5031),X5032))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5034),X5032))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5034),X5033))|~class_Groups_Ocomm__monoid__mult(X5035))&(c_Groups_Oone__class_Oone(X5035)!=hAPP(X5031,esk161_5(X5031,X5032,X5033,X5034,X5035))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5034,X5035),X5031),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5034,tc_HOL_Obool)),X5033),X5032))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5035),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5034,X5035),X5031),X5033)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5034,X5035),X5031),X5032))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5034),X5032))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5034),X5033))|~class_Groups_Ocomm__monoid__mult(X5035))), 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])])])])])). 6.97/7.22 cnf(c_0_6084, 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_4865])). 6.97/7.22 cnf(c_0_6085, 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_4866])). 6.97/7.22 cnf(c_0_6086, 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_4867]), ['final']). 6.97/7.22 fof(c_0_6087, plain, ![X2635, X2636, X2637, X2638, X2639]:((hBOOL(hAPP(hAPP(c_member(X2638),esk85_5(X2635,X2636,X2637,X2638,X2639)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2638,tc_HOL_Obool)),X2637),X2636)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2638,X2639),X2635),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2638,tc_HOL_Obool)),X2637),X2636))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2639),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2638,X2639),X2635),X2637)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2638,X2639),X2635),X2636))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2638),X2636))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2638),X2637))|~class_Groups_Ocomm__monoid__add(X2639))&(c_Groups_Ozero__class_Ozero(X2639)!=hAPP(X2635,esk85_5(X2635,X2636,X2637,X2638,X2639))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2638,X2639),X2635),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2638,tc_HOL_Obool)),X2637),X2636))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2639),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2638,X2639),X2635),X2637)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2638,X2639),X2635),X2636))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2638),X2636))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2638),X2637))|~class_Groups_Ocomm__monoid__add(X2639))), 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])])])])])). 6.97/7.22 fof(c_0_6088, plain, ![X4822, X4823, X4824, X4825, X4826, X4827, X4828, X4829]:((hBOOL(hAPP(hAPP(c_member(X4825),esk158_8(X4822,X4823,X4824,X4825,X4826,X4827,X4828,X4829)),X4824))|(~hBOOL(hAPP(hAPP(c_member(X4825),X4822),X4824))|hAPP(c_Set_Oimage(X4829,X4828,X4827),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4825,tc_fun(X4829,tc_HOL_Obool)),X4824),X4823))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4825,tc_fun(X4828,tc_HOL_Obool)),X4824),hAPP(hAPP(c_COMBB(tc_fun(X4829,tc_HOL_Obool),tc_fun(X4828,tc_HOL_Obool),X4825),c_Set_Oimage(X4829,X4828,X4827)),X4823)))|~c_Fun_Oinj__on(X4829,X4828,X4827,X4826))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4829,tc_HOL_Obool)),hAPP(X4823,esk158_8(X4822,X4823,X4824,X4825,X4826,X4827,X4828,X4829))),X4826))|(~hBOOL(hAPP(hAPP(c_member(X4825),X4822),X4824))|hAPP(c_Set_Oimage(X4829,X4828,X4827),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4825,tc_fun(X4829,tc_HOL_Obool)),X4824),X4823))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4825,tc_fun(X4828,tc_HOL_Obool)),X4824),hAPP(hAPP(c_COMBB(tc_fun(X4829,tc_HOL_Obool),tc_fun(X4828,tc_HOL_Obool),X4825),c_Set_Oimage(X4829,X4828,X4827)),X4823)))|~c_Fun_Oinj__on(X4829,X4828,X4827,X4826))), 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])])])])])). 6.97/7.22 cnf(c_0_6089, plain, (X3=X2|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)))),esk599_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_4868])). 6.97/7.22 cnf(c_0_6090, 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)))),esk598_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_4869])). 6.97/7.22 fof(c_0_6091, plain, ![X9554, X9555, X9556, X9557, X9558]:((X9558=c_Orderings_Obot__class_Obot(tc_fun(X9557,tc_HOL_Obool))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9556,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X9557,tc_fun(X9556,tc_HOL_Obool)),X9558),X9555)),X9554)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X9557,tc_fun(X9556,tc_HOL_Obool)),X9558),hAPP(hAPP(c_COMBC(X9557,tc_fun(X9556,tc_HOL_Obool),tc_fun(X9556,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9556,tc_HOL_Obool),tc_fun(tc_fun(X9556,tc_HOL_Obool),tc_fun(X9556,tc_HOL_Obool)),X9557),c_Groups_Ominus__class_Ominus(tc_fun(X9556,tc_HOL_Obool))),X9555)),X9554)))&(c_Orderings_Obot__class_Obot(tc_fun(X9557,tc_HOL_Obool))!=X9558|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9556,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X9556,tc_HOL_Obool))),X9554)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9556,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X9557,tc_fun(X9556,tc_HOL_Obool)),X9558),X9555)),X9554))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INT__extend__simps_I3_J])])])). 6.97/7.22 cnf(c_0_6092, plain, (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)))=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_Ominus__class_Ominus(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),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)],[c_0_4870, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.22 cnf(c_0_6093, 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_4858])). 6.97/7.22 cnf(c_0_6094, 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(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),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_4860])). 6.97/7.22 cnf(c_0_6095, plain, (c_Divides_OposDivAlg(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),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)],[inference(rw,[status(thm)],[c_0_4871, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_6096, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),X2)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),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)],[c_0_4872, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_6097, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),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)),c_Int_OMin)),c_Int_OMin))=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_4873, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4742]), ['final']). 6.97/7.22 cnf(c_0_6098, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4874, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_6099, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4875, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_6100, plain, (c_Groups_Ozero__class_Ozero(X1)!=X3|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_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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[c_0_4876, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_6101, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[c_0_4877, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 fof(c_0_6102, plain, ![X15088, X15089, X15090, X15091, X15092]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X15092,X15092)),hAPP(hAPP(c_Product__Type_OPair(X15092,X15092),X15091),esk509_5(X15088,X15089,X15090,X15091,X15092))),c_Transitive__Closure_Ortrancl(X15092,X15089)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X15092,X15092)),hAPP(hAPP(c_Product__Type_OPair(X15092,X15092),X15091),X15090)),c_Transitive__Closure_Ortrancl(X15092,X15089)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X15092,X15092)),hAPP(hAPP(c_Product__Type_OPair(X15092,X15092),X15091),X15090)),c_Transitive__Closure_Ortrancl(X15092,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X15092,X15092),tc_HOL_Obool)),X15089),X15088)))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X15092,X15092)),hAPP(hAPP(c_Product__Type_OPair(X15092,X15092),esk509_5(X15088,X15089,X15090,X15091,X15092)),esk510_5(X15088,X15089,X15090,X15091,X15092))),X15088))|hBOOL(hAPP(hAPP(c_member(tc_prod(X15092,X15092)),hAPP(hAPP(c_Product__Type_OPair(X15092,X15092),X15091),X15090)),c_Transitive__Closure_Ortrancl(X15092,X15089)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X15092,X15092)),hAPP(hAPP(c_Product__Type_OPair(X15092,X15092),X15091),X15090)),c_Transitive__Closure_Ortrancl(X15092,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X15092,X15092),tc_HOL_Obool)),X15089),X15088)))))&(esk509_5(X15088,X15089,X15090,X15091,X15092)!=esk510_5(X15088,X15089,X15090,X15091,X15092)|hBOOL(hAPP(hAPP(c_member(tc_prod(X15092,X15092)),hAPP(hAPP(c_Product__Type_OPair(X15092,X15092),X15091),X15090)),c_Transitive__Closure_Ortrancl(X15092,X15089)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X15092,X15092)),hAPP(hAPP(c_Product__Type_OPair(X15092,X15092),X15091),X15090)),c_Transitive__Closure_Ortrancl(X15092,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X15092,X15092),tc_HOL_Obool)),X15089),X15088))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rtrancl__Un__separatorE])])])])])). 6.97/7.22 fof(c_0_6103, plain, ![X2939, X2940, X2941, X2942, X2943]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X2943,X2943)),hAPP(hAPP(c_Product__Type_OPair(X2943,X2943),esk96_5(X2939,X2940,X2941,X2942,X2943)),X2941)),c_Transitive__Closure_Ortrancl(X2943,X2940)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X2943,X2943)),hAPP(hAPP(c_Product__Type_OPair(X2943,X2943),X2942),X2941)),c_Transitive__Closure_Ortrancl(X2943,X2940)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2943,X2943)),hAPP(hAPP(c_Product__Type_OPair(X2943,X2943),X2942),X2941)),c_Transitive__Closure_Ortrancl(X2943,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2943,X2943),tc_HOL_Obool)),X2940),X2939)))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X2943,X2943)),hAPP(hAPP(c_Product__Type_OPair(X2943,X2943),esk97_5(X2939,X2940,X2941,X2942,X2943)),esk96_5(X2939,X2940,X2941,X2942,X2943))),X2939))|hBOOL(hAPP(hAPP(c_member(tc_prod(X2943,X2943)),hAPP(hAPP(c_Product__Type_OPair(X2943,X2943),X2942),X2941)),c_Transitive__Closure_Ortrancl(X2943,X2940)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2943,X2943)),hAPP(hAPP(c_Product__Type_OPair(X2943,X2943),X2942),X2941)),c_Transitive__Closure_Ortrancl(X2943,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2943,X2943),tc_HOL_Obool)),X2940),X2939)))))&(esk97_5(X2939,X2940,X2941,X2942,X2943)!=esk96_5(X2939,X2940,X2941,X2942,X2943)|hBOOL(hAPP(hAPP(c_member(tc_prod(X2943,X2943)),hAPP(hAPP(c_Product__Type_OPair(X2943,X2943),X2942),X2941)),c_Transitive__Closure_Ortrancl(X2943,X2940)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2943,X2943)),hAPP(hAPP(c_Product__Type_OPair(X2943,X2943),X2942),X2941)),c_Transitive__Closure_Ortrancl(X2943,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2943,X2943),tc_HOL_Obool)),X2940),X2939))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rtrancl__Un__separator__converseE])])])])])). 6.97/7.22 cnf(c_0_6104, 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_4878])). 6.97/7.22 cnf(c_0_6105, 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(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4))),X2))=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(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4))),X4))|hBOOL(hAPP(X5,hAPP(hAPP(c_List_Ozip(X1,X3),X2),X4)))), inference(split_conjunct,[status(thm)],[c_0_4879])). 6.97/7.22 cnf(c_0_6106, 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_4880, c_0_4881]), ['final']). 6.97/7.22 fof(c_0_6107, plain, ![X13815, X13816, X13817, X13818]:(((hBOOL(hAPP(hAPP(c_member(tc_fun(X13817,tc_HOL_Obool)),esk465_4(X13815,X13816,X13817,X13818)),X13816))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13817,X13818),X13815),c_Complete__Lattice_OSup__class_OSup(tc_fun(X13817,tc_HOL_Obool),X13816))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X13817,tc_HOL_Obool),X13818),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13817,X13818),X13815)),X13816)|hBOOL(hAPP(hAPP(c_member(tc_fun(X13817,tc_HOL_Obool)),esk464_4(X13815,X13816,X13817,X13818)),X13816))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X13817,tc_HOL_Obool)),X13816))|~class_Groups_Ocomm__monoid__add(X13818))&((hBOOL(hAPP(hAPP(c_member(tc_fun(X13817,tc_HOL_Obool)),esk466_4(X13815,X13816,X13817,X13818)),X13816))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13817,X13818),X13815),c_Complete__Lattice_OSup__class_OSup(tc_fun(X13817,tc_HOL_Obool),X13816))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X13817,tc_HOL_Obool),X13818),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13817,X13818),X13815)),X13816)|hBOOL(hAPP(hAPP(c_member(tc_fun(X13817,tc_HOL_Obool)),esk464_4(X13815,X13816,X13817,X13818)),X13816))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X13817,tc_HOL_Obool)),X13816))|~class_Groups_Ocomm__monoid__add(X13818))&((esk466_4(X13815,X13816,X13817,X13818)!=esk465_4(X13815,X13816,X13817,X13818)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13817,X13818),X13815),c_Complete__Lattice_OSup__class_OSup(tc_fun(X13817,tc_HOL_Obool),X13816))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X13817,tc_HOL_Obool),X13818),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13817,X13818),X13815)),X13816)|hBOOL(hAPP(hAPP(c_member(tc_fun(X13817,tc_HOL_Obool)),esk464_4(X13815,X13816,X13817,X13818)),X13816))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X13817,tc_HOL_Obool)),X13816))|~class_Groups_Ocomm__monoid__add(X13818))&((hBOOL(hAPP(hAPP(c_member(X13817),esk467_4(X13815,X13816,X13817,X13818)),esk465_4(X13815,X13816,X13817,X13818)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13817,X13818),X13815),c_Complete__Lattice_OSup__class_OSup(tc_fun(X13817,tc_HOL_Obool),X13816))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X13817,tc_HOL_Obool),X13818),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13817,X13818),X13815)),X13816)|hBOOL(hAPP(hAPP(c_member(tc_fun(X13817,tc_HOL_Obool)),esk464_4(X13815,X13816,X13817,X13818)),X13816))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X13817,tc_HOL_Obool)),X13816))|~class_Groups_Ocomm__monoid__add(X13818))&((hBOOL(hAPP(hAPP(c_member(X13817),esk467_4(X13815,X13816,X13817,X13818)),esk466_4(X13815,X13816,X13817,X13818)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13817,X13818),X13815),c_Complete__Lattice_OSup__class_OSup(tc_fun(X13817,tc_HOL_Obool),X13816))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X13817,tc_HOL_Obool),X13818),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13817,X13818),X13815)),X13816)|hBOOL(hAPP(hAPP(c_member(tc_fun(X13817,tc_HOL_Obool)),esk464_4(X13815,X13816,X13817,X13818)),X13816))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X13817,tc_HOL_Obool)),X13816))|~class_Groups_Ocomm__monoid__add(X13818))&(c_Groups_Ozero__class_Ozero(X13818)!=hAPP(X13815,esk467_4(X13815,X13816,X13817,X13818))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13817,X13818),X13815),c_Complete__Lattice_OSup__class_OSup(tc_fun(X13817,tc_HOL_Obool),X13816))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X13817,tc_HOL_Obool),X13818),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13817,X13818),X13815)),X13816)|hBOOL(hAPP(hAPP(c_member(tc_fun(X13817,tc_HOL_Obool)),esk464_4(X13815,X13816,X13817,X13818)),X13816))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X13817,tc_HOL_Obool)),X13816))|~class_Groups_Ocomm__monoid__add(X13818)))))))&((hBOOL(hAPP(hAPP(c_member(tc_fun(X13817,tc_HOL_Obool)),esk465_4(X13815,X13816,X13817,X13818)),X13816))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13817,X13818),X13815),c_Complete__Lattice_OSup__class_OSup(tc_fun(X13817,tc_HOL_Obool),X13816))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X13817,tc_HOL_Obool),X13818),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13817,X13818),X13815)),X13816)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13817),esk464_4(X13815,X13816,X13817,X13818)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X13817,tc_HOL_Obool)),X13816))|~class_Groups_Ocomm__monoid__add(X13818))&((hBOOL(hAPP(hAPP(c_member(tc_fun(X13817,tc_HOL_Obool)),esk466_4(X13815,X13816,X13817,X13818)),X13816))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13817,X13818),X13815),c_Complete__Lattice_OSup__class_OSup(tc_fun(X13817,tc_HOL_Obool),X13816))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X13817,tc_HOL_Obool),X13818),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13817,X13818),X13815)),X13816)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13817),esk464_4(X13815,X13816,X13817,X13818)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X13817,tc_HOL_Obool)),X13816))|~class_Groups_Ocomm__monoid__add(X13818))&((esk466_4(X13815,X13816,X13817,X13818)!=esk465_4(X13815,X13816,X13817,X13818)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13817,X13818),X13815),c_Complete__Lattice_OSup__class_OSup(tc_fun(X13817,tc_HOL_Obool),X13816))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X13817,tc_HOL_Obool),X13818),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13817,X13818),X13815)),X13816)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13817),esk464_4(X13815,X13816,X13817,X13818)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X13817,tc_HOL_Obool)),X13816))|~class_Groups_Ocomm__monoid__add(X13818))&((hBOOL(hAPP(hAPP(c_member(X13817),esk467_4(X13815,X13816,X13817,X13818)),esk465_4(X13815,X13816,X13817,X13818)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13817,X13818),X13815),c_Complete__Lattice_OSup__class_OSup(tc_fun(X13817,tc_HOL_Obool),X13816))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X13817,tc_HOL_Obool),X13818),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13817,X13818),X13815)),X13816)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13817),esk464_4(X13815,X13816,X13817,X13818)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X13817,tc_HOL_Obool)),X13816))|~class_Groups_Ocomm__monoid__add(X13818))&((hBOOL(hAPP(hAPP(c_member(X13817),esk467_4(X13815,X13816,X13817,X13818)),esk466_4(X13815,X13816,X13817,X13818)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13817,X13818),X13815),c_Complete__Lattice_OSup__class_OSup(tc_fun(X13817,tc_HOL_Obool),X13816))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X13817,tc_HOL_Obool),X13818),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13817,X13818),X13815)),X13816)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13817),esk464_4(X13815,X13816,X13817,X13818)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X13817,tc_HOL_Obool)),X13816))|~class_Groups_Ocomm__monoid__add(X13818))&(c_Groups_Ozero__class_Ozero(X13818)!=hAPP(X13815,esk467_4(X13815,X13816,X13817,X13818))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13817,X13818),X13815),c_Complete__Lattice_OSup__class_OSup(tc_fun(X13817,tc_HOL_Obool),X13816))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X13817,tc_HOL_Obool),X13818),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13817,X13818),X13815)),X13816)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13817),esk464_4(X13815,X13816,X13817,X13818)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X13817,tc_HOL_Obool)),X13816))|~class_Groups_Ocomm__monoid__add(X13818)))))))), 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])])])])])). 6.97/7.22 cnf(c_0_6108, 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_4882])). 6.97/7.22 fof(c_0_6109, plain, ![X17276, X17277, X17278, X17279, X17280, X17281]:((((X17277=X17279|hBOOL(hAPP(hAPP(c_member(tc_prod(X17281,X17281)),hAPP(hAPP(c_Product__Type_OPair(X17281,X17281),X17279),X17277)),X17276))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17281),tc_List_Olist(X17281))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17281),tc_List_Olist(X17281)),hAPP(hAPP(c_List_Oappend(X17281),X17280),hAPP(hAPP(c_List_Olist_OCons(X17281),X17279),c_List_Olist_ONil(X17281)))),hAPP(hAPP(c_List_Oappend(X17281),X17278),hAPP(hAPP(c_List_Olist_OCons(X17281),X17277),c_List_Olist_ONil(X17281))))),c_List_Olistrel1(X17281,X17276))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17281),tc_List_Olist(X17281))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17281),tc_List_Olist(X17281)),X17280),X17278)),c_List_Olistrel1(X17281,X17276)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X17281,X17281)),hAPP(hAPP(c_Product__Type_OPair(X17281,X17281),X17279),X17277)),X17276))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17281),tc_List_Olist(X17281))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17281),tc_List_Olist(X17281)),hAPP(hAPP(c_List_Oappend(X17281),X17280),hAPP(hAPP(c_List_Olist_OCons(X17281),X17279),c_List_Olist_ONil(X17281)))),hAPP(hAPP(c_List_Oappend(X17281),X17278),hAPP(hAPP(c_List_Olist_OCons(X17281),X17277),c_List_Olist_ONil(X17281))))),c_List_Olistrel1(X17281,X17276)))))&((X17277=X17279|X17280=X17278|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17281),tc_List_Olist(X17281))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17281),tc_List_Olist(X17281)),hAPP(hAPP(c_List_Oappend(X17281),X17280),hAPP(hAPP(c_List_Olist_OCons(X17281),X17279),c_List_Olist_ONil(X17281)))),hAPP(hAPP(c_List_Oappend(X17281),X17278),hAPP(hAPP(c_List_Olist_OCons(X17281),X17277),c_List_Olist_ONil(X17281))))),c_List_Olistrel1(X17281,X17276))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17281),tc_List_Olist(X17281))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17281),tc_List_Olist(X17281)),X17280),X17278)),c_List_Olistrel1(X17281,X17276)))|X17280=X17278|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17281),tc_List_Olist(X17281))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17281),tc_List_Olist(X17281)),hAPP(hAPP(c_List_Oappend(X17281),X17280),hAPP(hAPP(c_List_Olist_OCons(X17281),X17279),c_List_Olist_ONil(X17281)))),hAPP(hAPP(c_List_Oappend(X17281),X17278),hAPP(hAPP(c_List_Olist_OCons(X17281),X17277),c_List_Olist_ONil(X17281))))),c_List_Olistrel1(X17281,X17276))))))&((~hBOOL(hAPP(hAPP(c_member(tc_prod(X17281,X17281)),hAPP(hAPP(c_Product__Type_OPair(X17281,X17281),X17279),X17277)),X17276))|X17280!=X17278|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17281),tc_List_Olist(X17281))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17281),tc_List_Olist(X17281)),hAPP(hAPP(c_List_Oappend(X17281),X17280),hAPP(hAPP(c_List_Olist_OCons(X17281),X17279),c_List_Olist_ONil(X17281)))),hAPP(hAPP(c_List_Oappend(X17281),X17278),hAPP(hAPP(c_List_Olist_OCons(X17281),X17277),c_List_Olist_ONil(X17281))))),c_List_Olistrel1(X17281,X17276))))&(X17277!=X17279|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17281),tc_List_Olist(X17281))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17281),tc_List_Olist(X17281)),X17280),X17278)),c_List_Olistrel1(X17281,X17276)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17281),tc_List_Olist(X17281))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17281),tc_List_Olist(X17281)),hAPP(hAPP(c_List_Oappend(X17281),X17280),hAPP(hAPP(c_List_Olist_OCons(X17281),X17279),c_List_Olist_ONil(X17281)))),hAPP(hAPP(c_List_Oappend(X17281),X17278),hAPP(hAPP(c_List_Olist_OCons(X17281),X17277),c_List_Olist_ONil(X17281))))),c_List_Olistrel1(X17281,X17276)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snoc__listrel1__snoc__iff])])])). 6.97/7.22 fof(c_0_6110, plain, ![X3667, X3668, X3669, X3670, X3671]:(~class_Groups_Oab__group__add(X3671)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3670),X3669))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3670),X3668))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3671),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3671),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3670,X3671),X3667),X3669)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3670,X3671),X3667),X3668))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3670,X3671),X3667),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3670,tc_HOL_Obool)),X3669),X3668)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3670,X3671),X3667),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3670,tc_HOL_Obool)),X3669),X3668))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__Un])])])). 6.97/7.22 fof(c_0_6111, plain, ![X5462, X5463, X5464, X5465]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5465),X5464))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5465),X5463))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5465,tc_Nat_Onat),X5462),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5465,tc_HOL_Obool)),X5464),X5463))=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(X5465,tc_Nat_Onat),X5462),X5464)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5465,tc_Nat_Onat),X5462),X5463))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5465,tc_Nat_Onat),X5462),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5465,tc_HOL_Obool)),X5464),X5463))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__Un__nat])])])). 6.97/7.22 fof(c_0_6112, plain, ![X8847, X8848, X8849, X8850, X8851]:(~class_Groups_Ocomm__monoid__add(X8851)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8850),X8849))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8850),X8848))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8851),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8850,X8851),X8847),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8850,tc_HOL_Obool)),X8849),X8848))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8850,X8851),X8847),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8850,tc_HOL_Obool)),X8849),X8848)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8851),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8850,X8851),X8847),X8849)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8850,X8851),X8847),X8848))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Un__Int])])). 6.97/7.22 cnf(c_0_6113, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[c_0_4883, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 fof(c_0_6114, plain, ![X10410, X10411, X10412, X10413, X10414]:(~class_Groups_Ocomm__monoid__mult(X10414)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10413),X10412))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10413),X10411))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10414),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10413,X10414),X10410),X10412)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10413,X10414),X10410),X10411))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10414),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10413,X10414),X10410),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10413,tc_HOL_Obool)),X10412),X10411))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10413,X10414),X10410),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10413,tc_HOL_Obool)),X10412),X10411)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__Un__Int])])])). 6.97/7.22 cnf(c_0_6115, 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)))),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)|~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_4884])). 6.97/7.22 cnf(c_0_6116, 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_4885]), ['final']). 6.97/7.22 cnf(c_0_6117, 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_4885]), ['final']). 6.97/7.22 fof(c_0_6118, plain, ![X4141, X4142, X4143]:(~class_Orderings_Olinorder(X4143)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4143),X4142))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4143),X4141))|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4143,tc_HOL_Obool)),X4142),X4141)=c_Orderings_Obot__class_Obot(tc_fun(X4143,tc_HOL_Obool))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X4143),c_Big__Operators_Olattice_OSup__fin(X4143,c_Orderings_Oord__class_Omax(X4143),X4142)),c_Big__Operators_Olattice_OSup__fin(X4143,c_Orderings_Oord__class_Omax(X4143),X4141))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4143),c_Big__Operators_Olattice_OSup__fin(X4143,c_Orderings_Oord__class_Omax(X4143),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4143,tc_HOL_Obool)),X4142),X4141))),c_Big__Operators_Olattice_OSup__fin(X4143,c_Orderings_Oord__class_Omax(X4143),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4143,tc_HOL_Obool)),X4142),X4141))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Ounion__inter])])])). 6.97/7.22 fof(c_0_6119, plain, ![X16010, X16011, X16012, X16013, X16014, X16015, X16016, X16017]:((hBOOL(hAPP(hAPP(c_member(X16016),esk541_7(X16010,X16011,X16012,X16013,X16014,X16015,X16016)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16016,tc_HOL_Obool)),X16011),X16010)))|hAPP(X16012,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16016,tc_HOL_Obool)),X16011),X16010))=hAPP(hAPP(X16015,hAPP(X16012,X16011)),hAPP(X16012,X16010))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16016),X16010))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16016),X16011))|~c_Finite__Set_Ofolding__image__simple(X16017,X16016,X16015,X16014,X16013,X16012))&(hAPP(X16013,esk541_7(X16010,X16011,X16012,X16013,X16014,X16015,X16016))!=X16014|hAPP(X16012,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16016,tc_HOL_Obool)),X16011),X16010))=hAPP(hAPP(X16015,hAPP(X16012,X16011)),hAPP(X16012,X16010))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16016),X16010))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16016),X16011))|~c_Finite__Set_Ofolding__image__simple(X16017,X16016,X16015,X16014,X16013,X16012))), 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])])])])])])])). 6.97/7.22 cnf(c_0_6120, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[c_0_4886, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_6121, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4887, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 fof(c_0_6122, plain, ![X10197, X10198, X10199, X10200, X10201]:(~class_Groups_Ocomm__monoid__mult(X10201)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10200),X10199))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10200),X10198))|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10200,tc_HOL_Obool)),X10199),X10198)!=c_Orderings_Obot__class_Obot(tc_fun(X10200,tc_HOL_Obool))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10201),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X10201,X10200,c_Groups_Otimes__class_Otimes(X10201)),X10197),c_Groups_Oone__class_Oone(X10201)),X10199)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X10201,X10200,c_Groups_Otimes__class_Otimes(X10201)),X10197),c_Groups_Oone__class_Oone(X10201)),X10198))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X10201,X10200,c_Groups_Otimes__class_Otimes(X10201)),X10197),c_Groups_Oone__class_Oone(X10201)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10200,tc_HOL_Obool)),X10199),X10198)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__Un__disjoint])])])). 6.97/7.22 fof(c_0_6123, plain, ![X10898, X10899, X10900]:(~class_Orderings_Olinorder(X10900)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10900),X10899))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10900),X10898))|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10900,tc_HOL_Obool)),X10899),X10898)=c_Orderings_Obot__class_Obot(tc_fun(X10900,tc_HOL_Obool))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X10900),c_Big__Operators_Olattice_OInf__fin(X10900,c_Orderings_Oord__class_Omin(X10900),X10899)),c_Big__Operators_Olattice_OInf__fin(X10900,c_Orderings_Oord__class_Omin(X10900),X10898))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X10900),c_Big__Operators_Olattice_OInf__fin(X10900,c_Orderings_Oord__class_Omin(X10900),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10900,tc_HOL_Obool)),X10899),X10898))),c_Big__Operators_Olattice_OInf__fin(X10900,c_Orderings_Oord__class_Omin(X10900),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10900,tc_HOL_Obool)),X10899),X10898))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Ounion__inter])])])). 6.97/7.22 cnf(c_0_6124, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[c_0_4888, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_6125, 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),esk202_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_4889])). 6.97/7.22 cnf(c_0_6126, 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_4889])). 6.97/7.22 cnf(c_0_6127, 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_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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4890, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_6128, 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_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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4891, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.22 fof(c_0_6129, plain, ![X9744, X9745, X9746, X9747, X9749]:((hBOOL(hAPP(hAPP(c_member(X9747),esk321_4(X9744,X9745,X9746,X9747)),X9746))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X9747,tc_HOL_Obool),tc_fun(X9747,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X9747,tc_HOL_Obool),tc_fun(X9747,tc_HOL_Obool)),X9746),X9745)),c_Wellfounded_Omax__ext(X9747,X9744)))|c_Orderings_Obot__class_Obot(tc_fun(X9747,tc_HOL_Obool))=X9745|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9747),X9745))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9747),X9746)))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X9747,X9747)),hAPP(hAPP(c_Product__Type_OPair(X9747,X9747),esk321_4(X9744,X9745,X9746,X9747)),X9749)),X9744))|~hBOOL(hAPP(hAPP(c_member(X9747),X9749),X9745))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X9747,tc_HOL_Obool),tc_fun(X9747,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X9747,tc_HOL_Obool),tc_fun(X9747,tc_HOL_Obool)),X9746),X9745)),c_Wellfounded_Omax__ext(X9747,X9744)))|c_Orderings_Obot__class_Obot(tc_fun(X9747,tc_HOL_Obool))=X9745|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9747),X9745))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9747),X9746)))), 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])])])])])])). 6.97/7.22 cnf(c_0_6130, plain, (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)))=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))))|~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_4892])). 6.97/7.22 cnf(c_0_6131, plain, (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))=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))|~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_4893, c_0_4573]), c_0_4573])). 6.97/7.22 fof(c_0_6132, plain, ![X4404, X4405, X4406, X4407, X4408, X4409, X4410]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X4410,X4410)),hAPP(hAPP(c_Product__Type_OPair(X4410,X4410),X4409),X4408)),X4407))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4410),tc_List_Olist(X4410))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4410),tc_List_Olist(X4410)),hAPP(hAPP(c_List_Oappend(X4410),X4406),hAPP(hAPP(c_List_Olist_OCons(X4410),X4409),X4405))),hAPP(hAPP(c_List_Oappend(X4410),X4406),hAPP(hAPP(c_List_Olist_OCons(X4410),X4408),X4404)))),c_List_Olexord(X4410,X4407)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lexord__append__left__rightI])])])). 6.97/7.22 fof(c_0_6133, plain, ![X4518, X4519, X4520, X4521, X4522]:(~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X4522,X4521),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X4520),X4519)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4521))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4518))|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X4522,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4521),X4518)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X4520),X4518)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4521),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4520,X4518))),X4519))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__nat__rel__mult2__eq])])])). 6.97/7.22 fof(c_0_6134, plain, ![X9032, X9033, X9034]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9034),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X9033))),c_List_Otranspose(X9033,X9032))))|hAPP(hAPP(c_List_Onth(tc_List_Olist(X9033)),c_List_Otranspose(X9033,X9032)),X9034)=hAPP(hAPP(c_List_Omap(tc_List_Olist(X9033),X9033),hAPP(hAPP(c_COMBC(tc_List_Olist(X9033),tc_Nat_Onat,X9033),c_List_Onth(X9033)),X9034)),hAPP(c_List_Ofilter(tc_List_Olist(X9033),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X9033)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9034)),c_Nat_Osize__class_Osize(tc_List_Olist(X9033)))),X9032))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__transpose])])). 6.97/7.22 fof(c_0_6135, plain, ![X17634, X17635, X17636, X17637, X17638]:(~class_Groups_Ocomm__monoid__add(X17638)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X17638),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X17638,tc_Nat_Onat),X17637),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X17635))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X17636),X17634))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X17638),X17637),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17636),X17635)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17634),X17635)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__nat__ivl])])). 6.97/7.22 fof(c_0_6136, plain, ![X12704, X12705, X12706, X12707, X12708, X12709, X12710]:(~hBOOL(hAPP(X12710,X12709))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X12708,X12708)),hAPP(hAPP(c_Product__Type_OPair(X12708,X12708),X12707),X12706)),hAPP(X12705,X12709)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X12704,X12708),tc_prod(X12704,X12708))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X12704,X12708),tc_prod(X12704,X12708)),hAPP(hAPP(c_Product__Type_OPair(X12704,X12708),X12709),X12707)),hAPP(hAPP(c_Product__Type_OPair(X12704,X12708),X12709),X12706))),c_Recdef_Osame__fst(X12704,X12708,X12710,X12705))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__fstI])])). 6.97/7.22 fof(c_0_6137, plain, ![X16101, X16102, X16103, X16104, X16105, X16106]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X16106,X16106)),hAPP(hAPP(c_Product__Type_OPair(X16106,X16106),X16105),X16104)),X16103))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X16106,X16106)),hAPP(hAPP(c_Product__Type_OPair(X16106,X16106),X16104),X16102)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X16106,X16106),tc_HOL_Obool),X16101),X16103)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X16106,X16106)),hAPP(hAPP(c_Product__Type_OPair(X16106,X16106),X16105),X16102)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X16106,X16106),tc_HOL_Obool),hAPP(c_Nat_OSuc,X16101)),X16103))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rel__pow__Suc__I2])])])). 6.97/7.22 cnf(c_0_6138, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[c_0_4894, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_6139, 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(c_fequal,X2))),X5)),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_4895])). 6.97/7.22 cnf(c_0_6140, 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(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_4896])). 6.97/7.22 fof(c_0_6141, plain, ![X10589, X10590, X10591, X10592]:(((~hBOOL(hAPP(hAPP(c_member(tc_prod(X10592,X10592)),hAPP(hAPP(c_Product__Type_OPair(X10592,X10592),esk347_4(X10589,X10590,X10591,X10592)),esk348_4(X10589,X10590,X10591,X10592))),X10591))|(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10592),tc_List_Olist(X10592))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10592),tc_List_Olist(X10592)),X10590),X10589)),c_List_Olexord(X10592,X10591)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10592),tc_List_Olist(X10592))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10592),tc_List_Olist(X10592)),X10589),X10590)),c_List_Olexord(X10592,X10591)))|X10589=X10590))&(esk347_4(X10589,X10590,X10591,X10592)!=esk348_4(X10589,X10590,X10591,X10592)|(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10592),tc_List_Olist(X10592))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10592),tc_List_Olist(X10592)),X10590),X10589)),c_List_Olexord(X10592,X10591)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10592),tc_List_Olist(X10592))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10592),tc_List_Olist(X10592)),X10589),X10590)),c_List_Olexord(X10592,X10591)))|X10589=X10590)))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X10592,X10592)),hAPP(hAPP(c_Product__Type_OPair(X10592,X10592),esk348_4(X10589,X10590,X10591,X10592)),esk347_4(X10589,X10590,X10591,X10592))),X10591))|(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10592),tc_List_Olist(X10592))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10592),tc_List_Olist(X10592)),X10590),X10589)),c_List_Olexord(X10592,X10591)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10592),tc_List_Olist(X10592))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10592),tc_List_Olist(X10592)),X10589),X10590)),c_List_Olexord(X10592,X10591)))|X10589=X10590))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lexord__linear])])])])])). 6.97/7.22 cnf(c_0_6142, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[c_0_4897, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 fof(c_0_6143, plain, ![X13677, X13678, X13679, X13680, X13681, X13682]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X13682,X13682)),hAPP(hAPP(c_Product__Type_OPair(X13682,X13682),X13681),X13680)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X13682,X13682),tc_HOL_Obool),X13679),X13678)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X13682,X13682)),hAPP(hAPP(c_Product__Type_OPair(X13682,X13682),X13680),X13677)),X13678))|hBOOL(hAPP(hAPP(c_member(tc_prod(X13682,X13682)),hAPP(hAPP(c_Product__Type_OPair(X13682,X13682),X13681),X13677)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X13682,X13682),tc_HOL_Obool),hAPP(c_Nat_OSuc,X13679)),X13678))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rel__pow__Suc__I])])])). 6.97/7.22 cnf(c_0_6144, plain, (c_Orderings_Oord__class_OLeast(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),hAPP(c_Set_Oimage(X1,X5,X4),X3)))=hAPP(X4,c_Orderings_Oord__class_OLeast(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk554_5(X3,X4,X1,X5,X2)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~c_Orderings_Oorder__class_Omono(X1,X5,X4)|~class_Orderings_Oorder(X1)|~class_Orderings_Oorder(X5)), inference(split_conjunct,[status(thm)],[c_0_4863])). 6.97/7.22 fof(c_0_6145, plain, ![X4444, X4445, X4446, X4447, X4448]:(~class_Groups_Oordered__ab__group__add__abs(X4448)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4448),hAPP(c_Groups_Oabs__class_Oabs(X4448),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4448),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4448),X4447),X4446)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4448),X4445),X4444)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4448),hAPP(c_Groups_Oabs__class_Oabs(X4448),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4448),X4447),X4445))),hAPP(c_Groups_Oabs__class_Oabs(X4448),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4448),X4446),X4444)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__diff__triangle__ineq])])). 6.97/7.22 cnf(c_0_6146, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))))|~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)],[c_0_4898, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 fof(c_0_6147, plain, ![X2630, X2631, X2632, X2633, X2634]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2634),tc_List_Olist(X2634))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2634),tc_List_Olist(X2634)),X2633),X2632)),c_List_Olexord(X2634,X2631)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2634),tc_List_Olist(X2634))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2634),tc_List_Olist(X2634)),X2632),X2630)),c_List_Olexord(X2634,X2631)))|(~c_Relation_Otrans(X2634,X2631)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2634),tc_List_Olist(X2634))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2634),tc_List_Olist(X2634)),X2633),X2630)),c_List_Olexord(X2634,X2631)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lexord__trans])])])). 6.97/7.22 fof(c_0_6148, plain, ![X17460, X17461, X17462, X17463, X17464, X17465]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X17465,X17465)),hAPP(hAPP(c_Product__Type_OPair(X17465,X17465),X17464),X17463)),X17462))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17465),tc_List_Olist(X17465))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17465),tc_List_Olist(X17465)),X17461),X17460)),c_List_Olistrel(X17465,X17462)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17465),tc_List_Olist(X17465))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17465),tc_List_Olist(X17465)),hAPP(hAPP(c_List_Olist_OCons(X17465),X17464),X17461)),hAPP(hAPP(c_List_Olist_OCons(X17465),X17463),X17460))),c_List_Olistrel(X17465,X17462))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel_OCons])])])). 6.97/7.22 cnf(c_0_6149, plain, (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))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))),hAPP(c_Int_Onumber__class_Onumber__of(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)),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_4899, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411])). 6.97/7.22 fof(c_0_6150, plain, ![X1563, X1564, X1565]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1565,tc_HOL_Obool)),X1564),hAPP(hAPP(c_Set_Oinsert(X1565),X1563),c_Orderings_Obot__class_Obot(tc_fun(X1565,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1565,tc_HOL_Obool))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X1565),X1563),c_Big__Operators_Olattice_OInf__fin(X1565,c_Orderings_Oord__class_Omin(X1565),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1565,tc_HOL_Obool)),X1564),hAPP(hAPP(c_Set_Oinsert(X1565),X1563),c_Orderings_Obot__class_Obot(tc_fun(X1565,tc_HOL_Obool))))))=c_Big__Operators_Olattice_OInf__fin(X1565,c_Orderings_Oord__class_Omin(X1565),X1564)|~hBOOL(hAPP(hAPP(c_member(X1565),X1563),X1564))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1565),X1564))|~class_Orderings_Olinorder(X1565))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1565,tc_HOL_Obool)),X1564),hAPP(hAPP(c_Set_Oinsert(X1565),X1563),c_Orderings_Obot__class_Obot(tc_fun(X1565,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X1565,tc_HOL_Obool))|X1563=c_Big__Operators_Olattice_OInf__fin(X1565,c_Orderings_Oord__class_Omin(X1565),X1564)|~hBOOL(hAPP(hAPP(c_member(X1565),X1563),X1564))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1565),X1564))|~class_Orderings_Olinorder(X1565))), 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])])])])). 6.97/7.22 fof(c_0_6151, plain, ![X15378, X15379, X15380, X15381, X15382]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X15382,X15381),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X15380),X15379)))|(X15381=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)),X15378))|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X15382,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15381),X15378)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X15380),X15378)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15381),c_Divides_Odiv__class_Omod(tc_Int_Oint,X15380,X15378))),X15379))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmult2__lemma])])])). 6.97/7.22 fof(c_0_6152, plain, ![X7951, X7952, X7953, X7954, X7955]:((hBOOL(hAPP(hAPP(c_member(X7954),esk258_5(X7951,X7952,X7953,X7954,X7955)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7954,tc_HOL_Obool)),X7953),X7952)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7955),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7954,X7955),X7951),X7952)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7954,X7955),X7951),X7953)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7954,tc_HOL_Obool)),X7952),X7953))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7954),X7953))|(~class_Groups_Oordered__ab__semigroup__add(X7955)|~class_Groups_Ocomm__monoid__add(X7955)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7955),c_Groups_Ozero__class_Ozero(X7955)),hAPP(X7951,esk258_5(X7951,X7952,X7953,X7954,X7955))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7955),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7954,X7955),X7951),X7952)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7954,X7955),X7951),X7953)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7954,tc_HOL_Obool)),X7952),X7953))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7954),X7953))|(~class_Groups_Oordered__ab__semigroup__add(X7955)|~class_Groups_Ocomm__monoid__add(X7955)))), 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])])])])])). 6.97/7.22 cnf(c_0_6153, 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),X6),X2)),hAPP(hAPP(c_Product__Type_OPair(X7,X1),X5),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_4900])). 6.97/7.22 fof(c_0_6154, plain, ![X12569, X12570, X12571]:((c_Orderings_Obot__class_Obot(tc_fun(X12571,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12571,tc_HOL_Obool)),X12570),hAPP(hAPP(c_Set_Oinsert(X12571),X12569),c_Orderings_Obot__class_Obot(tc_fun(X12571,tc_HOL_Obool))))|c_Big__Operators_Olattice_OSup__fin(X12571,c_Orderings_Oord__class_Omax(X12571),X12570)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X12571),X12569),c_Big__Operators_Olattice_OSup__fin(X12571,c_Orderings_Oord__class_Omax(X12571),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12571,tc_HOL_Obool)),X12570),hAPP(hAPP(c_Set_Oinsert(X12571),X12569),c_Orderings_Obot__class_Obot(tc_fun(X12571,tc_HOL_Obool))))))|~hBOOL(hAPP(hAPP(c_member(X12571),X12569),X12570))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12571),X12570))|~class_Orderings_Olinorder(X12571))&(c_Orderings_Obot__class_Obot(tc_fun(X12571,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12571,tc_HOL_Obool)),X12570),hAPP(hAPP(c_Set_Oinsert(X12571),X12569),c_Orderings_Obot__class_Obot(tc_fun(X12571,tc_HOL_Obool))))|c_Big__Operators_Olattice_OSup__fin(X12571,c_Orderings_Oord__class_Omax(X12571),X12570)=X12569|~hBOOL(hAPP(hAPP(c_member(X12571),X12569),X12570))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12571),X12570))|~class_Orderings_Olinorder(X12571))), 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])])])])). 6.97/7.22 cnf(c_0_6155, plain, (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))))))=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))|~class_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_4901])). 6.97/7.22 fof(c_0_6156, plain, ![X8391, X8392, X8393, X8394, X8395]:(~class_Groups_Ocomm__monoid__add(X8395)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X8395),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X8395,tc_Nat_Onat),X8394),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X8392))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X8393,X8391))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X8395),X8394),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X8393),X8392),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X8391),X8392)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__shift__bounds__cl__nat__ivl])])])). 6.97/7.22 cnf(c_0_6157, plain, (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))=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))|~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_4902, c_0_4573]), c_0_4573])). 6.97/7.22 fof(c_0_6158, plain, ![X6189, X6190, X6191]:(~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X6191),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X6191))),X6190)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6189),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X6191))),X6190)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X6191))),hAPP(c_List_Ofilter(tc_List_Olist(X6191),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X6191)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6189)),c_Nat_Osize__class_Osize(tc_List_Olist(X6191)))),c_List_Otranspose(X6191,X6190)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6191)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X6191)),X6190),X6189)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transpose__column__length])])])). 6.97/7.22 cnf(c_0_6159, 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_4903])). 6.97/7.22 cnf(c_0_6160, 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_4904])). 6.97/7.22 fof(c_0_6161, plain, ![X6781, X6782, X6783, X6784, X6785, X6786, X6787, X6788]:((hBOOL(hAPP(hAPP(c_member(X6788),esk221_8(X6781,X6782,X6783,X6784,X6785,X6786,X6787,X6788)),hAPP(c_List_Oset(X6788),X6787)))|hAPP(c_List_Ofoldl(X6786,X6788,hAPP(c_COMBC(X6788,X6786,X6786),X6784),hAPP(X6783,X6781)),X6787)=hAPP(X6783,hAPP(c_List_Ofoldl(X6785,X6788,hAPP(c_COMBC(X6788,X6785,X6785),X6782),X6781),X6787)))&(hAPP(c_Fun_Ocomp(X6785,X6786,X6785,X6783),hAPP(X6782,esk221_8(X6781,X6782,X6783,X6784,X6785,X6786,X6787,X6788)))!=hAPP(c_Fun_Ocomp(X6786,X6786,X6785,hAPP(X6784,esk221_8(X6781,X6782,X6783,X6784,X6785,X6786,X6787,X6788))),X6783)|hAPP(c_List_Ofoldl(X6786,X6788,hAPP(c_COMBC(X6788,X6786,X6786),X6784),hAPP(X6783,X6781)),X6787)=hAPP(X6783,hAPP(c_List_Ofoldl(X6785,X6788,hAPP(c_COMBC(X6788,X6785,X6785),X6782),X6781),X6787)))), 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])])])])])). 6.97/7.22 cnf(c_0_6162, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[c_0_4905, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_6163, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))|c_Divides_Odivmod__nat(X2,X1)=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),X2),X1),X1))), inference(split_conjunct,[status(thm)],[c_0_4906])). 6.97/7.22 cnf(c_0_6164, plain, (c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2))=c_Divides_Odivmod__nat(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_4907])). 6.97/7.22 cnf(c_0_6165, 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),esk202_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_4889])). 6.97/7.22 fof(c_0_6166, plain, ![X12514, X12515, X12516, X12517, X12518]:((hBOOL(hAPP(hAPP(c_member(X12517),esk411_5(X12514,X12515,X12516,X12517,X12518)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12517,tc_HOL_Obool)),X12516),X12515)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12518),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12517,X12518),X12514),X12515)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12517,X12518),X12514),X12516)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12517,tc_HOL_Obool)),X12515),X12516))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12517),X12516))|~class_Groups_Oordered__comm__monoid__add(X12518))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12518),c_Groups_Ozero__class_Ozero(X12518)),hAPP(X12514,esk411_5(X12514,X12515,X12516,X12517,X12518))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12518),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12517,X12518),X12514),X12515)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12517,X12518),X12514),X12516)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12517,tc_HOL_Obool)),X12515),X12516))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12517),X12516))|~class_Groups_Oordered__comm__monoid__add(X12518))), 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])])])])])). 6.97/7.22 cnf(c_0_6167, plain, (X3=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk599_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))))|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_4868])). 6.97/7.22 cnf(c_0_6168, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk598_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_4869])). 6.97/7.22 fof(c_0_6169, plain, ![X7428, X7429, X7430]:((c_Orderings_Obot__class_Obot(tc_fun(X7430,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7430,tc_HOL_Obool)),X7429),hAPP(hAPP(c_Set_Oinsert(X7430),X7428),c_Orderings_Obot__class_Obot(tc_fun(X7430,tc_HOL_Obool))))|c_Big__Operators_Olattice_OSup__fin(X7430,c_Orderings_Oord__class_Omax(X7430),hAPP(hAPP(c_Set_Oinsert(X7430),X7428),X7429))=X7428|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7430),X7429))|~class_Orderings_Olinorder(X7430))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7430,tc_HOL_Obool)),X7429),hAPP(hAPP(c_Set_Oinsert(X7430),X7428),c_Orderings_Obot__class_Obot(tc_fun(X7430,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X7430,tc_HOL_Obool))|c_Big__Operators_Olattice_OSup__fin(X7430,c_Orderings_Oord__class_Omax(X7430),hAPP(hAPP(c_Set_Oinsert(X7430),X7428),X7429))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X7430),X7428),c_Big__Operators_Olattice_OSup__fin(X7430,c_Orderings_Oord__class_Omax(X7430),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7430,tc_HOL_Obool)),X7429),hAPP(hAPP(c_Set_Oinsert(X7430),X7428),c_Orderings_Obot__class_Obot(tc_fun(X7430,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7430),X7429))|~class_Orderings_Olinorder(X7430))), 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])])])])). 6.97/7.22 fof(c_0_6170, plain, ![X8629, X8630, X8631, X8632, X8633]:(~class_Fields_Ofield__inverse__zero(X8633)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8632),X8631))|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8633),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8632,X8633),X8630),X8631)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8632,X8633),X8629),X8631))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8632,X8633),hAPP(hAPP(c_COMBS(X8632,X8633,X8633),hAPP(hAPP(c_COMBB(X8633,tc_fun(X8633,X8633),X8632),c_Rings_Oinverse__class_Odivide(X8633)),X8630)),X8629)),X8631))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__dividef])])])). 6.97/7.22 cnf(c_0_6171, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk108_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_4908])). 6.97/7.22 cnf(c_0_6172, 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_4837])). 6.97/7.22 cnf(c_0_6173, 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_4909])). 6.97/7.22 fof(c_0_6174, plain, ![X3092, X3093, X3094]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3094,tc_HOL_Obool)),X3093),hAPP(hAPP(c_Set_Oinsert(X3094),X3092),c_Orderings_Obot__class_Obot(tc_fun(X3094,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X3094,tc_HOL_Obool))|c_Big__Operators_Olattice_OInf__fin(X3094,c_Orderings_Oord__class_Omin(X3094),hAPP(hAPP(c_Set_Oinsert(X3094),X3092),X3093))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X3094),X3092),c_Big__Operators_Olattice_OInf__fin(X3094,c_Orderings_Oord__class_Omin(X3094),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3094,tc_HOL_Obool)),X3093),hAPP(hAPP(c_Set_Oinsert(X3094),X3092),c_Orderings_Obot__class_Obot(tc_fun(X3094,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3094),X3093))|~class_Orderings_Olinorder(X3094))&(c_Orderings_Obot__class_Obot(tc_fun(X3094,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3094,tc_HOL_Obool)),X3093),hAPP(hAPP(c_Set_Oinsert(X3094),X3092),c_Orderings_Obot__class_Obot(tc_fun(X3094,tc_HOL_Obool))))|c_Big__Operators_Olattice_OInf__fin(X3094,c_Orderings_Oord__class_Omin(X3094),hAPP(hAPP(c_Set_Oinsert(X3094),X3092),X3093))=X3092|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3094),X3093))|~class_Orderings_Olinorder(X3094))), 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])])])])). 6.97/7.22 fof(c_0_6175, plain, ![X2367, X2368, X2369, X2370, X2371]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2371),tc_List_Olist(X2371))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2371),tc_List_Olist(X2371)),X2370),X2369)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X2371),c_List_Olistrel1(X2371,X2368))))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2371),tc_List_Olist(X2371))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2371),tc_List_Olist(X2371)),hAPP(hAPP(c_List_Olist_OCons(X2371),X2367),X2370)),hAPP(hAPP(c_List_Olist_OCons(X2371),X2367),X2369))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X2371),c_List_Olistrel1(X2371,X2368))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__ConsI1])])). 6.97/7.22 cnf(c_0_6176, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[c_0_4910, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 fof(c_0_6177, plain, ![X4787, X4788, X4789, X4790, X4791]:((c_Orderings_Obot__class_Obot(tc_fun(X4791,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4791,tc_HOL_Obool)),X4788),hAPP(hAPP(c_Set_Oinsert(X4791),X4787),c_Orderings_Obot__class_Obot(tc_fun(X4791,tc_HOL_Obool))))|hAPP(hAPP(X4790,X4787),hAPP(X4789,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4791,tc_HOL_Obool)),X4788),hAPP(hAPP(c_Set_Oinsert(X4791),X4787),c_Orderings_Obot__class_Obot(tc_fun(X4791,tc_HOL_Obool))))))=hAPP(X4789,X4788)|~hBOOL(hAPP(hAPP(c_member(X4791),X4787),X4788))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4791),X4788))|~c_Finite__Set_Ofolding__one(X4791,X4790,X4789))&(c_Orderings_Obot__class_Obot(tc_fun(X4791,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4791,tc_HOL_Obool)),X4788),hAPP(hAPP(c_Set_Oinsert(X4791),X4787),c_Orderings_Obot__class_Obot(tc_fun(X4791,tc_HOL_Obool))))|hAPP(X4789,X4788)=X4787|~hBOOL(hAPP(hAPP(c_member(X4791),X4787),X4788))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4791),X4788))|~c_Finite__Set_Ofolding__one(X4791,X4790,X4789))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one_Oremove])])])])). 6.97/7.22 fof(c_0_6178, plain, ![X6892, X6893, X6894, X6895, X6896]:(~c_Equiv__Relations_Oequiv(X6896,X6895,X6894)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X6896,X6896)),hAPP(hAPP(c_Product__Type_OPair(X6896,X6896),X6893),X6892)),X6894))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6896,tc_HOL_Obool)),hAPP(c_Relation_OImage(X6896,X6896,X6894),hAPP(hAPP(c_Set_Oinsert(X6896),X6893),c_Orderings_Obot__class_Obot(tc_fun(X6896,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X6896,X6896,X6894),hAPP(hAPP(c_Set_Oinsert(X6896),X6892),c_Orderings_Obot__class_Obot(tc_fun(X6896,tc_HOL_Obool)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equiv__class__subset])])])). 6.97/7.22 cnf(c_0_6179, 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_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),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_4911, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_6180, 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_4912])). 6.97/7.22 fof(c_0_6181, plain, ![X5617, X5618, X5619, X5620, X5621]:(((X5618=hAPP(c_Nat_OSuc,esk186_5(X5617,X5618,X5619,X5620,X5621))|X5618=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5621,X5621)),hAPP(hAPP(c_Product__Type_OPair(X5621,X5621),X5620),X5619)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5621,X5621),tc_HOL_Obool),X5618),X5617))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X5621,X5621)),hAPP(hAPP(c_Product__Type_OPair(X5621,X5621),X5620),esk185_5(X5617,X5618,X5619,X5620,X5621))),X5617))|X5618=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5621,X5621)),hAPP(hAPP(c_Product__Type_OPair(X5621,X5621),X5620),X5619)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5621,X5621),tc_HOL_Obool),X5618),X5617))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X5621,X5621)),hAPP(hAPP(c_Product__Type_OPair(X5621,X5621),esk185_5(X5617,X5618,X5619,X5620,X5621)),X5619)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5621,X5621),tc_HOL_Obool),esk186_5(X5617,X5618,X5619,X5620,X5621)),X5617)))|X5618=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5621,X5621)),hAPP(hAPP(c_Product__Type_OPair(X5621,X5621),X5620),X5619)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5621,X5621),tc_HOL_Obool),X5618),X5617))))))&((X5618=hAPP(c_Nat_OSuc,esk186_5(X5617,X5618,X5619,X5620,X5621))|X5619=X5620|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5621,X5621)),hAPP(hAPP(c_Product__Type_OPair(X5621,X5621),X5620),X5619)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5621,X5621),tc_HOL_Obool),X5618),X5617))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X5621,X5621)),hAPP(hAPP(c_Product__Type_OPair(X5621,X5621),X5620),esk185_5(X5617,X5618,X5619,X5620,X5621))),X5617))|X5619=X5620|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5621,X5621)),hAPP(hAPP(c_Product__Type_OPair(X5621,X5621),X5620),X5619)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5621,X5621),tc_HOL_Obool),X5618),X5617))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X5621,X5621)),hAPP(hAPP(c_Product__Type_OPair(X5621,X5621),esk185_5(X5617,X5618,X5619,X5620,X5621)),X5619)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5621,X5621),tc_HOL_Obool),esk186_5(X5617,X5618,X5619,X5620,X5621)),X5617)))|X5619=X5620|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5621,X5621)),hAPP(hAPP(c_Product__Type_OPair(X5621,X5621),X5620),X5619)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5621,X5621),tc_HOL_Obool),X5618),X5617))))))), 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])])])])])). 6.97/7.22 fof(c_0_6182, plain, ![X964, X965, X966, X967, X968]:(((hAPP(c_Nat_OSuc,esk29_5(X964,X965,X966,X967,X968))=X965|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X965|~hBOOL(hAPP(hAPP(c_member(tc_prod(X968,X968)),hAPP(hAPP(c_Product__Type_OPair(X968,X968),X967),X966)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X968,X968),tc_HOL_Obool),X965),X964))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X968,X968)),hAPP(hAPP(c_Product__Type_OPair(X968,X968),X967),esk28_5(X964,X965,X966,X967,X968))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X968,X968),tc_HOL_Obool),esk29_5(X964,X965,X966,X967,X968)),X964)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X965|~hBOOL(hAPP(hAPP(c_member(tc_prod(X968,X968)),hAPP(hAPP(c_Product__Type_OPair(X968,X968),X967),X966)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X968,X968),tc_HOL_Obool),X965),X964))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X968,X968)),hAPP(hAPP(c_Product__Type_OPair(X968,X968),esk28_5(X964,X965,X966,X967,X968)),X966)),X964))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X965|~hBOOL(hAPP(hAPP(c_member(tc_prod(X968,X968)),hAPP(hAPP(c_Product__Type_OPair(X968,X968),X967),X966)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X968,X968),tc_HOL_Obool),X965),X964))))))&((hAPP(c_Nat_OSuc,esk29_5(X964,X965,X966,X967,X968))=X965|X967=X966|~hBOOL(hAPP(hAPP(c_member(tc_prod(X968,X968)),hAPP(hAPP(c_Product__Type_OPair(X968,X968),X967),X966)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X968,X968),tc_HOL_Obool),X965),X964))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X968,X968)),hAPP(hAPP(c_Product__Type_OPair(X968,X968),X967),esk28_5(X964,X965,X966,X967,X968))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X968,X968),tc_HOL_Obool),esk29_5(X964,X965,X966,X967,X968)),X964)))|X967=X966|~hBOOL(hAPP(hAPP(c_member(tc_prod(X968,X968)),hAPP(hAPP(c_Product__Type_OPair(X968,X968),X967),X966)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X968,X968),tc_HOL_Obool),X965),X964))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X968,X968)),hAPP(hAPP(c_Product__Type_OPair(X968,X968),esk28_5(X964,X965,X966,X967,X968)),X966)),X964))|X967=X966|~hBOOL(hAPP(hAPP(c_member(tc_prod(X968,X968)),hAPP(hAPP(c_Product__Type_OPair(X968,X968),X967),X966)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X968,X968),tc_HOL_Obool),X965),X964))))))), 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])])])])])). 6.97/7.22 cnf(c_0_6183, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_4913, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.22 cnf(c_0_6184, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[c_0_4914, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 fof(c_0_6185, plain, ![X7231]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X7231))|(X7231=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))),X7231)),c_FunDef_Omax__strict)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smax__emptyI])])). 6.97/7.22 fof(c_0_6186, plain, ![X15309, X15310, X15311]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15311),X15310))|(~c_Fun_Oinj__on(X15311,tc_fun(tc_fun(X15311,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X15311,tc_fun(tc_prod(X15311,X15311),tc_HOL_Obool),tc_fun(tc_fun(X15311,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X15311,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X15311,X15311),tc_HOL_Obool),tc_fun(tc_fun(X15311,tc_HOL_Obool),tc_HOL_Obool)),X15311),c_Equiv__Relations_Oquotient(X15311)),hAPP(hAPP(c_COMBC(X15311,tc_fun(X15311,tc_HOL_Obool),tc_fun(X15311,tc_HOL_Obool)),c_Set_Oinsert(X15311)),c_Orderings_Obot__class_Obot(tc_fun(X15311,tc_HOL_Obool))))),X15309),X15310)|hAPP(c_Finite__Set_Ocard(tc_fun(X15311,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X15311),X15310),X15309))=hAPP(c_Finite__Set_Ocard(X15311),X15310))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__quotient__disjoint])])])). 6.97/7.22 cnf(c_0_6187, 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_4915])). 6.97/7.22 fof(c_0_6188, plain, ![X2968, X2969, X2970, X2971, X2972, X2973]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2970),X2969)),X2968)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2973),X2972)),X2971)|(~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),X2970),X2969)),X2968)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2971),X2973))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2968))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2970))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2970),X2973))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2969),X2972)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__mono2__neg__lemma])])])). 6.97/7.22 fof(c_0_6189, plain, ![X17219, X17220, X17221, X17222, X17223, X17224]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17221),X17220)),X17219)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17224),X17223)),X17222)|(~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),X17221),X17220)),X17219)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17219),X17221))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17222))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17221))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X17221),X17224))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X17223),X17220)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__mono2__lemma])])])). 6.97/7.22 fof(c_0_6190, plain, ![X14954, X14955, X14956, X14957, X14958]:((c_Orderings_Obot__class_Obot(tc_fun(X14958,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X14958,tc_HOL_Obool)),X14955),hAPP(hAPP(c_Set_Oinsert(X14958),X14954),c_Orderings_Obot__class_Obot(tc_fun(X14958,tc_HOL_Obool))))|X14954=hAPP(X14956,hAPP(hAPP(c_Set_Oinsert(X14958),X14954),X14955))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14958),X14955))|~c_Finite__Set_Ofolding__one(X14958,X14957,X14956))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X14958,tc_HOL_Obool)),X14955),hAPP(hAPP(c_Set_Oinsert(X14958),X14954),c_Orderings_Obot__class_Obot(tc_fun(X14958,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X14958,tc_HOL_Obool))|hAPP(hAPP(X14957,X14954),hAPP(X14956,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X14958,tc_HOL_Obool)),X14955),hAPP(hAPP(c_Set_Oinsert(X14958),X14954),c_Orderings_Obot__class_Obot(tc_fun(X14958,tc_HOL_Obool))))))=hAPP(X14956,hAPP(hAPP(c_Set_Oinsert(X14958),X14954),X14955))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14958),X14955))|~c_Finite__Set_Ofolding__one(X14958,X14957,X14956))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one_Oinsert__remove])])])])). 6.97/7.22 fof(c_0_6191, plain, ![X16353, X16354, X16355, X16356, X16357, X16358]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X16355,X16358),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X16355,X16358),X16354),hAPP(c_COMBK(tc_fun(X16358,tc_HOL_Obool),X16355),X16356))),hAPP(hAPP(c_Product__Type_OSigma(X16355,X16358),X16353),hAPP(c_COMBK(tc_fun(X16358,tc_HOL_Obool),X16355),X16356))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16355,tc_HOL_Obool)),X16354),X16353))|~hBOOL(hAPP(hAPP(c_member(X16358),X16357),X16356)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16355,tc_HOL_Obool)),X16354),X16353))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X16355,X16358),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X16355,X16358),X16354),hAPP(c_COMBK(tc_fun(X16358,tc_HOL_Obool),X16355),X16356))),hAPP(hAPP(c_Product__Type_OSigma(X16355,X16358),X16353),hAPP(c_COMBK(tc_fun(X16358,tc_HOL_Obool),X16355),X16356))))|~hBOOL(hAPP(hAPP(c_member(X16358),X16357),X16356)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Times__subset__cancel2])])])])). 6.97/7.22 fof(c_0_6192, plain, ![X16817, X16818, X16819]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16819,tc_HOL_Obool)),X16818),hAPP(hAPP(c_Set_Oinsert(X16819),X16817),c_Orderings_Obot__class_Obot(tc_fun(X16819,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X16819,tc_HOL_Obool))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X16819),X16817),c_Big__Operators_Olinorder__class_OMax(X16819,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16819,tc_HOL_Obool)),X16818),hAPP(hAPP(c_Set_Oinsert(X16819),X16817),c_Orderings_Obot__class_Obot(tc_fun(X16819,tc_HOL_Obool))))))=c_Big__Operators_Olinorder__class_OMax(X16819,X16818)|~hBOOL(hAPP(hAPP(c_member(X16819),X16817),X16818))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16819),X16818))|~class_Orderings_Olinorder(X16819))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16819,tc_HOL_Obool)),X16818),hAPP(hAPP(c_Set_Oinsert(X16819),X16817),c_Orderings_Obot__class_Obot(tc_fun(X16819,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X16819,tc_HOL_Obool))|X16817=c_Big__Operators_Olinorder__class_OMax(X16819,X16818)|~hBOOL(hAPP(hAPP(c_member(X16819),X16817),X16818))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16819),X16818))|~class_Orderings_Olinorder(X16819))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max_Oremove])])])])). 6.97/7.22 cnf(c_0_6193, 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_4916, c_0_4565])). 6.97/7.22 cnf(c_0_6194, 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_4917, c_0_4565])). 6.97/7.22 fof(c_0_6195, plain, ![X14554, X14555, X14556, X14557, X14558]:(~class_Groups_Oab__semigroup__mult(X14558)|(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X14558,X14558,c_Groups_Otimes__class_Otimes(X14558),X14557,X14556),X14555))|(~hBOOL(hAPP(hAPP(c_member(X14558),X14554),X14556))|(hBOOL(hAPP(hAPP(c_member(X14558),X14557),X14556))|hBOOL(hAPP(c_Finite__Set_Ofold__graph(X14558,X14558,c_Groups_Otimes__class_Otimes(X14558),X14554,hAPP(hAPP(c_Set_Oinsert(X14558),X14557),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X14558,tc_HOL_Obool)),X14556),hAPP(hAPP(c_Set_Oinsert(X14558),X14554),c_Orderings_Obot__class_Obot(tc_fun(X14558,tc_HOL_Obool)))))),X14555)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__graph__permute__diff])])])). 6.97/7.22 cnf(c_0_6196, 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)),X7),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))|hAPP(hAPP(c_List_Oappend(X1),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X6))!=X7|X8!=hAPP(hAPP(c_List_Oappend(X1),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X6))), inference(split_conjunct,[status(thm)],[c_0_4918])). 6.97/7.22 fof(c_0_6197, plain, ![X17044, X17045, X17046]:(~class_Orderings_Olinorder(X17046)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17046),X17045))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17046),X17044))|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17046,tc_HOL_Obool)),X17045),X17044)=c_Orderings_Obot__class_Obot(tc_fun(X17046,tc_HOL_Obool))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X17046),c_Big__Operators_Olinorder__class_OMin(X17046,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17046,tc_HOL_Obool)),X17045),X17044))),c_Big__Operators_Olinorder__class_OMin(X17046,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17046,tc_HOL_Obool)),X17045),X17044)))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X17046),c_Big__Operators_Olinorder__class_OMin(X17046,X17045)),c_Big__Operators_Olinorder__class_OMin(X17046,X17044)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min_Ounion__inter])])])). 6.97/7.22 fof(c_0_6198, plain, ![X987, X988, X989]:(~class_Lattices_Olattice(X989)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X989),X988))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X989),X987))|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X989,tc_HOL_Obool)),X988),X987)=c_Orderings_Obot__class_Obot(tc_fun(X989,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X989),c_Big__Operators_Olattice__class_OInf__fin(X989,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X989,tc_HOL_Obool)),X988),X987))),c_Big__Operators_Olattice__class_OInf__fin(X989,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X989,tc_HOL_Obool)),X988),X987)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X989),c_Big__Operators_Olattice__class_OInf__fin(X989,X988)),c_Big__Operators_Olattice__class_OInf__fin(X989,X987)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Ounion__inter])])])). 6.97/7.22 fof(c_0_6199, plain, ![X10755, X10756, X10757]:(~class_Lattices_Olattice(X10757)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10757),X10756))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10757),X10755))|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10757,tc_HOL_Obool)),X10756),X10755)=c_Orderings_Obot__class_Obot(tc_fun(X10757,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10757),c_Big__Operators_Olattice__class_OSup__fin(X10757,X10756)),c_Big__Operators_Olattice__class_OSup__fin(X10757,X10755))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10757),c_Big__Operators_Olattice__class_OSup__fin(X10757,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10757,tc_HOL_Obool)),X10756),X10755))),c_Big__Operators_Olattice__class_OSup__fin(X10757,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10757,tc_HOL_Obool)),X10756),X10755))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Ounion__inter])])])). 6.97/7.22 fof(c_0_6200, plain, ![X10842, X10843, X10844]:(~class_Orderings_Olinorder(X10844)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10844),X10843))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10844),X10842))|(c_Orderings_Obot__class_Obot(tc_fun(X10844,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10844,tc_HOL_Obool)),X10843),X10842)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X10844),c_Big__Operators_Olinorder__class_OMax(X10844,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10844,tc_HOL_Obool)),X10843),X10842))),c_Big__Operators_Olinorder__class_OMax(X10844,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10844,tc_HOL_Obool)),X10843),X10842)))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X10844),c_Big__Operators_Olinorder__class_OMax(X10844,X10843)),c_Big__Operators_Olinorder__class_OMax(X10844,X10842)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max_Ounion__inter])])])). 6.97/7.22 fof(c_0_6201, plain, ![X6456, X6457, X6458, X6459, X6460, X6461, X6462, X6465, X6466, X6467, X6468, X6469, X6470, X6471, X6472, X6473]:(((((X6459=hAPP(hAPP(X6460,X6457),X6456)|hBOOL(hAPP(hAPP(c_member(X6462),esk212_7(X6456,X6457,X6458,X6459,X6460,X6461,X6462)),X6458))|~c_Nitpick_Ofold__graph_H(X6462,X6461,X6460,X6459,X6458,hAPP(hAPP(X6460,X6457),X6456)))&(X6458=c_Orderings_Obot__class_Obot(tc_fun(X6462,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X6462),esk212_7(X6456,X6457,X6458,X6459,X6460,X6461,X6462)),X6458))|~c_Nitpick_Ofold__graph_H(X6462,X6461,X6460,X6459,X6458,hAPP(hAPP(X6460,X6457),X6456))))&((X6459=hAPP(hAPP(X6460,X6457),X6456)|c_Nitpick_Ofold__graph_H(X6462,X6461,X6460,X6459,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6462,tc_HOL_Obool)),X6458),hAPP(hAPP(c_Set_Oinsert(X6462),esk212_7(X6456,X6457,X6458,X6459,X6460,X6461,X6462)),c_Orderings_Obot__class_Obot(tc_fun(X6462,tc_HOL_Obool)))),esk213_7(X6456,X6457,X6458,X6459,X6460,X6461,X6462))|~c_Nitpick_Ofold__graph_H(X6462,X6461,X6460,X6459,X6458,hAPP(hAPP(X6460,X6457),X6456)))&(X6458=c_Orderings_Obot__class_Obot(tc_fun(X6462,tc_HOL_Obool))|c_Nitpick_Ofold__graph_H(X6462,X6461,X6460,X6459,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6462,tc_HOL_Obool)),X6458),hAPP(hAPP(c_Set_Oinsert(X6462),esk212_7(X6456,X6457,X6458,X6459,X6460,X6461,X6462)),c_Orderings_Obot__class_Obot(tc_fun(X6462,tc_HOL_Obool)))),esk213_7(X6456,X6457,X6458,X6459,X6460,X6461,X6462))|~c_Nitpick_Ofold__graph_H(X6462,X6461,X6460,X6459,X6458,hAPP(hAPP(X6460,X6457),X6456)))))&((X6459=hAPP(hAPP(X6460,X6457),X6456)|hAPP(hAPP(X6460,X6457),X6456)=hAPP(hAPP(X6460,esk212_7(X6456,X6457,X6458,X6459,X6460,X6461,X6462)),esk213_7(X6456,X6457,X6458,X6459,X6460,X6461,X6462))|~c_Nitpick_Ofold__graph_H(X6462,X6461,X6460,X6459,X6458,hAPP(hAPP(X6460,X6457),X6456)))&(X6458=c_Orderings_Obot__class_Obot(tc_fun(X6462,tc_HOL_Obool))|hAPP(hAPP(X6460,X6457),X6456)=hAPP(hAPP(X6460,esk212_7(X6456,X6457,X6458,X6459,X6460,X6461,X6462)),esk213_7(X6456,X6457,X6458,X6459,X6460,X6461,X6462))|~c_Nitpick_Ofold__graph_H(X6462,X6461,X6460,X6459,X6458,hAPP(hAPP(X6460,X6457),X6456)))))&((~hBOOL(hAPP(hAPP(c_member(X6471),X6472),X6467))|~c_Nitpick_Ofold__graph_H(X6471,X6470,X6469,X6468,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6471,tc_HOL_Obool)),X6467),hAPP(hAPP(c_Set_Oinsert(X6471),X6472),c_Orderings_Obot__class_Obot(tc_fun(X6471,tc_HOL_Obool)))),X6473)|hAPP(hAPP(X6469,X6466),X6465)!=hAPP(hAPP(X6469,X6472),X6473)|c_Nitpick_Ofold__graph_H(X6471,X6470,X6469,X6468,X6467,hAPP(hAPP(X6469,X6466),X6465)))&(X6468!=hAPP(hAPP(X6469,X6466),X6465)|X6467!=c_Orderings_Obot__class_Obot(tc_fun(X6471,tc_HOL_Obool))|c_Nitpick_Ofold__graph_H(X6471,X6470,X6469,X6468,X6467,hAPP(hAPP(X6469,X6466),X6465))))), 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])])])])])])). 6.97/7.22 fof(c_0_6202, plain, ![X3273, X3274, X3275, X3276, X3277]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3277),X3276))|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),X3276),X3275)),X3274)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3277),X3275)),X3273))=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),X3276),X3277)),X3275)),X3274)),X3273)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__diff__add__eq1])])])). 6.97/7.22 fof(c_0_6203, plain, ![X2670, X2671, X2672, X2673, X2674]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2674),X2673))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2671),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),X2673),X2674)),X2672)),X2670))=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),X2674),X2672)),X2671)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2673),X2672)),X2670))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__diff__add__eq2])])])). 6.97/7.22 fof(c_0_6204, plain, ![X15686, X15687, X15688, X15689]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15689),X15688))|(~hBOOL(hAPP(hAPP(c_member(X15689),X15687),X15688))|(hBOOL(hAPP(hAPP(c_member(X15689),X15687),X15686))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X15689),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15689,tc_HOL_Obool)),X15688),X15686))),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Finite__Set_Ocard(X15689),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15689,tc_HOL_Obool)),X15688),hAPP(hAPP(c_Set_Oinsert(X15689),X15687),X15686)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Diff__insert])])])). 6.97/7.22 fof(c_0_6205, plain, ![X12492, X12493, X12494, X12495, X12496]:(~c_Finite__Set_Ofolding__one(X12496,X12495,X12494)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12496),X12493))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12496),X12492))|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12496,tc_HOL_Obool)),X12493),X12492)=c_Orderings_Obot__class_Obot(tc_fun(X12496,tc_HOL_Obool))|hAPP(hAPP(X12495,hAPP(X12494,X12493)),hAPP(X12494,X12492))=hAPP(hAPP(X12495,hAPP(X12494,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12496,tc_HOL_Obool)),X12493),X12492))),hAPP(X12494,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12496,tc_HOL_Obool)),X12493),X12492))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one_Ounion__inter])])])). 6.97/7.22 cnf(c_0_6206, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk385_5(X2,X3,X4,X1,X5)),X2))|hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),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)),X4))|c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),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)),X4))!=X5), inference(split_conjunct,[status(thm)],[c_0_4919])). 6.97/7.22 cnf(c_0_6207, plain, (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)))=c_Nitpick_Oof__frac(X2,X1,X3)|~class_Rings_Oring__1(X1)|~class_Rings_Oinverse(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4920, c_0_4921]), c_0_4922])). 6.97/7.22 cnf(c_0_6208, plain, (hAPP(X1,hAPP(X2,X3))=hAPP(hAPP(c_Fun_Ocomp(X4,X5,X6,X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_4923]), ['final']). 6.97/7.22 fof(c_0_6209, plain, ![X885, X886, X887, X888, X889]:(~class_Groups_Ocomm__monoid__add(X889)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X888,X889),hAPP(hAPP(c_COMBS(X888,X889,X889),hAPP(hAPP(c_COMBB(X889,tc_fun(X889,X889),X888),c_Groups_Oplus__class_Oplus(X889)),X887)),X886)),X885)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X889),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X888,X889),X887),X885)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X888,X889),X886),X885))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__addf])])). 6.97/7.22 fof(c_0_6210, plain, ![X1302, X1303, X1304]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1304,tc_HOL_Obool)),X1303),hAPP(hAPP(c_Set_Oinsert(X1304),X1302),c_Orderings_Obot__class_Obot(tc_fun(X1304,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1304,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1304),X1302),c_Big__Operators_Olattice__class_OInf__fin(X1304,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1304,tc_HOL_Obool)),X1303),hAPP(hAPP(c_Set_Oinsert(X1304),X1302),c_Orderings_Obot__class_Obot(tc_fun(X1304,tc_HOL_Obool))))))=c_Big__Operators_Olattice__class_OInf__fin(X1304,X1303)|~hBOOL(hAPP(hAPP(c_member(X1304),X1302),X1303))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1304),X1303))|~class_Lattices_Olattice(X1304))&(c_Orderings_Obot__class_Obot(tc_fun(X1304,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1304,tc_HOL_Obool)),X1303),hAPP(hAPP(c_Set_Oinsert(X1304),X1302),c_Orderings_Obot__class_Obot(tc_fun(X1304,tc_HOL_Obool))))|X1302=c_Big__Operators_Olattice__class_OInf__fin(X1304,X1303)|~hBOOL(hAPP(hAPP(c_member(X1304),X1302),X1303))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1304),X1303))|~class_Lattices_Olattice(X1304))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oremove])])])])). 6.97/7.22 fof(c_0_6211, plain, ![X14239, X14240, X14241, X14242, X14243, X14244]:((hBOOL(hAPP(hAPP(c_member(X14244),esk484_6(X14239,X14240,X14241,X14242,X14243,X14244)),X14243))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14241,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14244,tc_fun(X14241,tc_HOL_Obool)),X14243),X14240)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14244,tc_fun(X14241,tc_HOL_Obool)),X14242),X14239)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14244,tc_HOL_Obool)),X14243),X14242)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14241,tc_HOL_Obool)),hAPP(X14240,esk484_6(X14239,X14240,X14241,X14242,X14243,X14244))),hAPP(X14239,esk484_6(X14239,X14240,X14241,X14242,X14243,X14244))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14241,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14244,tc_fun(X14241,tc_HOL_Obool)),X14243),X14240)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14244,tc_fun(X14241,tc_HOL_Obool)),X14242),X14239)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14244,tc_HOL_Obool)),X14243),X14242)))), 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__mono])])])])])). 6.97/7.22 fof(c_0_6212, plain, ![X11167, X11168, X11169, X11170, X11171, X11172]:((hBOOL(hAPP(hAPP(c_member(X11172),esk371_6(X11167,X11168,X11169,X11170,X11171,X11172)),X11170))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11169,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11172,tc_fun(X11169,tc_HOL_Obool)),X11170),X11168)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11172,tc_fun(X11169,tc_HOL_Obool)),X11170),X11167)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11172,tc_HOL_Obool)),X11171),X11170)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11169,tc_HOL_Obool)),hAPP(X11168,esk371_6(X11167,X11168,X11169,X11170,X11171,X11172))),hAPP(X11167,esk371_6(X11167,X11168,X11169,X11170,X11171,X11172))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11169,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11172,tc_fun(X11169,tc_HOL_Obool)),X11170),X11168)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11172,tc_fun(X11169,tc_HOL_Obool)),X11170),X11167)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11172,tc_HOL_Obool)),X11171),X11170)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__anti__mono])])])])). 6.97/7.22 cnf(c_0_6213, plain, (hBOOL(hAPP(X1,esk108_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_4908])). 6.97/7.22 fof(c_0_6214, plain, ![X464, X465, X466, X467]:((~hBOOL(hAPP(hAPP(c_member(X466),X464),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X467,tc_fun(X466,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X467,tc_HOL_Obool))),X465)))|hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X467,tc_fun(X466,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X467,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X466,tc_HOL_Obool),tc_fun(X466,tc_HOL_Obool),X467),hAPP(c_COMBC(X466,tc_fun(X466,tc_HOL_Obool),tc_HOL_Obool),c_member(X466))),X465)),X464)))&(~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X467,tc_fun(X466,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X467,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X466,tc_HOL_Obool),tc_fun(X466,tc_HOL_Obool),X467),hAPP(c_COMBC(X466,tc_fun(X466,tc_HOL_Obool),tc_HOL_Obool),c_member(X466))),X465)),X464))|hBOOL(hAPP(hAPP(c_member(X466),X464),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X467,tc_fun(X466,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X467,tc_HOL_Obool))),X465))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__INT__eq])])). 6.97/7.22 fof(c_0_6215, plain, ![X2855, X2856, X2857, X2858, X2859]:(~class_Groups_Oab__group__add(X2859)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2859),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2858,X2859),X2857),X2855)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2858,X2859),X2856),X2855))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2858,X2859),hAPP(hAPP(c_COMBS(X2858,X2859,X2859),hAPP(hAPP(c_COMBB(X2859,tc_fun(X2859,X2859),X2858),c_Groups_Ominus__class_Ominus(X2859)),X2857)),X2856)),X2855)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__subtractf])])). 6.97/7.22 fof(c_0_6216, plain, ![X14765, X14766, X14767, X14768, X14769, X14770]:((((X14766=X14768|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X14770),tc_List_Olist(X14770))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X14770),tc_List_Olist(X14770)),X14768),X14766)),c_List_Olistrel1(X14770,X14765)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X14770),tc_List_Olist(X14770))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X14770),tc_List_Olist(X14770)),hAPP(hAPP(c_List_Olist_OCons(X14770),X14769),X14768)),hAPP(hAPP(c_List_Olist_OCons(X14770),X14767),X14766))),c_List_Olistrel1(X14770,X14765))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X14770,X14770)),hAPP(hAPP(c_Product__Type_OPair(X14770,X14770),X14769),X14767)),X14765))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X14770),tc_List_Olist(X14770))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X14770),tc_List_Olist(X14770)),X14768),X14766)),c_List_Olistrel1(X14770,X14765)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X14770),tc_List_Olist(X14770))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X14770),tc_List_Olist(X14770)),hAPP(hAPP(c_List_Olist_OCons(X14770),X14769),X14768)),hAPP(hAPP(c_List_Olist_OCons(X14770),X14767),X14766))),c_List_Olistrel1(X14770,X14765)))))&((X14766=X14768|X14769=X14767|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X14770),tc_List_Olist(X14770))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X14770),tc_List_Olist(X14770)),hAPP(hAPP(c_List_Olist_OCons(X14770),X14769),X14768)),hAPP(hAPP(c_List_Olist_OCons(X14770),X14767),X14766))),c_List_Olistrel1(X14770,X14765))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X14770,X14770)),hAPP(hAPP(c_Product__Type_OPair(X14770,X14770),X14769),X14767)),X14765))|X14769=X14767|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X14770),tc_List_Olist(X14770))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X14770),tc_List_Olist(X14770)),hAPP(hAPP(c_List_Olist_OCons(X14770),X14769),X14768)),hAPP(hAPP(c_List_Olist_OCons(X14770),X14767),X14766))),c_List_Olistrel1(X14770,X14765))))))&((~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X14770),tc_List_Olist(X14770))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X14770),tc_List_Olist(X14770)),X14768),X14766)),c_List_Olistrel1(X14770,X14765)))|X14769!=X14767|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X14770),tc_List_Olist(X14770))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X14770),tc_List_Olist(X14770)),hAPP(hAPP(c_List_Olist_OCons(X14770),X14769),X14768)),hAPP(hAPP(c_List_Olist_OCons(X14770),X14767),X14766))),c_List_Olistrel1(X14770,X14765))))&(X14766!=X14768|~hBOOL(hAPP(hAPP(c_member(tc_prod(X14770,X14770)),hAPP(hAPP(c_Product__Type_OPair(X14770,X14770),X14769),X14767)),X14765))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X14770),tc_List_Olist(X14770))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X14770),tc_List_Olist(X14770)),hAPP(hAPP(c_List_Olist_OCons(X14770),X14769),X14768)),hAPP(hAPP(c_List_Olist_OCons(X14770),X14767),X14766))),c_List_Olistrel1(X14770,X14765)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__listrel1__Cons])])])). 6.97/7.22 fof(c_0_6217, plain, ![X8609, X8610, X8611, X8612, X8613]:(~class_Groups_Ocomm__monoid__mult(X8613)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8613),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8612,X8613),X8611),X8609)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8612,X8613),X8610),X8609))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8612,X8613),hAPP(hAPP(c_COMBS(X8612,X8613,X8613),hAPP(hAPP(c_COMBB(X8613,tc_fun(X8613,X8613),X8612),c_Groups_Otimes__class_Otimes(X8613)),X8611)),X8610)),X8609)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__timesf])])])). 6.97/7.22 fof(c_0_6218, plain, ![X7892, X7893, X7894]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7894,tc_HOL_Obool)),X7893),hAPP(hAPP(c_Set_Oinsert(X7894),X7892),c_Orderings_Obot__class_Obot(tc_fun(X7894,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X7894,tc_HOL_Obool))|c_Big__Operators_Olattice__class_OSup__fin(X7894,X7893)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7894),X7892),c_Big__Operators_Olattice__class_OSup__fin(X7894,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7894,tc_HOL_Obool)),X7893),hAPP(hAPP(c_Set_Oinsert(X7894),X7892),c_Orderings_Obot__class_Obot(tc_fun(X7894,tc_HOL_Obool))))))|~hBOOL(hAPP(hAPP(c_member(X7894),X7892),X7893))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7894),X7893))|~class_Lattices_Olattice(X7894))&(c_Orderings_Obot__class_Obot(tc_fun(X7894,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7894,tc_HOL_Obool)),X7893),hAPP(hAPP(c_Set_Oinsert(X7894),X7892),c_Orderings_Obot__class_Obot(tc_fun(X7894,tc_HOL_Obool))))|X7892=c_Big__Operators_Olattice__class_OSup__fin(X7894,X7893)|~hBOOL(hAPP(hAPP(c_member(X7894),X7892),X7893))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7894),X7893))|~class_Lattices_Olattice(X7894))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oremove])])])])). 6.97/7.22 fof(c_0_6219, plain, ![X2090, X2091, X2092, X2093]:((~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2093,tc_fun(X2092,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2093,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2092,tc_HOL_Obool),tc_fun(X2092,tc_HOL_Obool),X2093),hAPP(c_COMBC(X2092,tc_fun(X2092,tc_HOL_Obool),tc_HOL_Obool),c_member(X2092))),X2091)),X2090))|hBOOL(hAPP(hAPP(c_member(X2092),X2090),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2093,tc_fun(X2092,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2093,tc_HOL_Obool))),X2091))))&(~hBOOL(hAPP(hAPP(c_member(X2092),X2090),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2093,tc_fun(X2092,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2093,tc_HOL_Obool))),X2091)))|hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2093,tc_fun(X2092,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2093,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2092,tc_HOL_Obool),tc_fun(X2092,tc_HOL_Obool),X2093),hAPP(c_COMBC(X2092,tc_fun(X2092,tc_HOL_Obool),tc_HOL_Obool),c_member(X2092))),X2091)),X2090)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__UN__eq])])). 6.97/7.22 fof(c_0_6220, plain, ![X6395, X6396, X6397]:((~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X6396),hAPP(hAPP(c_COMBB(tc_fun(X6397,tc_HOL_Obool),tc_HOL_Obool,X6396),c_Enum_Oenum__class_Oenum__all(X6397)),hAPP(hAPP(c_COMBB(tc_fun(X6397,tc_prod(X6396,X6397)),tc_fun(X6397,tc_HOL_Obool),X6396),hAPP(c_COMBB(tc_prod(X6396,X6397),tc_HOL_Obool,X6397),X6395)),c_Product__Type_OPair(X6396,X6397)))))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X6396,X6397)),X6395))|(~class_Enum_Oenum(X6396)|~class_Enum_Oenum(X6397)))&(~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X6396,X6397)),X6395))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X6396),hAPP(hAPP(c_COMBB(tc_fun(X6397,tc_HOL_Obool),tc_HOL_Obool,X6396),c_Enum_Oenum__class_Oenum__all(X6397)),hAPP(hAPP(c_COMBB(tc_fun(X6397,tc_prod(X6396,X6397)),tc_fun(X6397,tc_HOL_Obool),X6396),hAPP(c_COMBB(tc_prod(X6396,X6397),tc_HOL_Obool,X6397),X6395)),c_Product__Type_OPair(X6396,X6397)))))|(~class_Enum_Oenum(X6396)|~class_Enum_Oenum(X6397)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__all__prod__def])])])). 6.97/7.22 fof(c_0_6221, plain, ![X1375, X1376, X1377]:((~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1376),hAPP(hAPP(c_COMBB(tc_fun(X1377,tc_HOL_Obool),tc_HOL_Obool,X1376),c_Enum_Oenum__class_Oenum__ex(X1377)),hAPP(hAPP(c_COMBB(tc_fun(X1377,tc_prod(X1376,X1377)),tc_fun(X1377,tc_HOL_Obool),X1376),hAPP(c_COMBB(tc_prod(X1376,X1377),tc_HOL_Obool,X1377),X1375)),c_Product__Type_OPair(X1376,X1377)))))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X1376,X1377)),X1375))|(~class_Enum_Oenum(X1376)|~class_Enum_Oenum(X1377)))&(~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X1376,X1377)),X1375))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1376),hAPP(hAPP(c_COMBB(tc_fun(X1377,tc_HOL_Obool),tc_HOL_Obool,X1376),c_Enum_Oenum__class_Oenum__ex(X1377)),hAPP(hAPP(c_COMBB(tc_fun(X1377,tc_prod(X1376,X1377)),tc_fun(X1377,tc_HOL_Obool),X1376),hAPP(c_COMBB(tc_prod(X1376,X1377),tc_HOL_Obool,X1377),X1375)),c_Product__Type_OPair(X1376,X1377)))))|(~class_Enum_Oenum(X1376)|~class_Enum_Oenum(X1377)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__ex__prod__def])])])). 6.97/7.22 cnf(c_0_6222, 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_4924])). 6.97/7.22 fof(c_0_6223, plain, ![X2860, X2861, X2862, X2865, X2866, X2867, X2868, X2869]:(((hBOOL(hAPP(hAPP(c_member(X2862),esk91_3(X2860,X2861,X2862)),X2861))|c_Relation_Ototal__on(X2862,X2861,X2860))&((hBOOL(hAPP(hAPP(c_member(X2862),esk92_3(X2860,X2861,X2862)),X2861))|c_Relation_Ototal__on(X2862,X2861,X2860))&((esk92_3(X2860,X2861,X2862)!=esk91_3(X2860,X2861,X2862)|c_Relation_Ototal__on(X2862,X2861,X2860))&((~hBOOL(hAPP(hAPP(c_member(tc_prod(X2862,X2862)),hAPP(hAPP(c_Product__Type_OPair(X2862,X2862),esk91_3(X2860,X2861,X2862)),esk92_3(X2860,X2861,X2862))),X2860))|c_Relation_Ototal__on(X2862,X2861,X2860))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X2862,X2862)),hAPP(hAPP(c_Product__Type_OPair(X2862,X2862),esk92_3(X2860,X2861,X2862)),esk91_3(X2860,X2861,X2862))),X2860))|c_Relation_Ototal__on(X2862,X2861,X2860))))))&(~c_Relation_Ototal__on(X2867,X2866,X2865)|(~hBOOL(hAPP(hAPP(c_member(X2867),X2868),X2866))|(~hBOOL(hAPP(hAPP(c_member(X2867),X2869),X2866))|(X2869=X2868|(hBOOL(hAPP(hAPP(c_member(tc_prod(X2867,X2867)),hAPP(hAPP(c_Product__Type_OPair(X2867,X2867),X2868),X2869)),X2865))|hBOOL(hAPP(hAPP(c_member(tc_prod(X2867,X2867)),hAPP(hAPP(c_Product__Type_OPair(X2867,X2867),X2869),X2868)),X2865)))))))), 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])])])])])])])). 6.97/7.22 cnf(c_0_6224, 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)),esk478_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),esk478_4(X2,X3,X4,X1)),X3))),X2)), inference(split_conjunct,[status(thm)],[c_0_4925])). 6.97/7.22 cnf(c_0_6225, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[c_0_4926, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 fof(c_0_6226, plain, ![X12254, X12255, X12256]:((c_Orderings_Obot__class_Obot(tc_fun(X12256,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12256,tc_HOL_Obool)),X12255),hAPP(hAPP(c_Set_Oinsert(X12256),X12254),c_Orderings_Obot__class_Obot(tc_fun(X12256,tc_HOL_Obool))))|c_Big__Operators_Olinorder__class_OMin(X12256,X12255)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X12256),X12254),c_Big__Operators_Olinorder__class_OMin(X12256,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12256,tc_HOL_Obool)),X12255),hAPP(hAPP(c_Set_Oinsert(X12256),X12254),c_Orderings_Obot__class_Obot(tc_fun(X12256,tc_HOL_Obool))))))|~hBOOL(hAPP(hAPP(c_member(X12256),X12254),X12255))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12256),X12255))|~class_Orderings_Olinorder(X12256))&(c_Orderings_Obot__class_Obot(tc_fun(X12256,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12256,tc_HOL_Obool)),X12255),hAPP(hAPP(c_Set_Oinsert(X12256),X12254),c_Orderings_Obot__class_Obot(tc_fun(X12256,tc_HOL_Obool))))|c_Big__Operators_Olinorder__class_OMin(X12256,X12255)=X12254|~hBOOL(hAPP(hAPP(c_member(X12256),X12254),X12255))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12256),X12255))|~class_Orderings_Olinorder(X12256))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min_Oremove])])])])). 6.97/7.22 fof(c_0_6227, plain, ![X17047, X17048, X17049, X17050, X17051]:((hBOOL(hAPP(hAPP(c_member(X17050),esk576_5(X17047,X17048,X17049,X17050,X17051)),hAPP(c_List_Oset(X17050),X17049)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17051),hAPP(c_List_Omonoid__add__class_Olistsum(X17051),hAPP(hAPP(c_List_Omap(X17050,X17051),X17048),X17049))),hAPP(c_List_Omonoid__add__class_Olistsum(X17051),hAPP(hAPP(c_List_Omap(X17050,X17051),X17047),X17049))))|(~class_Groups_Oordered__ab__semigroup__add(X17051)|~class_Groups_Omonoid__add(X17051)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17051),hAPP(X17048,esk576_5(X17047,X17048,X17049,X17050,X17051))),hAPP(X17047,esk576_5(X17047,X17048,X17049,X17050,X17051))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17051),hAPP(c_List_Omonoid__add__class_Olistsum(X17051),hAPP(hAPP(c_List_Omap(X17050,X17051),X17048),X17049))),hAPP(c_List_Omonoid__add__class_Olistsum(X17051),hAPP(hAPP(c_List_Omap(X17050,X17051),X17047),X17049))))|(~class_Groups_Oordered__ab__semigroup__add(X17051)|~class_Groups_Omonoid__add(X17051)))), 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])])])])])). 6.97/7.22 fof(c_0_6228, plain, ![X10470, X10471, X10472, X10473, X10474, X10475]:(~class_Groups_Oab__semigroup__mult(X10475)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10474),X10473))|(hBOOL(hAPP(hAPP(c_member(X10474),X10472),X10473))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X10475,X10474,c_Groups_Otimes__class_Otimes(X10475)),X10471),X10470),hAPP(hAPP(c_Set_Oinsert(X10474),X10472),X10473))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10475),hAPP(X10471,X10472)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X10475,X10474,c_Groups_Otimes__class_Otimes(X10475)),X10471),X10470),X10473))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__image__insert])])])). 6.97/7.22 fof(c_0_6229, plain, ![X4995, X4996, X4997, X4998]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4998),X4997))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4996),X4995))|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),X4998),X4996)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X4997),X4995))),c_FunDef_Opair__less)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__lessI2])])). 6.97/7.22 fof(c_0_6230, plain, ![X2920, X2921, X2922, X2923]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2923),X2922))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2921),X2920))|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),X2923),X2921)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2922),X2920))),c_FunDef_Opair__leq)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pair__leqI2])])])). 6.97/7.22 cnf(c_0_6231, 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_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))))))=c_Partial__Function_Oflat__lub(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_4927])). 6.97/7.22 cnf(c_0_6232, 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_4928])). 6.97/7.22 fof(c_0_6233, plain, ![X12883, X12884, X12885, X12886, X12888, X12889, X12890, X12891, X12892]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk421_4(X12883,X12884,X12885,X12886)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12886)),X12885)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12886)),X12884)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12886)),X12885)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X12886),tc_List_Olist(X12886))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X12886),tc_List_Olist(X12886)),X12885),X12884)),c_List_Olistrel(X12886,X12883))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X12886,X12886)),hAPP(hAPP(c_Product__Type_OPair(X12886,X12886),hAPP(hAPP(c_List_Onth(X12886),X12885),esk421_4(X12883,X12884,X12885,X12886))),hAPP(hAPP(c_List_Onth(X12886),X12884),esk421_4(X12883,X12884,X12885,X12886)))),X12883))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12886)),X12884)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12886)),X12885)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X12886),tc_List_Olist(X12886))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X12886),tc_List_Olist(X12886)),X12885),X12884)),c_List_Olistrel(X12886,X12883)))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12892),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12891)),X12890)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X12891,X12891)),hAPP(hAPP(c_Product__Type_OPair(X12891,X12891),hAPP(hAPP(c_List_Onth(X12891),X12890),X12892)),hAPP(hAPP(c_List_Onth(X12891),X12889),X12892))),X12888))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X12891),tc_List_Olist(X12891))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X12891),tc_List_Olist(X12891)),X12890),X12889)),c_List_Olistrel(X12891,X12888))))&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12891)),X12889)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12891)),X12890)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X12891),tc_List_Olist(X12891))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X12891),tc_List_Olist(X12891)),X12890),X12889)),c_List_Olistrel(X12891,X12888)))))), 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_listrel__iff__nth])])])])])])])). 6.97/7.22 cnf(c_0_6234, 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),X6)),hAPP(hAPP(c_List_Oappend(X1),X3),X5))),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)))|X5!=X6), inference(split_conjunct,[status(thm)],[c_0_4929])). 6.97/7.22 cnf(c_0_6235, 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),X6),X2)),hAPP(hAPP(c_List_Olist_OCons(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)))|X5!=X6), inference(split_conjunct,[status(thm)],[c_0_4930])). 6.97/7.22 cnf(c_0_6236, 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_4929])). 6.97/7.22 fof(c_0_6237, plain, ![X13968, X13969, X13970, X13971, X13972, X13973, X13974, X13975]:((hAPP(hAPP(c_Product__Type_OPair(X13975,X13974),hAPP(X13970,esk470_8(X13968,X13969,X13970,X13971,X13972,X13973,X13974,X13975))),hAPP(X13969,esk471_8(X13968,X13969,X13970,X13971,X13972,X13973,X13974,X13975)))=X13973|~hBOOL(hAPP(hAPP(c_member(tc_prod(X13975,X13974)),X13973),hAPP(c_Set_Oimage(tc_prod(X13972,X13971),tc_prod(X13975,X13974),c_Product__Type_Omap__pair(X13972,X13975,X13971,X13974,X13970,X13969)),X13968))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X13972,X13971)),hAPP(hAPP(c_Product__Type_OPair(X13972,X13971),esk470_8(X13968,X13969,X13970,X13971,X13972,X13973,X13974,X13975)),esk471_8(X13968,X13969,X13970,X13971,X13972,X13973,X13974,X13975))),X13968))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X13975,X13974)),X13973),hAPP(c_Set_Oimage(tc_prod(X13972,X13971),tc_prod(X13975,X13974),c_Product__Type_Omap__pair(X13972,X13975,X13971,X13974,X13970,X13969)),X13968))))), 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])])])])])). 6.97/7.22 cnf(c_0_6238, 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))|X6!=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(split_conjunct,[status(thm)],[c_0_4931])). 6.97/7.22 cnf(c_0_6239, 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_4932])). 6.97/7.22 cnf(c_0_6240, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk289_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)),esk287_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_4933])). 6.97/7.22 cnf(c_0_6241, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk288_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)),esk287_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_4933])). 6.97/7.22 cnf(c_0_6242, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[c_0_4934, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_6243, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),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_4935, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_6244, 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_4936])). 6.97/7.22 fof(c_0_6245, plain, ![X11136, X11137, X11138, X11139, X11140, X11141, X11142, X11143]:(~c_Finite__Set_Ofolding(X11143,X11142,X11141,X11140)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11143),X11139))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11143),X11138))|hAPP(c_Fun_Ocomp(X11142,X11142,X11137,hAPP(X11140,X11138)),hAPP(c_Fun_Ocomp(X11142,X11142,X11137,hAPP(X11140,X11139)),X11136))=hAPP(c_Fun_Ocomp(X11142,X11142,X11137,hAPP(X11140,X11139)),hAPP(c_Fun_Ocomp(X11142,X11142,X11137,hAPP(X11140,X11138)),X11136))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Ocommute__left__comp_H_H])])])). 6.97/7.22 fof(c_0_6246, plain, ![X16524, X16525, X16526, X16527, X16528, X16529, X16530]:((hBOOL(hAPP(hAPP(c_member(X16530),esk550_7(X16524,X16525,X16526,X16527,X16528,X16529,X16530)),X16529))|X16524=X16525|~hBOOL(hAPP(hAPP(c_member(tc_fun(X16530,tc_HOL_Obool)),X16524),hAPP(hAPP(c_Equiv__Relations_Oquotient(X16530),X16529),X16528)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X16530,tc_HOL_Obool)),X16525),hAPP(hAPP(c_Equiv__Relations_Oquotient(X16530),X16529),X16528)))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16530,tc_fun(X16527,tc_HOL_Obool)),X16525),X16526)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16530,tc_fun(X16527,tc_HOL_Obool)),X16524),X16526)|~c_Equiv__Relations_Ocongruent(X16530,tc_fun(X16527,tc_HOL_Obool),X16528,X16526)|~c_Equiv__Relations_Oequiv(X16530,X16529,X16528))&((hBOOL(hAPP(hAPP(c_member(X16530),esk551_7(X16524,X16525,X16526,X16527,X16528,X16529,X16530)),X16529))|X16524=X16525|~hBOOL(hAPP(hAPP(c_member(tc_fun(X16530,tc_HOL_Obool)),X16524),hAPP(hAPP(c_Equiv__Relations_Oquotient(X16530),X16529),X16528)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X16530,tc_HOL_Obool)),X16525),hAPP(hAPP(c_Equiv__Relations_Oquotient(X16530),X16529),X16528)))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16530,tc_fun(X16527,tc_HOL_Obool)),X16525),X16526)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16530,tc_fun(X16527,tc_HOL_Obool)),X16524),X16526)|~c_Equiv__Relations_Ocongruent(X16530,tc_fun(X16527,tc_HOL_Obool),X16528,X16526)|~c_Equiv__Relations_Oequiv(X16530,X16529,X16528))&((hAPP(X16526,esk551_7(X16524,X16525,X16526,X16527,X16528,X16529,X16530))=hAPP(X16526,esk550_7(X16524,X16525,X16526,X16527,X16528,X16529,X16530))|X16524=X16525|~hBOOL(hAPP(hAPP(c_member(tc_fun(X16530,tc_HOL_Obool)),X16524),hAPP(hAPP(c_Equiv__Relations_Oquotient(X16530),X16529),X16528)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X16530,tc_HOL_Obool)),X16525),hAPP(hAPP(c_Equiv__Relations_Oquotient(X16530),X16529),X16528)))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16530,tc_fun(X16527,tc_HOL_Obool)),X16525),X16526)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16530,tc_fun(X16527,tc_HOL_Obool)),X16524),X16526)|~c_Equiv__Relations_Ocongruent(X16530,tc_fun(X16527,tc_HOL_Obool),X16528,X16526)|~c_Equiv__Relations_Oequiv(X16530,X16529,X16528))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X16530,X16530)),hAPP(hAPP(c_Product__Type_OPair(X16530,X16530),esk550_7(X16524,X16525,X16526,X16527,X16528,X16529,X16530)),esk551_7(X16524,X16525,X16526,X16527,X16528,X16529,X16530))),X16528))|X16524=X16525|~hBOOL(hAPP(hAPP(c_member(tc_fun(X16530,tc_HOL_Obool)),X16524),hAPP(hAPP(c_Equiv__Relations_Oquotient(X16530),X16529),X16528)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X16530,tc_HOL_Obool)),X16525),hAPP(hAPP(c_Equiv__Relations_Oquotient(X16530),X16529),X16528)))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16530,tc_fun(X16527,tc_HOL_Obool)),X16525),X16526)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16530,tc_fun(X16527,tc_HOL_Obool)),X16524),X16526)|~c_Equiv__Relations_Ocongruent(X16530,tc_fun(X16527,tc_HOL_Obool),X16528,X16526)|~c_Equiv__Relations_Oequiv(X16530,X16529,X16528))))), 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])])])])])). 6.97/7.22 fof(c_0_6247, plain, ![X1635, X1636, X1637]:((c_Orderings_Obot__class_Obot(tc_fun(X1637,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1637,tc_HOL_Obool)),X1636),hAPP(hAPP(c_Set_Oinsert(X1637),X1635),c_Orderings_Obot__class_Obot(tc_fun(X1637,tc_HOL_Obool))))|X1635=c_Big__Operators_Olinorder__class_OMin(X1637,hAPP(hAPP(c_Set_Oinsert(X1637),X1635),X1636))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1637),X1636))|~class_Orderings_Olinorder(X1637))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1637,tc_HOL_Obool)),X1636),hAPP(hAPP(c_Set_Oinsert(X1637),X1635),c_Orderings_Obot__class_Obot(tc_fun(X1637,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1637,tc_HOL_Obool))|c_Big__Operators_Olinorder__class_OMin(X1637,hAPP(hAPP(c_Set_Oinsert(X1637),X1635),X1636))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1637),X1635),c_Big__Operators_Olinorder__class_OMin(X1637,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1637,tc_HOL_Obool)),X1636),hAPP(hAPP(c_Set_Oinsert(X1637),X1635),c_Orderings_Obot__class_Obot(tc_fun(X1637,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1637),X1636))|~class_Orderings_Olinorder(X1637))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min_Oinsert__remove])])])])). 6.97/7.22 cnf(c_0_6248, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[c_0_4937, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_6249, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[c_0_4938, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_6250, 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_4939])). 6.97/7.22 cnf(c_0_6251, 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_4940])). 6.97/7.22 cnf(c_0_6252, 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_4941]), ['final']). 6.97/7.22 cnf(c_0_6253, 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_4942]), ['final']). 6.97/7.22 fof(c_0_6254, plain, ![X16991, X16992, X16993, X16994, X16995, X16996, X16997]:((hBOOL(hAPP(hAPP(c_member(X16997),esk572_7(X16991,X16992,X16993,X16994,X16995,X16996,X16997)),X16996))|hBOOL(hAPP(hAPP(c_member(tc_fun(X16994,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16997,tc_fun(X16994,tc_HOL_Obool)),X16992),X16993)),X16991))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X16997,tc_HOL_Obool)),X16992),hAPP(hAPP(c_Equiv__Relations_Oquotient(X16997),X16996),X16995)))|~c_Equiv__Relations_Ocongruent(X16997,tc_fun(X16994,tc_HOL_Obool),X16995,X16993)|~c_Equiv__Relations_Oequiv(X16997,X16996,X16995))&(~hBOOL(hAPP(hAPP(c_member(tc_fun(X16994,tc_HOL_Obool)),hAPP(X16993,esk572_7(X16991,X16992,X16993,X16994,X16995,X16996,X16997))),X16991))|hBOOL(hAPP(hAPP(c_member(tc_fun(X16994,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16997,tc_fun(X16994,tc_HOL_Obool)),X16992),X16993)),X16991))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X16997,tc_HOL_Obool)),X16992),hAPP(hAPP(c_Equiv__Relations_Oquotient(X16997),X16996),X16995)))|~c_Equiv__Relations_Ocongruent(X16997,tc_fun(X16994,tc_HOL_Obool),X16995,X16993)|~c_Equiv__Relations_Oequiv(X16997,X16996,X16995))), 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__type])])])])])). 6.97/7.22 fof(c_0_6255, plain, ![X6490, X6491, X6492, X6493, X6494, X6495]:((hBOOL(hAPP(hAPP(c_member(X6494),esk214_6(X6490,X6491,X6492,X6493,X6494,X6495)),X6493))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6494,X6495),hAPP(c_Fun_Ocomp(X6490,X6495,X6494,X6491),X6492)),X6493)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6490,X6495),X6491),hAPP(c_Set_Oimage(X6494,X6490,X6492),X6493))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6494),X6493))|~class_Groups_Ocomm__monoid__add(X6495))&((hBOOL(hAPP(hAPP(c_member(X6494),esk215_6(X6490,X6491,X6492,X6493,X6494,X6495)),X6493))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6494,X6495),hAPP(c_Fun_Ocomp(X6490,X6495,X6494,X6491),X6492)),X6493)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6490,X6495),X6491),hAPP(c_Set_Oimage(X6494,X6490,X6492),X6493))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6494),X6493))|~class_Groups_Ocomm__monoid__add(X6495))&((esk214_6(X6490,X6491,X6492,X6493,X6494,X6495)!=esk215_6(X6490,X6491,X6492,X6493,X6494,X6495)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6494,X6495),hAPP(c_Fun_Ocomp(X6490,X6495,X6494,X6491),X6492)),X6493)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6490,X6495),X6491),hAPP(c_Set_Oimage(X6494,X6490,X6492),X6493))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6494),X6493))|~class_Groups_Ocomm__monoid__add(X6495))&((hAPP(X6492,esk214_6(X6490,X6491,X6492,X6493,X6494,X6495))=hAPP(X6492,esk215_6(X6490,X6491,X6492,X6493,X6494,X6495))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6494,X6495),hAPP(c_Fun_Ocomp(X6490,X6495,X6494,X6491),X6492)),X6493)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6490,X6495),X6491),hAPP(c_Set_Oimage(X6494,X6490,X6492),X6493))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6494),X6493))|~class_Groups_Ocomm__monoid__add(X6495))&(c_Groups_Ozero__class_Ozero(X6495)!=hAPP(X6491,hAPP(X6492,esk214_6(X6490,X6491,X6492,X6493,X6494,X6495)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6494,X6495),hAPP(c_Fun_Ocomp(X6490,X6495,X6494,X6491),X6492)),X6493)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6490,X6495),X6491),hAPP(c_Set_Oimage(X6494,X6490,X6492),X6493))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6494),X6493))|~class_Groups_Ocomm__monoid__add(X6495)))))), 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])])])])])). 6.97/7.22 cnf(c_0_6256, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk230_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_4943])). 6.97/7.22 fof(c_0_6257, plain, ![X5398, X5399, X5400]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5400,tc_HOL_Obool)),X5399),hAPP(hAPP(c_Set_Oinsert(X5400),X5398),c_Orderings_Obot__class_Obot(tc_fun(X5400,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X5400,tc_HOL_Obool))|c_Big__Operators_Olattice__class_OInf__fin(X5400,hAPP(hAPP(c_Set_Oinsert(X5400),X5398),X5399))=X5398|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5400),X5399))|~class_Lattices_Olattice(X5400))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5400,tc_HOL_Obool)),X5399),hAPP(hAPP(c_Set_Oinsert(X5400),X5398),c_Orderings_Obot__class_Obot(tc_fun(X5400,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X5400,tc_HOL_Obool))|c_Big__Operators_Olattice__class_OInf__fin(X5400,hAPP(hAPP(c_Set_Oinsert(X5400),X5398),X5399))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5400),X5398),c_Big__Operators_Olattice__class_OInf__fin(X5400,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5400,tc_HOL_Obool)),X5399),hAPP(hAPP(c_Set_Oinsert(X5400),X5398),c_Orderings_Obot__class_Obot(tc_fun(X5400,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5400),X5399))|~class_Lattices_Olattice(X5400))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oinsert__remove])])])])). 6.97/7.22 fof(c_0_6258, plain, ![X2977, X2978, X2979, X2980, X2981]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2981),tc_List_Olist(X2981))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2981),tc_List_Olist(X2981)),X2980),X2979)),c_List_Olexord(X2981,X2978)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2981),tc_List_Olist(X2981))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2981),tc_List_Olist(X2981)),hAPP(hAPP(c_List_Oappend(X2981),X2977),X2980)),hAPP(hAPP(c_List_Oappend(X2981),X2977),X2979))),c_List_Olexord(X2981,X2978)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lexord__append__leftI])])])). 6.97/7.22 fof(c_0_6259, plain, ![X13657, X13658, X13659, X13660, X13661]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X13661),tc_List_Olist(X13661))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X13661),tc_List_Olist(X13661)),X13660),X13659)),c_List_Olistrel1(X13661,X13658)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X13661),tc_List_Olist(X13661))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X13661),tc_List_Olist(X13661)),hAPP(hAPP(c_List_Olist_OCons(X13661),X13657),X13660)),hAPP(hAPP(c_List_Olist_OCons(X13661),X13657),X13659))),c_List_Olistrel1(X13661,X13658)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel1I2])])])). 6.97/7.22 fof(c_0_6260, plain, ![X6628, X6629, X6630, X6631]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6631),X6628)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6629),X6630)|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),X6631),X6630)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6629),X6628))),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),X6631),X6630)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6629),X6628))),c_Int_Ointrel))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6631),X6628)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6629),X6630))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_intrel__iff])])). 6.97/7.22 cnf(c_0_6261, 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),X1))|~hBOOL(hAPP(hAPP(c_member(X3),X4),X2))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X7),X6)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X7),X6)))|~c_Equiv__Relations_Oequiv(X3,X7,X6)), inference(split_conjunct,[status(thm)],[c_0_4944])). 6.97/7.22 cnf(c_0_6262, plain, (hBOOL(hAPP(hAPP(c_member(X2),X5),X4))|~hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4)),esk385_5(X3,X5,X1,X2,X4)))|~hBOOL(hAPP(hAPP(c_member(X2),X5),X3))|~c_Orderings_Oorder__class_Omono(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),c_Set_OCollect(X2)),X1))|c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),c_Set_OCollect(X2)),X1))!=X4), inference(split_conjunct,[status(thm)],[c_0_4919])). 6.97/7.22 cnf(c_0_6263, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))=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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4945, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 fof(c_0_6264, plain, ![X682, X683, X684, X685, X686, X687]:((hBOOL(hAPP(hAPP(c_member(X687),esk15_6(X682,X683,X684,X685,X686,X687)),X686))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X687,X684),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X687,X684),X686),X683)),hAPP(hAPP(c_Product__Type_OSigma(X687,X684),X685),X682)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X687,tc_HOL_Obool)),X686),X685)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X684,tc_HOL_Obool)),hAPP(X683,esk15_6(X682,X683,X684,X685,X686,X687))),hAPP(X682,esk15_6(X682,X683,X684,X685,X686,X687))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X687,X684),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X687,X684),X686),X683)),hAPP(hAPP(c_Product__Type_OSigma(X687,X684),X685),X682)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X687,tc_HOL_Obool)),X686),X685)))), 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])])])])])). 6.97/7.22 fof(c_0_6265, plain, ![X1208, X1209, X1210, X1211, X1212, X1213]:((hBOOL(hAPP(hAPP(c_member(X1213),X1212),X1211))|hAPP(c_Set_Oimage(X1213,X1210,c_Fun_Ofun__upd(X1213,X1210,X1209,X1212,X1208)),X1211)=hAPP(c_Set_Oimage(X1213,X1210,X1209),X1211))&(~hBOOL(hAPP(hAPP(c_member(X1213),X1212),X1211))|hAPP(c_Set_Oimage(X1213,X1210,c_Fun_Ofun__upd(X1213,X1210,X1209,X1212,X1208)),X1211)=hAPP(hAPP(c_Set_Oinsert(X1210),X1208),hAPP(c_Set_Oimage(X1213,X1210,X1209),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1213,tc_HOL_Obool)),X1211),hAPP(hAPP(c_Set_Oinsert(X1213),X1212),c_Orderings_Obot__class_Obot(tc_fun(X1213,tc_HOL_Obool)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__upd__image])])])). 6.97/7.22 fof(c_0_6266, plain, ![X16539]:(X16539=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)),X16539),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])])])). 6.97/7.22 cnf(c_0_6267, 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_4946])). 6.97/7.22 fof(c_0_6268, plain, ![X2768, X2769, X2770, X2771]:(~c_FunDef_Oreduction__pair(X2771,X2770)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2771,X2771),tc_HOL_Obool)),X2769),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X2771,X2771),tc_HOL_Obool),tc_fun(tc_prod(X2771,X2771),tc_HOL_Obool)),X2770)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2771,X2771),tc_HOL_Obool)),X2768),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X2771,X2771),tc_HOL_Obool),tc_fun(tc_prod(X2771,X2771),tc_HOL_Obool)),X2770)))|(~c_Wellfounded_Owf(X2771,X2768)|c_Wellfounded_Owf(X2771,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2771,X2771),tc_HOL_Obool)),X2769),X2768)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_reduction__pair__lemma])])])). 6.97/7.22 fof(c_0_6269, plain, ![X6073, X6074, X6075, X6076, X6077, X6078, X6079]:((~c_List_Olist__all2(X6079,X6075,hAPP(hAPP(c_COMBC(X6079,tc_fun(X6075,X6078),tc_fun(X6075,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6078,tc_HOL_Obool),tc_fun(tc_fun(X6075,X6078),tc_fun(X6075,tc_HOL_Obool)),X6079),c_COMBB(X6078,tc_HOL_Obool,X6075)),X6077)),X6074),X6076,X6073)|c_List_Olist__all2(X6079,X6078,X6077,X6076,hAPP(hAPP(c_List_Omap(X6075,X6078),X6074),X6073)))&(~c_List_Olist__all2(X6079,X6078,X6077,X6076,hAPP(hAPP(c_List_Omap(X6075,X6078),X6074),X6073))|c_List_Olist__all2(X6079,X6075,hAPP(hAPP(c_COMBC(X6079,tc_fun(X6075,X6078),tc_fun(X6075,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6078,tc_HOL_Obool),tc_fun(tc_fun(X6075,X6078),tc_fun(X6075,tc_HOL_Obool)),X6079),c_COMBB(X6078,tc_HOL_Obool,X6075)),X6077)),X6074),X6076,X6073))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__map2])])). 6.97/7.22 fof(c_0_6270, plain, ![X12236, X12237, X12238]:((c_Orderings_Obot__class_Obot(tc_fun(X12238,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12238,tc_HOL_Obool)),X12237),hAPP(hAPP(c_Set_Oinsert(X12238),X12236),c_Orderings_Obot__class_Obot(tc_fun(X12238,tc_HOL_Obool))))|c_Big__Operators_Olinorder__class_OMax(X12238,hAPP(hAPP(c_Set_Oinsert(X12238),X12236),X12237))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X12238),X12236),c_Big__Operators_Olinorder__class_OMax(X12238,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12238,tc_HOL_Obool)),X12237),hAPP(hAPP(c_Set_Oinsert(X12238),X12236),c_Orderings_Obot__class_Obot(tc_fun(X12238,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12238),X12237))|~class_Orderings_Olinorder(X12238))&(c_Orderings_Obot__class_Obot(tc_fun(X12238,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12238,tc_HOL_Obool)),X12237),hAPP(hAPP(c_Set_Oinsert(X12238),X12236),c_Orderings_Obot__class_Obot(tc_fun(X12238,tc_HOL_Obool))))|c_Big__Operators_Olinorder__class_OMax(X12238,hAPP(hAPP(c_Set_Oinsert(X12238),X12236),X12237))=X12236|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12238),X12237))|~class_Orderings_Olinorder(X12238))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max_Oinsert__remove])])])])). 6.97/7.22 fof(c_0_6271, plain, ![X17629, X17630, X17631, X17632, X17633]:((((c_Fun_Oinj__on(X17633,X17632,X17631,X17629)|~c_Fun_Oinj__on(X17633,X17632,X17631,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17633,tc_HOL_Obool)),X17630),X17629)))&(c_Orderings_Obot__class_Obot(tc_fun(X17632,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17632,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17633,X17632,X17631),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17633,tc_HOL_Obool)),X17630),X17629))),hAPP(c_Set_Oimage(X17633,X17632,X17631),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17633,tc_HOL_Obool)),X17629),X17630)))|~c_Fun_Oinj__on(X17633,X17632,X17631,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17633,tc_HOL_Obool)),X17630),X17629))))&(c_Fun_Oinj__on(X17633,X17632,X17631,X17630)|~c_Fun_Oinj__on(X17633,X17632,X17631,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17633,tc_HOL_Obool)),X17630),X17629))))&(~c_Fun_Oinj__on(X17633,X17632,X17631,X17629)|c_Orderings_Obot__class_Obot(tc_fun(X17632,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17632,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17633,X17632,X17631),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17633,tc_HOL_Obool)),X17630),X17629))),hAPP(c_Set_Oimage(X17633,X17632,X17631),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17633,tc_HOL_Obool)),X17629),X17630)))|~c_Fun_Oinj__on(X17633,X17632,X17631,X17630)|c_Fun_Oinj__on(X17633,X17632,X17631,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17633,tc_HOL_Obool)),X17630),X17629)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__Un])])])). 6.97/7.22 fof(c_0_6272, plain, ![X1513, X1514, X1515, X1516, X1517]:((~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),X1516),X1517)),X1515)),X1514)),X1513))|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),X1516),X1515)),X1514)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1517),X1515)),X1513)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1517),X1516)))&(~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),X1516),X1515)),X1514)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1517),X1515)),X1513)))|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),X1516),X1517)),X1515)),X1514)),X1513))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1517),X1516)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff1])])])). 6.97/7.22 fof(c_0_6273, plain, ![X11012, X11013, X11014, X11015, X11016]:((~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),X11015),X11014)),X11013)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11016),X11014)),X11012)))|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),X11015),X11016)),X11014)),X11013)),X11012))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11016),X11015)))&(~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),X11015),X11016)),X11014)),X11013)),X11012))|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),X11015),X11014)),X11013)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11016),X11014)),X11012)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11016),X11015)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__le__add__iff1])])])])). 6.97/7.22 fof(c_0_6274, plain, ![X8457, X8458, X8459, X8460, X8461]:((~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),X8461),X8459)),X8458)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8460),X8459)),X8457)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8458),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),X8460),X8461)),X8459)),X8457)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8461),X8460)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8458),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),X8460),X8461)),X8459)),X8457)))|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),X8461),X8459)),X8458)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8460),X8459)),X8457)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8461),X8460)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff2])])])). 6.97/7.22 fof(c_0_6275, plain, ![X17593, X17594, X17595, X17596, X17597, X17598]:(~c_Relation_Osingle__valued(X17598,X17597,hAPP(c_Relation_Oconverse(X17597,X17598),X17596))|(X17595=c_Orderings_Obot__class_Obot(tc_fun(X17594,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17594,tc_fun(X17598,tc_HOL_Obool)),X17595),hAPP(hAPP(c_COMBB(tc_fun(X17597,tc_HOL_Obool),tc_fun(X17598,tc_HOL_Obool),X17594),c_Relation_OImage(X17597,X17598,X17596)),X17593))=hAPP(c_Relation_OImage(X17597,X17598,X17596),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17594,tc_fun(X17597,tc_HOL_Obool)),X17595),X17593)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Image__INT__eq])])])). 6.97/7.22 fof(c_0_6276, plain, ![X1977, X1978, X1979]:((c_Orderings_Obot__class_Obot(tc_fun(X1979,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1979,tc_HOL_Obool)),X1978),hAPP(hAPP(c_Set_Oinsert(X1979),X1977),c_Orderings_Obot__class_Obot(tc_fun(X1979,tc_HOL_Obool))))|X1977=c_Big__Operators_Olattice__class_OSup__fin(X1979,hAPP(hAPP(c_Set_Oinsert(X1979),X1977),X1978))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1979),X1978))|~class_Lattices_Olattice(X1979))&(c_Orderings_Obot__class_Obot(tc_fun(X1979,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1979,tc_HOL_Obool)),X1978),hAPP(hAPP(c_Set_Oinsert(X1979),X1977),c_Orderings_Obot__class_Obot(tc_fun(X1979,tc_HOL_Obool))))|c_Big__Operators_Olattice__class_OSup__fin(X1979,hAPP(hAPP(c_Set_Oinsert(X1979),X1977),X1978))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1979),X1977),c_Big__Operators_Olattice__class_OSup__fin(X1979,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1979,tc_HOL_Obool)),X1978),hAPP(hAPP(c_Set_Oinsert(X1979),X1977),c_Orderings_Obot__class_Obot(tc_fun(X1979,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1979),X1978))|~class_Lattices_Olattice(X1979))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oinsert__remove])])])])). 6.97/7.22 fof(c_0_6277, plain, ![X3920, X3921, X3922, X3923, X3924]:((~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),X3924),X3922)),X3921)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3923),X3922)),X3920)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3921),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),X3923),X3924)),X3922)),X3920)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3924),X3923)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3921),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),X3923),X3924)),X3922)),X3920)))|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),X3924),X3922)),X3921)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3923),X3922)),X3920)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3924),X3923)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff2])])])). 6.97/7.22 fof(c_0_6278, plain, ![X12285, X12286, X12287, X12288, X12289]:(~class_Groups_Ocomm__monoid__mult(X12289)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12288),X12287))|(~hBOOL(hAPP(hAPP(c_member(X12288),X12286),X12287))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12289),hAPP(X12285,X12286)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12288,X12289),X12285),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12288,tc_HOL_Obool)),X12287),hAPP(hAPP(c_Set_Oinsert(X12288),X12286),c_Orderings_Obot__class_Obot(tc_fun(X12288,tc_HOL_Obool))))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12288,X12289),X12285),X12287)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod_Oremove])])])). 6.97/7.22 fof(c_0_6279, plain, ![X283, X284, X285, X286, X287]:(~c_Equiv__Relations_Oequiv(X287,X286,X285)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X287,X287)),hAPP(hAPP(c_Product__Type_OPair(X287,X287),X284),X283)),X285))|hAPP(c_Relation_OImage(X287,X287,X285),hAPP(hAPP(c_Set_Oinsert(X287),X283),c_Orderings_Obot__class_Obot(tc_fun(X287,tc_HOL_Obool))))=hAPP(c_Relation_OImage(X287,X287,X285),hAPP(hAPP(c_Set_Oinsert(X287),X284),c_Orderings_Obot__class_Obot(tc_fun(X287,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equiv__class__eq])])])). 6.97/7.22 cnf(c_0_6280, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk23_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)),esk21_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_4947])). 6.97/7.22 cnf(c_0_6281, 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_4948]), ['final']). 6.97/7.22 cnf(c_0_6282, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk22_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)),esk21_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_4947])). 6.97/7.22 cnf(c_0_6283, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))=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))|~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_4949, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411])). 6.97/7.22 cnf(c_0_6284, plain, (hBOOL(hAPP(X3,esk121_2(X3,X2)))|hBOOL(hAPP(X3,esk118_2(X3,X2)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk118_2(X3,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk119_2(X3,X2)),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_4950])). 6.97/7.22 cnf(c_0_6285, 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_4951]), ['final']). 6.97/7.22 fof(c_0_6286, plain, ![X14460, X14461, X14462, X14463, X14464, X14465, X14466, X14467, X14468]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X14468,X14467)),hAPP(hAPP(c_Product__Type_OPair(X14468,X14467),X14466),X14465)),X14464))|hBOOL(hAPP(hAPP(c_member(tc_prod(X14463,X14462)),hAPP(hAPP(c_Product__Type_OPair(X14463,X14462),hAPP(X14461,X14466)),hAPP(X14460,X14465))),hAPP(c_Set_Oimage(tc_prod(X14468,X14467),tc_prod(X14463,X14462),c_Product__Type_Omap__pair(X14468,X14463,X14467,X14462,X14461,X14460)),X14464)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__pair__imageI])])])). 6.97/7.22 cnf(c_0_6287, 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)))|~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),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X2))),c_List_Olex(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_4932])). 6.97/7.22 cnf(c_0_6288, 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)))), inference(split_conjunct,[status(thm)],[c_0_4952]), ['final']). 6.97/7.22 fof(c_0_6289, plain, ![X7207, X7208, X7209, X7210, X7211, X7212, X7213, X7214]:(~c_Finite__Set_Ofolding__image(X7214,X7213,X7212,X7211,X7210)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7213),X7209))|hAPP(hAPP(X7212,hAPP(hAPP(X7210,X7208),X7209)),hAPP(hAPP(X7210,X7207),X7209))=hAPP(hAPP(X7210,hAPP(hAPP(c_COMBS(X7213,X7214,X7214),hAPP(hAPP(c_COMBB(X7214,tc_fun(X7214,X7214),X7213),X7212),X7208)),X7207)),X7209))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image_Odistrib])])])). 6.97/7.22 cnf(c_0_6290, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X2),X1))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),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(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))!=X3), inference(split_conjunct,[status(thm)],[c_0_4953])). 6.97/7.22 cnf(c_0_6291, 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_4954]), ['final']). 6.97/7.22 fof(c_0_6292, plain, ![X16465, X16466, X16467, X16468, X16469, X16470]:(~c_Finite__Set_Ofun__left__comm(X16470,X16469,X16468)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16470),X16467))|hAPP(hAPP(c_Finite__Set_Ofold(X16470,X16469,X16468),X16466),hAPP(hAPP(c_Set_Oinsert(X16470),X16465),X16467))=hAPP(hAPP(X16468,X16465),hAPP(hAPP(c_Finite__Set_Ofold(X16470,X16469,X16468),X16466),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16470,tc_HOL_Obool)),X16467),hAPP(hAPP(c_Set_Oinsert(X16470),X16465),c_Orderings_Obot__class_Obot(tc_fun(X16470,tc_HOL_Obool)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__insert__remove])])])). 6.97/7.22 fof(c_0_6293, plain, ![X6985, X6986, X6987, X6988]:(~hBOOL(hAPP(c_List_Odistinct(X6988),X6987))|(hBOOL(hAPP(hAPP(c_member(X6988),X6986),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6988,tc_HOL_Obool)),hAPP(c_List_Oset(X6988),X6987)),hAPP(hAPP(c_Set_Oinsert(X6988),hAPP(hAPP(c_List_Onth(X6988),X6987),X6985)),c_Orderings_Obot__class_Obot(tc_fun(X6988,tc_HOL_Obool))))))|hBOOL(hAPP(c_List_Odistinct(X6988),hAPP(hAPP(c_List_Olist__update(X6988,X6987),X6985),X6986))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__list__update])])])). 6.97/7.22 fof(c_0_6294, plain, ![X2127, X2128, X2129]:(~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,X2129),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X2129)),X2128))))|hBOOL(hAPP(hAPP(c_member(X2129),hAPP(c_Product__Type_Ofst(X2129,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(X2129,X2128),X2127))),hAPP(c_List_Oset(X2129),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X2129),X2129),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X2129)),X2128))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_select__weight__member])])])). 6.97/7.22 fof(c_0_6295, plain, ![X5466, X5467, X5468, X5469, X5470, X5471]:(~c_Finite__Set_Ofun__left__comm(X5471,X5470,X5469)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5471),X5468))|(~hBOOL(hAPP(hAPP(c_member(X5471),X5467),X5468))|hAPP(hAPP(X5469,X5467),hAPP(hAPP(c_Finite__Set_Ofold(X5471,X5470,X5469),X5466),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5471,tc_HOL_Obool)),X5468),hAPP(hAPP(c_Set_Oinsert(X5471),X5467),c_Orderings_Obot__class_Obot(tc_fun(X5471,tc_HOL_Obool))))))=hAPP(hAPP(c_Finite__Set_Ofold(X5471,X5470,X5469),X5466),X5468)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__rec])])])). 6.97/7.22 fof(c_0_6296, plain, ![X12572, X12573, X12574, X12575, X12576, X12577]:(~c_Fun_Obij__betw(X12577,X12576,X12575,c_Orderings_Otop__class_Otop(tc_fun(X12577,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X12576,tc_HOL_Obool)))|hAPP(c_Set_Oimage(X12577,X12576,X12575),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12574,tc_fun(X12577,tc_HOL_Obool)),X12573),X12572))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12574,tc_fun(X12576,tc_HOL_Obool)),X12573),hAPP(hAPP(c_COMBB(tc_fun(X12577,tc_HOL_Obool),tc_fun(X12576,tc_HOL_Obool),X12574),c_Set_Oimage(X12577,X12576,X12575)),X12572))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bij__image__INT])])])). 6.97/7.22 cnf(c_0_6297, plain, (X1=X2|hAPP(c_List_Ofilter(X3,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot),hAPP(c_fequal,X2))),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X4))=hAPP(hAPP(c_List_Olist_OCons(X3),X1),hAPP(c_List_Ofilter(X3,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot),hAPP(c_fequal,X2))),X4))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4955, c_0_4573]), c_0_4573])). 6.97/7.22 fof(c_0_6298, plain, ![X414, X415, X416, X417, X418]:(~class_Groups_Ocomm__monoid__add(X418)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X417),X416))|(~hBOOL(hAPP(hAPP(c_member(X417),X415),X416))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X417,X418),X414),X416)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X418),hAPP(X414,X415)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X417,X418),X414),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X417,tc_HOL_Obool)),X416),hAPP(hAPP(c_Set_Oinsert(X417),X415),c_Orderings_Obot__class_Obot(tc_fun(X417,tc_HOL_Obool))))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff1_H])])). 6.97/7.22 fof(c_0_6299, plain, ![X4185]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X4185))|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))),X4185)),c_FunDef_Omax__weak))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wmax__emptyI])])])). 6.97/7.22 cnf(c_0_6300, 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,esk108_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_4908])). 6.97/7.22 fof(c_0_6301, plain, ![X2239, X2240, X2241, X2242, X2243, X2244, X2245, X2246]:(~c_Finite__Set_Ofolding(X2246,X2245,X2244,X2243)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2246),X2242))|hAPP(c_Fun_Ocomp(X2245,X2245,X2241,hAPP(X2243,X2242)),hAPP(c_Fun_Ocomp(X2245,X2245,X2241,hAPP(X2244,X2240)),X2239))=hAPP(c_Fun_Ocomp(X2245,X2245,X2241,hAPP(X2244,X2240)),hAPP(c_Fun_Ocomp(X2245,X2245,X2241,hAPP(X2243,X2242)),X2239)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Ocommute__left__comp_H])])])). 6.97/7.22 fof(c_0_6302, plain, ![X13807, X13808, X13809, X13810, X13811, X13812, X13813]:((X13808=hAPP(hAPP(X13811,X13807),esk463_7(X13807,X13808,X13809,X13810,X13811,X13812,X13813))|~hBOOL(hAPP(hAPP(c_member(X13813),X13807),X13809))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X13813,X13812,X13811,X13810,X13809),X13808))|~c_Finite__Set_Ofun__left__comm(X13813,X13812,X13811))&(hBOOL(hAPP(c_Finite__Set_Ofold__graph(X13813,X13812,X13811,X13810,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13813,tc_HOL_Obool)),X13809),hAPP(hAPP(c_Set_Oinsert(X13813),X13807),c_Orderings_Obot__class_Obot(tc_fun(X13813,tc_HOL_Obool))))),esk463_7(X13807,X13808,X13809,X13810,X13811,X13812,X13813)))|~hBOOL(hAPP(hAPP(c_member(X13813),X13807),X13809))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X13813,X13812,X13811,X13810,X13809),X13808))|~c_Finite__Set_Ofun__left__comm(X13813,X13812,X13811))), 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])])])])])). 6.97/7.22 cnf(c_0_6303, plain, (hAPP(hAPP(c_List_Oappend(X2),X4),X5)=hAPP(hAPP(c_List_Oappend(X2),X3),X1)|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)|X3!=hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),X4)|X5!=hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)),X3)),X1)|X4!=hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)),X3)), inference(split_conjunct,[status(thm)],[c_0_4956])). 6.97/7.22 fof(c_0_6304, plain, ![X13427, X13428, X13429, X13430, X13431]:((X13431=c_Orderings_Obot__class_Obot(tc_fun(X13430,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13430,tc_fun(X13429,tc_HOL_Obool)),X13431),hAPP(hAPP(c_COMBB(tc_fun(X13429,tc_HOL_Obool),tc_fun(X13429,tc_HOL_Obool),X13430),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13429,tc_HOL_Obool)),X13428)),X13427))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13429,tc_HOL_Obool)),X13428),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13430,tc_fun(X13429,tc_HOL_Obool)),X13431),X13427)))&(X13431!=c_Orderings_Obot__class_Obot(tc_fun(X13430,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13429,tc_HOL_Obool)),X13428),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13430,tc_fun(X13429,tc_HOL_Obool)),X13431),X13427))=X13428)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INT__extend__simps_I2_J])])])). 6.97/7.22 fof(c_0_6305, plain, ![X9931, X9932, X9933, X9934, X9935, X9936, X9937, X9938]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X9938,X9937)),hAPP(hAPP(c_Product__Type_OPair(X9938,X9937),X9936),X9935)),X9934))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X9937,X9933)),hAPP(hAPP(c_Product__Type_OPair(X9937,X9933),X9935),X9932)),X9931))|hBOOL(hAPP(hAPP(c_member(tc_prod(X9938,X9933)),hAPP(hAPP(c_Product__Type_OPair(X9938,X9933),X9936),X9932)),hAPP(hAPP(c_Relation_Orel__comp(X9938,X9937,X9933),X9934),X9931))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__compI])])). 6.97/7.22 cnf(c_0_6306, 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_4957])). 6.97/7.22 cnf(c_0_6307, plain, (hAPP(c_Hilbert__Choice_Oinv__into(X4,X2,X6,hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5)),X7)=hAPP(hAPP(c_Fun_Ocomp(X1,X4,X2,c_Hilbert__Choice_Oinv__into(X4,X1,X6,X5)),c_Hilbert__Choice_Oinv__into(X1,X2,hAPP(c_Set_Oimage(X4,X1,X5),X6),X3)),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_4958])). 6.97/7.22 fof(c_0_6308, plain, ![X3469, X3470, X3471, X3472, X3473]:((hBOOL(hAPP(hAPP(c_member(X3472),esk111_5(X3469,X3470,X3471,X3472,X3473)),X3471))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3473),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3472,X3473),X3470),X3471)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3472,X3473),X3469),X3471)))|X3471=c_Orderings_Obot__class_Obot(tc_fun(X3472,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3472),X3471))|(~class_Groups_Ocomm__monoid__add(X3473)|~class_Groups_Oordered__cancel__ab__semigroup__add(X3473)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3473),hAPP(X3470,esk111_5(X3469,X3470,X3471,X3472,X3473))),hAPP(X3469,esk111_5(X3469,X3470,X3471,X3472,X3473))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3473),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3472,X3473),X3470),X3471)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3472,X3473),X3469),X3471)))|X3471=c_Orderings_Obot__class_Obot(tc_fun(X3472,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3472),X3471))|(~class_Groups_Ocomm__monoid__add(X3473)|~class_Groups_Oordered__cancel__ab__semigroup__add(X3473)))), 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])])])])])). 6.97/7.22 fof(c_0_6309, plain, ![X2304, X2305, X2306]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2306),X2305))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2306),X2304))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X2306),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2306,tc_HOL_Obool)),X2305),X2304))),hAPP(c_Finite__Set_Ocard(X2306),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2306,tc_HOL_Obool)),X2305),X2304)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X2306),X2305)),hAPP(c_Finite__Set_Ocard(X2306),X2304)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Un__Int])])])). 6.97/7.22 fof(c_0_6310, plain, ![X8380, X8381, X8382, X8383, X8384, X8385]:(~class_Rings_Olinordered__semiring__1__strict(X8385)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8385),X8384),X8383))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8385),X8382),X8383))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8385),c_Groups_Ozero__class_Ozero(X8385)),X8381))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8385),c_Groups_Ozero__class_Ozero(X8385)),X8380))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8385),X8381),X8380)!=c_Groups_Oone__class_Oone(X8385)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8385),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8385),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8385),X8381),X8384)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8385),X8380),X8382))),X8383)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_convex__bound__lt])])])). 6.97/7.22 fof(c_0_6311, plain, ![X14408, X14409, X14410, X14411, X14412, X14413]:(~class_Rings_Olinordered__semiring__1(X14413)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14413),X14412),X14411))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14413),X14410),X14411))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14413),c_Groups_Ozero__class_Ozero(X14413)),X14409))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14413),c_Groups_Ozero__class_Ozero(X14413)),X14408))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14413),X14409),X14408)!=c_Groups_Oone__class_Oone(X14413)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14413),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14413),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14413),X14409),X14412)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14413),X14408),X14410))),X14411)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_convex__bound__le])])])). 6.97/7.22 fof(c_0_6312, plain, ![X6214, X6215, X6216, X6217, X6218, X6219]:(~c_Finite__Set_Ofolding(X6219,X6218,X6217,X6216)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6219),X6215))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6219),X6214))|hAPP(c_Fun_Ocomp(X6218,X6218,X6218,hAPP(X6216,X6215)),hAPP(X6216,X6214))=hAPP(c_Fun_Ocomp(X6218,X6218,X6218,hAPP(X6216,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6219,tc_HOL_Obool)),X6215),X6214))),hAPP(X6216,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6219,tc_HOL_Obool)),X6215),X6214)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Ounion__inter])])])). 6.97/7.22 fof(c_0_6313, plain, ![X1706, X1707, X1708, X1709, X1710, X1711]:(~c_Fun_Oinj__on(X1711,X1710,X1709,X1708)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1711,tc_HOL_Obool)),X1707),X1708))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1711,tc_HOL_Obool)),X1706),X1708))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1710,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1711,X1710,X1709),X1707)),hAPP(c_Set_Oimage(X1711,X1710,X1709),X1706))=hAPP(c_Set_Oimage(X1711,X1710,X1709),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1711,tc_HOL_Obool)),X1707),X1706))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__image__set__diff])])])). 6.97/7.22 fof(c_0_6314, plain, ![X11806, X11807, X11808, X11809, X11810]:(~class_Fields_Ofield(X11810)|(c_Groups_Ozero__class_Ozero(X11810)=X11809|(c_Groups_Ozero__class_Ozero(X11810)=X11808|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X11810),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11810),X11807),X11809)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11810),X11806),X11808))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11810),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X11810),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11810),X11807),X11808)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11810),X11806),X11809))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11810),X11809),X11808))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__frac__eq])])])). 6.97/7.22 fof(c_0_6315, plain, ![X15573, X15574, X15575, X15576]:((hBOOL(hAPP(hAPP(c_member(X15576),esk525_4(X15573,X15574,X15575,X15576)),X15575))|hAPP(c_Finite__Set_Ocard(tc_prod(X15576,X15574)),hAPP(hAPP(c_Product__Type_OSigma(X15576,X15574),X15575),X15573))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X15576,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X15574,tc_HOL_Obool),tc_Nat_Onat,X15576),c_Finite__Set_Ocard(X15574)),X15573)),X15575)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X15576),X15575)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15574),hAPP(X15573,esk525_4(X15573,X15574,X15575,X15576))))|hAPP(c_Finite__Set_Ocard(tc_prod(X15576,X15574)),hAPP(hAPP(c_Product__Type_OSigma(X15576,X15574),X15575),X15573))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X15576,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X15574,tc_HOL_Obool),tc_Nat_Onat,X15576),c_Finite__Set_Ocard(X15574)),X15573)),X15575)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X15576),X15575)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__SigmaI])])])])). 6.97/7.22 cnf(c_0_6316, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk494_4(X2,X3,X4,X1)),hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),X3)),hAPP(c_Set_OCollect(X1),X2)))))|hBOOL(hAPP(X2,X4))|~c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3)|~hBOOL(hAPP(hAPP(c_member(X1),X4),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),X3)))), inference(split_conjunct,[status(thm)],[c_0_4959])). 6.97/7.22 fof(c_0_6317, plain, ![X1764, X1765, X1766, X1767, X1768, X1769]:((hBOOL(hAPP(hAPP(c_member(X1768),esk52_6(X1764,X1765,X1766,X1767,X1768,X1769)),X1767))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1769,X1768,c_Groups_Otimes__class_Otimes(X1769)),X1766),X1764),X1767)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1769,X1768,c_Groups_Otimes__class_Otimes(X1769)),X1765),X1764),X1767)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1768),X1767))|~class_Groups_Oab__semigroup__mult(X1769))&(hAPP(X1765,esk52_6(X1764,X1765,X1766,X1767,X1768,X1769))!=hAPP(X1766,esk52_6(X1764,X1765,X1766,X1767,X1768,X1769))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1769,X1768,c_Groups_Otimes__class_Otimes(X1769)),X1766),X1764),X1767)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1769,X1768,c_Groups_Otimes__class_Otimes(X1769)),X1765),X1764),X1767)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1768),X1767))|~class_Groups_Oab__semigroup__mult(X1769))), 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])])])])])). 6.97/7.22 fof(c_0_6318, plain, ![X8266, X8267, X8268, X8269]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8269),X8268))|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),X8269),X8267)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X8268),X8266))),c_FunDef_Opair__less))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__lessI1])])). 6.97/7.22 fof(c_0_6319, plain, ![X12945, X12946, X12947, X12948, X12949, X12950]:(~c_Fun_Oinj__on(X12950,X12949,X12948,X12947)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12950,tc_HOL_Obool)),X12946),X12947))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12950,tc_HOL_Obool)),X12945),X12947))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12949,tc_HOL_Obool)),hAPP(c_Set_Oimage(X12950,X12949,X12948),X12946)),hAPP(c_Set_Oimage(X12950,X12949,X12948),X12945))=hAPP(c_Set_Oimage(X12950,X12949,X12948),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12950,tc_HOL_Obool)),X12946),X12945))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__image__Int])])])). 6.97/7.22 fof(c_0_6320, plain, ![X12553, X12554, X12555, X12556, X12557]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X12557,X12557)),hAPP(hAPP(c_Product__Type_OPair(X12557,X12557),X12556),esk413_5(X12553,X12554,X12555,X12556,X12557))),X12553))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X12557,X12557)),hAPP(hAPP(c_Product__Type_OPair(X12557,X12557),X12556),X12555)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X12557,X12557),tc_HOL_Obool),hAPP(c_Nat_OSuc,X12554)),X12553))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X12557,X12557)),hAPP(hAPP(c_Product__Type_OPair(X12557,X12557),esk413_5(X12553,X12554,X12555,X12556,X12557)),X12555)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X12557,X12557),tc_HOL_Obool),X12554),X12553)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X12557,X12557)),hAPP(hAPP(c_Product__Type_OPair(X12557,X12557),X12556),X12555)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X12557,X12557),tc_HOL_Obool),hAPP(c_Nat_OSuc,X12554)),X12553))))), 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__D2])])])])])). 6.97/7.22 fof(c_0_6321, plain, ![X9398, X9399, X9400, X9401, X9402]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X9402,X9402)),hAPP(hAPP(c_Product__Type_OPair(X9402,X9402),X9401),esk308_5(X9398,X9399,X9400,X9401,X9402))),X9398))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X9402,X9402)),hAPP(hAPP(c_Product__Type_OPair(X9402,X9402),X9401),X9400)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X9402,X9402),tc_HOL_Obool),hAPP(c_Nat_OSuc,X9399)),X9398))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X9402,X9402)),hAPP(hAPP(c_Product__Type_OPair(X9402,X9402),esk308_5(X9398,X9399,X9400,X9401,X9402)),X9400)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X9402,X9402),tc_HOL_Obool),X9399),X9398)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X9402,X9402)),hAPP(hAPP(c_Product__Type_OPair(X9402,X9402),X9401),X9400)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X9402,X9402),tc_HOL_Obool),hAPP(c_Nat_OSuc,X9399)),X9398))))), 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])])])])])). 6.97/7.22 fof(c_0_6322, plain, ![X16166, X16167, X16168, X16169, X16170]:(~class_Fields_Ofield(X16170)|(c_Groups_Ozero__class_Ozero(X16170)=X16169|(X16168=c_Groups_Ozero__class_Ozero(X16170)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16170),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16170),X16167),X16169)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16170),X16166),X16168))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16170),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16170),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16170),X16167),X16168)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16170),X16166),X16169))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16170),X16169),X16168))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__frac__eq])])). 6.97/7.22 fof(c_0_6323, plain, ![X16670, X16671, X16672, X16673]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16673),X16672))|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),X16673),X16671)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X16672),X16670))),c_FunDef_Opair__leq))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pair__leqI1])])])). 6.97/7.22 fof(c_0_6324, plain, ![X7007, X7008, X7009, X7010, X7011]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X7011,X7011)),hAPP(hAPP(c_Product__Type_OPair(X7011,X7011),X7010),esk225_5(X7007,X7008,X7009,X7010,X7011))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7011,X7011),tc_HOL_Obool),X7008),X7007)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X7011,X7011)),hAPP(hAPP(c_Product__Type_OPair(X7011,X7011),X7010),X7009)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7011,X7011),tc_HOL_Obool),hAPP(c_Nat_OSuc,X7008)),X7007))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X7011,X7011)),hAPP(hAPP(c_Product__Type_OPair(X7011,X7011),esk225_5(X7007,X7008,X7009,X7010,X7011)),X7009)),X7007))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X7011,X7011)),hAPP(hAPP(c_Product__Type_OPair(X7011,X7011),X7010),X7009)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7011,X7011),tc_HOL_Obool),hAPP(c_Nat_OSuc,X7008)),X7007))))), 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])])])])])). 6.97/7.22 cnf(c_0_6325, 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,esk187_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_4960])). 6.97/7.22 fof(c_0_6326, plain, ![X17072, X17073, X17074, X17075, X17076, X17077]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17077),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17077),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17077),X17076),X17073)),X17075)),X17074)),X17072))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17077),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17077),X17076),X17075)),X17074)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17077),X17073),X17075)),X17072)))|~class_Rings_Oordered__ring(X17077))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17077),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17077),X17076),X17075)),X17074)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17077),X17073),X17075)),X17072)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17077),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17077),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17077),X17076),X17073)),X17075)),X17074)),X17072))|~class_Rings_Oordered__ring(X17077))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff1])])])). 6.97/7.22 fof(c_0_6327, plain, ![X5105, X5106, X5107, X5108, X5109, X5110]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5110),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5110),X5109),X5108)),X5107)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5110),X5106),X5108)),X5105)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5110),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5110),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5110),X5109),X5106)),X5108)),X5107)),X5105))|~class_Rings_Oordered__ring(X5110))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5110),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5110),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5110),X5109),X5106)),X5108)),X5107)),X5105))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5110),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5110),X5109),X5108)),X5107)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5110),X5106),X5108)),X5105)))|~class_Rings_Oordered__ring(X5110))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff1])])])). 6.97/7.22 fof(c_0_6328, plain, ![X14079, X14080, X14081, X14082, X14083]:(~class_Groups_Ocomm__monoid__mult(X14083)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14082),X14081))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14083),hAPP(X14080,X14079)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X14082,X14083),X14080),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X14082,tc_HOL_Obool)),X14081),hAPP(hAPP(c_Set_Oinsert(X14082),X14079),c_Orderings_Obot__class_Obot(tc_fun(X14082,tc_HOL_Obool))))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X14082,X14083),X14080),hAPP(hAPP(c_Set_Oinsert(X14082),X14079),X14081)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oinsert__remove])])). 6.97/7.22 fof(c_0_6329, plain, ![X12940, X12941, X12942, X12943, X12944]:((~c_Fun_Oinj__on(X12944,X12943,X12942,X12940)|hBOOL(hAPP(hAPP(c_member(X12943),hAPP(X12942,X12941)),hAPP(c_Set_Oimage(X12944,X12943,X12942),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12944,tc_HOL_Obool)),X12940),hAPP(hAPP(c_Set_Oinsert(X12944),X12941),c_Orderings_Obot__class_Obot(tc_fun(X12944,tc_HOL_Obool)))))))|c_Fun_Oinj__on(X12944,X12943,X12942,hAPP(hAPP(c_Set_Oinsert(X12944),X12941),X12940)))&((c_Fun_Oinj__on(X12944,X12943,X12942,X12940)|~c_Fun_Oinj__on(X12944,X12943,X12942,hAPP(hAPP(c_Set_Oinsert(X12944),X12941),X12940)))&(~hBOOL(hAPP(hAPP(c_member(X12943),hAPP(X12942,X12941)),hAPP(c_Set_Oimage(X12944,X12943,X12942),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12944,tc_HOL_Obool)),X12940),hAPP(hAPP(c_Set_Oinsert(X12944),X12941),c_Orderings_Obot__class_Obot(tc_fun(X12944,tc_HOL_Obool)))))))|~c_Fun_Oinj__on(X12944,X12943,X12942,hAPP(hAPP(c_Set_Oinsert(X12944),X12941),X12940))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__insert])])])])). 6.97/7.22 fof(c_0_6330, plain, ![X2650, X2651, X2652, X2653, X2654, X2655]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2655),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2655),X2654),X2653)),X2652)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2655),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2655),X2651),X2653)),X2650)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2655),X2652),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2655),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2655),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2655),X2651),X2654)),X2653)),X2650)))|~class_Rings_Oordered__ring(X2655))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2655),X2652),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2655),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2655),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2655),X2651),X2654)),X2653)),X2650)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2655),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2655),X2654),X2653)),X2652)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2655),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2655),X2651),X2653)),X2650)))|~class_Rings_Oordered__ring(X2655))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__add__iff2])])])])). 6.97/7.22 fof(c_0_6331, plain, ![X13878, X13879, X13880, X13881, X13882, X13883]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13883),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13883),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13883),X13882),X13881)),X13880)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13883),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13883),X13879),X13881)),X13878)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13883),X13880),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13883),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13883),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13883),X13879),X13882)),X13881)),X13878)))|~class_Rings_Oordered__ring(X13883))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13883),X13880),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13883),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13883),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13883),X13879),X13882)),X13881)),X13878)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13883),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13883),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13883),X13882),X13881)),X13880)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13883),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13883),X13879),X13881)),X13878)))|~class_Rings_Oordered__ring(X13883))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__add__iff2])])])])). 6.97/7.22 fof(c_0_6332, plain, ![X8745, X8746, X8747, X8748, X8749]:(~c_Fun_Obij__betw(X8749,X8748,X8747,c_Orderings_Otop__class_Otop(tc_fun(X8749,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X8748,tc_HOL_Obool)))|(~c_Fun_Obij__betw(X8746,X8749,X8745,c_Orderings_Otop__class_Otop(tc_fun(X8746,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X8749,tc_HOL_Obool)))|hAPP(c_Fun_Ocomp(X8749,X8746,X8748,c_Hilbert__Choice_Oinv__into(X8746,X8749,c_Orderings_Otop__class_Otop(tc_fun(X8746,tc_HOL_Obool)),X8745)),c_Hilbert__Choice_Oinv__into(X8749,X8748,c_Orderings_Otop__class_Otop(tc_fun(X8749,tc_HOL_Obool)),X8747))=c_Hilbert__Choice_Oinv__into(X8746,X8748,c_Orderings_Otop__class_Otop(tc_fun(X8746,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(X8749,X8748,X8746,X8747),X8745)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_o__inv__distrib])])])). 6.97/7.22 fof(c_0_6333, plain, ![X5527, X5528, X5529, X5530, X5531]:(~class_Groups_Ocomm__monoid__add(X5531)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5530),X5529))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5530,X5531),X5528),hAPP(hAPP(c_Set_Oinsert(X5530),X5527),X5529))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5531),hAPP(X5528,X5527)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5530,X5531),X5528),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5530,tc_HOL_Obool)),X5529),hAPP(hAPP(c_Set_Oinsert(X5530),X5527),c_Orderings_Obot__class_Obot(tc_fun(X5530,tc_HOL_Obool)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum_Oinsert__remove])])])). 6.97/7.22 cnf(c_0_6334, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[c_0_4961, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 fof(c_0_6335, plain, ![X4426, X4427, X4428, X4429, X4430]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X4430,X4430)),hAPP(hAPP(c_Product__Type_OPair(X4430,X4430),X4429),X4428)),X4427))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4430),tc_List_Olist(X4430))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4430),tc_List_Olist(X4430)),hAPP(hAPP(c_List_Olist_OCons(X4430),X4429),X4426)),hAPP(hAPP(c_List_Olist_OCons(X4430),X4428),X4426))),c_List_Olistrel1(X4430,X4427)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1I1])])). 6.97/7.22 cnf(c_0_6336, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk275_3(X3,X2,X1))),esk276_3(X3,X2,X1))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk273_3(X3,X2,X1))),esk274_3(X3,X2,X1))=X2|hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_4962])). 6.97/7.22 fof(c_0_6337, plain, ![X16303, X16304, X16305, X16306, X16307, X16308, X16309]:(~class_Groups_Oab__semigroup__mult(X16309)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16308),X16307))|(~c_Fun_Oinj__on(X16308,X16306,X16305,X16307)|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X16309,X16308,c_Groups_Otimes__class_Otimes(X16309)),hAPP(c_Fun_Ocomp(X16306,X16309,X16308,X16304),X16305)),X16303),X16307)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X16309,X16306,c_Groups_Otimes__class_Otimes(X16309)),X16304),X16303),hAPP(c_Set_Oimage(X16308,X16306,X16305),X16307))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__image__reindex])])])). 6.97/7.22 cnf(c_0_6338, 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)),esk21_3(X2,X3,X1)),X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),esk22_3(X2,X3,X1)),esk23_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_4947])). 6.97/7.22 fof(c_0_6339, plain, ![X16931, X16932, X16933, X16934, X16935]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X16935,X16934)),hAPP(X16935,X16933)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X16932,X16932)),hAPP(hAPP(c_Product__Type_OPair(X16932,X16932),X16934),X16933)),c_List_Omeasures(X16932,X16931)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X16932,X16932)),hAPP(hAPP(c_Product__Type_OPair(X16932,X16932),X16934),X16933)),c_List_Omeasures(X16932,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X16932,tc_Nat_Onat)),X16935),X16931)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_measures__lesseq])])). 6.97/7.22 cnf(c_0_6340, 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_4963])). 6.97/7.22 cnf(c_0_6341, plain, (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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))=c_Groups_Oone__class_Oone(X2)|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)],[inference(rw,[status(thm)],[c_0_4964, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_6342, plain, (c_Groups_Ozero__class_Ozero(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))|X1!=c_Groups_Ozero__class_Ozero(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)],[c_0_4965, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 fof(c_0_6343, plain, ![X6090, X6091, X6092, X6093, X6094]:(~class_Rings_Osemiring__0(X6094)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6094),hAPP(c_List_Omonoid__add__class_Olistsum(X6094),hAPP(hAPP(c_List_Omap(X6093,X6094),X6092),X6090))),X6091)=hAPP(c_List_Omonoid__add__class_Olistsum(X6094),hAPP(hAPP(c_List_Omap(X6093,X6094),hAPP(hAPP(c_COMBC(X6093,X6094,X6094),hAPP(hAPP(c_COMBB(X6094,tc_fun(X6094,X6094),X6093),c_Groups_Otimes__class_Otimes(X6094)),X6092)),X6091)),X6090))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__mult__const])])). 6.97/7.22 fof(c_0_6344, plain, ![X971, X972, X973, X974, X975]:((X974=hAPP(hAPP(c_List_Olist_OCons(X975),esk30_5(X971,X972,X973,X974,X975)),esk31_5(X971,X972,X973,X974,X975))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X975),tc_List_Olist(X975))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X975),tc_List_Olist(X975)),X974),hAPP(hAPP(c_List_Olist_OCons(X975),X973),X972))),c_List_Olistrel(X975,X971))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X975,X975)),hAPP(hAPP(c_Product__Type_OPair(X975,X975),esk30_5(X971,X972,X973,X974,X975)),X973)),X971))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X975),tc_List_Olist(X975))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X975),tc_List_Olist(X975)),X974),hAPP(hAPP(c_List_Olist_OCons(X975),X973),X972))),c_List_Olistrel(X975,X971))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X975),tc_List_Olist(X975))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X975),tc_List_Olist(X975)),esk31_5(X971,X972,X973,X974,X975)),X972)),c_List_Olistrel(X975,X971)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X975),tc_List_Olist(X975))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X975),tc_List_Olist(X975)),X974),hAPP(hAPP(c_List_Olist_OCons(X975),X973),X972))),c_List_Olistrel(X975,X971)))))), 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])])])])])). 6.97/7.22 cnf(c_0_6345, 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),X4)=hAPP(hAPP(c_List_Oappend(X1),X2),X5)|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)),X5)|X3!=hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2)), inference(split_conjunct,[status(thm)],[c_0_4956])). 6.97/7.22 fof(c_0_6346, plain, ![X16858, X16859, X16860]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X16860),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X16859),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X16859)),X16858))))|hBOOL(hAPP(hAPP(c_member(X16859),hAPP(c_Random_Opick(X16859,X16858),X16860)),hAPP(c_List_Oset(X16859),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X16859),X16859),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X16859)),X16858))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pick__member])])])). 6.97/7.22 fof(c_0_6347, plain, ![X3480, X3481, X3482, X3483, X3484]:((X3481=hAPP(hAPP(c_List_Olist_OCons(X3484),esk112_5(X3480,X3481,X3482,X3483,X3484)),esk113_5(X3480,X3481,X3482,X3483,X3484))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3484),tc_List_Olist(X3484))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3484),tc_List_Olist(X3484)),hAPP(hAPP(c_List_Olist_OCons(X3484),X3483),X3482)),X3481)),c_List_Olistrel(X3484,X3480))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X3484,X3484)),hAPP(hAPP(c_Product__Type_OPair(X3484,X3484),X3483),esk112_5(X3480,X3481,X3482,X3483,X3484))),X3480))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3484),tc_List_Olist(X3484))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3484),tc_List_Olist(X3484)),hAPP(hAPP(c_List_Olist_OCons(X3484),X3483),X3482)),X3481)),c_List_Olistrel(X3484,X3480))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3484),tc_List_Olist(X3484))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3484),tc_List_Olist(X3484)),X3482),esk113_5(X3480,X3481,X3482,X3483,X3484))),c_List_Olistrel(X3484,X3480)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3484),tc_List_Olist(X3484))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3484),tc_List_Olist(X3484)),hAPP(hAPP(c_List_Olist_OCons(X3484),X3483),X3482)),X3481)),c_List_Olistrel(X3484,X3480)))))), 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])])])])])). 6.97/7.22 fof(c_0_6348, plain, ![X11427, X11428, X11429, X11430, X11431, X11432, X11433, X11434]:(~c_Finite__Set_Ofolding__image__simple(X11434,X11433,X11432,X11431,X11430,X11429)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11433),X11428))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11433),X11427))|hAPP(hAPP(X11432,hAPP(X11429,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11433,tc_HOL_Obool)),X11428),X11427))),hAPP(X11429,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11433,tc_HOL_Obool)),X11428),X11427)))=hAPP(hAPP(X11432,hAPP(X11429,X11428)),hAPP(X11429,X11427))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Ounion__inter])])])). 6.97/7.22 fof(c_0_6349, plain, ![X6842, X6843, X6844, X6845, X6846]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X6843,X6845)),hAPP(X6843,X6844)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X6846,X6846)),hAPP(hAPP(c_Product__Type_OPair(X6846,X6846),X6845),X6844)),c_List_Omeasures(X6846,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X6846,tc_Nat_Onat)),X6843),X6842)))))&(hAPP(X6843,X6844)!=hAPP(X6843,X6845)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X6846,X6846)),hAPP(hAPP(c_Product__Type_OPair(X6846,X6846),X6845),X6844)),c_List_Omeasures(X6846,X6842)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X6846,X6846)),hAPP(hAPP(c_Product__Type_OPair(X6846,X6846),X6845),X6844)),c_List_Omeasures(X6846,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X6846,tc_Nat_Onat)),X6843),X6842))))))&((hAPP(X6843,X6844)=hAPP(X6843,X6845)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X6843,X6845)),hAPP(X6843,X6844)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X6846,X6846)),hAPP(hAPP(c_Product__Type_OPair(X6846,X6846),X6845),X6844)),c_List_Omeasures(X6846,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X6846,tc_Nat_Onat)),X6843),X6842)))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X6846,X6846)),hAPP(hAPP(c_Product__Type_OPair(X6846,X6846),X6845),X6844)),c_List_Omeasures(X6846,X6842)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X6843,X6845)),hAPP(X6843,X6844)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X6846,X6846)),hAPP(hAPP(c_Product__Type_OPair(X6846,X6846),X6845),X6844)),c_List_Omeasures(X6846,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X6846,tc_Nat_Onat)),X6843),X6842))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measures_I2_J])])])). 6.97/7.22 fof(c_0_6350, plain, ![X12181, X12182, X12183, X12184, X12185, X12186]:(~class_Complete__Lattice_Ocomplete__lattice(X12186)|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12185,X12186),X12184),hAPP(hAPP(c_COMBB(tc_fun(X12183,X12186),X12186,X12185),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12183,X12186),X12182)),X12181))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12183,X12186),X12182),hAPP(hAPP(c_COMBB(tc_fun(X12185,X12186),X12186,X12183),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12185,X12186),X12184)),hAPP(c_COMBC(X12185,X12183,X12186),X12181)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INF__commute])])])). 6.97/7.22 cnf(c_0_6351, plain, (c_Groups_Oone__class_Oone(X1)=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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))|~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)],[c_0_4966, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_6352, plain, (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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))|~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)],[c_0_4967, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 cnf(c_0_6353, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk120_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|hBOOL(hAPP(X1,esk118_2(X1,X2)))|hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk118_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk119_2(X1,X2)),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_4950])). 6.97/7.22 cnf(c_0_6354, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk497_3(X1,X2,X3)),esk498_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(X1,esk497_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk498_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_4968])). 6.97/7.22 cnf(c_0_6355, plain, (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),esk275_3(X1,X2,X3))),esk276_3(X1,X2,X3))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk273_3(X1,X2,X3))),esk274_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_4962])). 6.97/7.22 fof(c_0_6356, plain, ![X1967, X1968, X1969, X1970, X1971, X1972]:(~class_Complete__Lattice_Ocomplete__lattice(X1972)|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1971,X1972),X1970),hAPP(hAPP(c_COMBB(tc_fun(X1969,X1972),X1972,X1971),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1969,X1972),X1968)),X1967))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1969,X1972),X1968),hAPP(hAPP(c_COMBB(tc_fun(X1971,X1972),X1972,X1969),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1971,X1972),X1970)),hAPP(c_COMBC(X1971,X1969,X1972),X1967)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SUP__commute])])])). 6.97/7.22 cnf(c_0_6357, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X6,X3,X1),X2)),X5)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X6,X3,X4),X2)),X5)|hAPP(X1,esk517_6(X2,X3,X4,X1,X5,X6))!=hAPP(X4,esk517_6(X2,X3,X4,X1,X5,X6))), inference(split_conjunct,[status(thm)],[c_0_4969])). 6.97/7.22 fof(c_0_6358, plain, ![X4336, X4337, X4338, X4339, X4340]:(hAPP(c_Relation_OImage(X4340,X4340,X4339),hAPP(hAPP(c_Set_Oinsert(X4340),X4338),c_Orderings_Obot__class_Obot(tc_fun(X4340,tc_HOL_Obool))))!=hAPP(c_Relation_OImage(X4340,X4340,X4339),hAPP(hAPP(c_Set_Oinsert(X4340),X4337),c_Orderings_Obot__class_Obot(tc_fun(X4340,tc_HOL_Obool))))|(~c_Equiv__Relations_Oequiv(X4340,X4336,X4339)|(~hBOOL(hAPP(hAPP(c_member(X4340),X4337),X4336))|hBOOL(hAPP(hAPP(c_member(tc_prod(X4340,X4340)),hAPP(hAPP(c_Product__Type_OPair(X4340,X4340),X4338),X4337)),X4339))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__equiv__class])])])). 6.97/7.22 cnf(c_0_6359, plain, (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))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)|~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(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))!=X3), inference(split_conjunct,[status(thm)],[c_0_4953])). 6.97/7.22 cnf(c_0_6360, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X8),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X5),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X8),X1),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X6),X4))|hAPP(X1,esk209_8(X2,X1,X3,X4,X5,X6,X7,X8))!=hAPP(X2,esk209_8(X2,X1,X3,X4,X5,X6,X7,X8))|X4!=X3|X6!=X5|~class_Groups_Ocomm__monoid__add(X8)|~class_Orderings_Oord(X7)), inference(split_conjunct,[status(thm)],[c_0_4970])). 6.97/7.22 fof(c_0_6361, plain, ![X17394, X17395, X17396, X17397, X17398]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17398),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17397)),X17396)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17398),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17395)),X17394)))|hAPP(hAPP(c_Product__Type_OPair(X17397,X17395),hAPP(hAPP(c_List_Onth(X17397),X17396),X17398)),hAPP(hAPP(c_List_Onth(X17395),X17394),X17398))=hAPP(hAPP(c_List_Onth(tc_prod(X17397,X17395)),hAPP(hAPP(c_List_Ozip(X17397,X17395),X17396),X17394)),X17398))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__zip])])])). 6.97/7.22 fof(c_0_6362, plain, ![X17192, X17193, X17194, X17195, X17196, X17197]:(~hBOOL(hAPP(hAPP(c_member(X17197),X17196),X17195))|hAPP(hAPP(c_Set_Oinsert(X17194),X17193),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17197,tc_fun(X17194,tc_HOL_Obool)),X17195),X17192))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17197,tc_fun(X17194,tc_HOL_Obool)),X17195),hAPP(hAPP(c_COMBB(tc_fun(X17194,tc_HOL_Obool),tc_fun(X17194,tc_HOL_Obool),X17197),hAPP(c_Set_Oinsert(X17194),X17193)),X17192))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__insert__distrib])])])). 6.97/7.22 cnf(c_0_6363, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk23_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),esk21_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_4947])). 6.97/7.22 cnf(c_0_6364, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk22_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),esk21_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_4947])). 6.97/7.22 cnf(c_0_6365, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk265_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),esk264_4(X1,X2,X3,X4)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk264_4(X1,X2,X3,X4))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_4971])). 6.97/7.22 cnf(c_0_6366, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk265_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),esk264_4(X2,X3,X4,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X3,esk264_4(X2,X3,X4,X1))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_4971])). 6.97/7.22 fof(c_0_6367, plain, ![X13191, X13192, X13193, X13194, X13195, X13196, X13197, X13198]:(~c_Finite__Set_Ofolding(X13198,X13197,X13196,X13195)|hAPP(c_Fun_Ocomp(X13197,X13197,X13194,hAPP(X13196,X13193)),hAPP(c_Fun_Ocomp(X13197,X13197,X13194,hAPP(X13196,X13192)),X13191))=hAPP(c_Fun_Ocomp(X13197,X13197,X13194,hAPP(X13196,X13192)),hAPP(c_Fun_Ocomp(X13197,X13197,X13194,hAPP(X13196,X13193)),X13191))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp])])). 6.97/7.22 fof(c_0_6368, plain, ![X14035, X14036, X14037, X14038, X14039]:((hBOOL(hAPP(hAPP(c_member(X14038),esk476_5(X14035,X14036,X14037,X14038,X14039)),hAPP(c_List_Oset(X14038),X14037)))|hAPP(c_List_Omonoid__add__class_Olistsum(X14039),hAPP(hAPP(c_List_Omap(X14038,X14039),X14035),hAPP(c_List_Ofilter(X14038,X14036),X14037)))=hAPP(c_List_Omonoid__add__class_Olistsum(X14039),hAPP(hAPP(c_List_Omap(X14038,X14039),X14035),X14037))|~class_Groups_Omonoid__add(X14039))&((~hBOOL(hAPP(X14036,esk476_5(X14035,X14036,X14037,X14038,X14039)))|hAPP(c_List_Omonoid__add__class_Olistsum(X14039),hAPP(hAPP(c_List_Omap(X14038,X14039),X14035),hAPP(c_List_Ofilter(X14038,X14036),X14037)))=hAPP(c_List_Omonoid__add__class_Olistsum(X14039),hAPP(hAPP(c_List_Omap(X14038,X14039),X14035),X14037))|~class_Groups_Omonoid__add(X14039))&(hAPP(X14035,esk476_5(X14035,X14036,X14037,X14038,X14039))!=c_Groups_Ozero__class_Ozero(X14039)|hAPP(c_List_Omonoid__add__class_Olistsum(X14039),hAPP(hAPP(c_List_Omap(X14038,X14039),X14035),hAPP(c_List_Ofilter(X14038,X14036),X14037)))=hAPP(c_List_Omonoid__add__class_Olistsum(X14039),hAPP(hAPP(c_List_Omap(X14038,X14039),X14035),X14037))|~class_Groups_Omonoid__add(X14039)))), 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])])])])])). 6.97/7.22 cnf(c_0_6369, plain, (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)=hAPP(c_List_Orev(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_4972])). 6.97/7.22 cnf(c_0_6370, 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_4973]), ['final']). 6.97/7.22 cnf(c_0_6371, plain, (c_List_OdropWhile(X4,X1,hAPP(hAPP(c_List_Oappend(X4),X3),X2))=c_List_OdropWhile(X4,X1,X2)|~hBOOL(hAPP(X1,esk230_4(X2,X1,X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_4943])). 6.97/7.22 fof(c_0_6372, plain, ![X13150, X13151, X13152, X13153, X13154]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X13154,X13154)),hAPP(hAPP(c_Product__Type_OPair(X13154,X13154),X13153),X13152)),c_Transitive__Closure_Ortrancl(X13154,X13151)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X13154,X13154)),hAPP(hAPP(c_Product__Type_OPair(X13154,X13154),X13152),X13150)),c_Transitive__Closure_Ortrancl(X13154,X13151)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X13154,X13154)),hAPP(hAPP(c_Product__Type_OPair(X13154,X13154),X13153),X13150)),c_Transitive__Closure_Ortrancl(X13154,X13151))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rtrancl__trans])])])). 6.97/7.22 fof(c_0_6373, plain, ![X862, X863, X864, X865, X866]:((hBOOL(hAPP(hAPP(c_member(X865),X862),X864))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X865,X866),X863),X864)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X865,X866),X863),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X865,tc_HOL_Obool)),X864),hAPP(hAPP(c_Set_Oinsert(X865),X862),c_Orderings_Obot__class_Obot(tc_fun(X865,tc_HOL_Obool)))))|hAPP(X863,X862)=c_Groups_Ozero__class_Ozero(X866)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X865),X864))|~class_Fields_Ofield(X866))&(~hBOOL(hAPP(hAPP(c_member(X865),X862),X864))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X865,X866),X863),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X865,tc_HOL_Obool)),X864),hAPP(hAPP(c_Set_Oinsert(X865),X862),c_Orderings_Obot__class_Obot(tc_fun(X865,tc_HOL_Obool)))))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X866),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X865,X866),X863),X864)),hAPP(X863,X862))|hAPP(X863,X862)=c_Groups_Ozero__class_Ozero(X866)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X865),X864))|~class_Fields_Ofield(X866))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__diff1])])])])). 6.97/7.22 cnf(c_0_6374, 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_4974])). 6.97/7.22 cnf(c_0_6375, 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)), inference(split_conjunct,[status(thm)],[c_0_4975]), ['final']). 6.97/7.22 cnf(c_0_6376, 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_4976, c_0_4977]), c_0_4978]), ['final']). 6.97/7.22 fof(c_0_6377, plain, ![X13579, X13580, X13581, X13582, X13583]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13583),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13582)),X13581)))|hAPP(hAPP(c_List_Olist__update(X13582,hAPP(hAPP(c_List_Oappend(X13582),X13581),X13580)),X13583),X13579)=hAPP(hAPP(c_List_Oappend(X13582),hAPP(hAPP(c_List_Olist__update(X13582,X13581),X13583),X13579)),X13580))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13583),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13582)),X13581)))|hAPP(hAPP(c_List_Olist__update(X13582,hAPP(hAPP(c_List_Oappend(X13582),X13581),X13580)),X13583),X13579)=hAPP(hAPP(c_List_Oappend(X13582),X13581),hAPP(hAPP(c_List_Olist__update(X13582,X13580),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X13583),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13582)),X13581))),X13579)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__update__append])])])). 6.97/7.22 cnf(c_0_6378, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk53_5(X2,X3,X4,X1,X5)),hAPP(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(c_Set_OCollect(X1),X2)))))|hBOOL(hAPP(X2,X3))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X4)|c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),X4)!=X5), inference(split_conjunct,[status(thm)],[c_0_4979])). 6.97/7.22 fof(c_0_6379, plain, ![X9828, X9829, X9830, X9831, X9832, X9833, X9834, X9835]:(~c_Finite__Set_Ofolding__image__simple(X9835,X9834,X9833,X9832,X9831,X9830)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9834),X9829))|hAPP(X9830,hAPP(hAPP(c_Set_Oinsert(X9834),X9828),X9829))=hAPP(hAPP(X9833,hAPP(X9831,X9828)),hAPP(X9830,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9834,tc_HOL_Obool)),X9829),hAPP(hAPP(c_Set_Oinsert(X9834),X9828),c_Orderings_Obot__class_Obot(tc_fun(X9834,tc_HOL_Obool)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Oinsert__remove])])])). 6.97/7.22 fof(c_0_6380, plain, ![X1783, X1784, X1785, X1786, X1787, X1788, X1789, X1790]:(~c_Finite__Set_Ofolding__image__simple(X1790,X1789,X1788,X1787,X1786,X1785)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1789),X1784))|(~hBOOL(hAPP(hAPP(c_member(X1789),X1783),X1784))|hAPP(X1785,X1784)=hAPP(hAPP(X1788,hAPP(X1786,X1783)),hAPP(X1785,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1789,tc_HOL_Obool)),X1784),hAPP(hAPP(c_Set_Oinsert(X1789),X1783),c_Orderings_Obot__class_Obot(tc_fun(X1789,tc_HOL_Obool))))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Oremove])])])). 6.97/7.22 fof(c_0_6381, plain, ![X10137, X10138, X10139, X10140, X10141]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X10141,X10141)),hAPP(hAPP(c_Product__Type_OPair(X10141,X10141),hAPP(X10140,hAPP(c_Nat_OSuc,esk329_5(X10137,X10138,X10139,X10140,X10141)))),hAPP(X10140,esk329_5(X10137,X10138,X10139,X10140,X10141)))),c_Transitive__Closure_Ortrancl(X10141,X10139)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X10141,X10141)),hAPP(hAPP(c_Product__Type_OPair(X10141,X10141),hAPP(X10140,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10138),X10137))),hAPP(X10140,X10138))),c_Transitive__Closure_Ortrancl(X10141,X10139)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sequence__trans])])])). 6.97/7.22 fof(c_0_6382, plain, ![X12800, X12801, X12802, X12803, X12804]:((~hBOOL(hAPP(hAPP(c_member(X12803),X12801),X12802))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12803,X12804),X12800),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12803,tc_HOL_Obool)),X12802),hAPP(hAPP(c_Set_Oinsert(X12803),X12801),c_Orderings_Obot__class_Obot(tc_fun(X12803,tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X12804),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12803,X12804),X12800),X12802)),hAPP(X12800,X12801))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12803),X12802))|~class_Groups_Oab__group__add(X12804))&(hBOOL(hAPP(hAPP(c_member(X12803),X12801),X12802))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12803,X12804),X12800),X12802)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12803,X12804),X12800),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12803,tc_HOL_Obool)),X12802),hAPP(hAPP(c_Set_Oinsert(X12803),X12801),c_Orderings_Obot__class_Obot(tc_fun(X12803,tc_HOL_Obool)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12803),X12802))|~class_Groups_Oab__group__add(X12804))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__diff1])])])])). 6.97/7.22 cnf(c_0_6383, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3))),esk257_3(X1,X2,X3))=X2|X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk254_3(X1,X2,X3))),esk255_3(X1,X2,X3))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_4980])). 6.97/7.22 cnf(c_0_6384, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[c_0_4981, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 fof(c_0_6385, plain, ![X849, X850, X851, X852, X853]:(~c_Equiv__Relations_Oequiv(X853,X852,X851)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X853,tc_HOL_Obool)),hAPP(c_Relation_OImage(X853,X853,X851),hAPP(hAPP(c_Set_Oinsert(X853),X850),c_Orderings_Obot__class_Obot(tc_fun(X853,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X853,X853,X851),hAPP(hAPP(c_Set_Oinsert(X853),X849),c_Orderings_Obot__class_Obot(tc_fun(X853,tc_HOL_Obool))))))|(~hBOOL(hAPP(hAPP(c_member(X853),X850),X852))|hBOOL(hAPP(hAPP(c_member(tc_prod(X853,X853)),hAPP(hAPP(c_Product__Type_OPair(X853,X853),X849),X850)),X851))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_subset__equiv__class])])])). 6.97/7.22 fof(c_0_6386, plain, ![X12589, X12590, X12591, X12592, X12593]:(~class_Rings_Oring(X12593)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12592),X12591))|(~hBOOL(hAPP(hAPP(c_member(X12592),X12590),X12591))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12592,X12593),X12589),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12592,tc_HOL_Obool)),X12591),hAPP(hAPP(c_Set_Oinsert(X12592),X12590),c_Orderings_Obot__class_Obot(tc_fun(X12592,tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X12593),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12592,X12593),X12589),X12591)),hAPP(X12589,X12590))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff1__ring])])). 6.97/7.22 cnf(c_0_6387, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3))),esk257_3(X1,X2,X3))=X2|X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk254_3(X1,X2,X3))),esk255_3(X1,X2,X3))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_4980])). 6.97/7.22 fof(c_0_6388, plain, ![X9129, X9130, X9131]:(~class_Fields_Ofield(X9131)|(X9130=c_Groups_Oone__class_Oone(X9131)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9131),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9131),hAPP(hAPP(c_Power_Opower__class_Opower(X9131),X9130),X9129)),c_Groups_Oone__class_Oone(X9131))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9131),X9130),c_Groups_Oone__class_Oone(X9131)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X9131),hAPP(c_Power_Opower__class_Opower(X9131),X9130)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X9129)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_geometric__sum])])])). 6.97/7.22 fof(c_0_6389, plain, ![X12360, X12361, X12362, X12363, X12364, X12365]:(~c_Finite__Set_Ofolding(X12365,X12364,X12363,X12362)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12365),X12361))|hAPP(X12362,hAPP(hAPP(c_Set_Oinsert(X12365),X12360),X12361))=hAPP(c_Fun_Ocomp(X12364,X12364,X12364,hAPP(X12362,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12365,tc_HOL_Obool)),X12361),hAPP(hAPP(c_Set_Oinsert(X12365),X12360),c_Orderings_Obot__class_Obot(tc_fun(X12365,tc_HOL_Obool)))))),hAPP(X12363,X12360)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Oinsert__remove])])])). 6.97/7.22 fof(c_0_6390, plain, ![X8398, X8399, X8400, X8401, X8402]:(~class_Groups_Oab__group__add(X8402)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8401),X8400))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8400),X8399))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8402),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X8402),X8398),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X8401),X8399))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X8402),X8398),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X8401),X8400)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X8402),X8398),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X8400),X8399))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__diff__nat__ivl])])])). 6.97/7.22 fof(c_0_6391, plain, ![X10202, X10203, X10204, X10205, X10206, X10207]:(~c_Finite__Set_Ofolding(X10207,X10206,X10205,X10204)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10207),X10203))|(~hBOOL(hAPP(hAPP(c_member(X10207),X10202),X10203))|hAPP(c_Fun_Ocomp(X10206,X10206,X10206,hAPP(X10204,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10207,tc_HOL_Obool)),X10203),hAPP(hAPP(c_Set_Oinsert(X10207),X10202),c_Orderings_Obot__class_Obot(tc_fun(X10207,tc_HOL_Obool)))))),hAPP(X10205,X10202))=hAPP(X10204,X10203)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Oremove])])])). 6.97/7.22 cnf(c_0_6392, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk344_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_4982])). 6.97/7.22 fof(c_0_6393, plain, ![X7165, X7166, X7167, X7168, X7169]:(~class_Groups_Ocomm__monoid__add(X7169)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7168),X7167))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7167),X7166))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7169),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7169),X7165),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X7168),X7167))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7169),X7165),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X7167),X7166)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7169),X7165),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X7168),X7166))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__add__nat__ivl])])). 6.97/7.22 cnf(c_0_6394, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk135_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_4983])). 6.97/7.22 fof(c_0_6395, plain, ![X15505, X15506, X15507, X15508, X15509]:((hBOOL(hAPP(hAPP(c_member(X15508),esk524_5(X15505,X15506,X15507,X15508,X15509)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15508,tc_HOL_Obool)),X15507),X15506)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X15508,X15509),X15505),X15506)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X15508,X15509),X15505),X15507)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15508,tc_HOL_Obool)),X15506),X15507))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X15508),X15507))|~class_Groups_Ocomm__monoid__mult(X15509))&(c_Groups_Oone__class_Oone(X15509)!=hAPP(X15505,esk524_5(X15505,X15506,X15507,X15508,X15509))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X15508,X15509),X15505),X15506)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X15508,X15509),X15505),X15507)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15508,tc_HOL_Obool)),X15506),X15507))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X15508),X15507))|~class_Groups_Ocomm__monoid__mult(X15509))), 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])])])])])). 6.97/7.22 fof(c_0_6396, plain, ![X10988, X10989, X10990, X10991, X10992]:((hBOOL(hAPP(hAPP(c_member(X10991),esk367_5(X10988,X10989,X10990,X10991,X10992)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10991,tc_HOL_Obool)),X10990),X10989)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10991,X10992),X10988),X10990)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10991,X10992),X10988),X10989)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10991,tc_HOL_Obool)),X10989),X10990))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10991),X10990))|~class_Groups_Ocomm__monoid__mult(X10992))&(hAPP(X10988,esk367_5(X10988,X10989,X10990,X10991,X10992))!=c_Groups_Oone__class_Oone(X10992)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10991,X10992),X10988),X10990)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10991,X10992),X10988),X10989)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10991,tc_HOL_Obool)),X10989),X10990))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10991),X10990))|~class_Groups_Ocomm__monoid__mult(X10992))), 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])])])])])). 6.97/7.22 fof(c_0_6397, plain, ![X9600, X9601, X9602, X9603, X9604]:((hBOOL(hAPP(hAPP(c_member(X9603),esk316_5(X9600,X9601,X9602,X9603,X9604)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9603,tc_HOL_Obool)),X9602),X9601)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9603,X9604),X9600),X9602)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9603,X9604),X9600),X9601)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9603,tc_HOL_Obool)),X9601),X9602))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9603),X9602))|~class_Groups_Ocomm__monoid__add(X9604))&(hAPP(X9600,esk316_5(X9600,X9601,X9602,X9603,X9604))!=c_Groups_Ozero__class_Ozero(X9604)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9603,X9604),X9600),X9602)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9603,X9604),X9600),X9601)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9603,tc_HOL_Obool)),X9601),X9602))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9603),X9602))|~class_Groups_Ocomm__monoid__add(X9604))), 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])])])])])). 6.97/7.22 fof(c_0_6398, plain, ![X14357, X14358, X14359, X14360, X14361]:(~class_Groups_Ocomm__monoid__add(X14361)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14360),X14359))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14360),X14358))|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14360,tc_HOL_Obool)),X14359),X14358)!=c_Orderings_Obot__class_Obot(tc_fun(X14360,tc_HOL_Obool))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14361),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14360,X14361),X14357),X14359)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14360,X14361),X14357),X14358))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14360,X14361),X14357),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14360,tc_HOL_Obool)),X14359),X14358)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__Un__disjoint])])])). 6.97/7.22 fof(c_0_6399, plain, ![X14045, X14046, X14047, X14048, X14049]:(~class_Groups_Ocomm__monoid__mult(X14049)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14048),X14047))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14048),X14046))|(c_Orderings_Obot__class_Obot(tc_fun(X14048,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14048,tc_HOL_Obool)),X14047),X14046)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14049),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X14048,X14049),X14045),X14047)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X14048,X14049),X14045),X14046))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X14048,X14049),X14045),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14048,tc_HOL_Obool)),X14047),X14046)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod_Ounion__disjoint])])])). 6.97/7.22 fof(c_0_6400, plain, ![X7705, X7706, X7707, X7708, X7709]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X7709,X7709)),hAPP(hAPP(c_Product__Type_OPair(X7709,X7709),X7708),X7707)),X7706))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X7709,X7709)),hAPP(hAPP(c_Product__Type_OPair(X7709,X7709),X7707),X7705)),c_Transitive__Closure_Ortrancl(X7709,X7706)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X7709,X7709)),hAPP(hAPP(c_Product__Type_OPair(X7709,X7709),X7708),X7705)),c_Transitive__Closure_Ortrancl(X7709,X7706))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_converse__rtrancl__into__rtrancl])])])). 6.97/7.22 fof(c_0_6401, plain, ![X838, X839, X840, X841]:((~hBOOL(hAPP(hAPP(c_member(X841),X840),X839))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X841,tc_Nat_Onat),X838),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X841,tc_HOL_Obool)),X839),hAPP(hAPP(c_Set_Oinsert(X841),X840),c_Orderings_Obot__class_Obot(tc_fun(X841,tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X841,tc_Nat_Onat),X838),X839)),hAPP(X838,X840)))&(hBOOL(hAPP(hAPP(c_member(X841),X840),X839))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X841,tc_Nat_Onat),X838),X839)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X841,tc_Nat_Onat),X838),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X841,tc_HOL_Obool)),X839),hAPP(hAPP(c_Set_Oinsert(X841),X840),c_Orderings_Obot__class_Obot(tc_fun(X841,tc_HOL_Obool))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__diff1__nat])])])). 6.97/7.22 fof(c_0_6402, plain, ![X5570, X5571, X5572, X5573, X5574]:((hBOOL(hAPP(hAPP(c_member(X5573),esk183_5(X5570,X5571,X5572,X5573,X5574)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5573,tc_HOL_Obool)),X5572),X5571)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5573,X5574),X5570),X5572)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5573,X5574),X5570),X5571)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5573,tc_HOL_Obool)),X5571),X5572))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5573),X5572))|~class_Groups_Ocomm__monoid__add(X5574))&(hAPP(X5570,esk183_5(X5570,X5571,X5572,X5573,X5574))!=c_Groups_Ozero__class_Ozero(X5574)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5573,X5574),X5570),X5572)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5573,X5574),X5570),X5571)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5573,tc_HOL_Obool)),X5571),X5572))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5573),X5572))|~class_Groups_Ocomm__monoid__add(X5574))), 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])])])])])). 6.97/7.22 fof(c_0_6403, plain, ![X5928, X5929, X5930, X5931]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5931),X5930)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5929)),X5928)))|hAPP(hAPP(c_List_Oappend(X5929),hAPP(hAPP(c_List_Otake(X5929),X5931),X5928)),hAPP(hAPP(c_List_Otake(X5929),X5930),hAPP(hAPP(c_List_Odrop(X5929),X5931),X5928)))=hAPP(hAPP(c_List_Otake(X5929),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5931),X5930)),X5928)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_take__add])])])). 6.97/7.22 fof(c_0_6404, plain, ![X7808, X7809, X7810, X7811]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7811))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7810))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7810),X7809))|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),X7809),c_Divides_Odiv__class_Omod(tc_Int_Oint,X7808,X7811))),X7810)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7809),X7811)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmult2__lemma__aux4])])])). 6.97/7.22 fof(c_0_6405, plain, ![X7109, X7110, X7111, X7112]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7112))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7111),X7110))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7110),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),X7111),X7112)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7111),c_Divides_Odiv__class_Omod(tc_Int_Oint,X7109,X7112))),X7110)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmult2__lemma__aux1])])])). 6.97/7.22 fof(c_0_6406, plain, ![X14449, X14450, X14451, X14452, X14453]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X14453,X14453)),hAPP(hAPP(c_Product__Type_OPair(X14453,X14453),X14452),X14451)),c_Transitive__Closure_Ortrancl(X14453,X14450)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X14453,X14453)),hAPP(hAPP(c_Product__Type_OPair(X14453,X14453),X14451),X14449)),X14450))|hBOOL(hAPP(hAPP(c_member(tc_prod(X14453,X14453)),hAPP(hAPP(c_Product__Type_OPair(X14453,X14453),X14452),X14449)),c_Transitive__Closure_Ortrancl(X14453,X14450))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rtrancl_Ortrancl__into__rtrancl])])])). 6.97/7.22 cnf(c_0_6407, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oconcat(X1,X2)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk287_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(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_List_Oset(X1),esk288_2(X2,X1))),hAPP(c_List_Oset(X1),esk289_2(X2,X1)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_4933])). 6.97/7.22 fof(c_0_6408, plain, ![X2897, X2898, X2899, X2900, X2901, X2902]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2900)),X2899)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2902)),X2901)|(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2900)),X2897)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2902)),X2898)|hAPP(hAPP(c_List_Ozip(X2902,X2900),hAPP(hAPP(c_List_Oappend(X2902),X2901),X2898)),hAPP(hAPP(c_List_Oappend(X2900),X2899),X2897))=hAPP(hAPP(c_List_Oappend(tc_prod(X2902,X2900)),hAPP(hAPP(c_List_Ozip(X2902,X2900),X2901),X2899)),hAPP(hAPP(c_List_Ozip(X2902,X2900),X2898),X2897)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zip__append])])])). 6.97/7.22 fof(c_0_6409, plain, ![X12917, X12918, X12919]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12919),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12918)),X12917)))|hAPP(hAPP(c_List_Otake(X12918),hAPP(c_Nat_OSuc,X12919)),X12917)=hAPP(hAPP(c_List_Oappend(X12918),hAPP(hAPP(c_List_Otake(X12918),X12919),X12917)),hAPP(hAPP(c_List_Olist_OCons(X12918),hAPP(c_List_Ohd(X12918),hAPP(hAPP(c_List_Odrop(X12918),X12919),X12917))),c_List_Olist_ONil(X12918)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_take__hd__drop])])])). 6.97/7.22 cnf(c_0_6410, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk345_4(X1,X2,X3,X4)),esk344_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_4982])). 6.97/7.22 cnf(c_0_6411, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk136_4(X2,X3,X4,X1)),esk135_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_4983])). 6.97/7.22 fof(c_0_6412, plain, ![X9207, X9208, X9209]:(~class_Lattices_Oab__semigroup__idem__mult(X9209)|(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9209),hAPP(X9208,esk303_3(X9207,X9208,X9209))),hAPP(X9208,esk304_3(X9207,X9208,X9209)))!=hAPP(X9208,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9209),esk303_3(X9207,X9208,X9209)),esk304_3(X9207,X9208,X9209)))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9209),X9207))|(X9207=c_Orderings_Obot__class_Obot(tc_fun(X9209,tc_HOL_Obool))|hAPP(c_Finite__Set_Ofold1(X9209,c_Groups_Otimes__class_Otimes(X9209)),hAPP(c_Set_Oimage(X9209,X9209,X9208),X9207))=hAPP(X9208,hAPP(c_Finite__Set_Ofold1(X9209,c_Groups_Otimes__class_Otimes(X9209)),X9207)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_hom__fold1__commute])])])])). 6.97/7.22 cnf(c_0_6413, plain, (hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk370_3(X3,X2,X1)),X4))=hAPP(X2,esk370_3(X3,X2,X1))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(X2,hAPP(c_Nat_OSuc,esk369_3(X3,X2,X1)))),hAPP(X2,esk369_3(X3,X2,X1)))),c_Transitive__Closure_Ortrancl(X1,X3)))|~c_Wellfounded_Owf(X1,c_Transitive__Closure_Otrancl(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_4984])). 6.97/7.22 fof(c_0_6414, plain, ![X15838, X15839, X15840, X15841, X15843, X15844, X15845, X15846, X15847, X15848, X15851]:((((~hBOOL(hAPP(hAPP(c_member(X15841),X15843),X15839))|hBOOL(hAPP(X15838,X15843))|hBOOL(hAPP(hAPP(c_member(X15841),esk533_4(X15838,X15839,X15840,X15841)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15841,tc_HOL_Obool)),X15840),X15839))))&(~hBOOL(hAPP(hAPP(c_member(X15841),X15844),X15840))|hBOOL(hAPP(X15838,X15844))|hBOOL(hAPP(hAPP(c_member(X15841),esk533_4(X15838,X15839,X15840,X15841)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15841,tc_HOL_Obool)),X15840),X15839)))))&((~hBOOL(hAPP(hAPP(c_member(X15841),X15843),X15839))|hBOOL(hAPP(X15838,X15843))|~hBOOL(hAPP(X15838,esk533_4(X15838,X15839,X15840,X15841))))&(~hBOOL(hAPP(hAPP(c_member(X15841),X15844),X15840))|hBOOL(hAPP(X15838,X15844))|~hBOOL(hAPP(X15838,esk533_4(X15838,X15839,X15840,X15841))))))&(((hBOOL(hAPP(hAPP(c_member(X15848),esk535_4(X15845,X15846,X15847,X15848)),X15847))|hBOOL(hAPP(hAPP(c_member(X15848),esk534_4(X15845,X15846,X15847,X15848)),X15846))|(~hBOOL(hAPP(hAPP(c_member(X15848),X15851),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15848,tc_HOL_Obool)),X15847),X15846)))|hBOOL(hAPP(X15845,X15851))))&(~hBOOL(hAPP(X15845,esk535_4(X15845,X15846,X15847,X15848)))|hBOOL(hAPP(hAPP(c_member(X15848),esk534_4(X15845,X15846,X15847,X15848)),X15846))|(~hBOOL(hAPP(hAPP(c_member(X15848),X15851),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15848,tc_HOL_Obool)),X15847),X15846)))|hBOOL(hAPP(X15845,X15851)))))&((hBOOL(hAPP(hAPP(c_member(X15848),esk535_4(X15845,X15846,X15847,X15848)),X15847))|~hBOOL(hAPP(X15845,esk534_4(X15845,X15846,X15847,X15848)))|(~hBOOL(hAPP(hAPP(c_member(X15848),X15851),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15848,tc_HOL_Obool)),X15847),X15846)))|hBOOL(hAPP(X15845,X15851))))&(~hBOOL(hAPP(X15845,esk535_4(X15845,X15846,X15847,X15848)))|~hBOOL(hAPP(X15845,esk534_4(X15845,X15846,X15847,X15848)))|(~hBOOL(hAPP(hAPP(c_member(X15848),X15851),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15848,tc_HOL_Obool)),X15847),X15846)))|hBOOL(hAPP(X15845,X15851))))))), 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__Un])])])])])])). 6.97/7.22 cnf(c_0_6415, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X3)))=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)))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4985])). 6.97/7.22 cnf(c_0_6416, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk289_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),esk287_2(X2,X1)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_4933])). 6.97/7.22 cnf(c_0_6417, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk288_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),esk287_2(X2,X1)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_4933])). 6.97/7.22 fof(c_0_6418, plain, ![X17053, X17054, X17055, X17056, X17057]:((hBOOL(hAPP(hAPP(c_member(X17056),esk577_5(X17053,X17054,X17055,X17056,X17057)),X17055))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17057),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17056,X17057),X17054),X17055)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17057),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X17057),hAPP(c_Finite__Set_Ocard(X17056),X17055))),X17053)))|(~class_Groups_Oordered__ab__semigroup__add(X17057)|~class_Rings_Osemiring__1(X17057)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17057),hAPP(X17054,esk577_5(X17053,X17054,X17055,X17056,X17057))),X17053))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17057),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17056,X17057),X17054),X17055)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17057),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X17057),hAPP(c_Finite__Set_Ocard(X17056),X17055))),X17053)))|(~class_Groups_Oordered__ab__semigroup__add(X17057)|~class_Rings_Osemiring__1(X17057)))), 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])])])])])). 6.97/7.22 fof(c_0_6419, plain, ![X11117, X11118, X11119, X11120, X11121, X11122]:(~c_Equiv__Relations_Oequiv(X11122,X11121,X11120)|(~hBOOL(hAPP(hAPP(c_member(X11122),X11119),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11122,tc_HOL_Obool)),hAPP(c_Relation_OImage(X11122,X11122,X11120),hAPP(hAPP(c_Set_Oinsert(X11122),X11118),c_Orderings_Obot__class_Obot(tc_fun(X11122,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X11122,X11122,X11120),hAPP(hAPP(c_Set_Oinsert(X11122),X11117),c_Orderings_Obot__class_Obot(tc_fun(X11122,tc_HOL_Obool)))))))|hBOOL(hAPP(hAPP(c_member(tc_prod(X11122,X11122)),hAPP(hAPP(c_Product__Type_OPair(X11122,X11122),X11118),X11117)),X11120)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equiv__class__nondisjoint])])])). 6.97/7.22 fof(c_0_6420, plain, ![X6612, X6613, X6614, X6615]:(~class_Orderings_Olinorder(X6615)|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X6615,X6615,c_COMBI(X6615)),X6614),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X6615,X6615,c_COMBI(X6615)),X6613),X6612))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X6615,X6615,c_COMBI(X6615)),X6613),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X6615,X6615,c_COMBI(X6615)),X6614),X6612))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insort__left__comm])])])). 6.97/7.22 fof(c_0_6421, plain, ![X14383, X14384, X14385, X14386, X14387, X14388]:(~class_Orderings_Olinorder(X14388)|(hAPP(X14387,X14386)=hAPP(X14387,X14385)|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X14384,X14388,X14387),X14385),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X14384,X14388,X14387),X14386),X14383))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X14384,X14388,X14387),X14386),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X14384,X14388,X14387),X14385),X14383)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insort__key__left__comm])])])). 6.97/7.22 cnf(c_0_6422, 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_4577])). 6.97/7.22 cnf(c_0_6423, 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_4986, c_0_4467]), c_0_4467]), c_0_4467]), ['final']). 6.97/7.22 fof(c_0_6424, plain, ![X6726, X6727, X6728, X6729, X6730, X6731, X6732]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6732,X6731),tc_HOL_Obool)),X6730),X6729))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6731,X6728),tc_HOL_Obool)),X6727),X6726))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6732,X6728),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X6732,X6731,X6728),X6730),X6727)),hAPP(hAPP(c_Relation_Orel__comp(X6732,X6731,X6728),X6729),X6726))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rel__comp__mono])])])). 6.97/7.22 cnf(c_0_6425, 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)),esk21_3(X1,X2,X3)),X2))|esk23_3(X1,X2,X3)!=esk22_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_4947])). 6.97/7.22 cnf(c_0_6426, plain, (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))=hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_4987])). 6.97/7.22 cnf(c_0_6427, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6)=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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X4)),X5)!=X6|~class_Rings_Oring(X1)), inference(split_conjunct,[status(thm)],[c_0_4988])). 6.97/7.22 cnf(c_0_6428, 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_4989])). 6.97/7.22 cnf(c_0_6429, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk302_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_4990])). 6.97/7.22 cnf(c_0_6430, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk330_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_4991])). 6.97/7.22 cnf(c_0_6431, 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_4992])). 6.97/7.22 fof(c_0_6432, plain, ![X5078, X5079, X5080, X5081]:(~c_Finite__Set_Ofolding__one(X5081,X5080,X5079)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5081),X5078))|(c_Orderings_Obot__class_Obot(tc_fun(X5081,tc_HOL_Obool))=X5078|(~hBOOL(hAPP(hAPP(c_member(X5081),hAPP(hAPP(X5080,esk163_4(X5078,X5079,X5080,X5081)),esk164_4(X5078,X5079,X5080,X5081))),hAPP(hAPP(c_Set_Oinsert(X5081),esk163_4(X5078,X5079,X5080,X5081)),hAPP(hAPP(c_Set_Oinsert(X5081),esk164_4(X5078,X5079,X5080,X5081)),c_Orderings_Obot__class_Obot(tc_fun(X5081,tc_HOL_Obool))))))|hBOOL(hAPP(hAPP(c_member(X5081),hAPP(X5079,X5078)),X5078)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one_Oclosed])])])])). 6.97/7.22 cnf(c_0_6433, 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_4993])). 6.97/7.22 fof(c_0_6434, plain, ![X14167, X14168, X14169, X14170, X14171, X14172]:(~c_Finite__Set_Ofolding(X14172,X14171,X14170,X14169)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14172),X14168))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14172),X14167))|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14172,tc_HOL_Obool)),X14168),X14167)!=c_Orderings_Obot__class_Obot(tc_fun(X14172,tc_HOL_Obool))|hAPP(X14169,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14172,tc_HOL_Obool)),X14168),X14167))=hAPP(c_Fun_Ocomp(X14171,X14171,X14171,hAPP(X14169,X14168)),hAPP(X14169,X14167)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Ounion])])])). 6.97/7.22 fof(c_0_6435, plain, ![X13981, X13982, X13983, X13984, X13985, X13986]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13986),hAPP(X13985,X13984)),hAPP(X13985,X13983)))|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13982,X13986,X13985),X13984),hAPP(hAPP(c_List_Olist_OCons(X13982),X13983),X13981))=hAPP(hAPP(c_List_Olist_OCons(X13982),X13983),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13982,X13986,X13985),X13984),X13981))|~class_Orderings_Olinorder(X13986))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13986),hAPP(X13985,X13984)),hAPP(X13985,X13983)))|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13982,X13986,X13985),X13984),hAPP(hAPP(c_List_Olist_OCons(X13982),X13983),X13981))=hAPP(hAPP(c_List_Olist_OCons(X13982),X13984),hAPP(hAPP(c_List_Olist_OCons(X13982),X13983),X13981))|~class_Orderings_Olinorder(X13986))), 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])])])])). 6.97/7.22 fof(c_0_6436, plain, ![X6203, X6204, X6205]:((hBOOL(hAPP(hAPP(c_member(tc_fun(X6205,tc_HOL_Obool)),esk206_3(X6203,X6204,X6205)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X6205,tc_HOL_Obool)),X6204),X6203)))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6205,tc_HOL_Obool)),X6204),c_Complete__Lattice_OSup__class_OSup(tc_fun(X6205,tc_HOL_Obool),X6203))=c_Orderings_Obot__class_Obot(tc_fun(X6205,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(tc_fun(X6205,tc_HOL_Obool)),X6204),X6203)))&((hBOOL(hAPP(hAPP(c_member(tc_fun(X6205,tc_HOL_Obool)),esk207_3(X6203,X6204,X6205)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X6205,tc_HOL_Obool)),X6204),X6203)))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6205,tc_HOL_Obool)),X6204),c_Complete__Lattice_OSup__class_OSup(tc_fun(X6205,tc_HOL_Obool),X6203))=c_Orderings_Obot__class_Obot(tc_fun(X6205,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(tc_fun(X6205,tc_HOL_Obool)),X6204),X6203)))&((esk206_3(X6203,X6204,X6205)!=esk207_3(X6203,X6204,X6205)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6205,tc_HOL_Obool)),X6204),c_Complete__Lattice_OSup__class_OSup(tc_fun(X6205,tc_HOL_Obool),X6203))=c_Orderings_Obot__class_Obot(tc_fun(X6205,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(tc_fun(X6205,tc_HOL_Obool)),X6204),X6203)))&(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6205,tc_HOL_Obool)),esk206_3(X6203,X6204,X6205)),esk207_3(X6203,X6204,X6205))!=c_Orderings_Obot__class_Obot(tc_fun(X6205,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6205,tc_HOL_Obool)),X6204),c_Complete__Lattice_OSup__class_OSup(tc_fun(X6205,tc_HOL_Obool),X6203))=c_Orderings_Obot__class_Obot(tc_fun(X6205,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(tc_fun(X6205,tc_HOL_Obool)),X6204),X6203)))))), 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])])])])])). 6.97/7.22 fof(c_0_6437, plain, ![X12672, X12673, X12674, X12675, X12676, X12677]:(~c_Equiv__Relations_Oequiv(X12677,X12676,X12675)|(~c_Equiv__Relations_Ocongruent(X12677,tc_fun(X12674,tc_HOL_Obool),X12675,X12673)|(~hBOOL(hAPP(hAPP(c_member(X12677),X12672),X12676))|hAPP(X12673,X12672)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12677,tc_fun(X12674,tc_HOL_Obool)),hAPP(c_Relation_OImage(X12677,X12677,X12675),hAPP(hAPP(c_Set_Oinsert(X12677),X12672),c_Orderings_Obot__class_Obot(tc_fun(X12677,tc_HOL_Obool))))),X12673)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__equiv__class])])])). 6.97/7.22 cnf(c_0_6438, plain, (X1=hAPP(X2,esk265_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))|~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),esk264_4(X1,X2,X3,X4)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk264_4(X1,X2,X3,X4))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_4971])). 6.97/7.22 fof(c_0_6439, plain, ![X1061, X1062, X1063, X1064, X1065, X1066]:(hAPP(c_Set_Oimage(X1066,X1065,X1064),c_Orderings_Otop__class_Otop(tc_fun(X1066,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X1065,tc_HOL_Obool))|(c_Orderings_Otop__class_Otop(tc_fun(X1062,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X1063,X1062,X1061),c_Orderings_Otop__class_Otop(tc_fun(X1063,tc_HOL_Obool)))|c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1065,X1062),tc_HOL_Obool))=hAPP(c_Set_Oimage(tc_prod(X1066,X1063),tc_prod(X1065,X1062),c_Product__Type_Omap__pair(X1066,X1065,X1063,X1062,X1064,X1061)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1066,X1063),tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__pair__surj])])])). 6.97/7.22 fof(c_0_6440, plain, ![X11704, X11705, X11706]:(~class_Orderings_Olinorder(X11706)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11706),X11705))|c_List_Olinorder__class_Osorted__list__of__set(X11706,hAPP(hAPP(c_Set_Oinsert(X11706),X11704),X11705))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X11706,X11706,c_COMBI(X11706)),X11704),c_List_Olinorder__class_Osorted__list__of__set(X11706,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11706,tc_HOL_Obool)),X11705),hAPP(hAPP(c_Set_Oinsert(X11706),X11704),c_Orderings_Obot__class_Obot(tc_fun(X11706,tc_HOL_Obool)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__list__of__set__insert])])])). 6.97/7.22 fof(c_0_6441, plain, ![X4285, X4286, X4287]:((hBOOL(hAPP(hAPP(c_member(X4287),esk148_3(X4285,X4286,X4287)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4287,tc_HOL_Obool)),X4286),X4285)))|hAPP(c_Finite__Set_Ocard(X4287),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4287,tc_HOL_Obool)),X4286),X4285))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4287),X4286)),hAPP(c_Finite__Set_Ocard(X4287),X4285))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4287),X4285))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4287),X4286)))&(c_Groups_Oone__class_Oone(tc_Nat_Onat)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Finite__Set_Ocard(X4287),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4287,tc_HOL_Obool)),X4286),X4285))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4287),X4286)),hAPP(c_Finite__Set_Ocard(X4287),X4285))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4287),X4285))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4287),X4286)))), 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])])])])])). 6.97/7.22 fof(c_0_6442, plain, ![X16926, X16927, X16928, X16929, X16930]:(~c_Orderings_Oorder__class_Omono(tc_fun(X16930,tc_HOL_Obool),tc_fun(X16929,tc_HOL_Obool),X16928)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16929,tc_HOL_Obool)),hAPP(X16928,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16930,tc_HOL_Obool)),X16927),X16926))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16929,tc_HOL_Obool)),hAPP(X16928,X16927)),hAPP(X16928,X16926))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mono__Int])])])). 6.97/7.22 fof(c_0_6443, plain, ![X4066, X4067, X4068, X4069, X4070, X4072, X4073, X4074, X4075, X4076, X4077, X4078, X4081]:(((hBOOL(hAPP(hAPP(c_member(X4070),esk140_5(X4066,X4067,X4068,X4069,X4070)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4069,tc_fun(X4070,tc_HOL_Obool)),X4068),X4067)))|(~hBOOL(hAPP(hAPP(c_member(X4069),X4072),X4068))|(~hBOOL(hAPP(hAPP(c_member(X4070),X4073),hAPP(X4067,X4072)))|hBOOL(hAPP(X4066,X4073)))))&(~hBOOL(hAPP(X4066,esk140_5(X4066,X4067,X4068,X4069,X4070)))|(~hBOOL(hAPP(hAPP(c_member(X4069),X4072),X4068))|(~hBOOL(hAPP(hAPP(c_member(X4070),X4073),hAPP(X4067,X4072)))|hBOOL(hAPP(X4066,X4073))))))&((hBOOL(hAPP(hAPP(c_member(X4077),esk141_5(X4074,X4075,X4076,X4077,X4078)),X4076))|(~hBOOL(hAPP(hAPP(c_member(X4078),X4081),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4077,tc_fun(X4078,tc_HOL_Obool)),X4076),X4075)))|hBOOL(hAPP(X4074,X4081))))&((hBOOL(hAPP(hAPP(c_member(X4078),esk142_5(X4074,X4075,X4076,X4077,X4078)),hAPP(X4075,esk141_5(X4074,X4075,X4076,X4077,X4078))))|(~hBOOL(hAPP(hAPP(c_member(X4078),X4081),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4077,tc_fun(X4078,tc_HOL_Obool)),X4076),X4075)))|hBOOL(hAPP(X4074,X4081))))&(~hBOOL(hAPP(X4074,esk142_5(X4074,X4075,X4076,X4077,X4078)))|(~hBOOL(hAPP(hAPP(c_member(X4078),X4081),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4077,tc_fun(X4078,tc_HOL_Obool)),X4076),X4075)))|hBOOL(hAPP(X4074,X4081))))))), 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])])])])])])])). 6.97/7.22 cnf(c_0_6444, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X2),X1))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),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(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))!=X3), inference(split_conjunct,[status(thm)],[c_0_4953])). 6.97/7.22 fof(c_0_6445, plain, ![X15126, X15127, X15128, X15129, X15130]:(~c_Orderings_Oorder__class_Omono(tc_fun(X15130,tc_HOL_Obool),tc_fun(X15129,tc_HOL_Obool),X15128)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15129,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15129,tc_HOL_Obool)),hAPP(X15128,X15127)),hAPP(X15128,X15126))),hAPP(X15128,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15130,tc_HOL_Obool)),X15127),X15126))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mono__Un])])). 6.97/7.22 fof(c_0_6446, plain, ![X8232, X8233, X8234, X8235, X8236]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8236,tc_HOL_Obool)),hAPP(c_Relation_OImage(X8235,X8236,X8234),X8233)),X8232))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8235,tc_HOL_Obool)),X8233),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8235,tc_HOL_Obool)),hAPP(c_Relation_OImage(X8236,X8235,hAPP(c_Relation_Oconverse(X8235,X8236),X8234)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8236,tc_HOL_Obool)),X8232))))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8235,tc_HOL_Obool)),X8233),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8235,tc_HOL_Obool)),hAPP(c_Relation_OImage(X8236,X8235,hAPP(c_Relation_Oconverse(X8235,X8236),X8234)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8236,tc_HOL_Obool)),X8232)))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8236,tc_HOL_Obool)),hAPP(c_Relation_OImage(X8235,X8236,X8234),X8233)),X8232)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__subset__eq])])). 6.97/7.22 cnf(c_0_6447, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X1),X2))|~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),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))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(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(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2))!=X3), inference(split_conjunct,[status(thm)],[c_0_4953])). 6.97/7.22 cnf(c_0_6448, 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_4994]), ['final']). 6.97/7.22 fof(c_0_6449, plain, ![X730, X731, X732, X733, X734, X735, X736, X737]:(~c_Finite__Set_Ofolding__image__simple(X737,X736,X735,X734,X733,X732)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X736),X731))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X736),X730))|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X736,tc_HOL_Obool)),X731),X730)!=c_Orderings_Obot__class_Obot(tc_fun(X736,tc_HOL_Obool))|hAPP(hAPP(X735,hAPP(X732,X731)),hAPP(X732,X730))=hAPP(X732,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X736,tc_HOL_Obool)),X731),X730)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Ounion__disjoint])])])). 6.97/7.22 cnf(c_0_6450, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk129_7(X2,X3,X4,X5,X1,X6,X7)),hAPP(c_List_Oset(X1),X6)))|hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4)=hAPP(c_List_Ofilter(X1,X3),X2)|X4!=hAPP(c_List_Ofilter(X1,X3),X7)|~hBOOL(hAPP(X3,X5))|hAPP(hAPP(c_List_Oappend(X1),X6),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X7))!=X2), inference(split_conjunct,[status(thm)],[c_0_4995])). 6.97/7.22 fof(c_0_6451, plain, ![X11351, X11352, X11353, X11354]:((hBOOL(hAPP(hAPP(c_member(X11354),esk376_4(X11351,X11352,X11353,X11354)),X11353))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11354),hAPP(hAPP(c_Finite__Set_Ofold(X11354,X11354,c_Lattices_Osemilattice__sup__class_Osup(X11354)),X11351),X11353)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X11354),X11352),X11351)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11354),X11353))|~class_Lattices_Osemilattice__sup(X11354))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11354),esk376_4(X11351,X11352,X11353,X11354)),X11352))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11354),hAPP(hAPP(c_Finite__Set_Ofold(X11354,X11354,c_Lattices_Osemilattice__sup__class_Osup(X11354)),X11351),X11353)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X11354),X11352),X11351)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11354),X11353))|~class_Lattices_Osemilattice__sup(X11354))), 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])])])])])). 6.97/7.22 fof(c_0_6452, plain, ![X10701, X10702, X10703, X10704]:((hBOOL(hAPP(hAPP(c_member(X10704),esk354_4(X10701,X10702,X10703,X10704)),X10703))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10704),hAPP(hAPP(c_Finite__Set_Ofold(X10704,X10704,c_Orderings_Oord__class_Omax(X10704)),X10701),X10703)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X10704),X10702),X10701)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10704),X10703))|~class_Orderings_Olinorder(X10704))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10704),esk354_4(X10701,X10702,X10703,X10704)),X10702))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10704),hAPP(hAPP(c_Finite__Set_Ofold(X10704,X10704,c_Orderings_Oord__class_Omax(X10704)),X10701),X10703)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X10704),X10702),X10701)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10704),X10703))|~class_Orderings_Olinorder(X10704))), 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])])])])])). 6.97/7.22 fof(c_0_6453, plain, ![X12982, X12983, X12984, X12985]:((hBOOL(hAPP(hAPP(c_member(X12985),esk424_4(X12982,X12983,X12984,X12985)),X12984))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12985),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X12985),X12983),X12982)),hAPP(hAPP(c_Finite__Set_Ofold(X12985,X12985,c_Lattices_Osemilattice__inf__class_Oinf(X12985)),X12982),X12984)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12985),X12984))|~class_Lattices_Osemilattice__inf(X12985))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12985),X12983),esk424_4(X12982,X12983,X12984,X12985)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12985),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X12985),X12983),X12982)),hAPP(hAPP(c_Finite__Set_Ofold(X12985,X12985,c_Lattices_Osemilattice__inf__class_Oinf(X12985)),X12982),X12984)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12985),X12984))|~class_Lattices_Osemilattice__inf(X12985))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__le__fold__inf])])])])). 6.97/7.22 fof(c_0_6454, plain, ![X10131, X10132, X10133, X10134]:((hBOOL(hAPP(hAPP(c_member(X10134),esk328_4(X10131,X10132,X10133,X10134)),X10133))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10134),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10134),X10132),X10131)),hAPP(hAPP(c_Finite__Set_Ofold(X10134,X10134,c_Orderings_Oord__class_Omin(X10134)),X10131),X10133)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10134),X10133))|~class_Orderings_Olinorder(X10134))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10134),X10132),esk328_4(X10131,X10132,X10133,X10134)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10134),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10134),X10132),X10131)),hAPP(hAPP(c_Finite__Set_Ofold(X10134,X10134,c_Orderings_Oord__class_Omin(X10134)),X10131),X10133)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10134),X10133))|~class_Orderings_Olinorder(X10134))), 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])])])])])). 6.97/7.22 fof(c_0_6455, plain, ![X10405, X10406, X10407, X10408, X10409]:(~c_Relation_Otrans(X10409,X10408)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X10409,X10409)),hAPP(hAPP(c_Product__Type_OPair(X10409,X10409),X10407),X10406)),X10408))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X10409,X10409)),hAPP(hAPP(c_Product__Type_OPair(X10409,X10409),X10406),X10405)),X10408))|hBOOL(hAPP(hAPP(c_member(tc_prod(X10409,X10409)),hAPP(hAPP(c_Product__Type_OPair(X10409,X10409),X10407),X10405)),X10408))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transD])])])). 6.97/7.22 fof(c_0_6456, plain, ![X5511, X5512]:(~class_Groups_Oab__semigroup__mult(X5512)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5512),X5511))|(c_Orderings_Obot__class_Obot(tc_fun(X5512,tc_HOL_Obool))=X5511|(~hBOOL(hAPP(hAPP(c_member(X5512),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5512),esk179_2(X5511,X5512)),esk180_2(X5511,X5512))),hAPP(hAPP(c_Set_Oinsert(X5512),esk179_2(X5511,X5512)),hAPP(hAPP(c_Set_Oinsert(X5512),esk180_2(X5511,X5512)),c_Orderings_Obot__class_Obot(tc_fun(X5512,tc_HOL_Obool))))))|hBOOL(hAPP(hAPP(c_member(X5512),hAPP(c_Finite__Set_Ofold1(X5512,c_Groups_Otimes__class_Otimes(X5512)),X5511)),X5511)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__in])])])])). 6.97/7.22 cnf(c_0_6457, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk86_7(X2,X3,X4,X5,X1,X6,X7)),hAPP(c_List_Oset(X1),X6)))|hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2)=hAPP(c_List_Ofilter(X1,X5),X4)|X4!=hAPP(hAPP(c_List_Oappend(X1),X6),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X7))|~hBOOL(hAPP(X5,X3))|X2!=hAPP(c_List_Ofilter(X1,X5),X7)), inference(split_conjunct,[status(thm)],[c_0_4996])). 6.97/7.22 fof(c_0_6458, plain, ![X805, X806, X807, X808]:(c_Orderings_Otop__class_Otop(tc_fun(X807,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X808,X807,X806),c_Orderings_Otop__class_Otop(tc_fun(X808,tc_HOL_Obool)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X807,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X807,tc_HOL_Obool)),hAPP(c_Set_Oimage(X808,X807,X806),X805))),hAPP(c_Set_Oimage(X808,X807,X806),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X808,tc_HOL_Obool)),X805))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_surj__Compl__image__subset])])])). 6.97/7.22 cnf(c_0_6459, plain, (hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk250_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Int_Oint))),esk251_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk250_3(X1,X2,X3)),esk251_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_4997])). 6.97/7.22 cnf(c_0_6460, plain, (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)))=c_List_Oupt(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_4998])). 6.97/7.22 cnf(c_0_6461, plain, (hBOOL(hAPP(c_List_Odistinct(X2),c_List_Oconcat(X2,X1)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),esk287_2(X1,X2)),hAPP(c_List_Oset(tc_List_Olist(X2)),X1)))|esk289_2(X1,X2)!=esk288_2(X1,X2)|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),X1))), inference(split_conjunct,[status(thm)],[c_0_4933])). 6.97/7.22 fof(c_0_6462, plain, ![X4760, X4761, X4762, X4763, X4764]:(~class_Groups_Oab__group__add(X4764)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4763),X4762))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4763,tc_HOL_Obool)),X4761),X4762))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4764),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4763,X4764),X4760),X4762)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4763,X4764),X4760),X4761))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4763,X4764),X4760),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4763,tc_HOL_Obool)),X4762),X4761))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__diff])])])). 6.97/7.22 fof(c_0_6463, plain, ![X7076, X7077, X7078]:(~class_Groups_Oab__semigroup__mult(X7078)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7078),X7077))|(X7077=c_Orderings_Obot__class_Obot(tc_fun(X7078,tc_HOL_Obool))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7078),X7076))|(c_Orderings_Obot__class_Obot(tc_fun(X7078,tc_HOL_Obool))=X7076|(c_Orderings_Obot__class_Obot(tc_fun(X7078,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7078,tc_HOL_Obool)),X7077),X7076)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7078),hAPP(c_Finite__Set_Ofold1(X7078,c_Groups_Otimes__class_Otimes(X7078)),X7077)),hAPP(c_Finite__Set_Ofold1(X7078,c_Groups_Otimes__class_Otimes(X7078)),X7076))=hAPP(c_Finite__Set_Ofold1(X7078,c_Groups_Otimes__class_Otimes(X7078)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7078,tc_HOL_Obool)),X7077),X7076)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__Un])])])). 6.97/7.22 cnf(c_0_6464, 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_Orderings_Oorder(X2)|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_4999])). 6.97/7.22 fof(c_0_6465, plain, ![X11282, X11283, X11284, X11285]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X11284)),X11283))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11285),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X11285),X11282),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X11283,X11284))),hAPP(X11282,hAPP(c_Nat_OSuc,X11284)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X11285),X11282),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X11283,hAPP(c_Nat_OSuc,X11284)))|~class_Groups_Ocomm__monoid__add(X11285))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X11284)),X11283))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X11285),X11282),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X11283,hAPP(c_Nat_OSuc,X11284)))=c_Groups_Ozero__class_Ozero(X11285)|~class_Groups_Ocomm__monoid__add(X11285))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__cl__ivl__Suc])])])])). 6.97/7.22 fof(c_0_6466, plain, ![X8241, X8242, X8243, X8244, X8245, X8246]:(~c_Finite__Set_Ofun__left__comm(X8246,X8245,X8244)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8246),X8243))|(hBOOL(hAPP(hAPP(c_member(X8246),X8242),X8243))|hAPP(hAPP(X8244,X8242),hAPP(hAPP(c_Finite__Set_Ofold(X8246,X8245,X8244),X8241),X8243))=hAPP(hAPP(c_Finite__Set_Ofold(X8246,X8245,X8244),X8241),hAPP(hAPP(c_Set_Oinsert(X8246),X8242),X8243))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__insert])])])). 6.97/7.22 cnf(c_0_6467, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X1)=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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))|~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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5000, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.22 cnf(c_0_6468, 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_5001, c_0_5002]), ['final']). 6.97/7.22 cnf(c_0_6469, 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_5003, c_0_4413]), ['final']). 6.97/7.22 fof(c_0_6470, plain, ![X1848, X1849, X1850, X1851]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1851),X1850))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1851,tc_HOL_Obool)),X1850),X1849))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1851,tc_Nat_Onat),X1848),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1851,tc_HOL_Obool)),X1849),X1850))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1851,tc_Nat_Onat),X1848),X1849)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1851,tc_Nat_Onat),X1848),X1850)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__diff__nat])])])). 6.97/7.22 fof(c_0_6471, plain, ![X11742, X11743, X11744]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11744),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11743)),X11742)))|hAPP(hAPP(c_List_Oappend(X11743),hAPP(hAPP(c_List_Otake(X11743),X11744),X11742)),hAPP(hAPP(c_List_Olist_OCons(X11743),hAPP(hAPP(c_List_Onth(X11743),X11742),X11744)),hAPP(hAPP(c_List_Odrop(X11743),hAPP(c_Nat_OSuc,X11744)),X11742)))=X11742), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_id__take__nth__drop])])). 6.97/7.22 fof(c_0_6472, plain, ![X15242, X15243, X15244, X15245, X15246]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X15246,X15245)),esk514_5(X15242,X15243,X15244,X15245,X15246)),hAPP(c_List_Oset(tc_prod(X15246,X15245)),hAPP(hAPP(c_List_Ozip(X15246,X15245),X15244),X15243))))|(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15246)),X15244)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15245)),X15243)|c_List_Olist__all2(X15246,X15245,X15242,X15244,X15243)))&(~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X15246,X15245,tc_HOL_Obool),X15242),esk514_5(X15242,X15243,X15244,X15245,X15246)))|(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15246)),X15244)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15245)),X15243)|c_List_Olist__all2(X15246,X15245,X15242,X15244,X15243)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2I])])])])). 6.97/7.22 fof(c_0_6473, plain, ![X8607, X8608]:(~class_Rings_Ocomm__semiring__1(X8608)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8608),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8608),c_Groups_Oone__class_Oone(X8608)),c_Groups_Oone__class_Oone(X8608))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X8608),c_Nat_Osemiring__1__class_Oof__nat(X8608)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X8607)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8608),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8608),X8607)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8608),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8608),X8607)),c_Groups_Oone__class_Oone(X8608)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gauss__sum])])). 6.97/7.22 fof(c_0_6474, plain, ![X7446, X7447, X7448, X7449, X7450, X7452, X7453, X7454, X7455, X7456, X7457]:(((hBOOL(hAPP(hAPP(c_member(tc_prod(X7450,X7449)),esk240_5(X7446,X7447,X7448,X7449,X7450)),hAPP(c_List_Oset(tc_prod(X7450,X7449)),hAPP(hAPP(c_List_Ozip(X7450,X7449),X7447),X7446))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7449)),X7446)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7450)),X7447)|c_List_Olist__all2(X7450,X7449,X7448,X7447,X7446))&(~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X7450,X7449,tc_HOL_Obool),X7448),esk240_5(X7446,X7447,X7448,X7449,X7450)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7449)),X7446)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7450)),X7447)|c_List_Olist__all2(X7450,X7449,X7448,X7447,X7446)))&((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7455)),X7452)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7456)),X7453)|~c_List_Olist__all2(X7456,X7455,X7454,X7453,X7452))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X7456,X7455)),X7457),hAPP(c_List_Oset(tc_prod(X7456,X7455)),hAPP(hAPP(c_List_Ozip(X7456,X7455),X7453),X7452))))|hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X7456,X7455,tc_HOL_Obool),X7454),X7457))|~c_List_Olist__all2(X7456,X7455,X7454,X7453,X7452)))), 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__def])])])])])])])). 6.97/7.22 fof(c_0_6475, plain, ![X9986, X9987, X9988]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9988),X9987))|(~hBOOL(hAPP(hAPP(c_member(X9988),X9986),X9987))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X9988),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9988,tc_HOL_Obool)),X9987),hAPP(hAPP(c_Set_Oinsert(X9988),X9986),c_Orderings_Obot__class_Obot(tc_fun(X9988,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X9988),X9987))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Diff1__less])])])). 6.97/7.22 fof(c_0_6476, plain, ![X10015, X10016, X10017, X10018]:((((hBOOL(hAPP(hAPP(c_member(X10018),X10016),X10017))|~hBOOL(hAPP(hAPP(c_member(X10018),X10016),X10017))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10018,tc_HOL_Obool)),X10017),hAPP(hAPP(c_Set_Oinsert(X10018),X10016),X10015))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10018,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10018,tc_HOL_Obool)),X10017),hAPP(hAPP(c_Set_Oinsert(X10018),X10016),c_Orderings_Obot__class_Obot(tc_fun(X10018,tc_HOL_Obool))))),X10015))|~hBOOL(hAPP(hAPP(c_member(X10018),X10016),X10017))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10018,tc_HOL_Obool)),X10017),hAPP(hAPP(c_Set_Oinsert(X10018),X10016),X10015)))))&((hBOOL(hAPP(hAPP(c_member(X10018),X10016),X10017))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10018,tc_HOL_Obool)),X10017),X10015))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10018,tc_HOL_Obool)),X10017),hAPP(hAPP(c_Set_Oinsert(X10018),X10016),X10015))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10018,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10018,tc_HOL_Obool)),X10017),hAPP(hAPP(c_Set_Oinsert(X10018),X10016),c_Orderings_Obot__class_Obot(tc_fun(X10018,tc_HOL_Obool))))),X10015))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10018,tc_HOL_Obool)),X10017),X10015))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10018,tc_HOL_Obool)),X10017),hAPP(hAPP(c_Set_Oinsert(X10018),X10016),X10015))))))&((hBOOL(hAPP(hAPP(c_member(X10018),X10016),X10017))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10018,tc_HOL_Obool)),X10017),X10015))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10018,tc_HOL_Obool)),X10017),hAPP(hAPP(c_Set_Oinsert(X10018),X10016),X10015))))&(~hBOOL(hAPP(hAPP(c_member(X10018),X10016),X10017))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10018,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10018,tc_HOL_Obool)),X10017),hAPP(hAPP(c_Set_Oinsert(X10018),X10016),c_Orderings_Obot__class_Obot(tc_fun(X10018,tc_HOL_Obool))))),X10015))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10018,tc_HOL_Obool)),X10017),hAPP(hAPP(c_Set_Oinsert(X10018),X10016),X10015)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_subset__insert__iff])])])])). 6.97/7.22 fof(c_0_6477, plain, ![X11423, X11424, X11425, X11426]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X11426),tc_List_Olist(X11426))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X11426),tc_List_Olist(X11426)),X11425),X11424)),c_List_Olistrel(X11426,X11423)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X11426),tc_List_Olist(X11426))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X11426),tc_List_Olist(X11426)),X11425),X11424)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X11426),c_List_Olistrel1(X11426,X11423))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rtrancl__listrel1__if__listrel])])])). 6.97/7.22 cnf(c_0_6478, plain, (c_List_OdropWhile(X3,X1,X4)=c_List_OdropWhile(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5004])). 6.97/7.22 cnf(c_0_6479, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk128_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),esk127_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk127_3(X1,X2,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5005])). 6.97/7.22 cnf(c_0_6480, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk58_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),esk57_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk57_3(X1,X2,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5006])). 6.97/7.22 fof(c_0_6481, plain, ![X8691, X8692, X8693]:(~class_Orderings_Olinorder(X8693)|(hAPP(hAPP(c_Orderings_Oord__class_Omax(X8693),hAPP(X8692,esk281_3(X8691,X8692,X8693))),hAPP(X8692,esk282_3(X8691,X8692,X8693)))!=hAPP(X8692,hAPP(hAPP(c_Orderings_Oord__class_Omax(X8693),esk281_3(X8691,X8692,X8693)),esk282_3(X8691,X8692,X8693)))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8693),X8691))|(X8691=c_Orderings_Obot__class_Obot(tc_fun(X8693,tc_HOL_Obool))|c_Big__Operators_Olattice_OSup__fin(X8693,c_Orderings_Oord__class_Omax(X8693),hAPP(c_Set_Oimage(X8693,X8693,X8692),X8691))=hAPP(X8692,c_Big__Operators_Olattice_OSup__fin(X8693,c_Orderings_Oord__class_Omax(X8693),X8691)))))), 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])])])])). 6.97/7.22 fof(c_0_6482, plain, ![X13375, X13376, X13377]:(~class_Orderings_Olinorder(X13377)|(hAPP(X13376,hAPP(hAPP(c_Orderings_Oord__class_Omin(X13377),esk441_3(X13375,X13376,X13377)),esk442_3(X13375,X13376,X13377)))!=hAPP(hAPP(c_Orderings_Oord__class_Omin(X13377),hAPP(X13376,esk441_3(X13375,X13376,X13377))),hAPP(X13376,esk442_3(X13375,X13376,X13377)))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13377),X13375))|(X13375=c_Orderings_Obot__class_Obot(tc_fun(X13377,tc_HOL_Obool))|c_Big__Operators_Olattice_OInf__fin(X13377,c_Orderings_Oord__class_Omin(X13377),hAPP(c_Set_Oimage(X13377,X13377,X13376),X13375))=hAPP(X13376,c_Big__Operators_Olattice_OInf__fin(X13377,c_Orderings_Oord__class_Omin(X13377),X13375)))))), 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])])])])). 6.97/7.22 cnf(c_0_6483, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk209_8(X2,X3,X4,X5,X6,X7,X1,X8)),X4))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X8),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X6),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X8),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X7),X5))|X5!=X4|X7!=X6|~class_Groups_Ocomm__monoid__add(X8)|~class_Orderings_Oord(X1)), inference(split_conjunct,[status(thm)],[c_0_4970])). 6.97/7.22 cnf(c_0_6484, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk209_8(X3,X4,X5,X6,X2,X7,X1,X8)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X8),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X8),X4),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X7),X6))|X6!=X5|X7!=X2|~class_Groups_Ocomm__monoid__add(X8)|~class_Orderings_Oord(X1)), inference(split_conjunct,[status(thm)],[c_0_4970])). 6.97/7.22 cnf(c_0_6485, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_3(X2,X3,X1)),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),esk273_3(X2,X3,X1))),esk274_3(X2,X3,X1))=X3|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)))), inference(split_conjunct,[status(thm)],[c_0_4962])). 6.97/7.22 cnf(c_0_6486, 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_4879])). 6.97/7.22 cnf(c_0_6487, plain, (hAPP(hAPP(c_List_Otake(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_Otake(X1),X3),X4)),hAPP(hAPP(c_List_Otake(X2),X3),X5))), inference(split_conjunct,[status(thm)],[c_0_5007]), ['final']). 6.97/7.22 fof(c_0_6488, plain, ![X14582, X14583, X14584, X14585, X14586]:(~class_Rings_Osemiring__0(X14586)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14585,X14586),hAPP(hAPP(c_COMBC(X14585,X14586,X14586),hAPP(hAPP(c_COMBB(X14586,tc_fun(X14586,X14586),X14585),c_Groups_Otimes__class_Otimes(X14586)),X14584)),X14582)),X14583)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14586),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14585,X14586),X14584),X14583)),X14582)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__left__distrib])])])). 6.97/7.22 cnf(c_0_6489, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk275_3(X3,X2,X1))),esk276_3(X3,X2,X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk274_3(X3,X2,X1)))|hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_4962])). 6.97/7.22 fof(c_0_6490, plain, ![X1692, X1693, X1694]:((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),esk48_3(X1692,X1693,X1694)),esk49_3(X1692,X1693,X1694))))|hBOOL(hAPP(hAPP(X1692,X1694),X1693))|~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),X1694),X1693))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk49_3(X1692,X1693,X1694)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(X1692,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk48_3(X1692,X1693,X1694))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk49_3(X1692,X1693,X1694))))|hBOOL(hAPP(hAPP(X1692,X1694),X1693))|~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),X1694),X1693))))&(~hBOOL(hAPP(hAPP(X1692,esk48_3(X1692,X1693,X1694)),esk49_3(X1692,X1693,X1694)))|hBOOL(hAPP(hAPP(X1692,X1694),X1693))|~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),X1694),X1693)))))), 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])])])])])). 6.97/7.22 fof(c_0_6491, plain, ![X17513, X17514, X17515, X17516, X17517]:(~class_Rings_Osemiring(X17517)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17517),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17517),X17516),X17515)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17517),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17517),X17514),X17515)),X17513))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17517),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17517),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17517),X17516),X17514)),X17515)),X17513)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_combine__common__factor])])])). 6.97/7.22 cnf(c_0_6492, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_3(X1,X2,X3)),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),esk273_3(X1,X2,X3))),esk274_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_4962])). 6.97/7.22 cnf(c_0_6493, plain, (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),esk275_3(X1,X2,X3))),esk276_3(X1,X2,X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk274_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_4962])). 6.97/7.22 cnf(c_0_6494, plain, (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_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(split_conjunct,[status(thm)],[c_0_5008])). 6.97/7.22 cnf(c_0_6495, 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_5009])). 6.97/7.22 fof(c_0_6496, plain, ![X7998, X7999, X8000, X8001]:(~class_Orderings_Olinorder(X8001)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8001),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8001),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8001),X8000),X7999)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8001),X8000),X7998))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8001),X8000),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8001),X7999),X7998))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Odistrib__inf__le])])). 6.97/7.22 cnf(c_0_6497, 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_5010, c_0_4813]), c_0_4813])). 6.97/7.22 cnf(c_0_6498, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(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_Odrop(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_5011]), ['final']). 6.97/7.22 fof(c_0_6499, plain, ![X3562, X3563, X3564, X3565]:(~class_Lattices_Olattice(X3565)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3565),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3565),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3565),X3564),X3563)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3565),X3564),X3562))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3565),X3564),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3565),X3563),X3562))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distrib__inf__le])])])). 6.97/7.22 fof(c_0_6500, plain, ![X7578, X7579, X7580, X7581]:(~class_Orderings_Olinorder(X7581)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7581),hAPP(hAPP(c_Orderings_Oord__class_Omax(X7581),X7580),hAPP(hAPP(c_Orderings_Oord__class_Omin(X7581),X7579),X7578))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X7581),hAPP(hAPP(c_Orderings_Oord__class_Omax(X7581),X7580),X7579)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X7581),X7580),X7578))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Odistrib__sup__le])])). 6.97/7.22 fof(c_0_6501, plain, ![X3857, X3858, X3859, X3860]:(~class_Lattices_Olattice(X3860)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3860),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3860),X3859),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3860),X3858),X3857))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3860),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3860),X3859),X3858)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3860),X3859),X3857))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distrib__sup__le])])])). 6.97/7.22 fof(c_0_6502, plain, ![X16678, X16679, X16680, X16681]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk555_4(X16678,X16679,X16680,X16681)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X16680)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16681),X16679))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16681),X16680)),X16679)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X16679),X16678))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16680)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk556_4(X16678,X16679,X16680,X16681)),X16678))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16681),X16679))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16681),X16680)),X16679)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X16679),X16678))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16680)))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk556_4(X16678,X16679,X16680,X16681)),esk555_4(X16678,X16679,X16680,X16681))=X16681|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16681),X16679))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16681),X16680)),X16679)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X16679),X16678))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16680))))), 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])])])])])])). 6.97/7.22 fof(c_0_6503, plain, ![X16024, X16025, X16026, X16027]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk542_4(X16024,X16025,X16026,X16027)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X16026)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16025),X16027))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16025),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X16027),X16026))))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X16025),X16024))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16026)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk543_4(X16024,X16025,X16026,X16027)),X16024))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16025),X16027))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16025),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X16027),X16026))))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X16025),X16024))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16026)))&(X16027=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk543_4(X16024,X16025,X16026,X16027)),esk542_4(X16024,X16025,X16026,X16027))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16025),X16027))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16025),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X16027),X16026))))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X16025),X16024))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16026))))), 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])])])])])])). 6.97/7.22 fof(c_0_6504, plain, ![X11447, X11448, X11449, X11450, X11451]:(~class_Rings_Olinordered__idom(X11451)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11451),hAPP(c_Groups_Oabs__class_Oabs(X11451),X11450)),X11449))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11451),hAPP(c_Groups_Oabs__class_Oabs(X11451),X11448)),X11447))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11451),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11451),hAPP(c_Groups_Oabs__class_Oabs(X11451),X11450)),hAPP(c_Groups_Oabs__class_Oabs(X11451),X11448))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11451),X11449),X11447)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__mult__less])])])). 6.97/7.22 cnf(c_0_6505, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[c_0_5012, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.22 cnf(c_0_6506, plain, (c_Int_OMin=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[fact_Int_OMin__def]), ['final']). 6.97/7.22 cnf(c_0_6507, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5013, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.22 fof(c_0_6508, plain, ![X16721, X16722, X16723, X16724, X16725, X16728, X16729, X16730, X16731, X16732, X16733]:((((hBOOL(hAPP(hAPP(c_member(X16724),esk559_4(X16721,X16722,X16723,X16724)),X16722))|hBOOL(hAPP(hAPP(c_member(X16724),esk558_4(X16721,X16722,X16723,X16724)),X16723))|(~hBOOL(hAPP(X16721,X16725))|~hBOOL(hAPP(hAPP(c_member(X16724),X16725),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16724,tc_HOL_Obool)),X16723),X16722)))))&(hBOOL(hAPP(X16721,esk559_4(X16721,X16722,X16723,X16724)))|hBOOL(hAPP(hAPP(c_member(X16724),esk558_4(X16721,X16722,X16723,X16724)),X16723))|(~hBOOL(hAPP(X16721,X16725))|~hBOOL(hAPP(hAPP(c_member(X16724),X16725),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16724,tc_HOL_Obool)),X16723),X16722))))))&((hBOOL(hAPP(hAPP(c_member(X16724),esk559_4(X16721,X16722,X16723,X16724)),X16722))|hBOOL(hAPP(X16721,esk558_4(X16721,X16722,X16723,X16724)))|(~hBOOL(hAPP(X16721,X16725))|~hBOOL(hAPP(hAPP(c_member(X16724),X16725),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16724,tc_HOL_Obool)),X16723),X16722)))))&(hBOOL(hAPP(X16721,esk559_4(X16721,X16722,X16723,X16724)))|hBOOL(hAPP(X16721,esk558_4(X16721,X16722,X16723,X16724)))|(~hBOOL(hAPP(X16721,X16725))|~hBOOL(hAPP(hAPP(c_member(X16724),X16725),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16724,tc_HOL_Obool)),X16723),X16722)))))))&(((hBOOL(hAPP(X16728,esk560_4(X16728,X16729,X16730,X16731)))|(~hBOOL(hAPP(hAPP(c_member(X16731),X16732),X16730))|~hBOOL(hAPP(X16728,X16732))))&(hBOOL(hAPP(hAPP(c_member(X16731),esk560_4(X16728,X16729,X16730,X16731)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16731,tc_HOL_Obool)),X16730),X16729)))|(~hBOOL(hAPP(hAPP(c_member(X16731),X16732),X16730))|~hBOOL(hAPP(X16728,X16732)))))&((hBOOL(hAPP(X16728,esk560_4(X16728,X16729,X16730,X16731)))|(~hBOOL(hAPP(hAPP(c_member(X16731),X16733),X16729))|~hBOOL(hAPP(X16728,X16733))))&(hBOOL(hAPP(hAPP(c_member(X16731),esk560_4(X16728,X16729,X16730,X16731)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16731,tc_HOL_Obool)),X16730),X16729)))|(~hBOOL(hAPP(hAPP(c_member(X16731),X16733),X16729))|~hBOOL(hAPP(X16728,X16733))))))), 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])])])])])])). 6.97/7.22 fof(c_0_6509, plain, ![X6756, X6757, X6758, X6759, X6760, X6761]:((X6759=hAPP(hAPP(c_Product__Type_OPair(X6761,X6760),esk218_6(X6756,X6757,X6758,X6759,X6760,X6761)),esk220_6(X6756,X6757,X6758,X6759,X6760,X6761))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X6761,X6760)),X6759),hAPP(hAPP(c_Relation_Orel__comp(X6761,X6758,X6760),X6757),X6756))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X6761,X6758)),hAPP(hAPP(c_Product__Type_OPair(X6761,X6758),esk218_6(X6756,X6757,X6758,X6759,X6760,X6761)),esk219_6(X6756,X6757,X6758,X6759,X6760,X6761))),X6757))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X6761,X6760)),X6759),hAPP(hAPP(c_Relation_Orel__comp(X6761,X6758,X6760),X6757),X6756))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X6758,X6760)),hAPP(hAPP(c_Product__Type_OPair(X6758,X6760),esk219_6(X6756,X6757,X6758,X6759,X6760,X6761)),esk220_6(X6756,X6757,X6758,X6759,X6760,X6761))),X6756))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X6761,X6760)),X6759),hAPP(hAPP(c_Relation_Orel__comp(X6761,X6758,X6760),X6757),X6756)))))), 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])])])])])). 6.97/7.22 fof(c_0_6510, plain, ![X5878, X5879]:(~class_Orderings_Olinorder(X5879)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5879),X5878))|(c_Orderings_Obot__class_Obot(tc_fun(X5879,tc_HOL_Obool))=X5878|(~hBOOL(hAPP(hAPP(c_member(X5879),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5879),esk192_2(X5878,X5879)),esk193_2(X5878,X5879))),hAPP(hAPP(c_Set_Oinsert(X5879),esk192_2(X5878,X5879)),hAPP(hAPP(c_Set_Oinsert(X5879),esk193_2(X5878,X5879)),c_Orderings_Obot__class_Obot(tc_fun(X5879,tc_HOL_Obool))))))|hBOOL(hAPP(hAPP(c_member(X5879),c_Big__Operators_Olattice_OInf__fin(X5879,c_Orderings_Oord__class_Omin(X5879),X5878)),X5878)))))), 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])])])])). 6.97/7.22 fof(c_0_6511, plain, ![X10070, X10071, X10072, X10073, X10074, X10075]:((~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10073),X10072),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10073),X10074),X10070)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10073),X10072),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10073),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10073),X10074),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10073),X10075),X10071))),X10070)))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10073),X10072),X10071))|(~class_Rings_Ocomm__ring(X10073)|~class_Rings_Odvd(X10073)))&(~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10073),X10072),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10073),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10073),X10074),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10073),X10075),X10071))),X10070)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10073),X10072),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10073),X10074),X10070)))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10073),X10072),X10071))|(~class_Rings_Ocomm__ring(X10073)|~class_Rings_Odvd(X10073)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__period_I3_J])])])])). 6.97/7.22 cnf(c_0_6512, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))=X2|X2=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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))!=c_Groups_Oone__class_Oone(X1)|~class_Rings_Oring__1__no__zero__divisors(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)],[c_0_5014, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741])). 6.97/7.22 cnf(c_0_6513, plain, (X1=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|~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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),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_5015, c_0_4742]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741])). 6.97/7.22 fof(c_0_6514, plain, ![X2340, X2341]:(~class_Orderings_Olinorder(X2341)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2341),X2340))|(X2340=c_Orderings_Obot__class_Obot(tc_fun(X2341,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_member(X2341),hAPP(hAPP(c_Orderings_Oord__class_Omax(X2341),esk75_2(X2340,X2341)),esk76_2(X2340,X2341))),hAPP(hAPP(c_Set_Oinsert(X2341),esk75_2(X2340,X2341)),hAPP(hAPP(c_Set_Oinsert(X2341),esk76_2(X2340,X2341)),c_Orderings_Obot__class_Obot(tc_fun(X2341,tc_HOL_Obool))))))|hBOOL(hAPP(hAPP(c_member(X2341),c_Big__Operators_Olattice_OSup__fin(X2341,c_Orderings_Oord__class_Omax(X2341),X2340)),X2340)))))), 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])])])])). 6.97/7.22 fof(c_0_6515, plain, ![X5940, X5941, X5942]:(~class_Complete__Lattice_Ocomplete__lattice(X5942)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5942),X5941),hAPP(X5940,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5942),X5941),c_Inductive_Ocomplete__lattice__class_Ogfp(X5942,X5940)))))|(~c_Orderings_Oorder__class_Omono(X5942,X5942,X5940)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5942),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5942),X5941),c_Inductive_Ocomplete__lattice__class_Ogfp(X5942,X5940))),hAPP(X5940,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5942),X5941),c_Inductive_Ocomplete__lattice__class_Ogfp(X5942,X5940)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_coinduct__lemma])])])). 6.97/7.22 cnf(c_0_6516, 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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))), 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)],[c_0_5016, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741])])). 6.97/7.22 cnf(c_0_6517, 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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),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)],[inference(rw,[status(thm)],[c_0_5017, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741])). 6.97/7.22 fof(c_0_6518, plain, ![X8738, X8739, X8740, X8741]:(~class_Rings_Oring(X8741)|~class_Int_Onumber(X8741)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8741),hAPP(c_Int_Onumber__class_Onumber__of(X8741),X8740)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8741),X8739),X8738))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8741),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8741),hAPP(c_Int_Onumber__class_Onumber__of(X8741),X8740)),X8739)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8741),hAPP(c_Int_Onumber__class_Onumber__of(X8741),X8740)),X8738))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__diff__distrib__number__of])])). 6.97/7.22 cnf(c_0_6519, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk275_3(X3,X2,X1))),esk276_3(X3,X2,X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X3,X2,X1)),X3))|hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_4962])). 6.97/7.22 cnf(c_0_6520, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),esk276_3(X2,X3,X1)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk273_3(X2,X3,X1))),esk274_3(X2,X3,X1))=X3|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)))), inference(split_conjunct,[status(thm)],[c_0_4962])). 6.97/7.22 fof(c_0_6521, plain, ![X16175, X16176, X16177, X16178]:(~c_Fun_Oinj__on(X16178,X16177,X16176,c_Orderings_Otop__class_Otop(tc_fun(X16178,tc_HOL_Obool)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16177,tc_HOL_Obool)),hAPP(c_Set_Oimage(X16178,X16177,X16176),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X16178,tc_HOL_Obool)),X16175))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X16177,tc_HOL_Obool)),hAPP(c_Set_Oimage(X16178,X16177,X16176),X16175))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__image__Compl__subset])])). 6.97/7.22 fof(c_0_6522, plain, ![X12189, X12190, X12191, X12192]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12192),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12191)),X12190)))|hAPP(hAPP(c_List_Oappend(X12191),hAPP(hAPP(c_List_Otake(X12191),X12192),X12190)),hAPP(hAPP(c_List_Olist_OCons(X12191),X12189),hAPP(hAPP(c_List_Odrop(X12191),hAPP(c_Nat_OSuc,X12192)),X12190)))=hAPP(hAPP(c_List_Olist__update(X12191,X12190),X12192),X12189)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upd__conv__take__nth__drop])])). 6.97/7.22 fof(c_0_6523, plain, ![X9471, X9472, X9473, X9474, X9475]:(~class_Fields_Ofield(X9475)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9474,X9475),hAPP(hAPP(c_COMBC(X9474,X9475,X9475),hAPP(hAPP(c_COMBB(X9475,tc_fun(X9475,X9475),X9474),c_Rings_Oinverse__class_Odivide(X9475)),X9473)),X9471)),X9472)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9475),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9474,X9475),X9473),X9472)),X9471)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__divide__distrib])])])). 6.97/7.22 cnf(c_0_6524, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk330_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_4991])). 6.97/7.22 cnf(c_0_6525, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk302_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_4990])). 6.97/7.22 fof(c_0_6526, plain, ![X17266, X17267, X17268, X17269]:(~class_Int_Onumber(X17269)|~class_Rings_Osemiring(X17269)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17269),hAPP(c_Int_Onumber__class_Onumber__of(X17269),X17268)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17269),X17267),X17266))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17269),hAPP(c_Int_Onumber__class_Onumber__of(X17269),X17268)),X17267)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17269),hAPP(c_Int_Onumber__class_Onumber__of(X17269),X17268)),X17266))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__distrib__number__of])])). 6.97/7.22 fof(c_0_6527, plain, ![X8838, X8839, X8840, X8841, X8842, X8843]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X8840,X8840)),hAPP(hAPP(c_Product__Type_OPair(X8840,X8840),hAPP(X8838,X8842)),hAPP(X8838,X8841))),X8839))|hBOOL(hAPP(hAPP(c_member(tc_prod(X8843,X8843)),hAPP(hAPP(c_Product__Type_OPair(X8843,X8843),X8842),X8841)),hAPP(hAPP(c_Relation_Oinv__image(X8840,X8843),X8839),X8838))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X8843,X8843)),hAPP(hAPP(c_Product__Type_OPair(X8843,X8843),X8842),X8841)),hAPP(hAPP(c_Relation_Oinv__image(X8840,X8843),X8839),X8838)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X8840,X8840)),hAPP(hAPP(c_Product__Type_OPair(X8840,X8840),hAPP(X8838,X8842)),hAPP(X8838,X8841))),X8839)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__inv__image])])). 6.97/7.22 cnf(c_0_6528, 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)),esk22_3(X2,X3,X1)),esk23_3(X2,X3,X1))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(c_Finite__Set_Ocard(X1),esk21_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_4947])). 6.97/7.22 fof(c_0_6529, plain, ![X11226, X11227, X11228, X11229, X11230]:(~class_Divides_Osemiring__div(X11230)|(~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X11230),X11229),X11228))|(~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X11230),X11227),X11226))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X11230),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11230),X11228),X11226)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11230),X11229),X11227))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11230),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X11230),X11228),X11229)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X11230),X11226),X11227))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__mult__div__if__dvd])])])). 6.97/7.22 fof(c_0_6530, plain, ![X11270, X11271, X11272, X11273, X11274]:((hBOOL(hAPP(hAPP(c_member(X11274),esk375_5(X11270,X11271,X11272,X11273,X11274)),X11273))|c_Relation_Orefl__on(X11272,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11274,tc_fun(X11272,tc_HOL_Obool)),X11273),X11271),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11274,tc_fun(tc_prod(X11272,X11272),tc_HOL_Obool)),X11273),X11270)))&(~c_Relation_Orefl__on(X11272,hAPP(X11271,esk375_5(X11270,X11271,X11272,X11273,X11274)),hAPP(X11270,esk375_5(X11270,X11271,X11272,X11273,X11274)))|c_Relation_Orefl__on(X11272,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11274,tc_fun(X11272,tc_HOL_Obool)),X11273),X11271),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11274,tc_fun(tc_prod(X11272,X11272),tc_HOL_Obool)),X11273),X11270)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__INTER])])])])). 6.97/7.22 cnf(c_0_6531, 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),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),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),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_5018])). 6.97/7.22 cnf(c_0_6532, plain, (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)),X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,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),X2))), inference(split_conjunct,[status(thm)],[c_0_5019])). 6.97/7.22 fof(c_0_6533, plain, ![X5891, X5892, X5893, X5894, X5895]:((hBOOL(hAPP(hAPP(c_member(X5895),esk195_5(X5891,X5892,X5893,X5894,X5895)),X5894))|c_Relation_Orefl__on(X5893,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5895,tc_fun(X5893,tc_HOL_Obool)),X5894),X5892),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5895,tc_fun(tc_prod(X5893,X5893),tc_HOL_Obool)),X5894),X5891)))&(~c_Relation_Orefl__on(X5893,hAPP(X5892,esk195_5(X5891,X5892,X5893,X5894,X5895)),hAPP(X5891,esk195_5(X5891,X5892,X5893,X5894,X5895)))|c_Relation_Orefl__on(X5893,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5895,tc_fun(X5893,tc_HOL_Obool)),X5894),X5892),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5895,tc_fun(tc_prod(X5893,X5893),tc_HOL_Obool)),X5894),X5891)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__UNION])])])])). 6.97/7.22 cnf(c_0_6534, 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[c_0_5020, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.22 fof(c_0_6535, plain, ![X13081, X13082, X13083, X13084, X13085, X13086]:(~c_Finite__Set_Ofun__left__comm(X13086,X13085,X13084)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13086),X13083))|(hBOOL(hAPP(hAPP(c_member(X13086),X13082),X13083))|hAPP(hAPP(c_Finite__Set_Ofold(X13086,X13085,X13084),hAPP(hAPP(X13084,X13082),X13081)),X13083)=hAPP(hAPP(c_Finite__Set_Ofold(X13086,X13085,X13084),X13081),hAPP(hAPP(c_Set_Oinsert(X13086),X13082),X13083))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__insert2])])])). 6.97/7.22 cnf(c_0_6536, plain, (hBOOL(hAPP(X1,esk120_2(X1,X2)))|hBOOL(hAPP(X1,esk118_2(X1,X2)))|hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk118_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk119_2(X1,X2)),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_4950])). 6.97/7.22 cnf(c_0_6537, plain, (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),esk275_3(X1,X2,X3))),esk276_3(X1,X2,X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_4962])). 6.97/7.22 cnf(c_0_6538, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk276_3(X1,X2,X3)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk273_3(X1,X2,X3))),esk274_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_4962])). 6.97/7.22 cnf(c_0_6539, 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_4987])). 6.97/7.22 cnf(c_0_6540, 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_5021])). 6.97/7.22 cnf(c_0_6541, 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_5022])). 6.97/7.22 cnf(c_0_6542, 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_5023]), ['final']). 6.97/7.22 cnf(c_0_6543, plain, (hAPP(hAPP(c_List_Oappend(X2),X4),X5)=hAPP(hAPP(c_List_Oappend(X2),X3),X1)|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)|X3!=hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),X4)|~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)))), inference(split_conjunct,[status(thm)],[c_0_4956])). 6.97/7.22 fof(c_0_6544, plain, ![X4415, X4416, X4417, X4418]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4418,X4418)),hAPP(hAPP(c_Product__Type_OPair(X4418,X4418),esk149_4(X4415,X4416,X4417,X4418)),esk150_4(X4415,X4416,X4417,X4418))),X4415))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4418),tc_List_Olist(X4418))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4418),tc_List_Olist(X4418)),X4417),X4416)),c_List_Olistrel1(X4418,X4415))))&((hAPP(hAPP(c_List_Oappend(X4418),esk151_4(X4415,X4416,X4417,X4418)),hAPP(hAPP(c_List_Olist_OCons(X4418),esk149_4(X4415,X4416,X4417,X4418)),esk152_4(X4415,X4416,X4417,X4418)))=X4417|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4418),tc_List_Olist(X4418))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4418),tc_List_Olist(X4418)),X4417),X4416)),c_List_Olistrel1(X4418,X4415))))&(X4416=hAPP(hAPP(c_List_Oappend(X4418),esk151_4(X4415,X4416,X4417,X4418)),hAPP(hAPP(c_List_Olist_OCons(X4418),esk150_4(X4415,X4416,X4417,X4418)),esk152_4(X4415,X4416,X4417,X4418)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4418),tc_List_Olist(X4418))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4418),tc_List_Olist(X4418)),X4417),X4416)),c_List_Olistrel1(X4418,X4415)))))), 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])])])])])). 6.97/7.22 cnf(c_0_6545, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|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)))=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))|~class_Groups_Ocomm__monoid__add(X3)), inference(split_conjunct,[status(thm)],[c_0_5024])). 6.97/7.22 fof(c_0_6546, plain, ![X3864, X3865, X3866]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3866),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3865)),X3864)))|hAPP(hAPP(c_List_Oappend(X3865),hAPP(hAPP(c_List_Otake(X3865),X3866),X3864)),hAPP(hAPP(c_List_Olist_OCons(X3865),hAPP(hAPP(c_List_Onth(X3865),X3864),X3866)),c_List_Olist_ONil(X3865)))=hAPP(hAPP(c_List_Otake(X3865),hAPP(c_Nat_OSuc,X3866)),X3864)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__Suc__conv__app__nth])])). 6.97/7.22 fof(c_0_6547, plain, ![X7663, X7664, X7665, X7666, X7667]:(~class_Orderings_Olinorder(X7667)|(~hBOOL(hAPP(hAPP(c_member(X7666),X7665),hAPP(c_List_Oset(X7666),X7664)))|(~c_List_Olinorder__class_Osorted(X7667,hAPP(hAPP(c_List_Omap(X7666,X7667),X7663),X7664))|(X7665!=hAPP(c_List_Ohd(X7666),hAPP(c_List_Ofilter(X7666,hAPP(hAPP(c_COMBB(X7667,tc_HOL_Obool,X7666),hAPP(c_fequal,hAPP(X7663,X7665))),X7663)),X7664))|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7666,X7667,X7663),X7665),c_List_Oremove1(X7666,X7665,X7664))=X7664)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__key__remove1])])). 6.97/7.22 cnf(c_0_6548, 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_5025])). 6.97/7.22 fof(c_0_6549, plain, ![X10595, X10596, X10597, X10598, X10599]:(~c_Finite__Set_Ofolding__one(X10599,X10598,X10597)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10599),X10596))|(X10596=c_Orderings_Obot__class_Obot(tc_fun(X10599,tc_HOL_Obool))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10599),X10595))|(X10595=c_Orderings_Obot__class_Obot(tc_fun(X10599,tc_HOL_Obool))|(c_Orderings_Obot__class_Obot(tc_fun(X10599,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10599,tc_HOL_Obool)),X10596),X10595)|hAPP(X10597,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10599,tc_HOL_Obool)),X10596),X10595))=hAPP(hAPP(X10598,hAPP(X10597,X10596)),hAPP(X10597,X10595)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Ounion__disjoint])])). 6.97/7.22 fof(c_0_6550, plain, ![X15679, X15680, X15681, X15682, X15683]:(~class_Orderings_Olinorder(X15683)|c_List_Olinorder__class_Osorted(X15683,hAPP(hAPP(c_List_Omap(X15682,X15683),X15681),hAPP(c_List_Ofilter(X15682,hAPP(hAPP(c_COMBC(X15682,X15683,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X15683,tc_fun(X15683,tc_HOL_Obool),X15682),c_fequal),X15681)),hAPP(X15680,X15679))),X15679)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__map__same])])])). 6.97/7.22 fof(c_0_6551, plain, ![X5072, X5073, X5074]:(~class_Orderings_Olinorder(X5074)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5074),X5073))|(c_Orderings_Obot__class_Obot(tc_fun(X5074,tc_HOL_Obool))=X5073|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5074),X5072))|(X5072=c_Orderings_Obot__class_Obot(tc_fun(X5074,tc_HOL_Obool))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X5074),c_Big__Operators_Olattice_OInf__fin(X5074,c_Orderings_Oord__class_Omin(X5074),X5073)),c_Big__Operators_Olattice_OInf__fin(X5074,c_Orderings_Oord__class_Omin(X5074),X5072))=c_Big__Operators_Olattice_OInf__fin(X5074,c_Orderings_Oord__class_Omin(X5074),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5074,tc_HOL_Obool)),X5073),X5072))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Ounion__idem])])])). 6.97/7.22 fof(c_0_6552, plain, ![X3637, X3638, X3639]:((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),esk122_3(X3637,X3638,X3639)),esk123_3(X3637,X3638,X3639))))|hBOOL(hAPP(hAPP(X3637,X3639),X3638))|~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),X3639),X3638))))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=esk123_3(X3637,X3638,X3639)|hBOOL(hAPP(hAPP(X3637,esk123_3(X3637,X3638,X3639)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,esk122_3(X3637,X3638,X3639),esk123_3(X3637,X3638,X3639))))|hBOOL(hAPP(hAPP(X3637,X3639),X3638))|~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),X3639),X3638))))&(~hBOOL(hAPP(hAPP(X3637,esk122_3(X3637,X3638,X3639)),esk123_3(X3637,X3638,X3639)))|hBOOL(hAPP(hAPP(X3637,X3639),X3638))|~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),X3639),X3638)))))), 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])])])])])). 6.97/7.22 fof(c_0_6553, plain, ![X17225, X17226, X17227, X17228]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17228))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17227),X17226))|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),X17226),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X17225,X17228))),X17227)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17226),X17228))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__lemma])])])). 6.97/7.22 cnf(c_0_6554, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_3(X1,X2,X3)),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),esk254_3(X1,X2,X3))),esk255_3(X1,X2,X3))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_4980])). 6.97/7.22 cnf(c_0_6555, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3))),esk257_3(X1,X2,X3))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk255_3(X1,X2,X3)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_4980])). 6.97/7.22 fof(c_0_6556, plain, ![X1077, X1078, X1079, X1080, X1081, X1082]:(~class_Orderings_Olinorder(X1082)|(~c_List_Olinorder__class_Osorted(X1082,hAPP(hAPP(c_List_Omap(X1081,X1082),X1080),X1079))|(~hBOOL(hAPP(X1078,X1077))|hAPP(c_List_Ofilter(X1081,X1078),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1081,X1082,X1080),X1077),X1079))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1081,X1082,X1080),X1077),hAPP(c_List_Ofilter(X1081,X1078),X1079))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_filter__insort])])])). 6.97/7.22 fof(c_0_6557, plain, ![X16315, X16316, X16317]:(~class_Orderings_Olinorder(X16317)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16317),X16316))|(X16316=c_Orderings_Obot__class_Obot(tc_fun(X16317,tc_HOL_Obool))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16317),X16315))|(c_Orderings_Obot__class_Obot(tc_fun(X16317,tc_HOL_Obool))=X16315|c_Big__Operators_Olattice_OSup__fin(X16317,c_Orderings_Oord__class_Omax(X16317),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16317,tc_HOL_Obool)),X16316),X16315))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X16317),c_Big__Operators_Olattice_OSup__fin(X16317,c_Orderings_Oord__class_Omax(X16317),X16316)),c_Big__Operators_Olattice_OSup__fin(X16317,c_Orderings_Oord__class_Omax(X16317),X16315))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Ounion__idem])])])). 6.97/7.22 fof(c_0_6558, plain, ![X12014, X12015, X12016]:((hBOOL(hAPP(hAPP(c_member(X12016),esk398_3(X12014,X12015,X12016)),X12015))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12016,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X12016),c_Int_Onat),X12014)),X12015))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12016,tc_Int_Oint),X12014),X12015))&(~c_Nat__Transfer_Ois__nat(hAPP(X12014,esk398_3(X12014,X12015,X12016)))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12016,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X12016),c_Int_Onat),X12014)),X12015))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12016,tc_Int_Oint),X12014),X12015))), 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])])])])])). 6.97/7.22 fof(c_0_6559, plain, ![X16383, X16384, X16385]:((hBOOL(hAPP(hAPP(c_member(X16385),esk546_3(X16383,X16384,X16385)),X16384))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16385,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X16385),c_Int_Onat),X16383)),X16384))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16385,tc_Int_Oint),X16383),X16384))&(~c_Nat__Transfer_Ois__nat(hAPP(X16383,esk546_3(X16383,X16384,X16385)))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16385,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X16385),c_Int_Onat),X16383)),X16384))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16385,tc_Int_Oint),X16383),X16384))), 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])])])])])). 6.97/7.22 fof(c_0_6560, plain, ![X14934, X14935, X14936]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14936),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14936,tc_HOL_Obool)),X14935),X14934)))|hAPP(c_Finite__Set_Ocard(X14936),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X14936,tc_HOL_Obool)),X14935),X14934))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X14936),X14935)),hAPP(c_Finite__Set_Ocard(X14936),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14936,tc_HOL_Obool)),X14935),X14934)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff__subset__Int])])). 6.97/7.22 cnf(c_0_6561, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk345_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_4982])). 6.97/7.22 cnf(c_0_6562, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk136_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_4983])). 6.97/7.22 cnf(c_0_6563, 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_5026])). 6.97/7.22 cnf(c_0_6564, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_3(X1,X2,X3)),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),esk254_3(X1,X2,X3))),esk255_3(X1,X2,X3))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_4980])). 6.97/7.22 fof(c_0_6565, plain, ![X11640, X11641, X11642, X11643, X11644, X11645, X11646]:((hBOOL(hAPP(hAPP(X11646,esk390_7(X11640,X11641,X11642,X11643,X11644,X11645,X11646)),esk389_7(X11640,X11641,X11642,X11643,X11644,X11645,X11646)))|hBOOL(hAPP(X11642,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X11645,X11644,X11640),X11641),X11643)))|~hBOOL(hAPP(hAPP(X11646,hAPP(c_Product__Type_Osnd(X11645,X11644),X11643)),hAPP(c_Product__Type_Ofst(X11645,X11644),X11643))))&(~hBOOL(hAPP(X11642,hAPP(hAPP(X11641,esk389_7(X11640,X11641,X11642,X11643,X11644,X11645,X11646)),esk390_7(X11640,X11641,X11642,X11643,X11644,X11645,X11646))))|hBOOL(hAPP(X11642,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X11645,X11644,X11640),X11641),X11643)))|~hBOOL(hAPP(hAPP(X11646,hAPP(c_Product__Type_Osnd(X11645,X11644),X11643)),hAPP(c_Product__Type_Ofst(X11645,X11644),X11643))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_exE__realizer])])])])])). 6.97/7.22 cnf(c_0_6566, 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_5027])). 6.97/7.22 fof(c_0_6567, plain, ![X6673, X6674, X6675, X6676]:(~class_Int_Onumber(X6676)|~class_Rings_Osemiring(X6676)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6676),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6676),X6675),hAPP(c_Int_Onumber__class_Onumber__of(X6676),X6673))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6676),X6674),hAPP(c_Int_Onumber__class_Onumber__of(X6676),X6673)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6676),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6676),X6675),X6674)),hAPP(c_Int_Onumber__class_Onumber__of(X6676),X6673))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_left__distrib__number__of])])])). 6.97/7.22 cnf(c_0_6568, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3))),esk257_3(X1,X2,X3))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk255_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_4980])). 6.97/7.22 cnf(c_0_6569, 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_5028])). 6.97/7.22 fof(c_0_6570, plain, ![X2038, X2039, X2040, X2041, X2042]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2042,X2041)),hAPP(X2042,X2040)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X2039,X2039)),hAPP(hAPP(c_Product__Type_OPair(X2039,X2039),X2041),X2040)),c_List_Omeasures(X2039,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X2039,tc_Nat_Onat)),X2042),X2038))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_measures__less])])])). 6.97/7.22 cnf(c_0_6571, 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_5029])). 6.97/7.22 fof(c_0_6572, plain, ![X1995, X1996, X1997, X1998]:(~class_Groups_Ocomm__monoid__add(X1998)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1997),X1996))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1998),hAPP(X1995,X1997)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1998),X1995),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1997)),X1996)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1998),X1995),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1997),X1996)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__head__upt__Suc])])])). 6.97/7.22 fof(c_0_6573, plain, ![X5738, X5739, X5740, X5741]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5741))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5740),X5739))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5739),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),X5740),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5738,X5741))),X5739)),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])])])). 6.97/7.22 fof(c_0_6574, plain, ![X9428, X9429, X9430, X9431]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9431))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9430))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9430),X9429))|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),X9429),c_Divides_Odiv__class_Omod(tc_Int_Oint,X9428,X9431))),X9430)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmult2__lemma__aux3])])])). 6.97/7.22 fof(c_0_6575, plain, ![X3845, X3846, X3847, X3848, X3849]:(~class_Groups_Ocomm__monoid__add(X3849)|(~hBOOL(hAPP(hAPP(c_member(X3848),X3847),hAPP(c_List_Oset(X3848),X3846)))|hAPP(c_List_Omonoid__add__class_Olistsum(X3849),hAPP(hAPP(c_List_Omap(X3848,X3849),X3845),X3846))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3849),hAPP(X3845,X3847)),hAPP(c_List_Omonoid__add__class_Olistsum(X3849),hAPP(hAPP(c_List_Omap(X3848,X3849),X3845),c_List_Oremove1(X3848,X3847,X3846)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__map__remove1])])])). 6.97/7.22 fof(c_0_6576, plain, ![X11484, X11485, X11486, X11487, X11488, X11489]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X11489,X11489)),hAPP(hAPP(c_Product__Type_OPair(X11489,X11489),esk381_6(X11484,X11485,X11486,X11487,X11488,X11489)),esk382_6(X11484,X11485,X11486,X11487,X11488,X11489))),X11488))|c_Equiv__Relations_Ocongruent2(X11489,X11487,X11484,X11488,X11486,X11485))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X11487,X11487)),hAPP(hAPP(c_Product__Type_OPair(X11487,X11487),esk383_6(X11484,X11485,X11486,X11487,X11488,X11489)),esk384_6(X11484,X11485,X11486,X11487,X11488,X11489))),X11486))|c_Equiv__Relations_Ocongruent2(X11489,X11487,X11484,X11488,X11486,X11485))&(hAPP(hAPP(X11485,esk382_6(X11484,X11485,X11486,X11487,X11488,X11489)),esk384_6(X11484,X11485,X11486,X11487,X11488,X11489))!=hAPP(hAPP(X11485,esk381_6(X11484,X11485,X11486,X11487,X11488,X11489)),esk383_6(X11484,X11485,X11486,X11487,X11488,X11489))|c_Equiv__Relations_Ocongruent2(X11489,X11487,X11484,X11488,X11486,X11485)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_congruent2I_H])])])])])). 6.97/7.22 fof(c_0_6577, plain, ![X2120, X2121, X2122, X2123]:(~class_Rings_Oring(X2123)|~class_Int_Onumber(X2123)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2123),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2123),X2122),X2121)),hAPP(c_Int_Onumber__class_Onumber__of(X2123),X2120))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2123),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2123),X2122),hAPP(c_Int_Onumber__class_Onumber__of(X2123),X2120))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2123),X2121),hAPP(c_Int_Onumber__class_Onumber__of(X2123),X2120)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_left__diff__distrib__number__of])])])). 6.97/7.22 cnf(c_0_6578, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk275_3(X3,X2,X1))),esk276_3(X3,X2,X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_4962])). 6.97/7.22 cnf(c_0_6579, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(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),X2),esk273_3(X2,X3,X1))),esk274_3(X2,X3,X1))=X3|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)))), inference(split_conjunct,[status(thm)],[c_0_4962])). 6.97/7.22 fof(c_0_6580, plain, ![X2728, X2729]:(~c_Nat__Transfer_Onat__set(X2729)|(~c_Nat__Transfer_Onat__set(X2728)|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),X2729)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2728)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X2729),X2728))), 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])])])). 6.97/7.22 fof(c_0_6581, plain, ![X1130, X1131]:(~class_Lattices_Olattice(X1131)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1131),X1130))|(c_Orderings_Obot__class_Obot(tc_fun(X1131,tc_HOL_Obool))=X1130|(~hBOOL(hAPP(hAPP(c_member(X1131),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1131),esk34_2(X1130,X1131)),esk35_2(X1130,X1131))),hAPP(hAPP(c_Set_Oinsert(X1131),esk34_2(X1130,X1131)),hAPP(hAPP(c_Set_Oinsert(X1131),esk35_2(X1130,X1131)),c_Orderings_Obot__class_Obot(tc_fun(X1131,tc_HOL_Obool))))))|hBOOL(hAPP(hAPP(c_member(X1131),c_Big__Operators_Olattice__class_OSup__fin(X1131,X1130)),X1130)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oclosed])])])])). 6.97/7.22 fof(c_0_6582, plain, ![X8531, X8532]:(~class_Lattices_Olattice(X8532)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8532),X8531))|(X8531=c_Orderings_Obot__class_Obot(tc_fun(X8532,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_member(X8532),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8532),esk278_2(X8531,X8532)),esk279_2(X8531,X8532))),hAPP(hAPP(c_Set_Oinsert(X8532),esk278_2(X8531,X8532)),hAPP(hAPP(c_Set_Oinsert(X8532),esk279_2(X8531,X8532)),c_Orderings_Obot__class_Obot(tc_fun(X8532,tc_HOL_Obool))))))|hBOOL(hAPP(hAPP(c_member(X8532),c_Big__Operators_Olattice__class_OInf__fin(X8532,X8531)),X8531)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oclosed])])])])). 6.97/7.22 cnf(c_0_6583, 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_5030])). 6.97/7.22 cnf(c_0_6584, 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))), inference(split_conjunct,[status(thm)],[c_0_5031]), ['final']). 6.97/7.22 cnf(c_0_6585, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Oimage(X4,X1,X5),X6))=hAPP(c_Set_Oimage(X4,X2,hAPP(hAPP(c_COMBB(X1,X2,X4),X3),X5)),X6)), inference(split_conjunct,[status(thm)],[c_0_5032]), ['final']). 6.97/7.22 fof(c_0_6586, plain, ![X17466, X17467, X17468, X17469, X17470]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17470,tc_HOL_Obool)),X17469),X17468))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17470,tc_HOL_Obool)),X17467),X17466))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17470,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17470,tc_HOL_Obool)),X17469),X17466)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17470,tc_HOL_Obool)),X17468),X17467))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__mono])])). 6.97/7.22 fof(c_0_6587, plain, ![X11927, X11928, X11929, X11930, X11931]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11931,tc_HOL_Obool)),X11930),X11929))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11931,tc_HOL_Obool)),X11928),X11927))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11931,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11931,tc_HOL_Obool)),X11930),X11928)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11931,tc_HOL_Obool)),X11929),X11927))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__mono])])])). 6.97/7.22 fof(c_0_6588, plain, ![X12535, X12536, X12537, X12538, X12539]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12539,tc_HOL_Obool)),X12538),X12537))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12539,tc_HOL_Obool)),X12536),X12535))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12539,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12539,tc_HOL_Obool)),X12538),X12536)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12539,tc_HOL_Obool)),X12537),X12535))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Un__mono])])])). 6.97/7.22 cnf(c_0_6589, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk451_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_5027])). 6.97/7.22 cnf(c_0_6590, plain, (~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=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)))))), inference(split_conjunct,[status(thm)],[c_0_5033])). 6.97/7.22 cnf(c_0_6591, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3))),esk257_3(X1,X2,X3))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X1,X2,X3)),X1))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_4980])). 6.97/7.22 cnf(c_0_6592, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk257_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),X1),esk254_3(X1,X2,X3))),esk255_3(X1,X2,X3))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_4980])). 6.97/7.22 cnf(c_0_6593, plain, (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),esk275_3(X1,X2,X3))),esk276_3(X1,X2,X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_4962])). 6.97/7.22 cnf(c_0_6594, plain, (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)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk273_3(X1,X2,X3))),esk274_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_4962])). 6.97/7.22 fof(c_0_6595, plain, ![X17601, X17602, X17603, X17604, X17605]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X17605,X17605)),hAPP(hAPP(c_Product__Type_OPair(X17605,X17605),X17604),X17603)),c_Transitive__Closure_Ortrancl(X17605,X17602)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X17605,X17605),tc_HOL_Obool)),X17602),hAPP(hAPP(c_Product__Type_OSigma(X17605,X17605),X17601),hAPP(c_COMBK(tc_fun(X17605,tc_HOL_Obool),X17605),X17601))))|(hBOOL(hAPP(hAPP(c_member(X17605),X17604),X17601))|X17603=X17604))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_trancl__subset__Sigma__aux])])])). 6.97/7.22 fof(c_0_6596, plain, ![X2775, X2776, X2777]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2777),X2776))|(~hBOOL(hAPP(hAPP(c_member(X2777),X2775),X2776))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X2777),X2776)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Finite__Set_Ocard(X2777),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2777,tc_HOL_Obool)),X2776),hAPP(hAPP(c_Set_Oinsert(X2777),X2775),c_Orderings_Obot__class_Obot(tc_fun(X2777,tc_HOL_Obool))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Diff__singleton])])])). 6.97/7.22 fof(c_0_6597, plain, ![X3853, X3854, X3855, X3856]:(~class_Groups_Oordered__ab__group__add__abs(X3856)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3856),hAPP(c_Groups_Oabs__class_Oabs(X3856),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3855,X3856),X3854),X3853))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3855,X3856),hAPP(hAPP(c_COMBB(X3856,X3856,X3855),c_Groups_Oabs__class_Oabs(X3856)),X3854)),X3853)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__abs])])])). 6.97/7.22 cnf(c_0_6598, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3))),esk257_3(X1,X2,X3))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_4980])). 6.97/7.22 cnf(c_0_6599, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk257_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),X1),esk254_3(X1,X2,X3))),esk255_3(X1,X2,X3))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_4980])). 6.97/7.22 fof(c_0_6600, plain, ![X6237, X6238, X6239, X6240, X6241]:(~c_Relation_Osingle__valued(X6241,X6240,hAPP(c_Relation_Oconverse(X6240,X6241),X6239))|hAPP(c_Relation_OImage(X6240,X6241,X6239),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6240,tc_HOL_Obool)),X6238),X6237))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6241,tc_HOL_Obool)),hAPP(c_Relation_OImage(X6240,X6241,X6239),X6238)),hAPP(c_Relation_OImage(X6240,X6241,X6239),X6237))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Image__Int__eq])])])). 6.97/7.22 fof(c_0_6601, plain, ![X13642, X13643, X13644, X13645, X13646]:(~class_Rings_Olinordered__semiring__strict(X13646)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13646),X13645),X13644))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13646),X13643),X13642))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13646),c_Groups_Ozero__class_Ozero(X13646)),X13644))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13646),c_Groups_Ozero__class_Ozero(X13646)),X13643))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13646),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13646),X13645),X13643)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13646),X13644),X13642)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__strict__mono])])])). 6.97/7.22 cnf(c_0_6602, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk267_3(X1,X3,X2))),esk268_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_5034])). 6.97/7.22 cnf(c_0_6603, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk495_3(X2,X3,X1))),esk496_3(X2,X3,X1))=X2|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_5035])). 6.97/7.22 fof(c_0_6604, plain, ![X3278, X3279, X3280, X3281, X3282]:(~class_Rings_Olinordered__semiring__strict(X3282)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3282),X3281),X3280))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3282),X3279),X3278))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3282),c_Groups_Ozero__class_Ozero(X3282)),X3281))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3282),c_Groups_Ozero__class_Ozero(X3282)),X3279))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3282),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3282),X3281),X3279)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3282),X3280),X3278)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__strict__mono_H])])])). 6.97/7.22 fof(c_0_6605, plain, ![X10282, X10283, X10284, X10285, X10286]:(~class_Rings_Olinordered__semiring__strict(X10286)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10286),X10285),X10284))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10286),X10283),X10282))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10286),c_Groups_Ozero__class_Ozero(X10286)),X10285))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10286),c_Groups_Ozero__class_Ozero(X10286)),X10283))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10286),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10286),X10285),X10283)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10286),X10284),X10282)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__le__less__imp__less])])])). 6.97/7.22 fof(c_0_6606, plain, ![X8977, X8978, X8979, X8980, X8981]:(~class_Rings_Olinordered__semiring__strict(X8981)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8981),X8980),X8979))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8981),X8978),X8977))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8981),c_Groups_Ozero__class_Ozero(X8981)),X8980))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8981),c_Groups_Ozero__class_Ozero(X8981)),X8978))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8981),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8981),X8980),X8978)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8981),X8979),X8977)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__less__le__imp__less])])])). 6.97/7.22 fof(c_0_6607, plain, ![X17443, X17444, X17445, X17446, X17447]:(~class_Fields_Olinordered__field(X17447)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17447),c_Groups_Ozero__class_Ozero(X17447)),X17446))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17447),X17446),X17445))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17447),c_Groups_Ozero__class_Ozero(X17447)),X17444))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17447),X17444),X17443))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17447),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17447),X17446),X17443)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17447),X17445),X17444)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_frac__less2])])])). 6.97/7.22 cnf(c_0_6608, plain, (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(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)))))|~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_5036])). 6.97/7.22 cnf(c_0_6609, 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_5037, c_0_4415]), c_0_4415]), c_0_5038]), ['final']). 6.97/7.22 cnf(c_0_6610, 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))), inference(split_conjunct,[status(thm)],[c_0_5039]), ['final']). 6.97/7.22 cnf(c_0_6611, 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_5040]), ['final']). 6.97/7.22 fof(c_0_6612, plain, ![X3842, X3843, X3844]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3844),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X3843)))|hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,X3843),X3844),X3842))=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),X3843)),X3842)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X3843),X3844))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__update__nat])])])). 6.97/7.22 fof(c_0_6613, plain, ![X2912, X2913, X2914, X2915]:((~hBOOL(hAPP(X2915,hAPP(c_Nat_OSuc,esk95_4(X2912,X2913,X2914,X2915))))|~hBOOL(hAPP(X2913,esk95_4(X2912,X2913,X2914,X2915)))|hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,X2913))=c_Orderings_Oord__class_OLeast(tc_Nat_Onat,X2915)|hBOOL(hAPP(X2915,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X2913,X2912))|~hBOOL(hAPP(X2915,X2914)))&(hBOOL(hAPP(X2915,hAPP(c_Nat_OSuc,esk95_4(X2912,X2913,X2914,X2915))))|hBOOL(hAPP(X2913,esk95_4(X2912,X2913,X2914,X2915)))|hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,X2913))=c_Orderings_Oord__class_OLeast(tc_Nat_Onat,X2915)|hBOOL(hAPP(X2915,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X2913,X2912))|~hBOOL(hAPP(X2915,X2914)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Least__Suc2])])])])])). 6.97/7.22 fof(c_0_6614, plain, ![X4509, X4510, X4511, X4512, X4513]:(~class_Fields_Olinordered__field(X4513)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4513),c_Groups_Ozero__class_Ozero(X4513)),X4512))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4513),X4512),X4511))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4513),c_Groups_Ozero__class_Ozero(X4513)),X4510))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4513),X4510),X4509))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4513),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4513),X4512),X4509)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4513),X4511),X4510)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_frac__less])])])). 6.97/7.22 fof(c_0_6615, plain, ![X3970, X3971, X3972, X3973, X3974]:(~class_Rings_Oordered__semiring(X3974)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3974),X3973),X3972))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3974),X3971),X3970))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3974),c_Groups_Ozero__class_Ozero(X3974)),X3973))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3974),c_Groups_Ozero__class_Ozero(X3974)),X3971))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3974),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3974),X3973),X3971)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3974),X3972),X3970)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__mono_H])])])). 6.97/7.22 fof(c_0_6616, plain, ![X12409, X12410, X12411, X12412, X12413]:(~class_Rings_Oordered__semiring(X12413)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12413),X12412),X12411))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12413),X12410),X12409))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12413),c_Groups_Ozero__class_Ozero(X12413)),X12411))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12413),c_Groups_Ozero__class_Ozero(X12413)),X12410))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12413),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12413),X12412),X12410)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12413),X12411),X12409)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__mono])])])). 6.97/7.22 fof(c_0_6617, plain, ![X17568, X17569, X17570, X17571, X17572]:(~class_Fields_Olinordered__field(X17572)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17572),c_Groups_Ozero__class_Ozero(X17572)),X17571))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17572),X17571),X17570))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17572),c_Groups_Ozero__class_Ozero(X17572)),X17569))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17572),X17569),X17568))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17572),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17572),X17571),X17568)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17572),X17570),X17569)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_frac__le])])])). 6.97/7.22 fof(c_0_6618, plain, ![X14821, X14822, X14823]:(~class_Lattices_Oab__semigroup__idem__mult(X14823)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14823),X14822))|(c_Orderings_Obot__class_Obot(tc_fun(X14823,tc_HOL_Obool))=X14822|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14823),X14821))|(X14821=c_Orderings_Obot__class_Obot(tc_fun(X14823,tc_HOL_Obool))|hAPP(c_Finite__Set_Ofold1(X14823,c_Groups_Otimes__class_Otimes(X14823)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14823,tc_HOL_Obool)),X14822),X14821))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14823),hAPP(c_Finite__Set_Ofold1(X14823,c_Groups_Otimes__class_Otimes(X14823)),X14822)),hAPP(c_Finite__Set_Ofold1(X14823,c_Groups_Otimes__class_Otimes(X14823)),X14821))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__Un2])])])). 6.97/7.22 cnf(c_0_6619, plain, (X1=hAPP(X2,esk128_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),esk127_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk127_3(X1,X2,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5005])). 6.97/7.22 cnf(c_0_6620, plain, (X1=hAPP(X2,esk58_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),esk57_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk57_3(X1,X2,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5006])). 6.97/7.22 fof(c_0_6621, plain, ![X4526, X4527, X4528, X4529, X4530, X4531, X4532, X4533]:(~c_Fun_Oinj__on(X4533,X4532,X4531,X4530)|(~c_Fun_Oinj__on(X4529,X4528,X4527,X4526)|c_Fun_Oinj__on(tc_prod(X4533,X4529),tc_prod(X4532,X4528),c_Product__Type_Omap__pair(X4533,X4532,X4529,X4528,X4531,X4527),hAPP(hAPP(c_Product__Type_OSigma(X4533,X4529),X4530),hAPP(c_COMBK(tc_fun(X4529,tc_HOL_Obool),X4533),X4526))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__pair__inj__on])])])). 6.97/7.22 cnf(c_0_6622, 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),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__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))), inference(split_conjunct,[status(thm)],[c_0_5034])). 6.97/7.22 fof(c_0_6623, plain, ![X1960, X1961, X1962]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1962,tc_HOL_Obool)),X1961),X1960))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1962),X1960))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1962,tc_HOL_Obool),tc_fun(X1962,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1962,tc_HOL_Obool),tc_fun(X1962,tc_HOL_Obool)),X1961),X1960)),c_Wellfounded_Ofinite__psubset(X1962))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1962,tc_HOL_Obool)),X1961),X1960))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1962,tc_HOL_Obool),tc_fun(X1962,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1962,tc_HOL_Obool),tc_fun(X1962,tc_HOL_Obool)),X1961),X1960)),c_Wellfounded_Ofinite__psubset(X1962))))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X1962),X1960))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1962,tc_HOL_Obool),tc_fun(X1962,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1962,tc_HOL_Obool),tc_fun(X1962,tc_HOL_Obool)),X1961),X1960)),c_Wellfounded_Ofinite__psubset(X1962)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__finite__psubset])])])). 6.97/7.22 fof(c_0_6624, plain, ![X16800, X16801, X16802]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16802),X16801))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X16802),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16802,tc_HOL_Obool)),X16801),hAPP(hAPP(c_Set_Oinsert(X16802),X16800),c_Orderings_Obot__class_Obot(tc_fun(X16802,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X16802),X16801)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Diff1__le])])])). 6.97/7.22 fof(c_0_6625, plain, ![X7970, X7971, X7972]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7972),X7971))|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(X7972),X7970)),hAPP(c_Finite__Set_Ocard(X7972),X7971))),hAPP(c_Finite__Set_Ocard(X7972),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7972,tc_HOL_Obool)),X7970),X7971))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__card__le__card__Diff])])). 6.97/7.22 fof(c_0_6626, plain, ![X13523, X13524, X13525, X13526, X13527]:(~class_Rings_Osemiring__0(X13527)|hAPP(c_List_Omonoid__add__class_Olistsum(X13527),hAPP(hAPP(c_List_Omap(X13526,X13527),hAPP(hAPP(c_COMBB(X13527,X13527,X13526),hAPP(c_Groups_Otimes__class_Otimes(X13527),X13525)),X13524)),X13523))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13527),X13525),hAPP(c_List_Omonoid__add__class_Olistsum(X13527),hAPP(hAPP(c_List_Omap(X13526,X13527),X13524),X13523)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__const__mult])])). 6.97/7.22 fof(c_0_6627, plain, ![X8105, X8106, X8107, X8108, X8109]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X8109,X8108)),hAPP(X8109,X8107)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X8106,X8106)),hAPP(hAPP(c_Product__Type_OPair(X8106,X8106),X8108),X8107)),X8105))|hBOOL(hAPP(hAPP(c_member(tc_prod(X8106,X8106)),hAPP(hAPP(c_Product__Type_OPair(X8106,X8106),X8108),X8107)),c_Wellfounded_Omlex__prod(X8106,X8109,X8105))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mlex__leq])])])). 6.97/7.22 fof(c_0_6628, plain, ![X4314, X4315, X4316, X4317, X4318]:(~class_Orderings_Olinorder(X4318)|(~c_List_Olinorder__class_Osorted(X4318,hAPP(c_List_Orev(X4318),hAPP(hAPP(c_List_Omap(X4317,X4318),X4316),X4315)))|c_List_OtakeWhile(X4317,hAPP(hAPP(c_COMBB(X4318,tc_HOL_Obool,X4317),hAPP(c_Orderings_Oord__class_Oless(X4318),X4314)),X4316),X4315)=hAPP(c_List_Ofilter(X4317,hAPP(hAPP(c_COMBB(X4318,tc_HOL_Obool,X4317),hAPP(c_Orderings_Oord__class_Oless(X4318),X4314)),X4316)),X4315))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_filter__equals__takeWhile__sorted__rev])])])). 6.97/7.22 fof(c_0_6629, plain, ![X12655, X12656, X12657, X12659]:((hBOOL(hAPP(X12656,esk415_3(X12655,X12656,X12657)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12655))|(~hBOOL(hAPP(X12656,X12659))|hBOOL(hAPP(X12656,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X12659),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12655),X12657))))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12657)))&(~hBOOL(hAPP(X12656,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk415_3(X12655,X12656,X12657)),X12657)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12655))|(~hBOOL(hAPP(X12656,X12659))|hBOOL(hAPP(X12656,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X12659),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12655),X12657))))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12657)))), 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])])])])])])). 6.97/7.22 cnf(c_0_6630, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk517_6(X2,X3,X4,X5,X6,X1)),X6))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X3,X5),X2)),X6)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X3,X4),X2)),X6)), inference(split_conjunct,[status(thm)],[c_0_4969])). 6.97/7.22 cnf(c_0_6631, 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))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X5)),X4)!=X2|~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_5035])). 6.97/7.22 fof(c_0_6632, plain, ![X9481, X9482, X9483, X9484]:(~hBOOL(hAPP(hAPP(c_member(X9484),X9483),X9482))|hBOOL(hAPP(hAPP(c_member(tc_fun(X9484,tc_HOL_Obool)),hAPP(c_Relation_OImage(X9484,X9484,X9481),hAPP(hAPP(c_Set_Oinsert(X9484),X9483),c_Orderings_Obot__class_Obot(tc_fun(X9484,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(X9484),X9482),X9481)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotientI])])). 6.97/7.22 cnf(c_0_6633, 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_5041])). 6.97/7.22 cnf(c_0_6634, 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),esk100_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_5042])). 6.97/7.22 fof(c_0_6635, plain, ![X8670, X8671, X8672, X8673, X8674, X8675]:(~c_Finite__Set_Ofolding(X8675,X8674,X8673,X8672)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8675),X8671))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8675),X8670))|hAPP(c_Fun_Ocomp(X8674,X8674,X8674,hAPP(X8672,X8671)),hAPP(X8672,X8670))=hAPP(c_Fun_Ocomp(X8674,X8674,X8674,hAPP(X8672,X8670)),hAPP(X8672,X8671))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp_H_H])])). 6.97/7.22 fof(c_0_6636, plain, ![X9726, X9727, X9728, X9729, X9730, X9731]:((hAPP(hAPP(c_Product__Type_OPair(X9730,X9729),esk319_6(X9726,X9727,X9728,X9729,X9730,X9731)),esk320_6(X9726,X9727,X9728,X9729,X9730,X9731))=X9731|hBOOL(hAPP(hAPP(c_member(X9728),X9727),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X9730,X9729,tc_fun(X9728,tc_HOL_Obool)),X9726),X9731))))&(~hBOOL(hAPP(hAPP(c_member(X9728),X9727),hAPP(hAPP(X9726,esk319_6(X9726,X9727,X9728,X9729,X9730,X9731)),esk320_6(X9726,X9727,X9728,X9729,X9730,X9731))))|hBOOL(hAPP(hAPP(c_member(X9728),X9727),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X9730,X9729,tc_fun(X9728,tc_HOL_Obool)),X9726),X9731))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__splitI2])])])])). 6.97/7.22 cnf(c_0_6637, 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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))),X3)=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))), inference(split_conjunct,[status(thm)],[c_0_5043])). 6.97/7.22 cnf(c_0_6638, 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_5044])). 6.97/7.22 fof(c_0_6639, plain, ![X10221, X10222, X10223]:(~class_Rings_Olinordered__semidom(X10223)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10223),c_Groups_Ozero__class_Ozero(X10223)),X10222))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10223),X10222),c_Groups_Oone__class_Oone(X10223)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10223),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10223),X10222),hAPP(hAPP(c_Power_Opower__class_Opower(X10223),X10222),X10221))),hAPP(hAPP(c_Power_Opower__class_Opower(X10223),X10222),X10221)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__Suc__less])])])). 6.97/7.22 cnf(c_0_6640, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk346_2(X2,X1)),esk346_2(X2,X1))),c_Transitive__Closure_Otrancl(X1,X2)))|c_Wellfounded_Oacyclic(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5045])). 6.97/7.22 fof(c_0_6641, plain, ![X12795, X12796, X12797, X12798, X12799]:(~class_Groups_Oab__semigroup__mult(X12799)|(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X12799,X12799,c_Groups_Otimes__class_Otimes(X12799),X12798,X12797),X12796))|(hBOOL(hAPP(hAPP(c_member(X12799),X12798),X12797))|hBOOL(hAPP(c_Finite__Set_Ofold__graph(X12799,X12799,c_Groups_Otimes__class_Otimes(X12799),X12795,hAPP(hAPP(c_Set_Oinsert(X12799),X12798),X12797)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12799),X12795),X12796)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__graph__insert__swap])])])). 6.97/7.22 fof(c_0_6642, plain, ![X3034, X3035, X3036, X3037]:(~class_Complete__Lattice_Ocomplete__lattice(X3037)|hAPP(c_List_Ofoldl(X3037,X3036,hAPP(c_COMBC(X3036,X3037,X3037),hAPP(hAPP(c_COMBB(X3037,tc_fun(X3037,X3037),X3036),c_Lattices_Osemilattice__inf__class_Oinf(X3037)),X3034)),c_Orderings_Otop__class_Otop(X3037)),X3035)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3036,X3037),hAPP(c_List_Oset(X3036),X3035)),X3034)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INFI__set__fold])])). 6.97/7.22 cnf(c_0_6643, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk51_2(X2,X1)),esk51_2(X2,X1))),c_Transitive__Closure_Otrancl(X1,X2)))|c_Wellfounded_Oacyclic(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5046])). 6.97/7.22 fof(c_0_6644, plain, ![X1167, X1168, X1169]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1169),X1168))|hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1169),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1168),X1167))=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,X1169),X1168)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1168),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1168),X1167)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__add__Un])])])). 6.97/7.22 fof(c_0_6645, plain, ![X7266, X7267, X7268, X7269]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk233_4(X7266,X7267,X7268,X7269)),X7269))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7269),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7267)),X7266)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7269),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7267)),c_List_OtakeWhile(X7267,X7268,X7266))))))&(~hBOOL(hAPP(X7268,hAPP(hAPP(c_List_Onth(X7267),X7266),esk233_4(X7266,X7267,X7268,X7269))))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7269),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7267)),X7266)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7269),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7267)),c_List_OtakeWhile(X7267,X7268,X7266))))))), 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])])])])])). 6.97/7.22 fof(c_0_6646, plain, ![X17426, X17427, X17428, X17429]:(~class_Complete__Lattice_Ocomplete__lattice(X17429)|hAPP(c_List_Ofoldl(X17429,X17428,hAPP(c_COMBC(X17428,X17429,X17429),hAPP(hAPP(c_COMBB(X17429,tc_fun(X17429,X17429),X17428),c_Lattices_Osemilattice__sup__class_Osup(X17429)),X17426)),c_Orderings_Obot__class_Obot(X17429)),X17427)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17428,X17429),hAPP(c_List_Oset(X17428),X17427)),X17426)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUPR__set__fold])])). 6.97/7.22 fof(c_0_6647, plain, ![X13176, X13177, X13178, X13179, X13180]:(~c_Equiv__Relations_Oequiv(X13180,X13179,X13178)|(~hBOOL(hAPP(hAPP(c_member(tc_fun(X13180,tc_HOL_Obool)),X13177),hAPP(hAPP(c_Equiv__Relations_Oquotient(X13180),X13179),X13178)))|(~hBOOL(hAPP(hAPP(c_member(tc_fun(X13180,tc_HOL_Obool)),X13176),hAPP(hAPP(c_Equiv__Relations_Oquotient(X13180),X13179),X13178)))|(c_Orderings_Obot__class_Obot(tc_fun(X13180,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13180,tc_HOL_Obool)),X13177),X13176)|X13176=X13177)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_quotient__disj])])])). 6.97/7.22 fof(c_0_6648, plain, ![X2692, X2693, X2694, X2695]:(hAPP(hAPP(c_Relation_Orel__comp(X2695,X2695,X2695),X2694),X2693)!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2695,X2695),tc_HOL_Obool))|(hAPP(hAPP(c_Relation_Orel__comp(X2695,X2695,X2695),X2692),X2693)!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2695,X2695),tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2695,X2695),tc_HOL_Obool))=hAPP(hAPP(c_Relation_Orel__comp(X2695,X2695,X2695),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2695,X2695),tc_HOL_Obool)),X2694),X2692)),X2693))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_union__comp__emptyL])])])). 6.97/7.22 fof(c_0_6649, plain, ![X7463, X7464, X7465, X7466]:(hAPP(hAPP(c_Relation_Orel__comp(X7466,X7466,X7466),X7465),X7464)!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7466,X7466),tc_HOL_Obool))|(hAPP(hAPP(c_Relation_Orel__comp(X7466,X7466,X7466),X7465),X7463)!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7466,X7466),tc_HOL_Obool))|hAPP(hAPP(c_Relation_Orel__comp(X7466,X7466,X7466),X7465),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7466,X7466),tc_HOL_Obool)),X7464),X7463))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7466,X7466),tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_union__comp__emptyR])])])). 6.97/7.22 fof(c_0_6650, plain, ![X1340, X1341, X1342, X1343]:(~c_Fun_Obij__betw(X1343,X1342,X1341,c_Orderings_Otop__class_Otop(tc_fun(X1343,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1342,tc_HOL_Obool)))|hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1342,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1343,X1342,X1341),X1340))=hAPP(c_Set_Oimage(X1343,X1342,X1341),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1343,tc_HOL_Obool)),X1340))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__image__Compl__eq])])). 6.97/7.22 fof(c_0_6651, plain, ![X10718, X10719, X10720]:(~class_Groups_Oordered__ab__group__add__abs(X10720)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10720),hAPP(c_Groups_Oabs__class_Oabs(X10720),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10720),hAPP(c_Groups_Oabs__class_Oabs(X10720),X10719)),hAPP(c_Groups_Oabs__class_Oabs(X10720),X10718)))),hAPP(c_Groups_Oabs__class_Oabs(X10720),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10720),X10719),X10718))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__triangle__ineq3])])])). 6.97/7.22 cnf(c_0_6652, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[c_0_5047, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.22 cnf(c_0_6653, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),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)],[c_0_5048, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.22 fof(c_0_6654, plain, ![X1973, X1974, X1975]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1975,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1975,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk63_3(X1973,X1974,X1975))),X1974)),X1973))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1975,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1975,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X1974)),X1973))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__finite__subset])])])). 6.97/7.22 fof(c_0_6655, plain, ![X3213, X3214, X3215, X3216, X3217, X3218]:(~c_Finite__Set_Ofun__left__comm__idem(X3218,X3217,X3216)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3218),X3215))|hAPP(hAPP(X3216,X3213),hAPP(hAPP(c_Finite__Set_Ofold(X3218,X3217,X3216),X3214),X3215))=hAPP(hAPP(c_Finite__Set_Ofold(X3218,X3217,X3216),X3214),hAPP(hAPP(c_Set_Oinsert(X3218),X3213),X3215)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem])])])). 6.97/7.22 fof(c_0_6656, plain, ![X1040, X1041, X1042, X1043, X1044, X1045]:(~c_Finite__Set_Ofun__left__comm__idem(X1045,X1044,X1043)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1045),X1042))|hAPP(hAPP(c_Finite__Set_Ofold(X1045,X1044,X1043),hAPP(hAPP(X1043,X1040),X1041)),X1042)=hAPP(hAPP(c_Finite__Set_Ofold(X1045,X1044,X1043),X1041),hAPP(hAPP(c_Set_Oinsert(X1045),X1040),X1042)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem2])])])). 6.97/7.22 cnf(c_0_6657, plain, (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(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2))|~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),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X3))), inference(split_conjunct,[status(thm)],[c_0_4569])). 6.97/7.22 cnf(c_0_6658, 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_5049, c_0_5050]), ['final']). 6.97/7.22 cnf(c_0_6659, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk36_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_5051])). 6.97/7.22 cnf(c_0_6660, 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))|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_5052])). 6.97/7.22 fof(c_0_6661, plain, ![X8284, X8285, X8286, X8287]:(~hBOOL(hAPP(hAPP(c_member(X8287),X8286),hAPP(c_List_Oset(X8287),X8285)))|(hBOOL(hAPP(X8284,X8286))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8287)),hAPP(c_List_Ofilter(X8287,X8284),X8285))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8287)),X8285))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_length__filter__less])])])). 6.97/7.22 fof(c_0_6662, plain, ![X10350, X10351, X10352, X10353, X10354, X10355, X10356, X10357, X10358, X10359]:(~c_Equiv__Relations_Ocongruent2(X10359,X10358,X10357,X10356,X10355,X10354)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X10359,X10359)),hAPP(hAPP(c_Product__Type_OPair(X10359,X10359),X10353),X10352)),X10356))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X10358,X10358)),hAPP(hAPP(c_Product__Type_OPair(X10358,X10358),X10351),X10350)),X10355))|hAPP(hAPP(X10354,X10352),X10350)=hAPP(hAPP(X10354,X10353),X10351)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_congruent2D])])])). 6.97/7.22 fof(c_0_6663, plain, ![X16550, X16551, X16552, X16553]:(~class_Fields_Olinordered__field(X16553)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16553),X16552),X16551))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16553),c_Groups_Ozero__class_Ozero(X16553)),X16550))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16553),c_Groups_Ozero__class_Ozero(X16553)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16553),X16551),X16552)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16553),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16553),X16550),X16551)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16553),X16550),X16552))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__strict__left__mono])])])). 6.97/7.22 fof(c_0_6664, plain, ![X7941, X7942, X7943, X7944]:(~class_Fields_Olinordered__field(X7944)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7944),X7943),X7942))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7944),c_Groups_Ozero__class_Ozero(X7944)),X7941))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7944),c_Groups_Ozero__class_Ozero(X7944)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7944),X7942),X7943)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7944),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7944),X7941),X7942)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7944),X7941),X7943))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__left__mono])])])). 6.97/7.22 cnf(c_0_6665, 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)))|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_5053])). 6.97/7.22 fof(c_0_6666, plain, ![X10905, X10906, X10907, X10908]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk362_4(X10905,X10906,X10907,X10908)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X10907)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10908),X10905))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X10908),X10907)),X10905)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10907)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk363_4(X10905,X10906,X10907,X10908)),X10906))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10908),X10905))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X10908),X10907)),X10905)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10907)))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk363_4(X10905,X10906,X10907,X10908)),esk362_4(X10905,X10906,X10907,X10908))=X10908|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10908),X10905))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X10908),X10907)),X10905)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10907))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bset_I5_J])])])])])). 6.97/7.22 fof(c_0_6667, plain, ![X9720, X9721, X9722, X9723]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk317_4(X9720,X9721,X9722,X9723)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X9722)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9723),X9720))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X9723),X9722)),X9720)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9722)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk318_4(X9720,X9721,X9722,X9723)),X9721))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9723),X9720))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X9723),X9722)),X9720)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9722)))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk318_4(X9720,X9721,X9722,X9723)),esk317_4(X9720,X9721,X9722,X9723))=X9723|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9723),X9720))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X9723),X9722)),X9720)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9722))))), 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])])])])])])). 6.97/7.22 fof(c_0_6668, plain, ![X10315, X10316, X10317, X10318]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk342_4(X10315,X10316,X10317,X10318)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X10317)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10315),X10318))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10315),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X10318),X10317))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10317)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk343_4(X10315,X10316,X10317,X10318)),X10316))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10315),X10318))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10315),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X10318),X10317))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10317)))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk343_4(X10315,X10316,X10317,X10318)),esk342_4(X10315,X10316,X10317,X10318))=X10318|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10315),X10318))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10315),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X10318),X10317))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10317))))), 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])])])])])])). 6.97/7.22 fof(c_0_6669, plain, ![X9865, X9866, X9867, X9868]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk324_4(X9865,X9866,X9867,X9868)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X9867)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9865),X9868))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9865),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X9868),X9867))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9867)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk325_4(X9865,X9866,X9867,X9868)),X9866))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9865),X9868))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9865),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X9868),X9867))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9867)))&(X9868=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk325_4(X9865,X9866,X9867,X9868)),esk324_4(X9865,X9866,X9867,X9868))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9865),X9868))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9865),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X9868),X9867))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9867))))), 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])])])])])])). 6.97/7.22 fof(c_0_6670, plain, ![X1727, X1728, X1729, X1730]:(~class_Fields_Olinordered__field(X1730)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1730),X1729),X1728))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1730),X1727),c_Groups_Ozero__class_Ozero(X1730)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1730),c_Groups_Ozero__class_Ozero(X1730)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1730),X1729),X1728)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1730),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1730),X1727),X1729)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1730),X1727),X1728))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__strict__left__mono__neg])])])). 6.97/7.22 cnf(c_0_6671, 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_5054])). 6.97/7.22 cnf(c_0_6672, 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_4576])). 6.97/7.22 fof(c_0_6673, plain, ![X15919, X15920, X15921]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15921),X15920))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X15919))|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),X15919)),X15921)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X15919)),X15920))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmult__zless__mono2__lemma])])])). 6.97/7.22 cnf(c_0_6674, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3))),esk257_3(X1,X2,X3))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_4980])). 6.97/7.22 cnf(c_0_6675, 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),esk254_3(X1,X2,X3))),esk255_3(X1,X2,X3))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_4980])). 6.97/7.22 fof(c_0_6676, plain, ![X1508, X1509, X1510, X1511, X1512]:(~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),X1512),X1511)),X1510)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1512),X1509)),X1508)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1510))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1510),X1512))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1508),X1512))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1511),X1509)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_unique__quotient__lemma])])])). 6.97/7.22 fof(c_0_6677, plain, ![X4875, X4876, X4877, X4878, X4879]:(~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),X4879),X4878)),X4877)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4879),X4876)),X4875)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4875),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4879),X4875))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4879),X4877))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4876),X4878)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_unique__quotient__lemma__neg])])])). 6.97/7.22 cnf(c_0_6678, 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))|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_5052])). 6.97/7.22 cnf(c_0_6679, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3))),esk257_3(X1,X2,X3))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_4980])). 6.97/7.22 cnf(c_0_6680, 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),esk254_3(X1,X2,X3))),esk255_3(X1,X2,X3))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_4980])). 6.97/7.22 fof(c_0_6681, plain, ![X11391, X11392, X11393]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X11393,X11393)),hAPP(hAPP(c_Product__Type_OPair(X11393,X11393),esk378_3(X11391,X11392,X11393)),esk378_3(X11391,X11392,X11393))),X11392))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X11393),tc_List_Olist(X11393))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X11393),tc_List_Olist(X11393)),X11391),X11391)),c_List_Olexord(X11393,X11392)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lexord__irreflexive])])])])). 6.97/7.22 cnf(c_0_6682, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk568_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_5055])). 6.97/7.22 fof(c_0_6683, plain, ![X14143, X14144, X14145, X14146, X14147, X14148]:((hBOOL(hAPP(hAPP(c_member(X14147),esk482_6(X14143,X14144,X14145,X14146,X14147,X14148)),X14148))|c_Fun_Oinj__on(X14146,X14145,X14144,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X14147,tc_fun(X14146,tc_HOL_Obool)),X14148),X14143))|X14148=c_Orderings_Obot__class_Obot(tc_fun(X14147,tc_HOL_Obool)))&(~c_Fun_Oinj__on(X14146,X14145,X14144,hAPP(X14143,esk482_6(X14143,X14144,X14145,X14146,X14147,X14148)))|c_Fun_Oinj__on(X14146,X14145,X14144,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X14147,tc_fun(X14146,tc_HOL_Obool)),X14148),X14143))|X14148=c_Orderings_Obot__class_Obot(tc_fun(X14147,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_inj__on__INTER])])])])])). 6.97/7.22 cnf(c_0_6684, plain, (X1=c_List_Olist_ONil(X2)|hAPP(hAPP(c_List_Onth(X2),X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)))=hAPP(c_List_Ohd(X2),hAPP(c_List_Orotate(X2,X3),X1))), inference(split_conjunct,[status(thm)],[c_0_5056])). 6.97/7.22 fof(c_0_6685, plain, ![X11588, X11589, X11590, X11591]:(~class_Fields_Olinordered__field__inverse__zero(X11591)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11591),X11590),X11589))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11591),X11588),c_Groups_Ozero__class_Ozero(X11591)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11591),c_Groups_Ozero__class_Ozero(X11591)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11591),X11590),X11589)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11591),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11591),X11588),X11590)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11591),X11588),X11589))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__left__mono__neg])])])). 6.97/7.22 cnf(c_0_6686, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk106_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_5057])). 6.97/7.22 cnf(c_0_6687, 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_5058])). 6.97/7.22 cnf(c_0_6688, plain, (hBOOL(hAPP(hAPP(c_member(X2),X4),X1))|X1!=c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X2,tc_HOL_Obool),X3)|~c_Orderings_Oorder__class_Omono(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X3)|~hBOOL(hAPP(hAPP(c_member(X2),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X5),hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X5),X1))))), inference(split_conjunct,[status(thm)],[c_0_5059])). 6.97/7.22 fof(c_0_6689, plain, ![X8967, X8968, X8969]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8969),X8968))|hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X8969),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8969,tc_HOL_Obool)),X8968),hAPP(hAPP(c_Set_Oinsert(X8969),X8967),c_Orderings_Obot__class_Obot(tc_fun(X8969,tc_HOL_Obool))))))=hAPP(c_Finite__Set_Ocard(X8969),hAPP(hAPP(c_Set_Oinsert(X8969),X8967),X8968))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__insert])])])). 6.97/7.22 cnf(c_0_6690, 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),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)))))=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))|~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_5060])). 6.97/7.22 cnf(c_0_6691, 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_5061]), ['final']). 6.97/7.22 fof(c_0_6692, plain, ![X1582, X1583, X1584, X1585]:((hBOOL(hAPP(hAPP(c_member(X1585),X1584),X1583))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1585,tc_HOL_Obool)),X1583),X1582)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1585,tc_HOL_Obool)),X1583),hAPP(hAPP(c_Set_Oinsert(X1585),X1584),X1582)))&(~hBOOL(hAPP(hAPP(c_member(X1585),X1584),X1583))|hAPP(hAPP(c_Set_Oinsert(X1585),X1584),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1585,tc_HOL_Obool)),X1583),X1582))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1585,tc_HOL_Obool)),X1583),hAPP(hAPP(c_Set_Oinsert(X1585),X1584),X1582)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__insert__right])])])). 6.97/7.22 cnf(c_0_6693, plain, (hBOOL(hAPP(X1,X2))|c_List_OdropWhile(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))=hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)), inference(split_conjunct,[status(thm)],[c_0_5004])). 6.97/7.22 fof(c_0_6694, plain, ![X16838, X16839, X16840, X16841, X16842, X16843, X16844]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X16844,X16843)),hAPP(hAPP(c_Product__Type_OPair(X16844,X16843),X16842),X16841)),X16840))|hBOOL(hAPP(hAPP(c_member(X16839),hAPP(hAPP(X16838,X16842),X16841)),hAPP(c_Set_Oimage(tc_prod(X16844,X16843),X16839,hAPP(c_Product__Type_Oprod_Oprod__case(X16844,X16843,X16839),X16838)),X16840)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__imageI])])). 6.97/7.22 cnf(c_0_6695, 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)))|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_5053])). 6.97/7.22 cnf(c_0_6696, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk273_3(X2,X3,X1))),esk274_3(X2,X3,X1))=X3|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)))|~hBOOL(hAPP(X1,esk275_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_4962])). 6.97/7.22 cnf(c_0_6697, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk275_3(X3,X2,X1))),esk276_3(X3,X2,X1))|hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,esk273_3(X3,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_4962])). 6.97/7.22 fof(c_0_6698, plain, ![X2929, X2930, X2931]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2931),X2930))|(~hBOOL(hAPP(hAPP(c_member(X2931),X2929),X2930))|hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X2931),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2931,tc_HOL_Obool)),X2930),hAPP(hAPP(c_Set_Oinsert(X2931),X2929),c_Orderings_Obot__class_Obot(tc_fun(X2931,tc_HOL_Obool))))))=hAPP(c_Finite__Set_Ocard(X2931),X2930))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Suc__Diff1])])])). 6.97/7.22 fof(c_0_6699, plain, ![X9124, X9125, X9126, X9127, X9128]:(~c_Fun_Oinj__on(X9128,X9127,X9126,c_Orderings_Otop__class_Otop(tc_fun(X9128,tc_HOL_Obool)))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9127,tc_HOL_Obool)),hAPP(c_Set_Oimage(X9128,X9127,X9126),X9125)),hAPP(c_Set_Oimage(X9128,X9127,X9126),X9124))=hAPP(c_Set_Oimage(X9128,X9127,X9126),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9128,tc_HOL_Obool)),X9125),X9124))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__set__diff])])])). 6.97/7.22 fof(c_0_6700, plain, ![X2505, X2506, X2507, X2508, X2509]:(~c_Fun_Oinj__on(X2509,X2508,X2507,c_Orderings_Otop__class_Otop(tc_fun(X2509,tc_HOL_Obool)))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2508,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2509,X2508,X2507),X2506)),hAPP(c_Set_Oimage(X2509,X2508,X2507),X2505))=hAPP(c_Set_Oimage(X2509,X2508,X2507),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2509,tc_HOL_Obool)),X2506),X2505))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__Int])])])). 6.97/7.22 fof(c_0_6701, plain, ![X10009, X10010, X10011, X10012, X10013]:((hBOOL(hAPP(hAPP(c_member(X10013),esk327_5(X10009,X10010,X10011,X10012,X10013)),X10012))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10011,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10013,tc_fun(X10011,tc_HOL_Obool)),X10012),X10010)),X10009)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10011,tc_HOL_Obool)),hAPP(X10010,esk327_5(X10009,X10010,X10011,X10012,X10013))),X10009))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10011,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10013,tc_fun(X10011,tc_HOL_Obool)),X10012),X10010)),X10009)))), 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__least])])])])])). 6.97/7.22 fof(c_0_6702, plain, ![X12370, X12371, X12372, X12373]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12373),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12372)),X12371)))|hAPP(hAPP(c_List_Onth(X12372),hAPP(hAPP(c_List_Oappend(X12372),X12371),X12370)),X12373)=hAPP(hAPP(c_List_Onth(X12372),X12370),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12373),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12372)),X12371))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12373),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12372)),X12371)))|hAPP(hAPP(c_List_Onth(X12372),X12371),X12373)=hAPP(hAPP(c_List_Onth(X12372),hAPP(hAPP(c_List_Oappend(X12372),X12371),X12370)),X12373))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__append])])])). 6.97/7.22 cnf(c_0_6703, plain, (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))=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_5062])). 6.97/7.22 fof(c_0_6704, plain, ![X7712, X7713, X7714, X7715, X7716, X7718, X7719, X7720, X7721, X7722, X7723]:(((hBOOL(hAPP(hAPP(c_member(X7715),esk252_5(X7712,X7713,X7714,X7715,X7716)),X7714))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7716,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7715,tc_fun(X7716,tc_HOL_Obool)),X7714),X7713)),X7712)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7716,tc_HOL_Obool)),hAPP(X7713,esk252_5(X7712,X7713,X7714,X7715,X7716))),X7712))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7716,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7715,tc_fun(X7716,tc_HOL_Obool)),X7714),X7713)),X7712))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7722,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7721,tc_fun(X7722,tc_HOL_Obool)),X7720),X7719)),X7718))|(~hBOOL(hAPP(hAPP(c_member(X7721),X7723),X7720))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7722,tc_HOL_Obool)),hAPP(X7719,X7723)),X7718))))), 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])])])])])])])). 6.97/7.22 cnf(c_0_6705, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X1,X2,X3),X5)))|~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_Obij__betw(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_5063])). 6.97/7.22 cnf(c_0_6706, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X3,X1,X4),X2)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(X3,X1,X4),X5)))|~c_Fun_Obij__betw(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)))), inference(split_conjunct,[status(thm)],[c_0_5063])). 6.97/7.22 fof(c_0_6707, plain, ![X4494, X4495, X4496, X4497, X4498, X4499, X4500, X4501, X4502, X4503, X4504]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4498,tc_HOL_Obool)),X4497),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4496,tc_fun(X4498,tc_HOL_Obool)),X4495),X4494)))|(~hBOOL(hAPP(hAPP(c_member(X4496),X4499),X4495))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4498,tc_HOL_Obool)),X4497),hAPP(X4494,X4499)))))&((hBOOL(hAPP(hAPP(c_member(X4502),esk155_5(X4500,X4501,X4502,X4503,X4504)),X4501))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4504,tc_HOL_Obool)),X4503),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4502,tc_fun(X4504,tc_HOL_Obool)),X4501),X4500))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4504,tc_HOL_Obool)),X4503),hAPP(X4500,esk155_5(X4500,X4501,X4502,X4503,X4504))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4504,tc_HOL_Obool)),X4503),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4502,tc_fun(X4504,tc_HOL_Obool)),X4501),X4500)))))), 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__subset__iff])])])])])])). 6.97/7.22 fof(c_0_6708, plain, ![X6632, X6633, X6634, X6635, X6636]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6636),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6635)),X6634)))|hAPP(hAPP(c_List_Olist__update(X6635,hAPP(hAPP(c_List_Oappend(X6635),X6634),X6633)),X6636),X6632)=hAPP(hAPP(c_List_Oappend(X6635),hAPP(hAPP(c_List_Olist__update(X6635,X6634),X6636),X6632)),X6633)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__append1])])). 6.97/7.22 cnf(c_0_6709, plain, (X1=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),esk273_3(X1,X3,X2))),esk274_3(X1,X3,X2))=X3|hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X1)))|~hBOOL(hAPP(X2,esk275_3(X1,X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_4962])). 6.97/7.22 cnf(c_0_6710, plain, (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),esk275_3(X1,X2,X3))),esk276_3(X1,X2,X3))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk273_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_4962])). 6.97/7.22 fof(c_0_6711, plain, ![X3370, X3371, X3372, X3373, X3374]:((hBOOL(hAPP(hAPP(c_member(X3374),esk107_5(X3370,X3371,X3372,X3373,X3374)),X3373))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3372,tc_HOL_Obool)),X3371),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3374,tc_fun(X3372,tc_HOL_Obool)),X3373),X3370))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3372,tc_HOL_Obool)),X3371),hAPP(X3370,esk107_5(X3370,X3371,X3372,X3373,X3374))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3372,tc_HOL_Obool)),X3371),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3374,tc_fun(X3372,tc_HOL_Obool)),X3373),X3370))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__greatest])])])])). 6.97/7.22 fof(c_0_6712, plain, ![X13924, X13925, X13926, X13927, X13928, X13929]:(~hBOOL(hAPP(hAPP(c_member(X13929),X13928),X13927))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13926,tc_HOL_Obool)),hAPP(c_Set_Oimage(X13929,X13926,X13925),X13927)),hAPP(X13924,hAPP(c_Set_Oimage(X13929,X13926,X13925),X13927))))|hBOOL(hAPP(hAPP(c_member(X13926),hAPP(X13925,X13928)),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X13926,tc_HOL_Obool),X13924))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_weak__coinduct__image])])])). 6.97/7.22 fof(c_0_6713, plain, ![X11201, X11202, X11203, X11204]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11204,tc_HOL_Obool)),X11201),X11203))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11204,tc_HOL_Obool)),X11203),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11204,tc_HOL_Obool)),X11202),X11201))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11204,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11204,tc_HOL_Obool)),X11203),X11202)),X11201))&(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11204,tc_HOL_Obool)),X11203),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11204,tc_HOL_Obool)),X11202),X11201))!=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11204,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11204,tc_HOL_Obool)),X11203),X11202)),X11201)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11204,tc_HOL_Obool)),X11201),X11203)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__Int__assoc__eq])])). 6.97/7.22 fof(c_0_6714, plain, ![X12951, X12952, X12953, X12954]:((~c_Wellfounded_Oacyclic(X12954,X12951)|hBOOL(hAPP(hAPP(c_member(tc_prod(X12954,X12954)),hAPP(hAPP(c_Product__Type_OPair(X12954,X12954),X12952),X12953)),c_Transitive__Closure_Ortrancl(X12954,X12951)))|c_Wellfounded_Oacyclic(X12954,hAPP(hAPP(c_Set_Oinsert(tc_prod(X12954,X12954)),hAPP(hAPP(c_Product__Type_OPair(X12954,X12954),X12953),X12952)),X12951)))&((c_Wellfounded_Oacyclic(X12954,X12951)|~c_Wellfounded_Oacyclic(X12954,hAPP(hAPP(c_Set_Oinsert(tc_prod(X12954,X12954)),hAPP(hAPP(c_Product__Type_OPair(X12954,X12954),X12953),X12952)),X12951)))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X12954,X12954)),hAPP(hAPP(c_Product__Type_OPair(X12954,X12954),X12952),X12953)),c_Transitive__Closure_Ortrancl(X12954,X12951)))|~c_Wellfounded_Oacyclic(X12954,hAPP(hAPP(c_Set_Oinsert(tc_prod(X12954,X12954)),hAPP(hAPP(c_Product__Type_OPair(X12954,X12954),X12953),X12952)),X12951))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_acyclic__insert])])])])). 6.97/7.22 fof(c_0_6715, plain, ![X7903, X7904, X7905, X7906]:(((~hBOOL(hAPP(hAPP(c_member(tc_prod(X7906,X7906)),hAPP(hAPP(c_Product__Type_OPair(X7906,X7906),X7904),X7905)),c_Transitive__Closure_Ortrancl(X7906,X7903)))|~c_Wellfounded_Owf(X7906,hAPP(hAPP(c_Set_Oinsert(tc_prod(X7906,X7906)),hAPP(hAPP(c_Product__Type_OPair(X7906,X7906),X7905),X7904)),X7903)))&(c_Wellfounded_Owf(X7906,X7903)|~c_Wellfounded_Owf(X7906,hAPP(hAPP(c_Set_Oinsert(tc_prod(X7906,X7906)),hAPP(hAPP(c_Product__Type_OPair(X7906,X7906),X7905),X7904)),X7903))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X7906,X7906)),hAPP(hAPP(c_Product__Type_OPair(X7906,X7906),X7904),X7905)),c_Transitive__Closure_Ortrancl(X7906,X7903)))|~c_Wellfounded_Owf(X7906,X7903)|c_Wellfounded_Owf(X7906,hAPP(hAPP(c_Set_Oinsert(tc_prod(X7906,X7906)),hAPP(hAPP(c_Product__Type_OPair(X7906,X7906),X7905),X7904)),X7903)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__insert])])])])). 6.97/7.22 fof(c_0_6716, plain, ![X1026, X1027, X1028, X1029]:(~class_Orderings_Olinorder(X1029)|(~c_List_Olinorder__class_Osorted(X1029,hAPP(c_List_Orev(X1029),X1028))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1027),X1026))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1026),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1029)),X1028)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1029),hAPP(hAPP(c_List_Onth(X1029),X1028),X1026)),hAPP(hAPP(c_List_Onth(X1029),X1028),X1027))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__rev__nth__mono])])])). 6.97/7.22 fof(c_0_6717, plain, ![X7619, X7620, X7621]:(~c_Wellfounded_Owf(X7621,X7620)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7621,X7621),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X7621,X7621,X7621),X7620),X7619)),X7620))|c_FunDef_Oreduction__pair(X7621,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(X7621,X7621),tc_HOL_Obool),tc_fun(tc_prod(X7621,X7621),tc_HOL_Obool)),X7620),X7619)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_reduction__pairI])])])). 6.97/7.22 fof(c_0_6718, plain, ![X13219, X13220, X13221, X13222, X13223, X13224]:(~c_Finite__Set_Ofolding(X13224,X13223,X13222,X13221)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13224),X13220))|(hBOOL(hAPP(hAPP(c_member(X13224),X13219),X13220))|hAPP(X13221,hAPP(hAPP(c_Set_Oinsert(X13224),X13219),X13220))=hAPP(c_Fun_Ocomp(X13223,X13223,X13223,hAPP(X13221,X13220)),hAPP(X13222,X13219))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Oinsert])])])). 6.97/7.22 fof(c_0_6719, plain, ![X3317, X3318]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3318),X3317),c_Groups_Ozero__class_Ozero(X3318)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3318),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3318),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3318),c_Groups_Oone__class_Oone(X3318)),X3317)),X3317)),c_Groups_Ozero__class_Ozero(X3318)))|~hBOOL(hAPP(hAPP(c_member(X3318),X3317),c_Int_Oring__1__class_OInts(X3318)))|~class_Rings_Olinordered__idom(X3318))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3318),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3318),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3318),c_Groups_Oone__class_Oone(X3318)),X3317)),X3317)),c_Groups_Ozero__class_Ozero(X3318)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3318),X3317),c_Groups_Ozero__class_Ozero(X3318)))|~hBOOL(hAPP(hAPP(c_member(X3318),X3317),c_Int_Oring__1__class_OInts(X3318)))|~class_Rings_Olinordered__idom(X3318))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__less__0])])])). 6.97/7.22 fof(c_0_6720, plain, ![X15745, X15746, X15747, X15748]:(~class_Divides_Osemiring__div(X15748)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15748),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15748),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15748),X15747),X15746)),X15746)),c_Divides_Odiv__class_Omod(X15748,X15747,X15746))),X15745)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15748),X15747),X15745)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__mod__equality])])])). 6.97/7.22 fof(c_0_6721, plain, ![X7743, X7744, X7745, X7746]:(~class_Divides_Osemiring__div(X7746)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7746),X7744),X7743)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7746),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7746),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7746),X7745),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X7746),X7744),X7745))),c_Divides_Odiv__class_Omod(X7746,X7744,X7745))),X7743)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mod__equality2])])). 6.97/7.22 fof(c_0_6722, plain, ![X10763, X10764, X10765, X10766, X10767, X10768, X10769]:(~c_Fun_Obij__betw(X10769,X10768,X10767,X10766,X10765)|(~c_Fun_Obij__betw(X10769,X10768,X10767,X10764,X10763)|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10768,tc_HOL_Obool)),X10765),X10763)!=c_Orderings_Obot__class_Obot(tc_fun(X10768,tc_HOL_Obool))|c_Fun_Obij__betw(X10769,X10768,X10767,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10769,tc_HOL_Obool)),X10766),X10764),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10768,tc_HOL_Obool)),X10765),X10763))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bij__betw__combine])])])). 6.97/7.22 fof(c_0_6723, plain, ![X2207, X2208, X2209, X2210]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk70_4(X2207,X2208,X2209,X2210)),X2210))|hAPP(hAPP(c_List_Otake(X2209),X2210),X2208)=hAPP(hAPP(c_List_Otake(X2209),X2210),X2207)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2210),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2209)),X2207)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2210),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2209)),X2208))))&(hAPP(hAPP(c_List_Onth(X2209),X2208),esk70_4(X2207,X2208,X2209,X2210))!=hAPP(hAPP(c_List_Onth(X2209),X2207),esk70_4(X2207,X2208,X2209,X2210))|hAPP(hAPP(c_List_Otake(X2209),X2210),X2208)=hAPP(hAPP(c_List_Otake(X2209),X2210),X2207)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2210),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2209)),X2207)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2210),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2209)),X2208))))), 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])])])])])). 6.97/7.22 fof(c_0_6724, plain, ![X2476, X2477, X2478, X2479, X2480]:(hAPP(c_Set_Oimage(X2480,X2479,X2478),c_Orderings_Otop__class_Otop(tc_fun(X2480,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X2479,tc_HOL_Obool))|(hAPP(c_Set_Oimage(X2479,X2477,X2476),c_Orderings_Otop__class_Otop(tc_fun(X2479,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X2477,tc_HOL_Obool))|c_Orderings_Otop__class_Otop(tc_fun(X2477,tc_HOL_Obool))=hAPP(c_Set_Oimage(X2480,X2477,hAPP(c_Fun_Ocomp(X2479,X2477,X2480,X2476),X2478)),c_Orderings_Otop__class_Otop(tc_fun(X2480,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comp__surj])])])). 6.97/7.22 fof(c_0_6725, plain, ![X1035, X1036, X1037, X1038]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1038),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1037)),X1036)))|c_List_OtakeWhile(X1037,X1035,X1036)=hAPP(hAPP(c_List_Otake(X1037),X1038),X1036)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk32_4(X1035,X1036,X1037,X1038)),X1038)))&(hBOOL(hAPP(X1035,hAPP(hAPP(c_List_Onth(X1037),X1036),X1038)))|c_List_OtakeWhile(X1037,X1035,X1036)=hAPP(hAPP(c_List_Otake(X1037),X1038),X1036)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk32_4(X1035,X1036,X1037,X1038)),X1038))))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1038),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1037)),X1036)))|c_List_OtakeWhile(X1037,X1035,X1036)=hAPP(hAPP(c_List_Otake(X1037),X1038),X1036)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk32_4(X1035,X1036,X1037,X1038)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1037)),X1036))))&(hBOOL(hAPP(X1035,hAPP(hAPP(c_List_Onth(X1037),X1036),X1038)))|c_List_OtakeWhile(X1037,X1035,X1036)=hAPP(hAPP(c_List_Otake(X1037),X1038),X1036)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk32_4(X1035,X1036,X1037,X1038)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1037)),X1036)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1038),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1037)),X1036)))|c_List_OtakeWhile(X1037,X1035,X1036)=hAPP(hAPP(c_List_Otake(X1037),X1038),X1036)|~hBOOL(hAPP(X1035,hAPP(hAPP(c_List_Onth(X1037),X1036),esk32_4(X1035,X1036,X1037,X1038)))))&(hBOOL(hAPP(X1035,hAPP(hAPP(c_List_Onth(X1037),X1036),X1038)))|c_List_OtakeWhile(X1037,X1035,X1036)=hAPP(hAPP(c_List_Otake(X1037),X1038),X1036)|~hBOOL(hAPP(X1035,hAPP(hAPP(c_List_Onth(X1037),X1036),esk32_4(X1035,X1036,X1037,X1038)))))))), 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])])])])])). 6.97/7.22 cnf(c_0_6726, plain, (hBOOL(hAPP(X1,esk129_7(X2,X1,X3,X4,X5,X6,X7)))|hAPP(hAPP(c_List_Olist_OCons(X5),X4),X3)=hAPP(c_List_Ofilter(X5,X1),X2)|X3!=hAPP(c_List_Ofilter(X5,X1),X7)|~hBOOL(hAPP(X1,X4))|hAPP(hAPP(c_List_Oappend(X5),X6),hAPP(hAPP(c_List_Olist_OCons(X5),X4),X7))!=X2), inference(split_conjunct,[status(thm)],[c_0_4995])). 6.97/7.22 cnf(c_0_6727, plain, (hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,X2))),hAPP(c_List_Ofilter(X1,X3),X4))=hAPP(c_List_Ofilter(X1,X3),X4)|hBOOL(hAPP(X3,X2))), inference(rw,[status(thm)],[c_0_5064, c_0_5065])). 6.97/7.22 cnf(c_0_6728, 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_5066, c_0_4817]), ['final']). 6.97/7.22 cnf(c_0_6729, 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),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3)),hAPP(c_Nat_OSuc,X4)))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_5067])). 6.97/7.22 cnf(c_0_6730, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_OCollect(X1),X4))=hAPP(c_Set_OCollect(X2),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X4),c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3)))|~c_Fun_Obij__betw(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_5068])). 6.97/7.22 cnf(c_0_6731, 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_5069, c_0_4467])). 6.97/7.22 cnf(c_0_6732, plain, (hBOOL(hAPP(X1,esk86_7(X2,X3,X4,X1,X5,X6,X7)))|hAPP(hAPP(c_List_Olist_OCons(X5),X3),X2)=hAPP(c_List_Ofilter(X5,X1),X4)|X4!=hAPP(hAPP(c_List_Oappend(X5),X6),hAPP(hAPP(c_List_Olist_OCons(X5),X3),X7))|~hBOOL(hAPP(X1,X3))|X2!=hAPP(c_List_Ofilter(X5,X1),X7)), inference(split_conjunct,[status(thm)],[c_0_4996])). 6.97/7.22 cnf(c_0_6733, 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_5070])). 6.97/7.22 cnf(c_0_6734, 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_5070])). 6.97/7.22 fof(c_0_6735, plain, ![X12074, X12075, X12076, X12077]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X12077),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X12076),X12075)))|hAPP(c_Random_Opick(X12076,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X12076)),X12075),X12074)),X12077)=hAPP(c_Random_Opick(X12076,X12074),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X12077),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X12076),X12075))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X12077),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X12076),X12075)))|hAPP(c_Random_Opick(X12076,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X12076)),X12075),X12074)),X12077)=hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X12076),X12075))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pick_Osimps])])])). 6.97/7.22 cnf(c_0_6736, plain, (c_List_Olist_ONil(X1)=X2|hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_List_Onth(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3)=c_List_Ofoldr(X1,X1,c_Orderings_Oord__class_Omax(X1),X2,X3)|~c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Orev(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5071])). 6.97/7.22 fof(c_0_6737, plain, ![X17389, X17390, X17391, X17392, X17393]:(~class_Orderings_Olinorder(X17393)|(hBOOL(hAPP(hAPP(c_member(X17393),hAPP(X17392,X17391)),hAPP(c_Set_Oimage(X17390,X17393,X17392),hAPP(c_List_Oset(X17390),X17389))))|c_List_Olinorder__class_Oinsort__insert__key(X17390,X17393,X17392,X17391,X17389)=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X17390,X17393,X17392),X17391),X17389))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insort__insert__insort__key])])])). 6.97/7.22 cnf(c_0_6738, 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_5072])). 6.97/7.22 cnf(c_0_6739, 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(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2))),hAPP(c_fequal,X3)),X4)|~hBOOL(hAPP(X2,X3))), inference(rw,[status(thm)],[c_0_5073, c_0_5065])). 6.97/7.22 cnf(c_0_6740, 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(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(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2))),hAPP(c_fequal,X3)),X4)), inference(rw,[status(thm)],[c_0_5074, c_0_5065])). 6.97/7.22 fof(c_0_6741, plain, ![X12092, X12093, X12094, X12095, X12096, X12099, X12100, X12101, X12102, X12103, X12104, X12105]:((((hAPP(hAPP(c_Set_Oinsert(X12096),X12094),X12093)=hAPP(hAPP(c_Set_Oinsert(X12096),esk403_5(X12092,X12093,X12094,X12095,X12096)),esk404_5(X12092,X12093,X12094,X12095,X12096))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X12096,X12095,hAPP(hAPP(c_Set_Oinsert(X12096),X12094),X12093)),X12092)))&(~hBOOL(hAPP(hAPP(c_member(X12096),esk403_5(X12092,X12093,X12094,X12095,X12096)),esk404_5(X12092,X12093,X12094,X12095,X12096)))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X12096,X12095,hAPP(hAPP(c_Set_Oinsert(X12096),X12094),X12093)),X12092))))&(hBOOL(hAPP(c_Finite__Set_Ofold__graph(X12096,X12096,X12095,esk403_5(X12092,X12093,X12094,X12095,X12096),esk404_5(X12092,X12093,X12094,X12095,X12096)),X12092))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X12096,X12095,hAPP(hAPP(c_Set_Oinsert(X12096),X12094),X12093)),X12092))))&(hAPP(hAPP(c_Set_Oinsert(X12103),X12101),X12100)!=hAPP(hAPP(c_Set_Oinsert(X12103),X12104),X12105)|hBOOL(hAPP(hAPP(c_member(X12103),X12104),X12105))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X12103,X12103,X12102,X12104,X12105),X12099))|hBOOL(hAPP(c_Finite__Set_Ofold1Set(X12103,X12102,hAPP(hAPP(c_Set_Oinsert(X12103),X12101),X12100)),X12099)))), 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])])])])])])])). 6.97/7.22 cnf(c_0_6742, plain, (hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X4),X5),c_List_Oupt(X3,X2))),X1)=hAPP(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),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_5075])). 6.97/7.22 fof(c_0_6743, plain, ![X14892, X14893, X14894, X14896]:(((hBOOL(hAPP(hAPP(c_member(X14894),esk503_3(X14892,X14893,X14894)),X14893))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14894),X14892),hAPP(c_Finite__Set_Ofold1(X14894,c_Orderings_Oord__class_Omin(X14894)),X14893)))|c_Orderings_Obot__class_Obot(tc_fun(X14894,tc_HOL_Obool))=X14893|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14894),X14893))|~class_Orderings_Olinorder(X14894))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14894),X14892),esk503_3(X14892,X14893,X14894)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14894),X14892),hAPP(c_Finite__Set_Ofold1(X14894,c_Orderings_Oord__class_Omin(X14894)),X14893)))|c_Orderings_Obot__class_Obot(tc_fun(X14894,tc_HOL_Obool))=X14893|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14894),X14893))|~class_Orderings_Olinorder(X14894)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14894),X14892),hAPP(c_Finite__Set_Ofold1(X14894,c_Orderings_Oord__class_Omin(X14894)),X14893)))|(~hBOOL(hAPP(hAPP(c_member(X14894),X14896),X14893))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14894),X14892),X14896)))|c_Orderings_Obot__class_Obot(tc_fun(X14894,tc_HOL_Obool))=X14893|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14894),X14893))|~class_Orderings_Olinorder(X14894))), 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_strict__below__fold1__iff])])])])])])). 6.97/7.22 fof(c_0_6744, plain, ![X9878, X9879, X9880, X9881]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9880),X9878),hAPP(c_Finite__Set_Ofold1(X9880,c_Orderings_Oord__class_Omin(X9880)),X9879)))|(~hBOOL(hAPP(hAPP(c_member(X9880),X9881),X9879))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9880),X9878),X9881)))|X9879=c_Orderings_Obot__class_Obot(tc_fun(X9880,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9880),X9879))|~class_Orderings_Olinorder(X9880))&((hBOOL(hAPP(hAPP(c_member(X9880),esk326_3(X9878,X9879,X9880)),X9879))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9880),X9878),hAPP(c_Finite__Set_Ofold1(X9880,c_Orderings_Oord__class_Omin(X9880)),X9879)))|X9879=c_Orderings_Obot__class_Obot(tc_fun(X9880,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9880),X9879))|~class_Orderings_Olinorder(X9880))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9880),X9878),esk326_3(X9878,X9879,X9880)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9880),X9878),hAPP(c_Finite__Set_Ofold1(X9880,c_Orderings_Oord__class_Omin(X9880)),X9879)))|X9879=c_Orderings_Obot__class_Obot(tc_fun(X9880,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9880),X9879))|~class_Orderings_Olinorder(X9880)))), 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])])])])])])). 6.97/7.22 fof(c_0_6745, plain, ![X786, X787, X788, X789]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X788),X786),hAPP(c_Finite__Set_Ofold1(X788,c_Lattices_Osemilattice__inf__class_Oinf(X788)),X787)))|(~hBOOL(hAPP(hAPP(c_member(X788),X789),X787))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X788),X786),X789)))|X787=c_Orderings_Obot__class_Obot(tc_fun(X788,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X788),X787))|~class_Lattices_Osemilattice__inf(X788))&((hBOOL(hAPP(hAPP(c_member(X788),esk20_3(X786,X787,X788)),X787))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X788),X786),hAPP(c_Finite__Set_Ofold1(X788,c_Lattices_Osemilattice__inf__class_Oinf(X788)),X787)))|X787=c_Orderings_Obot__class_Obot(tc_fun(X788,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X788),X787))|~class_Lattices_Osemilattice__inf(X788))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X788),X786),esk20_3(X786,X787,X788)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X788),X786),hAPP(c_Finite__Set_Ofold1(X788,c_Lattices_Osemilattice__inf__class_Oinf(X788)),X787)))|X787=c_Orderings_Obot__class_Obot(tc_fun(X788,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X788),X787))|~class_Lattices_Osemilattice__inf(X788)))), 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])])])])])])). 6.97/7.22 fof(c_0_6746, plain, ![X9321, X9322, X9323, X9324, X9325, X9326, X9327]:(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X9327,X9326,X9325,X9324,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9327,tc_HOL_Obool)),X9323),hAPP(hAPP(c_Set_Oinsert(X9327),X9322),c_Orderings_Obot__class_Obot(tc_fun(X9327,tc_HOL_Obool))))),X9321))|(~hBOOL(hAPP(hAPP(c_member(X9327),X9322),X9323))|hBOOL(hAPP(c_Finite__Set_Ofold__graph(X9327,X9326,X9325,X9324,X9323),hAPP(hAPP(X9325,X9322),X9321))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Diff1__fold__graph])])])). 6.97/7.22 fof(c_0_6747, plain, ![X2625, X2626, X2627, X2628, X2629]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2629),hAPP(c_Set_Oimage(X2628,X2629,X2627),c_Orderings_Otop__class_Otop(tc_fun(X2628,tc_HOL_Obool)))))|hBOOL(hAPP(c_Finite__Set_Ofinite(X2626),hAPP(c_Set_Oimage(X2628,X2626,hAPP(hAPP(c_COMBB(X2629,X2626,X2628),X2625),X2627)),c_Orderings_Otop__class_Otop(tc_fun(X2628,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__range__imageI])])). 6.97/7.22 fof(c_0_6748, plain, ![X15106, X15107, X15108, X15109, X15110, X15111]:((X15106=hAPP(hAPP(c_Product__Type_OPair(X15109,X15108),esk511_6(X15106,X15107,X15108,X15109,X15110,X15111)),esk512_6(X15106,X15107,X15108,X15109,X15110,X15111))|~hBOOL(hAPP(hAPP(c_member(X15111),X15110),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X15109,X15108,tc_fun(X15111,tc_HOL_Obool)),X15107),X15106))))&(hBOOL(hAPP(hAPP(c_member(X15111),X15110),hAPP(hAPP(X15107,esk511_6(X15106,X15107,X15108,X15109,X15110,X15111)),esk512_6(X15106,X15107,X15108,X15109,X15110,X15111))))|~hBOOL(hAPP(hAPP(c_member(X15111),X15110),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X15109,X15108,tc_fun(X15111,tc_HOL_Obool)),X15107),X15106))))), 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])])])])])). 6.97/7.22 fof(c_0_6749, plain, ![X7738, X7739, X7740, X7741, X7742]:(~class_Rings_Ocomm__semiring__1(X7742)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7742),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7742),X7741),X7740)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7742),X7739),X7738))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7742),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7742),X7741),X7739)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7742),X7740),X7738))), 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])])])). 6.97/7.22 cnf(c_0_6750, plain, (c_Groups_Oone__class_Oone(X2)=hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(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),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5076, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.22 fof(c_0_6751, plain, ![X4099, X4100, X4101]:((hBOOL(hAPP(hAPP(c_member(X4101),X4099),X4100))|hAPP(c_Finite__Set_Ocard(X4101),X4100)=hAPP(c_Finite__Set_Ocard(X4101),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4101,tc_HOL_Obool)),X4100),hAPP(hAPP(c_Set_Oinsert(X4101),X4099),c_Orderings_Obot__class_Obot(tc_fun(X4101,tc_HOL_Obool)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4101),X4100)))&(~hBOOL(hAPP(hAPP(c_member(X4101),X4099),X4100))|hAPP(c_Finite__Set_Ocard(X4101),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4101,tc_HOL_Obool)),X4100),hAPP(hAPP(c_Set_Oinsert(X4101),X4099),c_Orderings_Obot__class_Obot(tc_fun(X4101,tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4101),X4100)),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4101),X4100)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Diff__singleton__if])])])])). 6.97/7.22 fof(c_0_6752, plain, ![X2803, X2804, X2805, X2806]:(~c_Orderings_Oorder__class_Omono(tc_fun(X2806,tc_HOL_Obool),tc_fun(X2806,tc_HOL_Obool),X2805)|(~hBOOL(hAPP(hAPP(c_member(X2806),X2804),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X2806,tc_HOL_Obool),X2805)))|hBOOL(hAPP(hAPP(c_member(X2806),X2804),hAPP(X2805,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2806,tc_HOL_Obool)),X2803),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X2806,tc_HOL_Obool),X2805))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gfp__fun__UnI2])])). 6.97/7.22 fof(c_0_6753, plain, ![X6770, X6771, X6772, X6773, X6774]:(~class_Lattices_Osemilattice__sup(X6774)|~class_Lattices_Osemilattice__sup(X6773)|(~c_Orderings_Oorder__class_Omono(X6773,X6774,X6772)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6774),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6774),hAPP(X6772,X6771)),hAPP(X6772,X6770))),hAPP(X6772,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6773),X6771),X6770)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mono__sup])])])). 6.97/7.22 fof(c_0_6754, plain, ![X1118, X1119, X1120, X1121, X1122, X1123]:(~c_Finite__Set_Ofolding__idem(X1123,X1122,X1121,X1120)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1123),X1119))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1123),X1118))|hAPP(c_Fun_Ocomp(X1122,X1122,X1122,hAPP(X1120,X1119)),hAPP(X1120,X1118))=hAPP(X1120,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1123,tc_HOL_Obool)),X1119),X1118))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__idem_Ounion__idem])])])). 6.97/7.22 fof(c_0_6755, plain, ![X7295, X7296, X7297, X7298, X7299, X7300, X7301, X7302, X7303, X7304, X7305, X7306]:(((hAPP(hAPP(c_List_Oappend(X7299),X7300),X7297)!=X7295|X7298!=hAPP(hAPP(c_List_Oappend(X7299),X7296),X7300)|hAPP(hAPP(c_List_Oappend(X7299),X7296),X7295)=hAPP(hAPP(c_List_Oappend(X7299),X7298),X7297))&(X7296!=hAPP(hAPP(c_List_Oappend(X7299),X7298),X7301)|X7297!=hAPP(hAPP(c_List_Oappend(X7299),X7301),X7295)|hAPP(hAPP(c_List_Oappend(X7299),X7296),X7295)=hAPP(hAPP(c_List_Oappend(X7299),X7298),X7297)))&(((X7303=hAPP(hAPP(c_List_Oappend(X7306),X7305),esk236_5(X7302,X7303,X7304,X7305,X7306))|hAPP(hAPP(c_List_Oappend(X7306),esk235_5(X7302,X7303,X7304,X7305,X7306)),X7304)=X7302|hAPP(hAPP(c_List_Oappend(X7306),X7303),X7302)!=hAPP(hAPP(c_List_Oappend(X7306),X7305),X7304))&(X7304=hAPP(hAPP(c_List_Oappend(X7306),esk236_5(X7302,X7303,X7304,X7305,X7306)),X7302)|hAPP(hAPP(c_List_Oappend(X7306),esk235_5(X7302,X7303,X7304,X7305,X7306)),X7304)=X7302|hAPP(hAPP(c_List_Oappend(X7306),X7303),X7302)!=hAPP(hAPP(c_List_Oappend(X7306),X7305),X7304)))&((X7303=hAPP(hAPP(c_List_Oappend(X7306),X7305),esk236_5(X7302,X7303,X7304,X7305,X7306))|X7305=hAPP(hAPP(c_List_Oappend(X7306),X7303),esk235_5(X7302,X7303,X7304,X7305,X7306))|hAPP(hAPP(c_List_Oappend(X7306),X7303),X7302)!=hAPP(hAPP(c_List_Oappend(X7306),X7305),X7304))&(X7304=hAPP(hAPP(c_List_Oappend(X7306),esk236_5(X7302,X7303,X7304,X7305,X7306)),X7302)|X7305=hAPP(hAPP(c_List_Oappend(X7306),X7303),esk235_5(X7302,X7303,X7304,X7305,X7306))|hAPP(hAPP(c_List_Oappend(X7306),X7303),X7302)!=hAPP(hAPP(c_List_Oappend(X7306),X7305),X7304))))), 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])])])])])])). 6.97/7.22 fof(c_0_6756, plain, ![X7863, X7864, X7865, X7866, X7867]:(~class_Rings_Ocomm__semiring__1(X7867)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7867),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7867),X7866),X7865)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7867),X7864),X7863))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7867),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7867),X7866),X7864)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7867),X7865),X7863))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J])])). 6.97/7.22 cnf(c_0_6757, 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_5077])). 6.97/7.22 cnf(c_0_6758, 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_5078])). 6.97/7.22 cnf(c_0_6759, 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_5079])). 6.97/7.22 cnf(c_0_6760, plain, (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)))=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_5080])). 6.97/7.22 fof(c_0_6761, plain, ![X5791, X5792, X5793, X5794, X5795, X5796, X5797, X5798]:(~c_Finite__Set_Ofolding__image__simple(X5798,X5797,X5796,X5795,X5794,X5793)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5797),X5792))|(hBOOL(hAPP(hAPP(c_member(X5797),X5791),X5792))|hAPP(X5793,hAPP(hAPP(c_Set_Oinsert(X5797),X5791),X5792))=hAPP(hAPP(X5796,hAPP(X5794,X5791)),hAPP(X5793,X5792))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Oinsert])])])). 6.97/7.22 fof(c_0_6762, plain, ![X13450, X13451, X13452]:((hAPP(X13451,esk447_3(X13450,X13451,X13452))!=hAPP(X13451,esk446_3(X13450,X13451,X13452))|c_Wellfounded_OwfP(X13452,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13450,tc_fun(X13452,tc_fun(X13452,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X13450,tc_HOL_Obool))),X13451))|~c_Wellfounded_OwfP(X13452,hAPP(X13451,esk445_3(X13450,X13451,X13452))))&(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13452,tc_HOL_Obool)),c_Predicate_ODomainP(X13452,X13452,hAPP(X13451,esk446_3(X13450,X13451,X13452)))),c_Predicate_ORangeP(X13452,X13452,hAPP(X13451,esk447_3(X13450,X13451,X13452))))!=c_Orderings_Obot__class_Obot(tc_fun(X13452,tc_HOL_Obool))|c_Wellfounded_OwfP(X13452,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13450,tc_fun(X13452,tc_fun(X13452,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X13450,tc_HOL_Obool))),X13451))|~c_Wellfounded_OwfP(X13452,hAPP(X13451,esk445_3(X13450,X13451,X13452))))), 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])])])])])). 6.97/7.22 cnf(c_0_6763, 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_5081])). 6.97/7.22 cnf(c_0_6764, 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),c_Int_OBit1(X2))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_5082])). 6.97/7.22 fof(c_0_6765, plain, ![X13495, X13496, X13497, X13498]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13498),X13497))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13496,tc_HOL_Obool)),hAPP(c_List_Oset(X13496),hAPP(hAPP(c_List_Odrop(X13496),X13497),X13495))),hAPP(c_List_Oset(X13496),hAPP(hAPP(c_List_Odrop(X13496),X13498),X13495))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__drop__subset__set__drop])])). 6.97/7.22 fof(c_0_6766, plain, ![X978, X979, X980, X981]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X981),X980))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X979,tc_HOL_Obool)),hAPP(c_List_Oset(X979),hAPP(hAPP(c_List_Otake(X979),X981),X978))),hAPP(c_List_Oset(X979),hAPP(hAPP(c_List_Otake(X979),X980),X978))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__take__subset__set__take])])). 6.97/7.22 fof(c_0_6767, plain, ![X1613, X1614, X1615]:(~class_Fields_Olinordered__field(X1615)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1615),X1614),X1613))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1615),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1615),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1615),X1614),X1613)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1615),c_Groups_Oone__class_Oone(X1615)),c_Groups_Oone__class_Oone(X1615)))),X1613)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_gt__half__sum])])])). 6.97/7.22 fof(c_0_6768, plain, ![X17448, X17449, X17450, X17451, X17452]:(~c_Finite__Set_Ofolding__one__idem(X17452,X17451,X17450)|(hAPP(hAPP(X17451,hAPP(X17449,esk594_5(X17448,X17449,X17450,X17451,X17452))),hAPP(X17449,esk595_5(X17448,X17449,X17450,X17451,X17452)))!=hAPP(X17449,hAPP(hAPP(X17451,esk594_5(X17448,X17449,X17450,X17451,X17452)),esk595_5(X17448,X17449,X17450,X17451,X17452)))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17452),X17448))|(c_Orderings_Obot__class_Obot(tc_fun(X17452,tc_HOL_Obool))=X17448|hAPP(X17450,hAPP(c_Set_Oimage(X17452,X17452,X17449),X17448))=hAPP(X17449,hAPP(X17450,X17448)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one__idem_Ohom__commute])])])])). 6.97/7.22 cnf(c_0_6769, plain, (hBOOL(hAPP(X3,esk121_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,esk118_2(X3,X2)))|~hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk118_2(X3,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk119_2(X3,X2)),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_4950])). 6.97/7.22 fof(c_0_6770, plain, ![X8013, X8014, X8015, X8016]:((hAPP(hAPP(c_Product__Type_OPair(X8016,X8015),esk261_4(X8013,X8014,X8015,X8016)),esk260_4(X8013,X8014,X8015,X8016))=X8014|~hBOOL(hAPP(hAPP(c_member(tc_prod(X8016,X8015)),X8014),hAPP(c_Relation_Oconverse(X8015,X8016),X8013))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X8015,X8016)),hAPP(hAPP(c_Product__Type_OPair(X8015,X8016),esk260_4(X8013,X8014,X8015,X8016)),esk261_4(X8013,X8014,X8015,X8016))),X8013))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X8016,X8015)),X8014),hAPP(c_Relation_Oconverse(X8015,X8016),X8013))))), 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])])])])])). 6.97/7.22 fof(c_0_6771, plain, ![X10321, X10322, X10323]:(~class_Fields_Olinordered__field(X10323)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10323),X10322),X10321))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10323),X10322),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10323),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10323),X10322),X10321)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10323),c_Groups_Oone__class_Oone(X10323)),c_Groups_Oone__class_Oone(X10323))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__half__sum])])])). 6.97/7.22 fof(c_0_6772, plain, ![X4054, X4055, X4056, X4057, X4058]:(~class_Orderings_Olinorder(X4057)|~class_Lattices_Osemilattice__sup(X4058)|(~c_Orderings_Oorder__class_Omono(X4057,X4058,X4056)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4058),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4058),hAPP(X4056,X4055)),hAPP(X4056,X4054))),hAPP(X4056,hAPP(hAPP(c_Orderings_Oord__class_Omax(X4057),X4055),X4054)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Omono__sup])])])). 6.97/7.22 fof(c_0_6773, plain, ![X11515, X11516, X11517, X11518]:((~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X11517),hAPP(hAPP(c_COMBS(X11517,X11518,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X11518,tc_fun(X11518,tc_HOL_Obool),X11517),c_Orderings_Oord__class_Oless__eq(X11518)),X11516)),X11515)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11517,X11518)),X11516),X11515))|(~class_Orderings_Oorder(X11518)|~class_Enum_Oenum(X11517)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11517,X11518)),X11516),X11515))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X11517),hAPP(hAPP(c_COMBS(X11517,X11518,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X11518,tc_fun(X11518,tc_HOL_Obool),X11517),c_Orderings_Oord__class_Oless__eq(X11518)),X11516)),X11515)))|(~class_Orderings_Oorder(X11518)|~class_Enum_Oenum(X11517)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__fun_I1_J])])])). 6.97/7.22 fof(c_0_6774, plain, ![X705, X706, X707, X708, X709, X710]:(~class_Groups_Ocomm__monoid__add(X710)|(~c_Fun_Oinj__on(X709,X708,X707,X706)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X709,X710),hAPP(c_Fun_Ocomp(X708,X710,X709,X705),X707)),X706)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X708,X710),X705),hAPP(c_Set_Oimage(X709,X708,X707),X706)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__reindex])])])). 6.97/7.22 fof(c_0_6775, plain, ![X696, X697, X698, X699]:(~class_Groups_Oordered__ab__group__add__abs(X699)|hAPP(c_Groups_Oabs__class_Oabs(X699),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X698,X699),hAPP(hAPP(c_COMBB(X699,X699,X698),c_Groups_Oabs__class_Oabs(X699)),X697)),X696))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X698,X699),hAPP(hAPP(c_COMBB(X699,X699,X698),c_Groups_Oabs__class_Oabs(X699)),X697)),X696)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__setsum__abs])])). 6.97/7.22 cnf(c_0_6776, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X2),X6),X8)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X4),X7)|hAPP(hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5),esk568_8(X4,X6,X7,X8,X5,X1,X3,X2))!=hAPP(X6,esk568_8(X4,X6,X7,X8,X5,X1,X3,X2))|X7!=hAPP(c_Set_Oimage(X3,X1,X5),X8)|~c_Fun_Oinj__on(X3,X1,X5,X8)|~class_Groups_Ocomm__monoid__mult(X2)), inference(split_conjunct,[status(thm)],[c_0_5055])). 6.97/7.22 fof(c_0_6777, plain, ![X12682, X12683, X12684]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12684),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12683)),X12682)))|hAPP(hAPP(c_List_Onth(X12683),X12682),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12683)),X12682)),hAPP(c_Nat_OSuc,X12684)))=hAPP(hAPP(c_List_Onth(X12683),hAPP(c_List_Orev(X12683),X12682)),X12684)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rev__nth])])])). 6.97/7.22 cnf(c_0_6778, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk314_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_5083])). 6.97/7.22 cnf(c_0_6779, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk248_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_5084])). 6.97/7.22 cnf(c_0_6780, 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_5085, c_0_4411])). 6.97/7.22 fof(c_0_6781, plain, ![X8405, X8406, X8407, X8408, X8409, X8410]:((~hBOOL(hAPP(hAPP(c_member(X8409),X8407),hAPP(X8405,X8408)))|~hBOOL(hAPP(hAPP(c_member(X8410),X8408),X8406))|hBOOL(hAPP(hAPP(c_member(tc_prod(X8410,X8409)),hAPP(hAPP(c_Product__Type_OPair(X8410,X8409),X8408),X8407)),hAPP(hAPP(c_Product__Type_OSigma(X8410,X8409),X8406),X8405))))&((hBOOL(hAPP(hAPP(c_member(X8409),X8407),hAPP(X8405,X8408)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X8410,X8409)),hAPP(hAPP(c_Product__Type_OPair(X8410,X8409),X8408),X8407)),hAPP(hAPP(c_Product__Type_OSigma(X8410,X8409),X8406),X8405))))&(hBOOL(hAPP(hAPP(c_member(X8410),X8408),X8406))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X8410,X8409)),hAPP(hAPP(c_Product__Type_OPair(X8410,X8409),X8408),X8407)),hAPP(hAPP(c_Product__Type_OSigma(X8410,X8409),X8406),X8405)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__Sigma__iff])])])). 6.97/7.22 cnf(c_0_6782, 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_5086])). 6.97/7.22 cnf(c_0_6783, 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_5087]), ['final']). 6.97/7.22 fof(c_0_6784, plain, ![X8482, X8483, X8484, X8485, X8486]:(~c_Finite__Set_Ofolding__one__idem(X8486,X8485,X8484)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8486),X8483))|(c_Orderings_Obot__class_Obot(tc_fun(X8486,tc_HOL_Obool))=X8483|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8486),X8482))|(X8482=c_Orderings_Obot__class_Obot(tc_fun(X8486,tc_HOL_Obool))|hAPP(X8484,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8486,tc_HOL_Obool)),X8483),X8482))=hAPP(hAPP(X8485,hAPP(X8484,X8483)),hAPP(X8484,X8482))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one__idem_Ounion__idem])])])). 6.97/7.22 cnf(c_0_6785, 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_5088, c_0_4922])). 6.97/7.22 cnf(c_0_6786, 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_5089, c_0_4922])). 6.97/7.22 cnf(c_0_6787, 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_5090])). 6.97/7.22 cnf(c_0_6788, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(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__sup__class_Osup(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_5091])). 6.97/7.22 fof(c_0_6789, plain, ![X4744, X4745, X4746, X4747, X4748, X4749]:(~c_Fun_Oinj__on(X4749,X4748,X4747,X4746)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4748,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4749,X4748,X4747),X4746)),X4745))|(~c_Fun_Oinj__on(X4748,X4749,X4744,X4745)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4749,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4748,X4749,X4744),X4745)),X4746))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4749),X4746))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4748),X4745))|hAPP(c_Finite__Set_Ocard(X4748),X4745)=hAPP(c_Finite__Set_Ocard(X4749),X4746))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__bij__eq])])])). 6.97/7.22 fof(c_0_6790, plain, ![X5354, X5355, X5356, X5357]:(~class_Rings_Olinordered__semidom(X5357)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5357),X5356),X5355))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5357),c_Groups_Ozero__class_Ozero(X5357)),X5356))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5354))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5357),hAPP(hAPP(c_Power_Opower__class_Opower(X5357),X5356),X5354)),hAPP(hAPP(c_Power_Opower__class_Opower(X5357),X5355),X5354))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__strict__mono])])])). 6.97/7.22 cnf(c_0_6791, plain, (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_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)))|~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_5092])). 6.97/7.22 fof(c_0_6792, plain, ![X6888, X6889, X6890, X6891]:(~class_Int_Onumber__ring(X6891)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6891),hAPP(c_Int_Onumber__class_Onumber__of(X6891),X6890)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6891),hAPP(c_Int_Onumber__class_Onumber__of(X6891),X6889)),X6888))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6891),hAPP(c_Int_Onumber__class_Onumber__of(X6891),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6890),X6889))),X6888)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__left])])). 6.97/7.22 fof(c_0_6793, plain, ![X5850, X5851, X5852]:(~class_Orderings_Olinorder(X5852)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5852),X5851))|(c_Orderings_Obot__class_Obot(tc_fun(X5852,tc_HOL_Obool))=X5850|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5852,tc_HOL_Obool)),X5850),X5851))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X5852),c_Big__Operators_Olattice_OInf__fin(X5852,c_Orderings_Oord__class_Omin(X5852),X5850)),c_Big__Operators_Olattice_OInf__fin(X5852,c_Orderings_Oord__class_Omin(X5852),X5851))=c_Big__Operators_Olattice_OInf__fin(X5852,c_Orderings_Oord__class_Omin(X5852),X5851))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Osubset__idem])])])). 6.97/7.22 fof(c_0_6794, plain, ![X17419, X17420, X17421]:(~class_Orderings_Olinorder(X17421)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17421),X17420))|(X17419=c_Orderings_Obot__class_Obot(tc_fun(X17421,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17421,tc_HOL_Obool)),X17419),X17420))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X17421),c_Big__Operators_Olattice_OSup__fin(X17421,c_Orderings_Oord__class_Omax(X17421),X17419)),c_Big__Operators_Olattice_OSup__fin(X17421,c_Orderings_Oord__class_Omax(X17421),X17420))=c_Big__Operators_Olattice_OSup__fin(X17421,c_Orderings_Oord__class_Omax(X17421),X17420))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Osubset__idem])])])). 6.97/7.22 fof(c_0_6795, plain, ![X11336, X11337, X11338, X11339]:(~class_Divides_Osemiring__div(X11339)|(~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X11339),X11338),X11337))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X11339),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11339),X11337),X11336)),X11338)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11339),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X11339),X11337),X11338)),X11336))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dvd__div__mult])])])). 6.97/7.22 cnf(c_0_6796, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))|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_5093, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.22 cnf(c_0_6797, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),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)],[c_0_5094, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.22 fof(c_0_6798, plain, ![X13325, X13326, X13327, X13328, X13329, X13330]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X13330,X13329),tc_HOL_Obool)),X13328),hAPP(hAPP(c_Product__Type_OSigma(X13330,X13329),X13327),hAPP(c_COMBK(tc_fun(X13329,tc_HOL_Obool),X13330),X13326))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13329,tc_HOL_Obool)),hAPP(c_Relation_OImage(X13330,X13329,X13328),X13325)),X13326))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__subset])])). 6.97/7.22 fof(c_0_6799, plain, ![X4624, X4625, X4626, X4627]:(~hBOOL(hAPP(hAPP(c_member(X4627),X4626),c_Wellfounded_Oacc(X4627,X4625)))|(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4627)),X4624),c_Wellfounded_Oacc(tc_List_Olist(X4627),c_List_Olistrel1(X4627,X4625))))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4627)),hAPP(hAPP(c_List_Olist_OCons(X4627),X4626),X4624)),c_Wellfounded_Oacc(tc_List_Olist(X4627),c_List_Olistrel1(X4627,X4625)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Cons__acc__listrel1I])])])). 6.97/7.22 fof(c_0_6800, plain, ![X16393, X16394, X16395, X16396]:(~class_Rings_Olinordered__semidom(X16396)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16395),X16394))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16396),c_Groups_Ozero__class_Ozero(X16396)),X16393))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16396),X16393),c_Groups_Oone__class_Oone(X16396)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16396),hAPP(hAPP(c_Power_Opower__class_Opower(X16396),X16393),X16394)),hAPP(hAPP(c_Power_Opower__class_Opower(X16396),X16393),X16395))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__strict__decreasing])])])). 6.97/7.22 fof(c_0_6801, plain, ![X16879, X16880, X16881, X16882]:(~class_Rings_Olinordered__semidom(X16882)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X16881),X16880))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16882),c_Groups_Ozero__class_Ozero(X16882)),X16879))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16882),X16879),c_Groups_Oone__class_Oone(X16882)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16882),hAPP(hAPP(c_Power_Opower__class_Opower(X16882),X16879),X16880)),hAPP(hAPP(c_Power_Opower__class_Opower(X16882),X16879),X16881))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__decreasing])])])). 6.97/7.22 cnf(c_0_6802, 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_5025])). 6.97/7.22 fof(c_0_6803, plain, ![X14982, X14983, X14984, X14985, X14986]:(~class_Orderings_Olinorder(X14985)|~class_Lattices_Osemilattice__inf(X14986)|(~c_Orderings_Oorder__class_Omono(X14985,X14986,X14984)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14986),hAPP(X14984,hAPP(hAPP(c_Orderings_Oord__class_Omin(X14985),X14983),X14982))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X14986),hAPP(X14984,X14983)),hAPP(X14984,X14982)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Omono__inf])])])). 6.97/7.22 fof(c_0_6804, plain, ![X1898, X1899, X1900, X1901, X1902]:(~class_Lattices_Osemilattice__inf(X1901)|~class_Lattices_Osemilattice__inf(X1902)|(~c_Orderings_Oorder__class_Omono(X1901,X1902,X1900)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1902),hAPP(X1900,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1901),X1899),X1898))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1902),hAPP(X1900,X1899)),hAPP(X1900,X1898)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mono__inf])])])). 6.97/7.22 fof(c_0_6805, plain, ![X11218, X11219, X11220]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11220),X11219))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11220),X11218))|(c_Orderings_Obot__class_Obot(tc_fun(X11220,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11220,tc_HOL_Obool)),X11219),X11218)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X11220),X11219)),hAPP(c_Finite__Set_Ocard(X11220),X11218))=hAPP(c_Finite__Set_Ocard(X11220),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11220,tc_HOL_Obool)),X11219),X11218))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Un__disjoint])])])). 6.97/7.22 fof(c_0_6806, plain, ![X9348, X9349, X9350, X9351, X9352, X9353, X9354, X9355]:(~c_Finite__Set_Ofolding__image__simple__idem(X9355,X9354,X9353,X9352,X9351,X9350)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9354),X9349))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9354),X9348))|hAPP(X9350,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9354,tc_HOL_Obool)),X9349),X9348))=hAPP(hAPP(X9353,hAPP(X9350,X9349)),hAPP(X9350,X9348))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image__simple__idem_Ounion__idem])])])). 6.97/7.22 fof(c_0_6807, plain, ![X15185, X15186, X15187, X15188, X15189, X15190]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X15190,X15189),tc_HOL_Obool)),X15188),X15187))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15190,tc_HOL_Obool)),X15186),X15185))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15189,tc_HOL_Obool)),hAPP(c_Relation_OImage(X15190,X15189,X15188),X15186)),hAPP(c_Relation_OImage(X15190,X15189,X15187),X15185))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Image__mono])])])). 6.97/7.22 fof(c_0_6808, plain, ![X6538, X6539, X6540, X6541, X6542, X6543]:(~class_Divides_Oring__div(X6543)|(c_Divides_Odiv__class_Omod(X6543,X6540,X6541)!=c_Divides_Odiv__class_Omod(X6543,X6542,X6541)|(c_Divides_Odiv__class_Omod(X6543,X6539,X6541)!=c_Divides_Odiv__class_Omod(X6543,X6538,X6541)|c_Divides_Odiv__class_Omod(X6543,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X6543),X6540),X6538),X6541)=c_Divides_Odiv__class_Omod(X6543,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X6543),X6542),X6539),X6541)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__diff__cong])])])). 6.97/7.22 fof(c_0_6809, plain, ![X13282, X13283, X13284]:(~class_Orderings_Olinorder(X13284)|(c_Orderings_Obot__class_Obot(tc_fun(X13284,tc_HOL_Obool))=X13283|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13284,tc_HOL_Obool)),X13283),X13282))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13284),X13282))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13284),hAPP(c_Finite__Set_Ofold1(X13284,c_Orderings_Oord__class_Omin(X13284)),X13282)),hAPP(c_Finite__Set_Ofold1(X13284,c_Orderings_Oord__class_Omin(X13284)),X13283))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__antimono])])])). 6.97/7.22 cnf(c_0_6810, 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_5095, c_0_4471]), c_0_4471])). 6.97/7.22 cnf(c_0_6811, 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_5096, c_0_4471]), ['final']). 6.97/7.22 fof(c_0_6812, plain, ![X2870, X2871, X2872, X2873]:((hBOOL(hAPP(hAPP(c_member(X2872),esk93_4(X2870,X2871,X2872,X2873)),X2871))|c_Groups_Oone__class_Oone(X2873)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X2873,X2872,c_Groups_Otimes__class_Otimes(X2873)),X2870),c_Groups_Oone__class_Oone(X2873)),X2871)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2872),X2871))|~class_Groups_Ocomm__monoid__mult(X2873))&(c_Groups_Oone__class_Oone(X2873)!=hAPP(X2870,esk93_4(X2870,X2871,X2872,X2873))|c_Groups_Oone__class_Oone(X2873)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X2873,X2872,c_Groups_Otimes__class_Otimes(X2873)),X2870),c_Groups_Oone__class_Oone(X2873)),X2871)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2872),X2871))|~class_Groups_Ocomm__monoid__mult(X2873))), 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])])])])])). 6.97/7.22 cnf(c_0_6813, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk120_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,esk118_2(X1,X2)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk118_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk119_2(X1,X2)),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_4950])). 6.97/7.22 fof(c_0_6814, plain, ![X1453, X1454, X1455, X1456, X1457, X1458]:(~c_Finite__Set_Ofolding(X1458,X1457,X1456,X1455)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1458),X1454))|hAPP(c_Fun_Ocomp(X1457,X1457,X1457,hAPP(X1456,X1453)),hAPP(X1455,X1454))=hAPP(c_Fun_Ocomp(X1457,X1457,X1457,hAPP(X1455,X1454)),hAPP(X1456,X1453)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Ocommute__comp_H])])])). 6.97/7.22 fof(c_0_6815, plain, ![X10300, X10301, X10302, X10303, X10304]:(~class_Fields_Ofield__inverse__zero(X10304)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10304),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10304),X10303),X10302)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10304),X10301),X10300))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10304),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10304),X10303),X10301)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10304),X10302),X10300))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times__divide__times__eq])])). 6.97/7.22 cnf(c_0_6816, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk165_6(X2,X3,X4,X5,X1,X6)),X5))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6),hAPP(X4,X2)),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X6),X4),X5)!=X3|~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_5097])). 6.97/7.22 cnf(c_0_6817, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3))),esk257_3(X1,X2,X3))=X2|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk255_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_4980])). 6.97/7.22 cnf(c_0_6818, plain, (X3=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk254_3(X2,X3,X1))),esk255_3(X2,X3,X1))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,esk257_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_4980])). 6.97/7.22 cnf(c_0_6819, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|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_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_4569])). 6.97/7.22 cnf(c_0_6820, 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_5098]), ['final']). 6.97/7.22 fof(c_0_6821, plain, ![X14280, X14281, X14282, X14283]:(~c_Equiv__Relations_Oequiv(X14283,X14282,X14281)|(~hBOOL(hAPP(hAPP(c_member(X14283),X14280),X14282))|hBOOL(hAPP(hAPP(c_member(X14283),X14280),hAPP(c_Relation_OImage(X14283,X14283,X14281),hAPP(hAPP(c_Set_Oinsert(X14283),X14280),c_Orderings_Obot__class_Obot(tc_fun(X14283,tc_HOL_Obool)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equiv__class__self])])])). 6.97/7.22 fof(c_0_6822, plain, ![X13367, X13368, X13369, X13370, X13372]:(((c_Fun_Oinj__on(X13370,X13368,esk440_4(X13367,X13368,X13369,X13370),X13369)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X13370),X13369)),hAPP(c_Finite__Set_Ocard(X13368),X13367)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13368),X13367))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13370),X13369)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13368,tc_HOL_Obool)),hAPP(c_Set_Oimage(X13370,X13368,esk440_4(X13367,X13368,X13369,X13370)),X13369)),X13367))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X13370),X13369)),hAPP(c_Finite__Set_Ocard(X13368),X13367)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13368),X13367))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13370),X13369))))&(~c_Fun_Oinj__on(X13370,X13368,X13372,X13369)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13368,tc_HOL_Obool)),hAPP(c_Set_Oimage(X13370,X13368,X13372),X13369)),X13367))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X13370),X13369)),hAPP(c_Finite__Set_Ocard(X13368),X13367)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13368),X13367))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13370),X13369)))), 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__card__le])])])])])). 6.97/7.22 cnf(c_0_6823, plain, (hAPP(c_Product__Type_Oapsnd(X3,X6,X2,X1),X4)=hAPP(c_Product__Type_Oapsnd(X3,X6,X2,X5),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_5099])). 6.97/7.22 cnf(c_0_6824, 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))|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_5052])). 6.97/7.22 fof(c_0_6825, plain, ![X11026, X11027, X11028]:(~class_Groups_Ocomm__monoid__mult(X11028)|~class_Groups_Ocomm__monoid__add(X11028)|(~c_Nat__Transfer_Onat__set(X11027)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X11028),X11026),X11027)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X11028),hAPP(hAPP(c_COMBB(tc_Int_Oint,X11028,tc_Nat_Onat),X11026),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X11027)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transfer__int__nat__sum__prod_I2_J])])])). 6.97/7.22 fof(c_0_6826, plain, ![X5732, X5733, X5734]:(~class_Groups_Ocomm__monoid__add(X5734)|~class_Groups_Ocomm__monoid__mult(X5734)|(~c_Nat__Transfer_Onat__set(X5733)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5734),X5732),X5733)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5734),hAPP(hAPP(c_COMBB(tc_Int_Oint,X5734,tc_Nat_Onat),X5732),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X5733)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transfer__int__nat__sum__prod_I1_J])])])). 6.97/7.22 fof(c_0_6827, plain, ![X12877, X12878, X12879]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12879))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12878))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12878),X12877))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12879),X12877)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12879),X12878)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__mono2])])])). 6.97/7.22 cnf(c_0_6828, plain, (hAPP(c_Product__Type_Oapfst(X2,X6,X3,X1),X4)=hAPP(c_Product__Type_Oapfst(X2,X6,X3,X5),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_5100])). 6.97/7.22 cnf(c_0_6829, 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_5101])). 6.97/7.22 cnf(c_0_6830, 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_4940])). 6.97/7.22 cnf(c_0_6831, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)=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),c_Groups_Ozero__class_Ozero(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)))|~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),X2),X4)),X1)), inference(split_conjunct,[status(thm)],[c_0_5102])). 6.97/7.22 fof(c_0_6832, plain, ![X2974, X2975, X2976]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2976),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)),X2975))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2975),X2974))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2976),X2975)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2976),X2974)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__mono2__neg])])])). 6.97/7.22 cnf(c_0_6833, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3))),esk257_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk255_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_4980])). 6.97/7.22 cnf(c_0_6834, plain, (X3=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk254_3(X2,X3,X1))),esk255_3(X2,X3,X1))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,esk257_3(X2,X3,X1)))|~hBOOL(hAPP(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_4980])). 6.97/7.22 fof(c_0_6835, plain, ![X3111, X3112, X3113, X3114]:((((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),c_Groups_Ozero__class_Ozero(X3114)),X3112))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),c_Groups_Ozero__class_Ozero(X3114)),X3112))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3114),X3113),X3112)),X3111))|~class_Fields_Olinordered__field__inverse__zero(X3114))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),X3112),c_Groups_Ozero__class_Ozero(X3114)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),X3112),c_Groups_Ozero__class_Ozero(X3114)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),c_Groups_Ozero__class_Ozero(X3114)),X3112))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3114),X3113),X3112)),X3111))|~class_Fields_Olinordered__field__inverse__zero(X3114))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3114),X3111),X3112)),X3113))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),X3112),c_Groups_Ozero__class_Ozero(X3114)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),c_Groups_Ozero__class_Ozero(X3114)),X3112))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3114),X3113),X3112)),X3111))|~class_Fields_Olinordered__field__inverse__zero(X3114)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),X3112),c_Groups_Ozero__class_Ozero(X3114)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),c_Groups_Ozero__class_Ozero(X3114)),X3111))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),c_Groups_Ozero__class_Ozero(X3114)),X3112))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3114),X3113),X3112)),X3111))|~class_Fields_Olinordered__field__inverse__zero(X3114))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3114),X3111),X3112)),X3113))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),c_Groups_Ozero__class_Ozero(X3114)),X3111))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),c_Groups_Ozero__class_Ozero(X3114)),X3112))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3114),X3113),X3112)),X3111))|~class_Fields_Olinordered__field__inverse__zero(X3114)))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),c_Groups_Ozero__class_Ozero(X3114)),X3112))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),X3113),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3114),X3111),X3112)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3114),X3113),X3112)),X3111))|~class_Fields_Olinordered__field__inverse__zero(X3114))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),X3112),c_Groups_Ozero__class_Ozero(X3114)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),X3112),c_Groups_Ozero__class_Ozero(X3114)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),X3113),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3114),X3111),X3112)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3114),X3113),X3112)),X3111))|~class_Fields_Olinordered__field__inverse__zero(X3114))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3114),X3111),X3112)),X3113))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),X3112),c_Groups_Ozero__class_Ozero(X3114)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),X3113),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3114),X3111),X3112)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3114),X3113),X3112)),X3111))|~class_Fields_Olinordered__field__inverse__zero(X3114)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),X3112),c_Groups_Ozero__class_Ozero(X3114)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),c_Groups_Ozero__class_Ozero(X3114)),X3111))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),X3113),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3114),X3111),X3112)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3114),X3113),X3112)),X3111))|~class_Fields_Olinordered__field__inverse__zero(X3114))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3114),X3111),X3112)),X3113))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),c_Groups_Ozero__class_Ozero(X3114)),X3111))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),X3113),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3114),X3111),X3112)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3114),X3113),X3112)),X3111))|~class_Fields_Olinordered__field__inverse__zero(X3114))))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),c_Groups_Ozero__class_Ozero(X3114)),X3112))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),X3113),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3114),X3111),X3112)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3114),X3113),X3112)),X3111))|~class_Fields_Olinordered__field__inverse__zero(X3114))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),X3112),c_Groups_Ozero__class_Ozero(X3114)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),c_Groups_Ozero__class_Ozero(X3114)),X3111))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),c_Groups_Ozero__class_Ozero(X3114)),X3112))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3114),X3113),X3112)),X3111))|~class_Fields_Olinordered__field__inverse__zero(X3114))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),X3112),c_Groups_Ozero__class_Ozero(X3114)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3114),X3111),X3112)),X3113))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),c_Groups_Ozero__class_Ozero(X3114)),X3112))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3114),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3114),X3113),X3112)),X3111))|~class_Fields_Olinordered__field__inverse__zero(X3114))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__less__eq])])])])). 6.97/7.22 cnf(c_0_6836, 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),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))),c_Groups_Ozero__class_Ozero(X1)))|c_Groups_Ozero__class_Ozero(X1)!=X2|c_Groups_Ozero__class_Ozero(X1)!=X3|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_5103])). 6.97/7.22 fof(c_0_6837, plain, ![X14575, X14576, X14577, X14578]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14578),c_Groups_Ozero__class_Ozero(X14578)),X14576))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),X14577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14578),X14575),X14576)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14578),X14577),X14576)),X14575))|~class_Fields_Olinordered__field__inverse__zero(X14578))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14578),X14576),c_Groups_Ozero__class_Ozero(X14578)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14578),X14575),X14576)),X14577))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14578),c_Groups_Ozero__class_Ozero(X14578)),X14576))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14578),X14577),X14576)),X14575))|~class_Fields_Olinordered__field__inverse__zero(X14578))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14578),X14576),c_Groups_Ozero__class_Ozero(X14578)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),c_Groups_Ozero__class_Ozero(X14578)),X14575))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14578),c_Groups_Ozero__class_Ozero(X14578)),X14576))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14578),X14577),X14576)),X14575))|~class_Fields_Olinordered__field__inverse__zero(X14578))))&(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14578),c_Groups_Ozero__class_Ozero(X14578)),X14576))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14578),c_Groups_Ozero__class_Ozero(X14578)),X14576))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14578),X14577),X14576)),X14575))|~class_Fields_Olinordered__field__inverse__zero(X14578))&(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14578),X14576),c_Groups_Ozero__class_Ozero(X14578)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14578),X14576),c_Groups_Ozero__class_Ozero(X14578)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14578),c_Groups_Ozero__class_Ozero(X14578)),X14576))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14578),X14577),X14576)),X14575))|~class_Fields_Olinordered__field__inverse__zero(X14578))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),c_Groups_Ozero__class_Ozero(X14578)),X14575))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14578),X14576),c_Groups_Ozero__class_Ozero(X14578)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14578),c_Groups_Ozero__class_Ozero(X14578)),X14576))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14578),X14577),X14576)),X14575))|~class_Fields_Olinordered__field__inverse__zero(X14578)))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14578),X14576),c_Groups_Ozero__class_Ozero(X14578)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14578),X14575),X14576)),X14577))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14578),c_Groups_Ozero__class_Ozero(X14578)),X14576))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14578),X14577),X14576)),X14575))|~class_Fields_Olinordered__field__inverse__zero(X14578))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),c_Groups_Ozero__class_Ozero(X14578)),X14575))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14578),X14575),X14576)),X14577))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14578),c_Groups_Ozero__class_Ozero(X14578)),X14576))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14578),X14577),X14576)),X14575))|~class_Fields_Olinordered__field__inverse__zero(X14578)))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14578),c_Groups_Ozero__class_Ozero(X14578)),X14576))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),X14577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14578),X14575),X14576)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14578),X14577),X14576)),X14575))|~class_Fields_Olinordered__field__inverse__zero(X14578))&(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14578),X14576),c_Groups_Ozero__class_Ozero(X14578)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14578),X14576),c_Groups_Ozero__class_Ozero(X14578)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),X14577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14578),X14575),X14576)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14578),X14577),X14576)),X14575))|~class_Fields_Olinordered__field__inverse__zero(X14578))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),c_Groups_Ozero__class_Ozero(X14578)),X14575))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14578),X14576),c_Groups_Ozero__class_Ozero(X14578)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),X14577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14578),X14575),X14576)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14578),X14577),X14576)),X14575))|~class_Fields_Olinordered__field__inverse__zero(X14578)))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14578),X14576),c_Groups_Ozero__class_Ozero(X14578)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14578),X14575),X14576)),X14577))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),X14577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14578),X14575),X14576)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14578),X14577),X14576)),X14575))|~class_Fields_Olinordered__field__inverse__zero(X14578))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),c_Groups_Ozero__class_Ozero(X14578)),X14575))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14578),X14575),X14576)),X14577))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),X14577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14578),X14575),X14576)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14578),X14577),X14576)),X14575))|~class_Fields_Olinordered__field__inverse__zero(X14578))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__le__eq])])])])). 6.97/7.22 fof(c_0_6838, plain, ![X14139, X14140, X14141, X14142]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14139),c_Groups_Ozero__class_Ozero(X14142)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14141),c_Groups_Ozero__class_Ozero(X14142)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),c_Groups_Ozero__class_Ozero(X14142)),X14139))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14141),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14142),X14140),X14139)))|~class_Fields_Olinordered__field__inverse__zero(X14142))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14139),c_Groups_Ozero__class_Ozero(X14142)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14140),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14142),X14141),X14139)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),c_Groups_Ozero__class_Ozero(X14142)),X14139))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14141),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14142),X14140),X14139)))|~class_Fields_Olinordered__field__inverse__zero(X14142)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),c_Groups_Ozero__class_Ozero(X14142)),X14139))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14142),X14141),X14139)),X14140))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14141),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14142),X14140),X14139)))|~class_Fields_Olinordered__field__inverse__zero(X14142)))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),c_Groups_Ozero__class_Ozero(X14142)),X14139))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),c_Groups_Ozero__class_Ozero(X14142)),X14139))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14141),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14142),X14140),X14139)))|~class_Fields_Olinordered__field__inverse__zero(X14142))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14142),X14141),X14139)),X14140))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),c_Groups_Ozero__class_Ozero(X14142)),X14139))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14141),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14142),X14140),X14139)))|~class_Fields_Olinordered__field__inverse__zero(X14142)))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),c_Groups_Ozero__class_Ozero(X14142)),X14139))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14139),c_Groups_Ozero__class_Ozero(X14142)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14139),c_Groups_Ozero__class_Ozero(X14142))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14141),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14142),X14140),X14139)))|~class_Fields_Olinordered__field__inverse__zero(X14142))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14142),X14141),X14139)),X14140))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14139),c_Groups_Ozero__class_Ozero(X14142)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14139),c_Groups_Ozero__class_Ozero(X14142))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14141),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14142),X14140),X14139)))|~class_Fields_Olinordered__field__inverse__zero(X14142)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),c_Groups_Ozero__class_Ozero(X14142)),X14139))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14140),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14142),X14141),X14139)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14139),c_Groups_Ozero__class_Ozero(X14142))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14141),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14142),X14140),X14139)))|~class_Fields_Olinordered__field__inverse__zero(X14142))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14142),X14141),X14139)),X14140))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14140),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14142),X14141),X14139)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14139),c_Groups_Ozero__class_Ozero(X14142))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14141),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14142),X14140),X14139)))|~class_Fields_Olinordered__field__inverse__zero(X14142))))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),c_Groups_Ozero__class_Ozero(X14142)),X14139))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14139),c_Groups_Ozero__class_Ozero(X14142)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14141),c_Groups_Ozero__class_Ozero(X14142))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14141),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14142),X14140),X14139)))|~class_Fields_Olinordered__field__inverse__zero(X14142))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14142),X14141),X14139)),X14140))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14139),c_Groups_Ozero__class_Ozero(X14142)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14141),c_Groups_Ozero__class_Ozero(X14142))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14141),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14142),X14140),X14139)))|~class_Fields_Olinordered__field__inverse__zero(X14142)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),c_Groups_Ozero__class_Ozero(X14142)),X14139))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14140),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14142),X14141),X14139)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14141),c_Groups_Ozero__class_Ozero(X14142))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14141),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14142),X14140),X14139)))|~class_Fields_Olinordered__field__inverse__zero(X14142))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14142),X14141),X14139)),X14140))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14140),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14142),X14141),X14139)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14141),c_Groups_Ozero__class_Ozero(X14142))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14142),X14141),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14142),X14140),X14139)))|~class_Fields_Olinordered__field__inverse__zero(X14142))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__divide__eq])])])])). 6.97/7.22 fof(c_0_6839, plain, ![X8292, X8293, X8294, X8295]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8295),c_Groups_Ozero__class_Ozero(X8295)),X8292))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8295),c_Groups_Ozero__class_Ozero(X8295)),X8292))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),X8294),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8295),X8293),X8292)))|~class_Fields_Olinordered__field__inverse__zero(X8295))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8295),X8294),X8292)),X8293))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8295),c_Groups_Ozero__class_Ozero(X8295)),X8292))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),X8294),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8295),X8293),X8292)))|~class_Fields_Olinordered__field__inverse__zero(X8295)))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8295),c_Groups_Ozero__class_Ozero(X8295)),X8292))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8295),X8292),c_Groups_Ozero__class_Ozero(X8295)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8295),X8292),c_Groups_Ozero__class_Ozero(X8295))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),X8294),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8295),X8293),X8292)))|~class_Fields_Olinordered__field__inverse__zero(X8295))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8295),X8294),X8292)),X8293))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8295),X8292),c_Groups_Ozero__class_Ozero(X8295)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8295),X8292),c_Groups_Ozero__class_Ozero(X8295))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),X8294),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8295),X8293),X8292)))|~class_Fields_Olinordered__field__inverse__zero(X8295)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8295),c_Groups_Ozero__class_Ozero(X8295)),X8292))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),X8294),c_Groups_Ozero__class_Ozero(X8295)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8295),X8292),c_Groups_Ozero__class_Ozero(X8295))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),X8294),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8295),X8293),X8292)))|~class_Fields_Olinordered__field__inverse__zero(X8295))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8295),X8294),X8292)),X8293))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),X8294),c_Groups_Ozero__class_Ozero(X8295)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8295),X8292),c_Groups_Ozero__class_Ozero(X8295))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),X8294),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8295),X8293),X8292)))|~class_Fields_Olinordered__field__inverse__zero(X8295))))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8295),c_Groups_Ozero__class_Ozero(X8295)),X8292))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8295),X8292),c_Groups_Ozero__class_Ozero(X8295)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),X8293),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8295),X8294),X8292))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),X8294),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8295),X8293),X8292)))|~class_Fields_Olinordered__field__inverse__zero(X8295))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8295),X8294),X8292)),X8293))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8295),X8292),c_Groups_Ozero__class_Ozero(X8295)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),X8293),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8295),X8294),X8292))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),X8294),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8295),X8293),X8292)))|~class_Fields_Olinordered__field__inverse__zero(X8295)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8295),c_Groups_Ozero__class_Ozero(X8295)),X8292))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),X8294),c_Groups_Ozero__class_Ozero(X8295)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),X8293),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8295),X8294),X8292))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),X8294),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8295),X8293),X8292)))|~class_Fields_Olinordered__field__inverse__zero(X8295))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8295),X8294),X8292)),X8293))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),X8294),c_Groups_Ozero__class_Ozero(X8295)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),X8293),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8295),X8294),X8292))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),X8294),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8295),X8293),X8292)))|~class_Fields_Olinordered__field__inverse__zero(X8295))))))&(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8295),X8292),c_Groups_Ozero__class_Ozero(X8295)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),X8293),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8295),X8294),X8292)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8295),c_Groups_Ozero__class_Ozero(X8295)),X8292))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),X8294),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8295),X8293),X8292)))|~class_Fields_Olinordered__field__inverse__zero(X8295))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8295),X8292),c_Groups_Ozero__class_Ozero(X8295)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),X8294),c_Groups_Ozero__class_Ozero(X8295)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8295),c_Groups_Ozero__class_Ozero(X8295)),X8292))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),X8294),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8295),X8293),X8292)))|~class_Fields_Olinordered__field__inverse__zero(X8295)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8295),c_Groups_Ozero__class_Ozero(X8295)),X8292))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8295),X8294),X8292)),X8293))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8295),X8294),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8295),X8293),X8292)))|~class_Fields_Olinordered__field__inverse__zero(X8295)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__divide__eq])])])])). 6.97/7.22 fof(c_0_6840, plain, ![X8868, X8869, X8870, X8871]:(~class_Groups_Ocomm__monoid__add(X8871)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X8871),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X8871,tc_Nat_Onat),X8870),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X8869,X8868))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X8871),X8870),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X8869),hAPP(c_Nat_OSuc,X8868)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__shift__bounds__cl__Suc__ivl])])])). 6.97/7.22 cnf(c_0_6841, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,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),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)), inference(split_conjunct,[status(thm)],[c_0_5102])). 6.97/7.22 fof(c_0_6842, plain, ![X9171, X9172, X9173]:(~class_Orderings_Olinorder(X9173)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9173),X9172))|c_List_Olinorder__class_Osorted__list__of__set(X9173,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9173,tc_HOL_Obool)),X9172),hAPP(hAPP(c_Set_Oinsert(X9173),X9171),c_Orderings_Obot__class_Obot(tc_fun(X9173,tc_HOL_Obool)))))=c_List_Oremove1(X9173,X9171,c_List_Olinorder__class_Osorted__list__of__set(X9173,X9172)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__list__of__set__remove])])])). 6.97/7.22 fof(c_0_6843, plain, ![X11749, X11750, X11751, X11752, X11753]:(~hBOOL(hAPP(hAPP(c_member(X11753),X11752),X11751))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11753,tc_fun(X11750,tc_HOL_Obool)),X11751),X11749)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11750,tc_HOL_Obool)),hAPP(X11749,X11752)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11753,tc_fun(X11750,tc_HOL_Obool)),X11751),X11749))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INT__absorb])])])). 6.97/7.22 fof(c_0_6844, plain, ![X9423, X9424, X9425, X9426, X9427]:(~hBOOL(hAPP(hAPP(c_member(X9427),X9426),X9425))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9427,tc_fun(X9424,tc_HOL_Obool)),X9425),X9423)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9424,tc_HOL_Obool)),hAPP(X9423,X9426)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9427,tc_fun(X9424,tc_HOL_Obool)),X9425),X9423))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__absorb])])])). 6.97/7.22 cnf(c_0_6845, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=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_Ominus__class_Ominus(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),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)],[c_0_5104, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.22 fof(c_0_6846, plain, ![X5759, X5760, X5761, X5763]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5761),esk188_3(X5759,X5760,X5761)),X5759))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5761),hAPP(c_Finite__Set_Ofold1(X5761,c_Orderings_Oord__class_Omin(X5761)),X5760)),X5759))|c_Orderings_Obot__class_Obot(tc_fun(X5761,tc_HOL_Obool))=X5760|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5761),X5760))|~class_Orderings_Olinorder(X5761))&(hBOOL(hAPP(hAPP(c_member(X5761),esk188_3(X5759,X5760,X5761)),X5760))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5761),hAPP(c_Finite__Set_Ofold1(X5761,c_Orderings_Oord__class_Omin(X5761)),X5760)),X5759))|c_Orderings_Obot__class_Obot(tc_fun(X5761,tc_HOL_Obool))=X5760|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5761),X5760))|~class_Orderings_Olinorder(X5761)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5761),X5763),X5759))|~hBOOL(hAPP(hAPP(c_member(X5761),X5763),X5760))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5761),hAPP(c_Finite__Set_Ofold1(X5761,c_Orderings_Oord__class_Omin(X5761)),X5760)),X5759))|c_Orderings_Obot__class_Obot(tc_fun(X5761,tc_HOL_Obool))=X5760|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5761),X5760))|~class_Orderings_Olinorder(X5761))), 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])])])])])])). 6.97/7.22 fof(c_0_6847, plain, ![X16616, X16617, X16618, X16620]:(((hBOOL(hAPP(hAPP(c_member(X16618),esk553_3(X16616,X16617,X16618)),X16617))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16618),hAPP(c_Finite__Set_Ofold1(X16618,c_Orderings_Oord__class_Omin(X16618)),X16617)),X16616))|X16617=c_Orderings_Obot__class_Obot(tc_fun(X16618,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16618),X16617))|~class_Orderings_Olinorder(X16618))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16618),esk553_3(X16616,X16617,X16618)),X16616))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16618),hAPP(c_Finite__Set_Ofold1(X16618,c_Orderings_Oord__class_Omin(X16618)),X16617)),X16616))|X16617=c_Orderings_Obot__class_Obot(tc_fun(X16618,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16618),X16617))|~class_Orderings_Olinorder(X16618)))&(~hBOOL(hAPP(hAPP(c_member(X16618),X16620),X16617))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16618),X16620),X16616))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16618),hAPP(c_Finite__Set_Ofold1(X16618,c_Orderings_Oord__class_Omin(X16618)),X16617)),X16616))|X16617=c_Orderings_Obot__class_Obot(tc_fun(X16618,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16618),X16617))|~class_Orderings_Olinorder(X16618))), 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])])])])])])). 6.97/7.22 fof(c_0_6848, plain, ![X16638, X16639, X16640, X16641, X16642]:(~c_Finite__Set_Ofolding__one__idem(X16642,X16641,X16640)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16642),X16639))|(X16638=c_Orderings_Obot__class_Obot(tc_fun(X16642,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16642,tc_HOL_Obool)),X16638),X16639))|hAPP(X16640,X16639)=hAPP(hAPP(X16641,hAPP(X16640,X16638)),hAPP(X16640,X16639)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one__idem_Osubset__idem])])])). 6.97/7.22 fof(c_0_6849, plain, ![X3556, X3557, X3558, X3559]:(~class_Int_Onumber__ring(X3559)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3559),hAPP(c_Int_Onumber__class_Onumber__of(X3559),X3558)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3559),hAPP(c_Int_Onumber__class_Onumber__of(X3559),X3557)),X3556))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3559),hAPP(c_Int_Onumber__class_Onumber__of(X3559),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3558),X3557))),X3556)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__number__of__left])])). 6.97/7.22 cnf(c_0_6850, 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))|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_5053])). 6.97/7.22 cnf(c_0_6851, 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)))=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)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5105, c_0_4471]), c_0_4471])). 6.97/7.22 fof(c_0_6852, plain, ![X9359, X9360, X9361, X9362]:(~class_Int_Onumber__ring(X9362)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9362),hAPP(c_Int_Onumber__class_Onumber__of(X9362),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X9361),X9360))),X9359)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9362),hAPP(c_Int_Onumber__class_Onumber__of(X9362),X9361)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9362),hAPP(c_Int_Onumber__class_Onumber__of(X9362),X9360)),X9359))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__number__of__diff1])])])). 6.97/7.22 cnf(c_0_6853, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oconcat(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_List_Oset(X1),esk288_2(X2,X1))),hAPP(c_List_Oset(X1),esk289_2(X2,X1)))|~hBOOL(hAPP(c_List_Odistinct(X1),esk287_2(X2,X1)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_4933])). 6.97/7.22 fof(c_0_6854, plain, ![X13751, X13752, X13753, X13754]:((~c_List_Olinorder__class_Osorted(X13752,X13751)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13753),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13752)),X13751)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13754),X13753))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13752),hAPP(hAPP(c_List_Onth(X13752),X13751),X13754)),hAPP(hAPP(c_List_Onth(X13752),X13751),X13753)))))|~class_Orderings_Olinorder(X13752))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk459_2(X13751,X13752)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13752)),X13751)))|c_List_Olinorder__class_Osorted(X13752,X13751)|~class_Orderings_Olinorder(X13752))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk460_2(X13751,X13752)),esk459_2(X13751,X13752)))|c_List_Olinorder__class_Osorted(X13752,X13751)|~class_Orderings_Olinorder(X13752))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13752),hAPP(hAPP(c_List_Onth(X13752),X13751),esk460_2(X13751,X13752))),hAPP(hAPP(c_List_Onth(X13752),X13751),esk459_2(X13751,X13752))))|c_List_Olinorder__class_Osorted(X13752,X13751)|~class_Orderings_Olinorder(X13752))))), 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])])])])])])). 6.97/7.22 fof(c_0_6855, plain, ![X9757, X9758, X9759, X9760, X9761]:((hBOOL(hAPP(hAPP(c_member(X9761),esk322_5(X9757,X9758,X9759,X9760,X9761)),X9760))|hBOOL(hAPP(hAPP(c_member(X9759),X9758),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X9761,tc_fun(X9759,tc_HOL_Obool)),X9760),X9757))))&(~hBOOL(hAPP(hAPP(c_member(X9759),X9758),hAPP(X9757,esk322_5(X9757,X9758,X9759,X9760,X9761))))|hBOOL(hAPP(hAPP(c_member(X9759),X9758),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X9761,tc_fun(X9759,tc_HOL_Obool)),X9760),X9757))))), 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__I])])])])])). 6.97/7.22 fof(c_0_6856, plain, ![X8296, X8297, X8298, X8299, X8300, X8301]:(~class_Divides_Osemiring__div(X8301)|(c_Divides_Odiv__class_Omod(X8301,X8300,X8299)!=c_Divides_Odiv__class_Omod(X8301,X8298,X8299)|(c_Divides_Odiv__class_Omod(X8301,X8297,X8299)!=c_Divides_Odiv__class_Omod(X8301,X8296,X8299)|c_Divides_Odiv__class_Omod(X8301,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8301),X8300),X8297),X8299)=c_Divides_Odiv__class_Omod(X8301,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8301),X8298),X8296),X8299)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__add__cong])])])). 6.97/7.22 fof(c_0_6857, plain, ![X5181, X5182, X5183, X5185, X5186, X5187, X5188, X5190]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk168_3(X5181,X5182,X5183)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5183)),X5182)))|(~hBOOL(hAPP(hAPP(c_member(X5183),X5185),hAPP(c_List_Oset(X5183),X5182)))|hBOOL(hAPP(X5181,X5185))))&(~hBOOL(hAPP(X5181,hAPP(hAPP(c_List_Onth(X5183),X5182),esk168_3(X5181,X5182,X5183))))|(~hBOOL(hAPP(hAPP(c_member(X5183),X5185),hAPP(c_List_Oset(X5183),X5182)))|hBOOL(hAPP(X5181,X5185)))))&((hBOOL(hAPP(hAPP(c_member(X5188),esk169_3(X5186,X5187,X5188)),hAPP(c_List_Oset(X5188),X5187)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5190),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5188)),X5187)))|hBOOL(hAPP(X5186,hAPP(hAPP(c_List_Onth(X5188),X5187),X5190)))))&(~hBOOL(hAPP(X5186,esk169_3(X5186,X5187,X5188)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5190),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5188)),X5187)))|hBOOL(hAPP(X5186,hAPP(hAPP(c_List_Onth(X5188),X5187),X5190))))))), 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__set__conv__all__nth])])])])])])). 6.97/7.22 fof(c_0_6858, plain, ![X13639, X13640, X13641]:(~class_Groups_Oordered__ab__group__add__abs(X13641)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13641),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13641),hAPP(c_Groups_Oabs__class_Oabs(X13641),X13640)),hAPP(c_Groups_Oabs__class_Oabs(X13641),X13639))),hAPP(c_Groups_Oabs__class_Oabs(X13641),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13641),X13640),X13639))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__triangle__ineq2])])])). 6.97/7.22 fof(c_0_6859, plain, ![X1170, X1171, X1172]:(~class_Groups_Oordered__ab__group__add__abs(X1172)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1172),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1172),hAPP(c_Groups_Oabs__class_Oabs(X1172),X1171)),hAPP(c_Groups_Oabs__class_Oabs(X1172),X1170))),hAPP(c_Groups_Oabs__class_Oabs(X1172),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1172),X1170),X1171))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2__sym])])). 6.97/7.22 fof(c_0_6860, plain, ![X3171, X3172, X3173, X3174, X3175, X3177, X3178, X3179, X3180, X3181, X3182]:(((hBOOL(hAPP(hAPP(c_member(X3173),esk102_5(X3171,X3172,X3173,X3174,X3175)),X3172))|hBOOL(hAPP(hAPP(c_member(X3175),X3174),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3173,tc_fun(X3175,tc_HOL_Obool)),X3172),X3171))))&(~hBOOL(hAPP(hAPP(c_member(X3175),X3174),hAPP(X3171,esk102_5(X3171,X3172,X3173,X3174,X3175))))|hBOOL(hAPP(hAPP(c_member(X3175),X3174),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3173,tc_fun(X3175,tc_HOL_Obool)),X3172),X3171)))))&(~hBOOL(hAPP(hAPP(c_member(X3181),X3180),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3179,tc_fun(X3181,tc_HOL_Obool)),X3178),X3177)))|(~hBOOL(hAPP(hAPP(c_member(X3179),X3182),X3178))|hBOOL(hAPP(hAPP(c_member(X3181),X3180),hAPP(X3177,X3182)))))), 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__iff])])])])])])])). 6.97/7.22 cnf(c_0_6861, 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))|esk23_3(X1,X2,X3)!=esk22_3(X1,X2,X3)|hAPP(c_Finite__Set_Ocard(X3),esk21_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_4947])). 6.97/7.22 fof(c_0_6862, plain, ![X10960, X10961, X10962, X10963]:((hBOOL(hAPP(hAPP(c_member(X10963),esk366_4(X10960,X10961,X10962,X10963)),hAPP(c_List_Oset(X10963),X10962)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X10963,X10961,X10962)),c_List_Olist_Olist__size(X10963,X10960,X10962))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X10961,esk366_4(X10960,X10961,X10962,X10963))),hAPP(X10960,esk366_4(X10960,X10961,X10962,X10963))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X10963,X10961,X10962)),c_List_Olist_Olist__size(X10963,X10960,X10962))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__size__pointwise])])])])). 6.97/7.22 fof(c_0_6863, plain, ![X17282, X17283, X17284, X17285, X17286, X17287]:(~class_Divides_Osemiring__div(X17287)|(c_Divides_Odiv__class_Omod(X17287,X17284,X17285)!=c_Divides_Odiv__class_Omod(X17287,X17286,X17285)|(c_Divides_Odiv__class_Omod(X17287,X17283,X17285)!=c_Divides_Odiv__class_Omod(X17287,X17282,X17285)|c_Divides_Odiv__class_Omod(X17287,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17287),X17286),X17283),X17285)=c_Divides_Odiv__class_Omod(X17287,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17287),X17284),X17282),X17285)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__mult__cong])])])). 6.97/7.22 fof(c_0_6864, plain, ![X16388, X16389, X16390]:(~class_Groups_Oordered__ab__group__add__abs(X16390)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16390),hAPP(c_Groups_Oabs__class_Oabs(X16390),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X16390),X16389),X16388))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16390),hAPP(c_Groups_Oabs__class_Oabs(X16390),X16389)),hAPP(c_Groups_Oabs__class_Oabs(X16390),X16388))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq4])])). 6.97/7.22 fof(c_0_6865, plain, ![X16093, X16094, X16095]:(~class_Groups_Oordered__ab__group__add__abs(X16095)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16095),hAPP(c_Groups_Oabs__class_Oabs(X16095),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16095),X16094),X16093))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16095),hAPP(c_Groups_Oabs__class_Oabs(X16095),X16094)),hAPP(c_Groups_Oabs__class_Oabs(X16095),X16093))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__triangle__ineq])])])). 6.97/7.22 fof(c_0_6866, plain, ![X15527, X15528, X15529]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15529),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15528)),X15527)))|hAPP(hAPP(c_List_Olist_OCons(X15528),hAPP(hAPP(c_List_Onth(X15528),X15527),X15529)),hAPP(hAPP(c_List_Odrop(X15528),hAPP(c_Nat_OSuc,X15529)),X15527))=hAPP(hAPP(c_List_Odrop(X15528),X15529),X15527)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__drop_H])])])). 6.97/7.22 cnf(c_0_6867, 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_5106])). 6.97/7.22 fof(c_0_6868, plain, ![X7253, X7254, X7255, X7256]:(~class_Fields_Ofield(X7256)|(X7255=c_Groups_Ozero__class_Ozero(X7256)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7254),X7253))|hAPP(hAPP(c_Power_Opower__class_Opower(X7256),X7255),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X7253),X7254))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7256),hAPP(hAPP(c_Power_Opower__class_Opower(X7256),X7255),X7253)),hAPP(hAPP(c_Power_Opower__class_Opower(X7256),X7255),X7254))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__diff])])])). 6.97/7.22 fof(c_0_6869, plain, ![X2582, X2583, X2584, X2585, X2586]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X2584,X2586)),hAPP(hAPP(c_Product__Type_OPair(X2584,X2586),X2582),X2585)),X2583))|hBOOL(hAPP(hAPP(c_member(X2586),X2585),hAPP(c_Relation_OImage(X2584,X2586,X2583),hAPP(hAPP(c_Set_Oinsert(X2584),X2582),c_Orderings_Obot__class_Obot(tc_fun(X2584,tc_HOL_Obool)))))))&(~hBOOL(hAPP(hAPP(c_member(X2586),X2585),hAPP(c_Relation_OImage(X2584,X2586,X2583),hAPP(hAPP(c_Set_Oinsert(X2584),X2582),c_Orderings_Obot__class_Obot(tc_fun(X2584,tc_HOL_Obool))))))|hBOOL(hAPP(hAPP(c_member(tc_prod(X2584,X2586)),hAPP(hAPP(c_Product__Type_OPair(X2584,X2586),X2582),X2585)),X2583)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__singleton__iff])])). 6.97/7.22 cnf(c_0_6870, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),X2))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5107, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.22 fof(c_0_6871, plain, ![X17406, X17407, X17409, X17410, X17411, X17412]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X17407,X17407)),hAPP(hAPP(c_Product__Type_OPair(X17407,X17407),hAPP(esk592_2(X17406,X17407),hAPP(c_Nat_OSuc,X17409))),hAPP(esk592_2(X17406,X17407),X17409))),X17406))|c_Wellfounded_Owf(X17407,X17406))&(~c_Wellfounded_Owf(X17411,X17410)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X17411,X17411)),hAPP(hAPP(c_Product__Type_OPair(X17411,X17411),hAPP(X17412,hAPP(c_Nat_OSuc,esk593_3(X17410,X17411,X17412)))),hAPP(X17412,esk593_3(X17410,X17411,X17412)))),X17410)))), 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])])])])])). 6.97/7.22 cnf(c_0_6872, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),X2))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5108, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.22 cnf(c_0_6873, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))|~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_Oone__class_Oone(X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5109, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.22 cnf(c_0_6874, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5110, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.22 cnf(c_0_6875, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(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))))|~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_4999])). 6.97/7.22 cnf(c_0_6876, 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),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X5))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5111])). 6.97/7.22 cnf(c_0_6877, 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_5112]), ['final']). 6.97/7.22 fof(c_0_6878, plain, ![X13077, X13078, X13079]:(~class_Rings_Oring__1(X13079)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13079),hAPP(hAPP(c_Power_Opower__class_Opower(X13079),hAPP(c_Groups_Ouminus__class_Ouminus(X13079),c_Groups_Oone__class_Oone(X13079))),X13077)),hAPP(hAPP(c_Power_Opower__class_Opower(X13079),X13078),X13077))=hAPP(hAPP(c_Power_Opower__class_Opower(X13079),hAPP(c_Groups_Ouminus__class_Ouminus(X13079),X13078)),X13077)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus])])). 6.97/7.22 cnf(c_0_6879, 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_5113])). 6.97/7.22 cnf(c_0_6880, 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_5114]), ['final']). 6.97/7.22 cnf(c_0_6881, 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_5115]), ['final']). 6.97/7.22 fof(c_0_6882, plain, ![X6233, X6234, X6235, X6236]:(~class_Fields_Ofield(X6236)|(c_Groups_Ozero__class_Ozero(X6236)=X6235|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X6236),X6234),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6236),X6233),X6235))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6236),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X6236),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6236),X6235),X6234)),X6233)),X6235))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__divide__eq__iff])])])). 6.97/7.22 fof(c_0_6883, plain, ![X343, X344, X345, X346]:(~class_Fields_Ofield(X346)|(c_Groups_Ozero__class_Ozero(X346)=X345|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X346),X344),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X346),X343),X345))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X346),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X346),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X346),X345),X344)),X343)),X345))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__divide__eq__iff])])). 6.97/7.22 cnf(c_0_6884, 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),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5111])). 6.97/7.22 fof(c_0_6885, plain, ![X3501, X3502, X3503, X3504, X3505]:(~class_Groups_Ocomm__monoid__mult(X3505)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3504),X3503))|(hBOOL(hAPP(hAPP(c_member(X3504),X3502),X3503))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3505),hAPP(X3501,X3502)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3504,X3505),X3501),X3503))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3504,X3505),X3501),hAPP(hAPP(c_Set_Oinsert(X3504),X3502),X3503))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__insert])])])). 6.97/7.22 fof(c_0_6886, plain, ![X10019, X10020, X10021, X10022]:(~class_Fields_Ofield__inverse__zero(X10022)|(c_Groups_Ozero__class_Ozero(X10022)=X10021|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10022),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10022),X10020),X10021)),X10019)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10022),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10022),X10020),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10022),X10019),X10021))),X10021))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__frac__num])])). 6.97/7.22 fof(c_0_6887, plain, ![X5718, X5719, X5720, X5721]:(~class_Fields_Ofield(X5721)|(X5720=c_Groups_Ozero__class_Ozero(X5721)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5721),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5721),X5719),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5721),X5720),X5718))),X5720)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5721),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5721),X5719),X5720)),X5718))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__diff__eq__iff])])). 6.97/7.22 fof(c_0_6888, plain, ![X1327, X1328, X1329, X1330]:(~class_Fields_Ofield(X1330)|(X1329=c_Groups_Ozero__class_Ozero(X1330)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1330),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1330),X1328),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1330),X1329),X1327))),X1329)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1330),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1330),X1328),X1329)),X1327))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__add__eq__iff])])])). 6.97/7.22 fof(c_0_6889, plain, ![X5164, X5165, X5166, X5167]:(~class_Divides_Osemiring__div(X5167)|(c_Groups_Ozero__class_Ozero(X5167)=X5166|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X5167),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5167),X5165),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5167),X5164),X5166))),X5166)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5167),X5164),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X5167),X5165),X5166)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__mult__self1])])])). 6.97/7.22 fof(c_0_6890, plain, ![X8892, X8893, X8894, X8895, X8896, X8897, X8898]:(hBOOL(hAPP(hAPP(c_member(X8898),X8897),X8896))|(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X8898,X8895,X8894,X8893,X8896),X8892))|hBOOL(hAPP(c_Finite__Set_Ofold__graph(X8898,X8895,X8894,X8893,hAPP(hAPP(c_Set_Oinsert(X8898),X8897),X8896)),hAPP(hAPP(X8894,X8897),X8892))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__graph_OinsertI])])])). 6.97/7.22 cnf(c_0_6891, plain, (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)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(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_5116])). 6.97/7.22 fof(c_0_6892, plain, ![X9642, X9643, X9644, X9645, X9646, X9647]:(X9646=X9647|hAPP(hAPP(c_List_Olist__update(X9645,hAPP(hAPP(c_List_Olist__update(X9645,X9644),X9647),X9643)),X9646),X9642)=hAPP(hAPP(c_List_Olist__update(X9645,hAPP(hAPP(c_List_Olist__update(X9645,X9644),X9646),X9642)),X9647),X9643)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__update__swap])])])). 6.97/7.22 fof(c_0_6893, plain, ![X3418, X3419, X3420, X3421, X3422]:(~class_Groups_Ocomm__monoid__add(X3422)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3421),X3420))|(hBOOL(hAPP(hAPP(c_member(X3421),X3419),X3420))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3421,X3422),X3418),hAPP(hAPP(c_Set_Oinsert(X3421),X3419),X3420))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3422),hAPP(X3418,X3419)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3421,X3422),X3418),X3420))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__insert])])])). 6.97/7.22 fof(c_0_6894, plain, ![X14539, X14540, X14541, X14542]:(~class_Fields_Ofield__inverse__zero(X14542)|(c_Groups_Ozero__class_Ozero(X14542)=X14541|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14542),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14542),X14539),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14542),X14540),X14541))),X14541)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14542),X14540),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14542),X14539),X14541)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__num__frac])])])). 6.97/7.22 fof(c_0_6895, plain, ![X10559, X10560, X10561, X10562]:(~class_Divides_Osemiring__div(X10562)|(X10561=c_Groups_Ozero__class_Ozero(X10562)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X10562),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10562),X10560),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10562),X10561),X10559))),X10561)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10562),X10559),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X10562),X10560),X10561)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self2])])). 6.97/7.22 fof(c_0_6896, plain, ![X1331, X1332, X1333, X1334, X1335]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1335,tc_HOL_Obool)),hAPP(c_List_Oset(X1335),X1334)),X1333))|(~hBOOL(hAPP(hAPP(c_member(X1335),X1332),X1333))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1335,tc_HOL_Obool)),hAPP(c_List_Oset(X1335),hAPP(hAPP(c_List_Olist__update(X1335,X1334),X1331),X1332))),X1333)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_set__update__subsetI])])])). 6.97/7.22 fof(c_0_6897, plain, ![X15250, X15251, X15252]:(~class_Rings_Olinordered__semidom(X15252)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15252),c_Groups_Oone__class_Oone(X15252)),X15251))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15252),hAPP(hAPP(c_Power_Opower__class_Opower(X15252),X15251),X15250)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15252),X15251),hAPP(hAPP(c_Power_Opower__class_Opower(X15252),X15251),X15250)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__less__power__Suc])])])). 6.97/7.22 cnf(c_0_6898, 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_5117])). 6.97/7.22 fof(c_0_6899, plain, ![X12454, X12455, X12456]:(~class_Groups_Ocomm__monoid__mult(X12456)|~class_Groups_Ocomm__monoid__add(X12456)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X12456),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X12456,tc_Int_Oint),X12455),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X12454))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X12456),X12455),X12454)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod_I2_J])])). 6.97/7.22 fof(c_0_6900, plain, ![X8953, X8954, X8955]:(~class_Groups_Ocomm__monoid__mult(X8955)|~class_Groups_Ocomm__monoid__add(X8955)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X8955),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X8955,tc_Int_Oint),X8954),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X8953))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X8955),X8954),X8953)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transfer__nat__int__sum__prod_I1_J])])])). 6.97/7.22 cnf(c_0_6901, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk315_3(X2,X1,X3)),esk314_3(X2,X1,X3))|X1=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X3)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(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_5083])). 6.97/7.22 cnf(c_0_6902, plain, (X1=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk249_3(X2,X1,X3)),esk248_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_5084])). 6.97/7.22 fof(c_0_6903, plain, ![X17009, X17010, X17011, X17012, X17013, X17014, X17015]:((hAPP(hAPP(X17013,X17011),esk574_7(X17009,X17010,X17011,X17012,X17013,X17014,X17015))=X17009|hBOOL(hAPP(hAPP(c_member(X17015),X17011),X17010))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X17015,X17014,X17013,X17012,hAPP(hAPP(c_Set_Oinsert(X17015),X17011),X17010)),X17009))|~c_Finite__Set_Ofun__left__comm(X17015,X17014,X17013))&(hBOOL(hAPP(c_Finite__Set_Ofold__graph(X17015,X17014,X17013,X17012,X17010),esk574_7(X17009,X17010,X17011,X17012,X17013,X17014,X17015)))|hBOOL(hAPP(hAPP(c_member(X17015),X17011),X17010))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X17015,X17014,X17013,X17012,hAPP(hAPP(c_Set_Oinsert(X17015),X17011),X17010)),X17009))|~c_Finite__Set_Ofun__left__comm(X17015,X17014,X17013))), 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])])])])])). 6.97/7.22 fof(c_0_6904, plain, ![X9519, X9520, X9521, X9522, X9523, X9524, X9525, X9526]:(~c_List_Olist__all2(X9526,X9525,X9524,X9523,X9522)|(~hBOOL(hAPP(hAPP(X9524,X9521),X9520))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9519),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9525)),X9522)))|c_List_Olist__all2(X9526,X9525,X9524,hAPP(hAPP(c_List_Olist__update(X9526,X9523),X9519),X9521),hAPP(hAPP(c_List_Olist__update(X9525,X9522),X9519),X9520))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__all2__update__cong2])])])). 6.97/7.22 fof(c_0_6905, plain, ![X11585, X11586, X11587]:(~class_Lattices_Olattice(X11587)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11587),X11586))|(X11586=c_Orderings_Obot__class_Obot(tc_fun(X11587,tc_HOL_Obool))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11587),X11585))|(c_Orderings_Obot__class_Obot(tc_fun(X11587,tc_HOL_Obool))=X11585|c_Big__Operators_Olattice__class_OSup__fin(X11587,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11587,tc_HOL_Obool)),X11586),X11585))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X11587),c_Big__Operators_Olattice__class_OSup__fin(X11587,X11586)),c_Big__Operators_Olattice__class_OSup__fin(X11587,X11585))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Ounion__idem])])])). 6.97/7.22 fof(c_0_6906, plain, ![X17538, X17539, X17540, X17541, X17542, X17543, X17544, X17545]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17545),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17544)),X17543)))|(~c_List_Olist__all2(X17544,X17542,X17541,X17543,X17540)|(~hBOOL(hAPP(hAPP(X17541,X17539),X17538))|c_List_Olist__all2(X17544,X17542,X17541,hAPP(hAPP(c_List_Olist__update(X17544,X17543),X17545),X17539),hAPP(hAPP(c_List_Olist__update(X17542,X17540),X17545),X17538))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__all2__update__cong])])])). 6.97/7.22 cnf(c_0_6907, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X8),X1),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,X8),X2),X3)|hAPP(X1,esk106_8(X2,X1,X3,X4,X5,X6,X7,X8))!=hAPP(X2,hAPP(X5,esk106_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__add(X8)), inference(split_conjunct,[status(thm)],[c_0_5057])). 6.97/7.22 cnf(c_0_6908, 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_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(split_conjunct,[status(thm)],[c_0_5118])). 6.97/7.22 cnf(c_0_6909, 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_5119]), ['final']). 6.97/7.22 cnf(c_0_6910, 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), inference(split_conjunct,[status(thm)],[c_0_5120]), ['final']). 6.97/7.22 fof(c_0_6911, plain, ![X13165, X13166, X13167, X13168, X13169]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X13166),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13168,tc_fun(X13166,tc_HOL_Obool)),X13167),X13165)))|(~hBOOL(hAPP(hAPP(c_member(X13168),X13169),X13167))|hBOOL(hAPP(c_Finite__Set_Ofinite(X13166),hAPP(X13165,X13169))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13168),X13167)))&((hBOOL(hAPP(hAPP(c_member(X13168),esk430_4(X13165,X13166,X13167,X13168)),X13167))|hBOOL(hAPP(c_Finite__Set_Ofinite(X13166),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13168,tc_fun(X13166,tc_HOL_Obool)),X13167),X13165)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13168),X13167)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13166),hAPP(X13165,esk430_4(X13165,X13166,X13167,X13168))))|hBOOL(hAPP(c_Finite__Set_Ofinite(X13166),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13168,tc_fun(X13166,tc_HOL_Obool)),X13167),X13165)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13168),X13167))))), 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])])])])])). 6.97/7.22 fof(c_0_6912, plain, ![X295, X296, X297, X298]:((hBOOL(hAPP(hAPP(c_member(X298),esk1_4(X295,X296,X297,X298)),X297))|hBOOL(hAPP(c_Finite__Set_Ofinite(X296),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X298,tc_fun(X296,tc_HOL_Obool)),X297),X295)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X298),X297)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X296),hAPP(X295,esk1_4(X295,X296,X297,X298))))|hBOOL(hAPP(c_Finite__Set_Ofinite(X296),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X298,tc_fun(X296,tc_HOL_Obool)),X297),X295)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X298),X297)))), 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__UN__I])])])])])). 6.97/7.22 fof(c_0_6913, plain, ![X1719, X1720, X1721, X1722]:((hBOOL(hAPP(hAPP(c_member(X1722),esk50_4(X1719,X1720,X1721,X1722)),X1721))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1722,X1720)),hAPP(hAPP(c_Product__Type_OSigma(X1722,X1720),X1721),X1719)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1722),X1721)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1720),hAPP(X1719,esk50_4(X1719,X1720,X1721,X1722))))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1722,X1720)),hAPP(hAPP(c_Product__Type_OSigma(X1722,X1720),X1721),X1719)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1722),X1721)))), 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])])])])])). 6.97/7.22 cnf(c_0_6914, 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_5028])). 6.97/7.22 fof(c_0_6915, plain, ![X3765, X3766, X3767, X3768]:(~class_Orderings_Olinorder(X3768)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3768),X3767),X3766))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3768),X3766),X3765))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3768,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X3768,X3767),X3766)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X3768,X3766),X3765))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X3768,X3767),X3765)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I17_J])])])). 6.97/7.22 cnf(c_0_6916, 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_5121])). 6.97/7.22 fof(c_0_6917, plain, ![X13568, X13569, X13570, X13571]:(~class_Orderings_Olinorder(X13571)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13571),X13570))|(~hBOOL(hAPP(hAPP(c_member(X13571),X13569),X13570))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13571),hAPP(hAPP(c_Finite__Set_Ofold(X13571,X13571,c_Orderings_Oord__class_Omin(X13571)),X13568),X13570)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X13571),X13569),X13568)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ofold__inf__le__inf])])])). 6.97/7.22 fof(c_0_6918, plain, ![X8756, X8757, X8758, X8759]:(~class_Lattices_Osemilattice__inf(X8759)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8759),X8758))|(~hBOOL(hAPP(hAPP(c_member(X8759),X8757),X8758))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8759),hAPP(hAPP(c_Finite__Set_Ofold(X8759,X8759,c_Lattices_Osemilattice__inf__class_Oinf(X8759)),X8756),X8758)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8759),X8757),X8756)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__inf__le__inf])])])). 6.97/7.22 fof(c_0_6919, plain, ![X8823, X8824, X8825, X8826]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X8826,X8826)),hAPP(hAPP(c_Product__Type_OPair(X8826,X8826),esk285_4(X8823,X8824,X8825,X8826)),esk286_4(X8823,X8824,X8825,X8826))),X8825))|c_Equiv__Relations_Ocongruent(X8826,X8823,X8825,X8824))&(hAPP(X8824,esk286_4(X8823,X8824,X8825,X8826))!=hAPP(X8824,esk285_4(X8823,X8824,X8825,X8826))|c_Equiv__Relations_Ocongruent(X8826,X8823,X8825,X8824))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_congruentI])])])])])). 6.97/7.22 fof(c_0_6920, plain, ![X1638, X1639, X1640]:(~class_Lattices_Olattice(X1640)|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1640),hAPP(X1639,esk45_3(X1638,X1639,X1640))),hAPP(X1639,esk46_3(X1638,X1639,X1640)))!=hAPP(X1639,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1640),esk45_3(X1638,X1639,X1640)),esk46_3(X1638,X1639,X1640)))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1640),X1638))|(c_Orderings_Obot__class_Obot(tc_fun(X1640,tc_HOL_Obool))=X1638|hAPP(X1639,c_Big__Operators_Olattice__class_OInf__fin(X1640,X1638))=c_Big__Operators_Olattice__class_OInf__fin(X1640,hAPP(c_Set_Oimage(X1640,X1640,X1639),X1638)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Ohom__commute])])])])). 6.97/7.22 fof(c_0_6921, plain, ![X12823, X12824, X12825]:(~class_Orderings_Olinorder(X12825)|(hAPP(X12824,hAPP(hAPP(c_Orderings_Oord__class_Omin(X12825),esk418_3(X12823,X12824,X12825)),esk419_3(X12823,X12824,X12825)))!=hAPP(hAPP(c_Orderings_Oord__class_Omin(X12825),hAPP(X12824,esk418_3(X12823,X12824,X12825))),hAPP(X12824,esk419_3(X12823,X12824,X12825)))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12825),X12823))|(c_Orderings_Obot__class_Obot(tc_fun(X12825,tc_HOL_Obool))=X12823|hAPP(X12824,c_Big__Operators_Olinorder__class_OMin(X12825,X12823))=c_Big__Operators_Olinorder__class_OMin(X12825,hAPP(c_Set_Oimage(X12825,X12825,X12824),X12823)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min_Ohom__commute])])])])). 6.97/7.22 fof(c_0_6922, plain, ![X628, X629, X630]:(~class_Lattices_Olattice(X630)|(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X630),hAPP(X629,esk11_3(X628,X629,X630))),hAPP(X629,esk12_3(X628,X629,X630)))!=hAPP(X629,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X630),esk11_3(X628,X629,X630)),esk12_3(X628,X629,X630)))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X630),X628))|(X628=c_Orderings_Obot__class_Obot(tc_fun(X630,tc_HOL_Obool))|c_Big__Operators_Olattice__class_OSup__fin(X630,hAPP(c_Set_Oimage(X630,X630,X629),X628))=hAPP(X629,c_Big__Operators_Olattice__class_OSup__fin(X630,X628)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Ohom__commute])])])])). 6.97/7.22 fof(c_0_6923, plain, ![X11717, X11718, X11719]:(~class_Orderings_Olinorder(X11719)|(hAPP(X11718,hAPP(hAPP(c_Orderings_Oord__class_Omax(X11719),esk394_3(X11717,X11718,X11719)),esk395_3(X11717,X11718,X11719)))!=hAPP(hAPP(c_Orderings_Oord__class_Omax(X11719),hAPP(X11718,esk394_3(X11717,X11718,X11719))),hAPP(X11718,esk395_3(X11717,X11718,X11719)))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11719),X11717))|(X11717=c_Orderings_Obot__class_Obot(tc_fun(X11719,tc_HOL_Obool))|c_Big__Operators_Olinorder__class_OMax(X11719,hAPP(c_Set_Oimage(X11719,X11719,X11718),X11717))=hAPP(X11718,c_Big__Operators_Olinorder__class_OMax(X11719,X11717)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max_Ohom__commute])])])])). 6.97/7.22 cnf(c_0_6924, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk338_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|X4=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_5122])). 6.97/7.22 fof(c_0_6925, plain, ![X4147, X4148, X4149, X4150]:(~class_Orderings_Olinorder(X4150)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4150),X4149))|(~hBOOL(hAPP(hAPP(c_member(X4150),X4148),X4149))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4150),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4150),X4148),X4147)),hAPP(hAPP(c_Finite__Set_Ofold(X4150,X4150,c_Orderings_Oord__class_Omax(X4150)),X4147),X4149)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup__le__fold__sup])])])). 6.97/7.22 fof(c_0_6926, plain, ![X9061, X9062, X9063, X9064]:(~class_Lattices_Osemilattice__sup(X9064)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9064),X9063))|(~hBOOL(hAPP(hAPP(c_member(X9064),X9062),X9063))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9064),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X9064),X9062),X9061)),hAPP(hAPP(c_Finite__Set_Ofold(X9064,X9064,c_Lattices_Osemilattice__sup__class_Osup(X9064)),X9061),X9063)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__le__fold__sup])])])). 6.97/7.22 fof(c_0_6927, plain, ![X2201, X2202, X2203, X2204, X2205]:((hBOOL(hAPP(hAPP(c_member(X2204),esk69_5(X2201,X2202,X2203,X2204,X2205)),hAPP(c_Set_Oimage(X2205,X2204,X2203),c_Orderings_Otop__class_Otop(tc_fun(X2205,tc_HOL_Obool)))))|hBOOL(hAPP(X2202,X2201))|~c_Fun_Oinj__on(X2205,X2204,X2203,c_Orderings_Otop__class_Otop(tc_fun(X2205,tc_HOL_Obool))))&(~hBOOL(hAPP(X2202,hAPP(c_Hilbert__Choice_Oinv__into(X2205,X2204,c_Orderings_Otop__class_Otop(tc_fun(X2205,tc_HOL_Obool)),X2203),esk69_5(X2201,X2202,X2203,X2204,X2205))))|hBOOL(hAPP(X2202,X2201))|~c_Fun_Oinj__on(X2205,X2204,X2203,c_Orderings_Otop__class_Otop(tc_fun(X2205,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_inj__transfer])])])])])). 6.97/7.22 cnf(c_0_6928, 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_5123])). 6.97/7.22 cnf(c_0_6929, 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_5124])). 6.97/7.22 cnf(c_0_6930, plain, (hAPP(hAPP(c_List_Omap(X1,X2),hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5)),X6)=hAPP(hAPP(c_List_Omap(X3,X2),X4),hAPP(hAPP(c_List_Omap(X1,X3),X5),X6))), inference(split_conjunct,[status(thm)],[c_0_5125]), ['final']). 6.97/7.22 cnf(c_0_6931, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk125_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_5126])). 6.97/7.22 cnf(c_0_6932, plain, (c_List_Olist_ONil(X1)=X2|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),c_List_Olast(X1,X2))),X2)=c_List_Obutlast(X1,X2)|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5127])). 6.97/7.22 fof(c_0_6933, plain, ![X9614, X9615, X9616, X9617]:(~class_Fields_Ofield(X9617)|(c_Groups_Ozero__class_Ozero(X9617)=X9616|hAPP(hAPP(c_Power_Opower__class_Opower(X9617),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9617),X9615),X9616)),X9614)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9617),hAPP(hAPP(c_Power_Opower__class_Opower(X9617),X9615),X9614)),hAPP(hAPP(c_Power_Opower__class_Opower(X9617),X9616),X9614)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nonzero__power__divide])])])). 6.97/7.22 fof(c_0_6934, plain, ![X2957, X2958, X2959, X2960, X2961]:(~class_Orderings_Olinorder(X2961)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2961,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X2961,X2960),X2959)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X2961,X2958),X2957))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X2961,hAPP(hAPP(c_Orderings_Oord__class_Omax(X2961),X2960),X2958)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X2961),X2959),X2957))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastLessThan])])). 6.97/7.22 fof(c_0_6935, plain, ![X4863, X4864, X4865, X4866]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4866),X4865))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4866,X4866),tc_HOL_Obool)),X4864),hAPP(hAPP(c_Product__Type_OSigma(X4866,X4866),X4865),hAPP(c_COMBK(tc_fun(X4866,tc_HOL_Obool),X4866),X4865))))|(~hBOOL(hAPP(hAPP(c_member(tc_fun(X4866,tc_HOL_Obool)),X4863),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4866),X4865),X4864)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X4866),X4863))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__equiv__class])])])). 6.97/7.22 cnf(c_0_6936, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,esk502_4(X3,X1,X2,X4)),X4)),X3))|X4=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hAPP(c_Set_Oimage(X1,X2,X5),X3)!=X4), inference(split_conjunct,[status(thm)],[c_0_5128])). 6.97/7.22 fof(c_0_6937, plain, ![X1495, X1496]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1496))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1495),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1496),X1495)=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),X1496),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1495)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__pos__neg])])])). 6.97/7.22 fof(c_0_6938, plain, ![X16548, X16549]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16549),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X16548),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X16549),X16548)=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),X16549),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X16548)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__neg__neg])])). 6.97/7.22 fof(c_0_6939, plain, ![X9417, X9418, X9419, X9420, X9421]:((hBOOL(hAPP(hAPP(c_member(X9421),esk309_5(X9417,X9418,X9419,X9420,X9421)),X9420))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9419,tc_HOL_Obool)),hAPP(c_Set_Oimage(X9421,X9419,X9418),X9420)),X9417)))&(~hBOOL(hAPP(hAPP(c_member(X9419),hAPP(X9418,esk309_5(X9417,X9418,X9419,X9420,X9421))),X9417))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9419,tc_HOL_Obool)),hAPP(c_Set_Oimage(X9421,X9419,X9418),X9420)),X9417)))), 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__subsetI])])])])])). 6.97/7.22 fof(c_0_6940, plain, ![X16705, X16706, X16707]:(~class_Orderings_Olinorder(X16707)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16707),X16706))|(X16706=c_Orderings_Obot__class_Obot(tc_fun(X16707,tc_HOL_Obool))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16707),X16705))|(c_Orderings_Obot__class_Obot(tc_fun(X16707,tc_HOL_Obool))=X16705|c_Big__Operators_Olinorder__class_OMin(X16707,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16707,tc_HOL_Obool)),X16706),X16705))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X16707),c_Big__Operators_Olinorder__class_OMin(X16707,X16706)),c_Big__Operators_Olinorder__class_OMin(X16707,X16705))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min__Un])])])). 6.97/7.22 fof(c_0_6941, plain, ![X12920, X12921, X12922, X12923, X12924, X12926]:(((hBOOL(hAPP(hAPP(c_member(X12923),esk422_5(X12920,X12921,X12922,X12923,X12924)),X12922))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12924),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12923,X12924),X12922),X12921)),X12920))|~class_Complete__Lattice_Ocomplete__lattice(X12924))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12924),hAPP(X12921,esk422_5(X12920,X12921,X12922,X12923,X12924))),X12920))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12924),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12923,X12924),X12922),X12921)),X12920))|~class_Complete__Lattice_Ocomplete__lattice(X12924)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12924),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12923,X12924),X12922),X12921)),X12920))|(~hBOOL(hAPP(hAPP(c_member(X12923),X12926),X12922))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12924),hAPP(X12921,X12926)),X12920)))|~class_Complete__Lattice_Ocomplete__lattice(X12924))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__le__iff])])])])])). 6.97/7.22 fof(c_0_6942, plain, ![X2565, X2566, X2567, X2568, X2569]:((hBOOL(hAPP(hAPP(c_member(X2568),esk83_5(X2565,X2566,X2567,X2568,X2569)),X2567))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2569),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2568,X2569),X2567),X2566)),X2565))|~class_Complete__Lattice_Ocomplete__lattice(X2569))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2569),hAPP(X2566,esk83_5(X2565,X2566,X2567,X2568,X2569))),X2565))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2569),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2568,X2569),X2567),X2566)),X2565))|~class_Complete__Lattice_Ocomplete__lattice(X2569))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SUP__leI])])])])])). 6.97/7.22 fof(c_0_6943, plain, ![X2251, X2252, X2253, X2254, X2255, X2257]:(((hBOOL(hAPP(hAPP(c_member(X2253),esk71_5(X2251,X2252,X2253,X2254,X2255)),X2252))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2255),X2254),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2253,X2255),X2252),X2251)))|~class_Complete__Lattice_Ocomplete__lattice(X2255))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2255),X2254),hAPP(X2251,esk71_5(X2251,X2252,X2253,X2254,X2255))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2255),X2254),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2253,X2255),X2252),X2251)))|~class_Complete__Lattice_Ocomplete__lattice(X2255)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2255),X2254),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2253,X2255),X2252),X2251)))|(~hBOOL(hAPP(hAPP(c_member(X2253),X2257),X2252))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2255),X2254),hAPP(X2251,X2257))))|~class_Complete__Lattice_Ocomplete__lattice(X2255))), 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])])])])])])). 6.97/7.22 fof(c_0_6944, plain, ![X1084, X1085, X1086, X1087, X1088]:((hBOOL(hAPP(hAPP(c_member(X1087),esk33_5(X1084,X1085,X1086,X1087,X1088)),X1086))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1088),X1085),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1087,X1088),X1086),X1084)))|~class_Complete__Lattice_Ocomplete__lattice(X1088))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1088),X1085),hAPP(X1084,esk33_5(X1084,X1085,X1086,X1087,X1088))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1088),X1085),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1087,X1088),X1086),X1084)))|~class_Complete__Lattice_Ocomplete__lattice(X1088))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__INFI])])])])])). 6.97/7.22 cnf(c_0_6945, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk590_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_5129])). 6.97/7.22 fof(c_0_6946, plain, ![X15318, X15319, X15320, X15321, X15322]:(~c_Fun_Oinj__on(X15322,X15321,X15320,X15319)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15321,tc_HOL_Obool)),hAPP(c_Set_Oimage(X15322,X15321,X15320),X15319)),X15318))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15321),X15318))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X15322),X15319)),hAPP(c_Finite__Set_Ocard(X15321),X15318)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__inj__on__le])])])). 6.97/7.22 fof(c_0_6947, plain, ![X11510, X11511, X11512, X11513, X11514]:(~class_Rings_Osemiring__0(X11514)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11514),X11513),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11512,X11514),X11511),X11510))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11512,X11514),hAPP(hAPP(c_COMBB(X11514,X11514,X11512),hAPP(c_Groups_Otimes__class_Otimes(X11514),X11513)),X11511)),X11510)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__right__distrib])])])). 6.97/7.22 fof(c_0_6948, plain, ![X9134, X9135, X9136, X9137, X9138, X9139, X9140, X9141]:((hBOOL(hAPP(hAPP(c_member(X9140),esk300_7(X9134,X9135,X9136,X9137,X9138,X9139,X9140)),X9136))|hAPP(hAPP(X9137,X9134),X9136)=hAPP(hAPP(X9137,X9135),X9136)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9140),X9136))|~c_Finite__Set_Ofolding__image(X9141,X9140,X9139,X9138,X9137))&(hAPP(X9134,esk300_7(X9134,X9135,X9136,X9137,X9138,X9139,X9140))!=hAPP(X9135,esk300_7(X9134,X9135,X9136,X9137,X9138,X9139,X9140))|hAPP(hAPP(X9137,X9134),X9136)=hAPP(hAPP(X9137,X9135),X9136)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9140),X9136))|~c_Finite__Set_Ofolding__image(X9141,X9140,X9139,X9138,X9137))), 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_Ocong])])])])])])])). 6.97/7.22 fof(c_0_6949, plain, ![X10681, X10682, X10683, X10685]:(((hBOOL(hAPP(hAPP(c_member(X10683),esk353_3(X10681,X10682,X10683)),X10682))|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(X10683,tc_Nat_Onat),X10681),X10682)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10683),X10682)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X10681,esk353_3(X10681,X10682,X10683))))|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(X10683,tc_Nat_Onat),X10681),X10682)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10683),X10682))))&(~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(X10683,tc_Nat_Onat),X10681),X10682)))|(~hBOOL(hAPP(hAPP(c_member(X10683),X10685),X10682))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X10681,X10685))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10683),X10682)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__pos__nat__iff])])])])])). 6.97/7.22 cnf(c_0_6950, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk462_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_5130])). 6.97/7.22 fof(c_0_6951, plain, ![X12645, X12646, X12647]:(~class_Lattices_Olattice(X12647)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12647),X12646))|(X12646=c_Orderings_Obot__class_Obot(tc_fun(X12647,tc_HOL_Obool))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12647),X12645))|(c_Orderings_Obot__class_Obot(tc_fun(X12647,tc_HOL_Obool))=X12645|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X12647),c_Big__Operators_Olattice__class_OInf__fin(X12647,X12646)),c_Big__Operators_Olattice__class_OInf__fin(X12647,X12645))=c_Big__Operators_Olattice__class_OInf__fin(X12647,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12647,tc_HOL_Obool)),X12646),X12645))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Ounion__idem])])])). 6.97/7.22 fof(c_0_6952, plain, ![X15867, X15868, X15869, X15870]:((hBOOL(hAPP(hAPP(c_member(X15869),esk536_4(X15867,X15868,X15869,X15870)),X15868))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15870),c_Groups_Ozero__class_Ozero(X15870)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X15869,X15870),X15867),X15868)))|~class_Rings_Olinordered__semidom(X15870))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15870),c_Groups_Ozero__class_Ozero(X15870)),hAPP(X15867,esk536_4(X15867,X15868,X15869,X15870))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15870),c_Groups_Ozero__class_Ozero(X15870)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X15869,X15870),X15867),X15868)))|~class_Rings_Olinordered__semidom(X15870))), 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])])])])])). 6.97/7.22 fof(c_0_6953, plain, ![X4634, X4635, X4636, X4637]:((hBOOL(hAPP(hAPP(c_member(X4636),esk156_4(X4634,X4635,X4636,X4637)),X4635))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4637),c_Groups_Ozero__class_Ozero(X4637)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4636,X4637),X4634),X4635)))|~class_Rings_Olinordered__semidom(X4637))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4637),c_Groups_Ozero__class_Ozero(X4637)),hAPP(X4634,esk156_4(X4634,X4635,X4636,X4637))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4637),c_Groups_Ozero__class_Ozero(X4637)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4636,X4637),X4634),X4635)))|~class_Rings_Olinordered__semidom(X4637))), 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])])])])])). 6.97/7.22 cnf(c_0_6954, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk529_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)|X3!=X4|~class_Groups_Ocomm__monoid__add(X5)|~class_Groups_Ocomm__monoid__mult(X5)), inference(split_conjunct,[status(thm)],[c_0_5131])). 6.97/7.22 cnf(c_0_6955, 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_5132])). 6.97/7.22 cnf(c_0_6956, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk561_5(X1,X2,X3,X4,X5)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X1),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X2),X4)|~c_Nat__Transfer_Onat__set(X3)|X4!=X3|~class_Groups_Ocomm__monoid__mult(X5)|~class_Groups_Ocomm__monoid__add(X5)), inference(split_conjunct,[status(thm)],[c_0_5133])). 6.97/7.22 cnf(c_0_6957, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk232_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(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(X2,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_5134])). 6.97/7.22 cnf(c_0_6958, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk269_3(X1,X2,X3))),esk270_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(split_conjunct,[status(thm)],[c_0_5135])). 6.97/7.22 fof(c_0_6959, plain, ![X9568, X9569, X9572, X9573, X9574, X9575]:(((hBOOL(hAPP(hAPP(c_member(tc_prod(X9569,X9569)),hAPP(hAPP(c_Product__Type_OPair(X9569,X9569),esk312_2(X9568,X9569)),esk313_2(X9568,X9569))),X9568))|c_Relation_Osym(X9569,X9568))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X9569,X9569)),hAPP(hAPP(c_Product__Type_OPair(X9569,X9569),esk313_2(X9568,X9569)),esk312_2(X9568,X9569))),X9568))|c_Relation_Osym(X9569,X9568)))&(~c_Relation_Osym(X9573,X9572)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X9573,X9573)),hAPP(hAPP(c_Product__Type_OPair(X9573,X9573),X9574),X9575)),X9572))|hBOOL(hAPP(hAPP(c_member(tc_prod(X9573,X9573)),hAPP(hAPP(c_Product__Type_OPair(X9573,X9573),X9575),X9574)),X9572))))), 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_sym__def])])])])])])). 6.97/7.22 fof(c_0_6960, plain, ![X2924, X2925, X2926]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2926),X2924),c_Groups_Ozero__class_Ozero(X2926)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2926),c_Groups_Ozero__class_Ozero(X2926)),X2925))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2926),hAPP(c_Groups_Oabs__class_Oabs(X2926),X2925)),hAPP(c_Groups_Oabs__class_Oabs(X2926),X2924))=hAPP(c_Groups_Oabs__class_Oabs(X2926),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2926),X2925),X2924))|~class_Rings_Oordered__ring__abs(X2926))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2926),c_Groups_Ozero__class_Ozero(X2926)),X2924))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2926),c_Groups_Ozero__class_Ozero(X2926)),X2925))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2926),hAPP(c_Groups_Oabs__class_Oabs(X2926),X2925)),hAPP(c_Groups_Oabs__class_Oabs(X2926),X2924))=hAPP(c_Groups_Oabs__class_Oabs(X2926),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2926),X2925),X2924))|~class_Rings_Oordered__ring__abs(X2926)))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2926),X2924),c_Groups_Ozero__class_Ozero(X2926)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2926),X2925),c_Groups_Ozero__class_Ozero(X2926)))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2926),hAPP(c_Groups_Oabs__class_Oabs(X2926),X2925)),hAPP(c_Groups_Oabs__class_Oabs(X2926),X2924))=hAPP(c_Groups_Oabs__class_Oabs(X2926),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2926),X2925),X2924))|~class_Rings_Oordered__ring__abs(X2926))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2926),c_Groups_Ozero__class_Ozero(X2926)),X2924))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2926),X2925),c_Groups_Ozero__class_Ozero(X2926)))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2926),hAPP(c_Groups_Oabs__class_Oabs(X2926),X2925)),hAPP(c_Groups_Oabs__class_Oabs(X2926),X2924))=hAPP(c_Groups_Oabs__class_Oabs(X2926),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2926),X2925),X2924))|~class_Rings_Oordered__ring__abs(X2926)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__eq__mult])])])])). 6.97/7.22 fof(c_0_6961, plain, ![X9204, X9205, X9206]:(~class_Orderings_Olinorder(X9206)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9206),X9205))|(c_Orderings_Obot__class_Obot(tc_fun(X9206,tc_HOL_Obool))=X9205|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9206),X9204))|(X9204=c_Orderings_Obot__class_Obot(tc_fun(X9206,tc_HOL_Obool))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X9206),c_Big__Operators_Olinorder__class_OMax(X9206,X9205)),c_Big__Operators_Olinorder__class_OMax(X9206,X9204))=c_Big__Operators_Olinorder__class_OMax(X9206,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9206,tc_HOL_Obool)),X9205),X9204))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max__Un])])])). 6.97/7.22 cnf(c_0_6962, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk570_6(X2,X3,X4,X1,X5,X6)),X5))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X5),X3)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X6),X4)|X6!=X5), inference(split_conjunct,[status(thm)],[c_0_5136])). 6.97/7.22 cnf(c_0_6963, plain, (c_List_Osublist(X1,X2,X3)=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)|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5137])). 6.97/7.22 cnf(c_0_6964, plain, (hBOOL(hAPP(X5,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),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)),X2)!=X4|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(X5,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X4),X1)))), inference(split_conjunct,[status(thm)],[c_0_4962])). 6.97/7.22 fof(c_0_6965, plain, ![X4977, X4978, X4979, X4980]:((hBOOL(hAPP(hAPP(c_member(X4980),X4979),X4978))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4980,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4980),X4979),X4977)),X4978)=hAPP(hAPP(c_Set_Oinsert(X4980),X4979),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4980,tc_HOL_Obool)),X4977),X4978)))&(~hBOOL(hAPP(hAPP(c_member(X4980),X4979),X4978))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4980,tc_HOL_Obool)),X4977),X4978)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4980,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4980),X4979),X4977)),X4978))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insert__Diff__if])])])). 6.97/7.22 cnf(c_0_6966, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk126_4(X1,X2,X3,X4)),esk125_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_5126])). 6.97/7.22 cnf(c_0_6967, plain, (hBOOL(hAPP(X5,X4))|~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)))|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),X1),X2))|~hBOOL(hAPP(X5,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X1)))), inference(split_conjunct,[status(thm)],[c_0_4962])). 6.97/7.22 fof(c_0_6968, plain, ![X8210, X8211]:(~class_Orderings_Oorder(X8211)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8211,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X8211),X8210),c_Orderings_Obot__class_Obot(tc_fun(X8211,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(X8211),X8210))=hAPP(hAPP(c_Set_Oinsert(X8211),X8210),c_Orderings_Obot__class_Obot(tc_fun(X8211,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_single__Diff__lessThan])])])). 6.97/7.22 fof(c_0_6969, plain, ![X2907, X2908, X2909]:(hBOOL(hAPP(hAPP(c_member(X2909),X2908),X2907))|X2907=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2909,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X2909),X2908),X2907)),hAPP(hAPP(c_Set_Oinsert(X2909),X2908),c_Orderings_Obot__class_Obot(tc_fun(X2909,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Diff__insert__absorb])])])). 6.97/7.22 cnf(c_0_6970, plain, (X1=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk339_4(X2,X3,X4,X1)),esk338_4(X2,X3,X4,X1))|X1=X3|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X4)!=X3|~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_5122])). 6.97/7.22 fof(c_0_6971, plain, ![X5344, X5345, X5346, X5347, X5348]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X5347,X5348)),hAPP(hAPP(c_Product__Type_OPair(X5347,X5348),X5345),X5346)),X5344))|hBOOL(hAPP(hAPP(c_member(tc_prod(X5348,X5347)),hAPP(hAPP(c_Product__Type_OPair(X5348,X5347),X5346),X5345)),hAPP(c_Relation_Oconverse(X5347,X5348),X5344))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X5348,X5347)),hAPP(hAPP(c_Product__Type_OPair(X5348,X5347),X5346),X5345)),hAPP(c_Relation_Oconverse(X5347,X5348),X5344)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X5347,X5348)),hAPP(hAPP(c_Product__Type_OPair(X5347,X5348),X5345),X5346)),X5344)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converse__iff])])). 6.97/7.22 cnf(c_0_6972, 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_5138])). 6.97/7.22 cnf(c_0_6973, plain, (c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)=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))))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5139])). 6.97/7.22 fof(c_0_6974, plain, ![X4217, X4218, X4219, X4220, X4221]:(~c_Finite__Set_Ofun__left__comm__idem(X4221,X4220,X4219)|hAPP(hAPP(c_Finite__Set_Ofold(X4221,X4220,X4219),X4218),hAPP(c_List_Oset(X4221),X4217))=hAPP(c_List_Ofoldl(X4220,X4221,hAPP(c_COMBC(X4221,X4220,X4220),X4219),X4218),X4217)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm__idem_Ofold__set])])])). 6.97/7.22 fof(c_0_6975, plain, ![X15613, X15614, X15615, X15616, X15617]:(~c_Finite__Set_Ofolding__one(X15617,X15616,X15615)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15617),X15614))|(hBOOL(hAPP(hAPP(c_member(X15617),X15613),X15614))|hAPP(hAPP(c_Finite__Set_Ofold(X15617,X15617,X15616),X15613),X15614)=hAPP(X15615,hAPP(hAPP(c_Set_Oinsert(X15617),X15613),X15614))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one_Oeq__fold_H])])])). 6.97/7.22 fof(c_0_6976, plain, ![X9922, X9923, X9924]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9924),X9923))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9924,tc_HOL_Obool)),X9923),X9922))|hAPP(c_Finite__Set_Ocard(X9924),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9924,tc_HOL_Obool)),X9922),X9923))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X9924),X9922)),hAPP(c_Finite__Set_Ocard(X9924),X9923)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Diff__subset])])])). 6.97/7.22 fof(c_0_6977, plain, ![X10750, X10751, X10752, X10753, X10754]:((hAPP(hAPP(c_Divides_Odiv__class_Odiv(X10754),X10750),X10752)!=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X10754),X10751),X10753)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10754),X10751),X10752)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10754),X10753),X10750)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10754),X10752),X10750))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10754),X10753),X10751))|X10752=c_Groups_Ozero__class_Ozero(X10754)|X10753=c_Groups_Ozero__class_Ozero(X10754)|~class_Divides_Osemiring__div(X10754))&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10754),X10751),X10752)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10754),X10753),X10750)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X10754),X10750),X10752)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X10754),X10751),X10753)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10754),X10752),X10750))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10754),X10753),X10751))|X10752=c_Groups_Ozero__class_Ozero(X10754)|X10753=c_Groups_Ozero__class_Ozero(X10754)|~class_Divides_Osemiring__div(X10754))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dvd__div__div__eq__mult])])])])). 6.97/7.22 cnf(c_0_6978, 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_5140])). 6.97/7.22 cnf(c_0_6979, 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_5141])). 6.97/7.22 cnf(c_0_6980, 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),esk493_2(X1,X2)),hAPP(X2,esk493_2(X1,X2))))), inference(split_conjunct,[status(thm)],[c_0_5142])). 6.97/7.22 fof(c_0_6981, plain, ![X5954, X5955, X5956, X5957, X5958, X5959, X5960, X5961, X5962, X5963, X5964, X5965, X5966, X5967, X5968]:((~hBOOL(hAPP(hAPP(c_member(X5960),X5961),X5957))|~hBOOL(hAPP(hAPP(hAPP(X5956,X5961),X5955),X5954))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5960,tc_fun(X5959,tc_fun(X5958,tc_HOL_Obool))),X5957),X5956),X5955),X5954)))&((hBOOL(hAPP(hAPP(c_member(X5968),esk196_7(X5962,X5963,X5964,X5965,X5966,X5967,X5968)),X5965))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5968,tc_fun(X5967,tc_fun(X5966,tc_HOL_Obool))),X5965),X5964),X5963),X5962)))&(hBOOL(hAPP(hAPP(hAPP(X5964,esk196_7(X5962,X5963,X5964,X5965,X5966,X5967,X5968)),X5963),X5962))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5968,tc_fun(X5967,tc_fun(X5966,tc_HOL_Obool))),X5965),X5964),X5963),X5962))))), 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])])])])])])). 6.97/7.22 fof(c_0_6982, plain, ![X11733, X11734, X11735, X11736]:(~class_Orderings_Olinorder(X11736)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11736),X11735))|hAPP(hAPP(c_Finite__Set_Ofold(X11736,X11736,c_Orderings_Oord__class_Omin(X11736)),X11734),hAPP(hAPP(c_Set_Oinsert(X11736),X11733),X11735))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X11736),X11733),hAPP(hAPP(c_Finite__Set_Ofold(X11736,X11736,c_Orderings_Oord__class_Omin(X11736)),X11734),X11735)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ofold__inf__insert])])])). 6.97/7.22 fof(c_0_6983, plain, ![X4423, X4424]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4424))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4423),X4424))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X4423),X4424)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4423),X4424)),X4424)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__geq])])])). 6.97/7.22 fof(c_0_6984, plain, ![X15915, X15916, X15917, X15918]:(~class_Lattices_Osemilattice__inf(X15918)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15918),X15917))|hAPP(hAPP(c_Finite__Set_Ofold(X15918,X15918,c_Lattices_Osemilattice__inf__class_Oinf(X15918)),X15916),hAPP(hAPP(c_Set_Oinsert(X15918),X15915),X15917))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15918),X15915),hAPP(hAPP(c_Finite__Set_Ofold(X15918,X15918,c_Lattices_Osemilattice__inf__class_Oinf(X15918)),X15916),X15917)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__inf__insert])])])). 6.97/7.22 fof(c_0_6985, plain, ![X11174, X11175, X11176, X11177]:(~class_Lattices_Osemilattice__sup(X11177)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11177),X11176))|hAPP(hAPP(c_Finite__Set_Ofold(X11177,X11177,c_Lattices_Osemilattice__sup__class_Osup(X11177)),X11175),hAPP(hAPP(c_Set_Oinsert(X11177),X11174),X11176))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X11177),X11174),hAPP(hAPP(c_Finite__Set_Ofold(X11177,X11177,c_Lattices_Osemilattice__sup__class_Osup(X11177)),X11175),X11176)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__sup__insert])])). 6.97/7.22 fof(c_0_6986, plain, ![X16540, X16541, X16542, X16543]:(~class_Orderings_Olinorder(X16543)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16543),X16542))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X16543),X16540),hAPP(hAPP(c_Finite__Set_Ofold(X16543,X16543,c_Orderings_Oord__class_Omax(X16543)),X16541),X16542))=hAPP(hAPP(c_Finite__Set_Ofold(X16543,X16543,c_Orderings_Oord__class_Omax(X16543)),X16541),hAPP(hAPP(c_Set_Oinsert(X16543),X16540),X16542)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ofold__sup__insert])])])). 6.97/7.22 fof(c_0_6987, plain, ![X9964, X9965, X9966, X9967]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X9967|hAPP(hAPP(c_List_Otake(X9966),X9967),hAPP(hAPP(c_List_Olist_OCons(X9966),X9965),X9964))=c_List_Olist_ONil(X9966))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X9967|hAPP(hAPP(c_List_Otake(X9966),X9967),hAPP(hAPP(c_List_Olist_OCons(X9966),X9965),X9964))=hAPP(hAPP(c_List_Olist_OCons(X9966),X9965),hAPP(hAPP(c_List_Otake(X9966),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X9967),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X9964)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_take__Cons_H])])])). 6.97/7.22 fof(c_0_6988, plain, ![X15823, X15824, X15825]:(~hBOOL(hAPP(c_List_Odistinct(X15825),X15824))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15825,tc_HOL_Obool)),hAPP(c_List_Oset(X15825),X15824)),hAPP(hAPP(c_Set_Oinsert(X15825),X15823),c_Orderings_Obot__class_Obot(tc_fun(X15825,tc_HOL_Obool))))=hAPP(c_List_Oset(X15825),c_List_Oremove1(X15825,X15823,X15824))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_set__remove1__eq])])])). 6.97/7.22 cnf(c_0_6989, 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_5143])). 6.97/7.22 cnf(c_0_6990, 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_5144])). 6.97/7.22 fof(c_0_6991, plain, ![X12337, X12338, X12339, X12340, X12341]:(~c_Fun_Oinj__on(X12341,X12340,X12339,X12338)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12341,tc_HOL_Obool)),X12337),X12338))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12340,tc_HOL_Obool)),hAPP(c_Set_Oimage(X12341,X12340,X12339),X12337)),hAPP(c_Set_Oimage(X12341,X12340,X12339),X12338))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__strict__subset])])])). 6.97/7.22 fof(c_0_6992, plain, ![X7960, X7961, X7962, X7963, X7964]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X7964,X7963)),hAPP(X7964,X7962)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X7961,X7961)),hAPP(hAPP(c_Product__Type_OPair(X7961,X7961),X7963),X7962)),c_Wellfounded_Omlex__prod(X7961,X7964,X7960)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mlex__less])])])). 6.97/7.22 fof(c_0_6993, plain, ![X15355, X15356, X15357, X15359, X15360, X15361, X15362]:(((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15356),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15355),hAPP(c_Nat_OSuc,esk516_3(X15355,X15356,X15357)))))|hBOOL(hAPP(X15357,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X15357,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X15356),X15355))))&(hBOOL(hAPP(X15357,esk516_3(X15355,X15356,X15357)))|hBOOL(hAPP(X15357,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X15357,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X15356),X15355)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15355),esk516_3(X15355,X15356,X15357))),X15356))|hBOOL(hAPP(X15357,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X15357,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X15356),X15355)))))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15356),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15355),hAPP(c_Nat_OSuc,esk516_3(X15355,X15356,X15357)))))|X15355=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(X15357,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X15356),X15355))))&(hBOOL(hAPP(X15357,esk516_3(X15355,X15356,X15357)))|X15355=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(X15357,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X15356),X15355)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15355),esk516_3(X15355,X15356,X15357))),X15356))|X15355=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(X15357,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X15356),X15355))))))&((~hBOOL(hAPP(X15361,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|X15359!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X15361,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X15360),X15359))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15360),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15359),hAPP(c_Nat_OSuc,X15362))))|~hBOOL(hAPP(X15361,X15362))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15359),X15362)),X15360))|hBOOL(hAPP(X15361,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X15360),X15359)))))), 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])])])])])])). 6.97/7.22 cnf(c_0_6994, 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_5145])). 6.97/7.22 cnf(c_0_6995, 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_5146])). 6.97/7.22 fof(c_0_6996, plain, ![X8212, X8213, X8214, X8215, X8216, X8217]:(~hBOOL(hAPP(hAPP(c_member(X8217),X8216),X8215))|(~hBOOL(hAPP(hAPP(c_member(X8214),X8213),hAPP(X8212,X8216)))|hBOOL(hAPP(hAPP(c_member(X8214),X8213),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8217,tc_fun(X8214,tc_HOL_Obool)),X8215),X8212))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__I])])])). 6.97/7.22 fof(c_0_6997, plain, ![X5145, X5146, X5147, X5148]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5148),X5146),c_Groups_Ozero__class_Ozero(X5148)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5148),X5147),X5145))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5148),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5148),X5147),X5146)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5148),X5145),X5146)))|~class_Rings_Olinordered__ring__strict(X5148))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5148),X5145),X5147))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5148),X5147),X5145))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5148),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5148),X5147),X5146)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5148),X5145),X5146)))|~class_Rings_Olinordered__ring__strict(X5148)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5148),X5146),c_Groups_Ozero__class_Ozero(X5148)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5148),c_Groups_Ozero__class_Ozero(X5148)),X5146))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5148),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5148),X5147),X5146)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5148),X5145),X5146)))|~class_Rings_Olinordered__ring__strict(X5148))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5148),X5145),X5147))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5148),c_Groups_Ozero__class_Ozero(X5148)),X5146))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5148),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5148),X5147),X5146)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5148),X5145),X5146)))|~class_Rings_Olinordered__ring__strict(X5148))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5148),X5147),X5145))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5148),c_Groups_Ozero__class_Ozero(X5148)),X5146))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5148),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5148),X5147),X5146)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5148),X5145),X5146)))|~class_Rings_Olinordered__ring__strict(X5148))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5148),X5146),c_Groups_Ozero__class_Ozero(X5148)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5148),X5145),X5147))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5148),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5148),X5147),X5146)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5148),X5145),X5146)))|~class_Rings_Olinordered__ring__strict(X5148)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj])])])). 6.97/7.22 fof(c_0_6998, plain, ![X4373, X4374, X4375, X4376]:(~class_Rings_Olinordered__semiring__strict(X4376)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4376),X4375),X4374))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4376),c_Groups_Ozero__class_Ozero(X4376)),X4373))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4376),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4376),X4375),X4373)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4376),X4374),X4373)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__strict__right__mono])])])). 6.97/7.22 fof(c_0_6999, plain, ![X4756, X4757, X4758, X4759]:(~class_Rings_Olinordered__comm__semiring__strict(X4759)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4759),X4758),X4757))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4759),c_Groups_Ozero__class_Ozero(X4759)),X4756))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4759),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4759),X4756),X4758)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4759),X4756),X4757)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__mult__strict__left__mono])])])). 6.97/7.22 fof(c_0_7000, plain, ![X4461, X4462, X4463, X4464]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4464),X4462),X4461))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4464),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4464),X4463),X4462)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4464),X4463),X4461)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4464),c_Groups_Ozero__class_Ozero(X4464)),X4463))|~class_Rings_Olinordered__ring__strict(X4464))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4464),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4464),X4463),X4462)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4464),X4463),X4461)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4464),X4462),X4461))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4464),c_Groups_Ozero__class_Ozero(X4464)),X4463))|~class_Rings_Olinordered__ring__strict(X4464))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos])])])). 6.97/7.22 fof(c_0_7001, plain, ![X14807, X14808, X14809, X14810]:(~class_Rings_Olinordered__semiring__strict(X14810)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14810),X14809),X14808))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14810),c_Groups_Ozero__class_Ozero(X14810)),X14807))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14810),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14810),X14807),X14809)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14810),X14807),X14808)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__strict__left__mono])])])). 6.97/7.22 fof(c_0_7002, plain, ![X7521, X7522, X7523, X7524]:(~class_Fields_Olinordered__field(X7524)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7524),X7523),X7522))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7524),c_Groups_Ozero__class_Ozero(X7524)),X7521))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7524),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7524),X7523),X7521)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7524),X7522),X7521)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono])])). 6.97/7.22 fof(c_0_7003, plain, ![X2514, X2515, X2516, X2517]:(~class_Rings_Oordered__semiring(X2517)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2517),X2516),X2515))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2517),c_Groups_Ozero__class_Ozero(X2517)),X2514))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2517),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2517),X2516),X2514)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2517),X2515),X2514)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__right__mono])])])). 6.97/7.22 fof(c_0_7004, plain, ![X15906, X15907, X15908, X15909]:(~class_Rings_Oordered__comm__semiring(X15909)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15909),X15908),X15907))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15909),c_Groups_Ozero__class_Ozero(X15909)),X15906))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15909),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15909),X15906),X15908)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15909),X15906),X15907)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__mult__left__mono])])])). 6.97/7.22 cnf(c_0_7005, 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_5147])). 6.97/7.22 cnf(c_0_7006, plain, (hAPP(c_Relation_ORange(X1,X2),X3)=hAPP(c_Set_Oimage(tc_prod(X1,X2),X2,c_Product__Type_Osnd(X1,X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_5148]), ['final']). 6.97/7.22 cnf(c_0_7007, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,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))=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)), inference(split_conjunct,[status(thm)],[c_0_5149])). 6.97/7.22 fof(c_0_7008, plain, ![X2752, X2753, X2754, X2755]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2755),X2753),X2752))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2755),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2755),X2754),X2753)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2755),X2754),X2752)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2755),c_Groups_Ozero__class_Ozero(X2755)),X2754))|~class_Rings_Olinordered__ring__strict(X2755))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2755),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2755),X2754),X2753)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2755),X2754),X2752)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2755),X2753),X2752))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2755),c_Groups_Ozero__class_Ozero(X2755)),X2754))|~class_Rings_Olinordered__ring__strict(X2755))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__pos])])])). 6.97/7.22 fof(c_0_7009, plain, ![X2286, X2287, X2288, X2289]:(~class_Rings_Oordered__semiring(X2289)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2289),X2288),X2287))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2289),c_Groups_Ozero__class_Ozero(X2289)),X2286))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2289),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2289),X2286),X2288)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2289),X2286),X2287)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__left__mono])])])). 6.97/7.22 cnf(c_0_7010, 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_5150])). 6.97/7.22 cnf(c_0_7011, plain, (hAPP(c_Relation_ODomain(X1,X2),X3)=hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_5151]), ['final']). 6.97/7.22 fof(c_0_7012, plain, ![X5435, X5436, X5437, X5438]:(~class_Rings_Olinordered__ring__strict(X5438)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5438),X5437),X5436))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5438),X5435),c_Groups_Ozero__class_Ozero(X5438)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5438),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5438),X5435),X5436)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5438),X5435),X5437)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__strict__left__mono__neg])])])). 6.97/7.22 fof(c_0_7013, plain, ![X6130, X6131, X6132, X6133]:(~class_Fields_Olinordered__field(X6133)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6133),X6132),X6131))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6133),X6130),c_Groups_Ozero__class_Ozero(X6133)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6133),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6133),X6131),X6130)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6133),X6132),X6130)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__strict__right__mono__neg])])])). 6.97/7.22 fof(c_0_7014, plain, ![X15647, X15648]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15648))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15647))|c_Divides_OposDivAlg(X15648,X15647)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X15648),X15647)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X15648,X15647)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_posDivAlg__div__mod])])])). 6.97/7.22 fof(c_0_7015, plain, ![X4362, X4363]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4363),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)),X4362))|hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X4363),X4362)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4363,X4362))=c_Divides_OnegDivAlg(X4363,X4362))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_negDivAlg__div__mod])])])). 6.97/7.22 fof(c_0_7016, plain, ![X10169, X10170, X10171, X10172]:(~class_Rings_Oordered__ring(X10172)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10172),X10171),X10170))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10172),X10169),c_Groups_Ozero__class_Ozero(X10172)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10172),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10172),X10170),X10169)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10172),X10171),X10169)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono__neg])])). 6.97/7.22 fof(c_0_7017, plain, ![X14395, X14396, X14397, X14398]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14398),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14398),X14397),X14396)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14398),X14397),X14395)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14398),X14395),X14396))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14398),X14397),c_Groups_Ozero__class_Ozero(X14398)))|~class_Rings_Olinordered__ring__strict(X14398))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14398),X14395),X14396))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14398),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14398),X14397),X14396)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14398),X14397),X14395)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14398),X14397),c_Groups_Ozero__class_Ozero(X14398)))|~class_Rings_Olinordered__ring__strict(X14398))), 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])])])])). 6.97/7.22 fof(c_0_7018, plain, ![X9635, X9636, X9637, X9638]:(~class_Rings_Oordered__ring(X9638)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9638),X9637),X9636))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9638),X9635),c_Groups_Ozero__class_Ozero(X9638)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9638),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9638),X9635),X9636)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9638),X9635),X9637)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__left__mono__neg])])])). 6.97/7.22 cnf(c_0_7019, plain, (hAPP(c_List_Oset(X1),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X4)),hAPP(c_List_Oset(X1),X5))|c_List_Opartition(X1,X2,X3)!=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X5)), inference(split_conjunct,[status(thm)],[c_0_5152])). 6.97/7.22 fof(c_0_7020, plain, ![X3796, X3797, X3798]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3798),X3797))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3797),X3796)),X3798)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3797),X3798)),X3796)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__diff__assoc2])])])). 6.97/7.22 fof(c_0_7021, plain, ![X2986, X2987, X2988]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2988,X2988),tc_HOL_Obool)),X2987),X2986))|(~c_Relation_Orefl__on(X2988,c_Orderings_Otop__class_Otop(tc_fun(X2988,tc_HOL_Obool)),X2986)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X2988),tc_List_Olist(X2988)),tc_HOL_Obool)),c_List_Olistrel1(X2988,X2987)),c_List_Olistrel(X2988,X2986))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel1__subset__listrel])])])). 6.97/7.22 fof(c_0_7022, plain, ![X2598, X2599]:((~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)),X2599)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2598)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X2599),X2598)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X2599),X2598))|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)),X2599)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2598))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I4_J])])). 6.97/7.22 fof(c_0_7023, plain, ![X13316, X13317, X13318]:((hBOOL(hAPP(hAPP(c_member(tc_fun(X13318,tc_HOL_Obool)),esk437_3(X13316,X13317,X13318)),X13317))|(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X13318,tc_HOL_Obool),tc_HOL_Obool))=X13317|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13318,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X13318,tc_HOL_Obool),X13317)),X13316))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13318,tc_HOL_Obool)),esk437_3(X13316,X13317,X13318)),X13316))|(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X13318,tc_HOL_Obool),tc_HOL_Obool))=X13317|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13318,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X13318,tc_HOL_Obool),X13317)),X13316))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inter__subset])])])])). 6.97/7.22 cnf(c_0_7024, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk269_3(X1,X2,X3))),esk270_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(split_conjunct,[status(thm)],[c_0_5135])). 6.97/7.22 fof(c_0_7025, plain, ![X13261, X13262, X13263, X13264]:((hBOOL(hAPP(hAPP(c_member(X13263),esk434_4(X13261,X13262,X13263,X13264)),hAPP(c_List_Oset(X13263),X13262)))|hBOOL(hAPP(X13261,hAPP(hAPP(c_List_Onth(X13263),X13262),X13264)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13264),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13263)),X13262))))&(~hBOOL(hAPP(X13261,esk434_4(X13261,X13262,X13263,X13264)))|hBOOL(hAPP(X13261,hAPP(hAPP(c_List_Onth(X13263),X13262),X13264)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13264),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13263)),X13262))))), 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])])])])])). 6.97/7.22 cnf(c_0_7026, 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_5153])). 6.97/7.22 fof(c_0_7027, plain, ![X12003, X12004, X12005, X12006]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X12006,X12006)),X12005),c_Transitive__Closure_Ortrancl(X12006,X12004)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X12006,X12006)),X12005),c_Transitive__Closure_Ortrancl(X12006,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X12006,X12006),tc_HOL_Obool)),X12004),X12003)))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X12006,X12006)),X12005),c_Transitive__Closure_Ortrancl(X12006,X12003)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X12006,X12006)),X12005),c_Transitive__Closure_Ortrancl(X12006,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X12006,X12006),tc_HOL_Obool)),X12004),X12003)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rtrancl__UnI])])])). 6.97/7.22 fof(c_0_7028, plain, ![X14088, X14089, X14090, X14091, X14092, X14093, X14094]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X14090,X14090)),X14089),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X14090,X14090),tc_HOL_Obool),X14091),X14088)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X14090,X14090)),X14089),c_Transitive__Closure_Ortrancl(X14090,X14088))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X14094,X14094)),X14093),c_Transitive__Closure_Ortrancl(X14094,X14092)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X14094,X14094)),X14093),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X14094,X14094),tc_HOL_Obool),esk479_3(X14092,X14093,X14094)),X14092))))), 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])])])])])). 6.97/7.22 fof(c_0_7029, plain, ![X13408, X13409, X13410, X13411, X13412]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X13410,X13412)),hAPP(hAPP(c_Product__Type_OPair(X13410,X13412),esk444_5(X13408,X13409,X13410,X13411,X13412)),X13411)),X13409))|~hBOOL(hAPP(hAPP(c_member(X13412),X13411),hAPP(c_Relation_OImage(X13410,X13412,X13409),X13408))))&(hBOOL(hAPP(hAPP(c_member(X13410),esk444_5(X13408,X13409,X13410,X13411,X13412)),X13408))|~hBOOL(hAPP(hAPP(c_member(X13412),X13411),hAPP(c_Relation_OImage(X13410,X13412,X13409),X13408))))), 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])])])])])). 6.97/7.22 fof(c_0_7030, plain, ![X9806, X9807, X9808, X9809, X9810, X9812, X9813, X9814, X9815, X9816, X9817]:(((hBOOL(hAPP(hAPP(c_member(X9808),esk323_5(X9806,X9807,X9808,X9809,X9810)),X9806))|~hBOOL(hAPP(hAPP(c_member(X9810),X9809),hAPP(c_Relation_OImage(X9808,X9810,X9807),X9806))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X9808,X9810)),hAPP(hAPP(c_Product__Type_OPair(X9808,X9810),esk323_5(X9806,X9807,X9808,X9809,X9810)),X9809)),X9807))|~hBOOL(hAPP(hAPP(c_member(X9810),X9809),hAPP(c_Relation_OImage(X9808,X9810,X9807),X9806)))))&(~hBOOL(hAPP(hAPP(c_member(X9814),X9817),X9812))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X9814,X9816)),hAPP(hAPP(c_Product__Type_OPair(X9814,X9816),X9817),X9815)),X9813))|hBOOL(hAPP(hAPP(c_member(X9816),X9815),hAPP(c_Relation_OImage(X9814,X9816,X9813),X9812))))), 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])])])])])])). 6.97/7.22 fof(c_0_7031, plain, ![X393, X394, X395, X396, X397, X398, X399]:(~hBOOL(hAPP(hAPP(c_member(X399),X398),X397))|(~c_Nitpick_Ofold__graph_H(X399,X396,X395,X394,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X399,tc_HOL_Obool)),X397),hAPP(hAPP(c_Set_Oinsert(X399),X398),c_Orderings_Obot__class_Obot(tc_fun(X399,tc_HOL_Obool)))),X393)|c_Nitpick_Ofold__graph_H(X399,X396,X395,X394,X397,hAPP(hAPP(X395,X398),X393)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__graph_H_Ointros_I2_J])])])). 6.97/7.22 cnf(c_0_7032, 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_5025])). 6.97/7.22 fof(c_0_7033, plain, ![X4227, X4228]:((~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),X4228)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X4227)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X4228),X4227))|~c_Nat__Transfer_Onat__set(X4227)|~c_Nat__Transfer_Onat__set(X4228))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X4228),X4227))|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),X4228)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X4227)))|~c_Nat__Transfer_Onat__set(X4227)|~c_Nat__Transfer_Onat__set(X4228))), 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_I4_J])])])])). 6.97/7.22 fof(c_0_7034, plain, ![X6961, X6962, X6963, X6964]:((hAPP(c_Relation_OImage(X6964,X6964,X6961),hAPP(hAPP(c_Set_Oinsert(X6964),esk224_4(X6961,X6962,X6963,X6964)),c_Orderings_Obot__class_Obot(tc_fun(X6964,tc_HOL_Obool))))=X6963|~hBOOL(hAPP(hAPP(c_member(tc_fun(X6964,tc_HOL_Obool)),X6963),hAPP(hAPP(c_Equiv__Relations_Oquotient(X6964),X6962),X6961))))&(hBOOL(hAPP(hAPP(c_member(X6964),esk224_4(X6961,X6962,X6963,X6964)),X6962))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X6964,tc_HOL_Obool)),X6963),hAPP(hAPP(c_Equiv__Relations_Oquotient(X6964),X6962),X6961))))), 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])])])])])). 6.97/7.22 fof(c_0_7035, plain, ![X14327, X14328, X14329, X14330, X14331, X14332]:(~c_Finite__Set_Ofolding(X14332,X14331,X14330,X14329)|hAPP(c_Fun_Ocomp(X14331,X14331,X14331,hAPP(X14330,X14327)),hAPP(X14330,X14328))=hAPP(c_Fun_Ocomp(X14331,X14331,X14331,hAPP(X14330,X14328)),hAPP(X14330,X14327))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp])])). 6.97/7.22 cnf(c_0_7036, 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_5154])). 6.97/7.22 fof(c_0_7037, plain, ![X4188, X4189, X4190, X4192, X4193, X4194, X4195]:(((hBOOL(hAPP(hAPP(c_member(X4190),esk146_3(X4188,X4189,X4190)),X4189))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4190,X4190),tc_HOL_Obool)),X4188),hAPP(hAPP(c_Product__Type_OSigma(X4190,X4190),X4189),hAPP(c_COMBK(tc_fun(X4190,tc_HOL_Obool),X4190),X4189))))|c_Relation_Orefl__on(X4190,X4189,X4188))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X4190,X4190)),hAPP(hAPP(c_Product__Type_OPair(X4190,X4190),esk146_3(X4188,X4189,X4190)),esk146_3(X4188,X4189,X4190))),X4188))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4190,X4190),tc_HOL_Obool)),X4188),hAPP(hAPP(c_Product__Type_OSigma(X4190,X4190),X4189),hAPP(c_COMBK(tc_fun(X4190,tc_HOL_Obool),X4190),X4189))))|c_Relation_Orefl__on(X4190,X4189,X4188)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4194,X4194),tc_HOL_Obool)),X4192),hAPP(hAPP(c_Product__Type_OSigma(X4194,X4194),X4193),hAPP(c_COMBK(tc_fun(X4194,tc_HOL_Obool),X4194),X4193))))|~c_Relation_Orefl__on(X4194,X4193,X4192))&(~hBOOL(hAPP(hAPP(c_member(X4194),X4195),X4193))|hBOOL(hAPP(hAPP(c_member(tc_prod(X4194,X4194)),hAPP(hAPP(c_Product__Type_OPair(X4194,X4194),X4195),X4195)),X4192))|~c_Relation_Orefl__on(X4194,X4193,X4192)))), 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])])])])])])). 6.97/7.22 fof(c_0_7038, plain, ![X340, X341, X342]:(~c_Equiv__Relations_Oequiv(X342,X341,X340)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X342,X342),tc_HOL_Obool)),X340),hAPP(hAPP(c_Product__Type_OSigma(X342,X342),X341),hAPP(c_COMBK(tc_fun(X342,tc_HOL_Obool),X342),X341))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__type])])). 6.97/7.22 fof(c_0_7039, plain, ![X15323, X15324, X15325, X15326, X15327, X15328]:(~c_Fun_Oinj__on(X15328,X15327,X15326,X15325)|(~hBOOL(hAPP(hAPP(c_member(X15327),X15324),hAPP(c_Set_Oimage(X15328,X15327,X15326),X15325)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15328,tc_HOL_Obool)),X15325),X15323))|hBOOL(hAPP(hAPP(c_member(X15328),hAPP(c_Fun_Othe__inv__into(X15328,X15327,X15325,X15326),X15324)),X15323))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__into])])). 6.97/7.22 fof(c_0_7040, plain, ![X10911, X10912, X10913]:(~c_Wellfounded_Owf(X10913,X10912)|(~c_Wellfounded_Owf(X10913,X10911)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10913,X10913),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10913,X10913,X10913),X10912),X10911)),X10912))|c_Wellfounded_Owf(X10913,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10913,X10913),tc_HOL_Obool)),X10912),X10911))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__union__compatible])])])). 6.97/7.22 fof(c_0_7041, plain, ![X13233, X13234]:(~class_Orderings_Olinorder(X13234)|hAPP(c_List_Ofoldl(tc_List_Olist(X13234),X13234,hAPP(c_COMBC(X13234,tc_List_Olist(X13234),tc_List_Olist(X13234)),c_List_Olinorder__class_Oinsort__key(X13234,X13234,c_COMBI(X13234))),c_List_Olist_ONil(X13234)),X13233)=c_List_Olinorder__class_Osort__key(X13234,X13234,c_COMBI(X13234),X13233)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sort__foldl__insort])])). 6.97/7.22 fof(c_0_7042, plain, ![X8334, X8335]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8335))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8334),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|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),X8335),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X8334))))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X8335,X8334))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__pos__neg])])])). 6.97/7.22 fof(c_0_7043, plain, ![X544, X545]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X545),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X544),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|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),X545),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X544))))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X545,X544))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__neg__neg])])])). 6.97/7.22 cnf(c_0_7044, 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_5155])). 6.97/7.22 fof(c_0_7045, plain, ![X10217, X10218, X10219, X10220]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10220),X10219)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10218)),X10217)))|hAPP(hAPP(c_List_Onth(X10218),hAPP(hAPP(c_List_Odrop(X10218),X10220),X10217)),X10219)=hAPP(hAPP(c_List_Onth(X10218),X10217),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10220),X10219))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__drop])])])). 6.97/7.22 fof(c_0_7046, plain, ![X6324, X6325, X6326, X6327]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6327)),X6326)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6325)),X6324)|hAPP(hAPP(c_List_Ozip(X6327,X6325),hAPP(c_List_Orev(X6327),X6326)),hAPP(c_List_Orev(X6325),X6324))=hAPP(c_List_Orev(tc_prod(X6327,X6325)),hAPP(hAPP(c_List_Ozip(X6327,X6325),X6326),X6324))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__rev])])). 6.97/7.22 cnf(c_0_7047, 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_5156])). 6.97/7.22 cnf(c_0_7048, 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_5157])). 6.97/7.22 fof(c_0_7049, plain, ![X8831, X8832, X8833]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8833),X8832))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X8832)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X8833),X8831))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X8832),X8833))),X8831)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq2])])). 6.97/7.22 fof(c_0_7050, plain, ![X8442, X8443, X8444]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8444),X8443))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X8442),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X8443),X8444)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X8442),X8444)),hAPP(c_Nat_OSuc,X8443))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__Suc__diff__eq1])])])). 6.97/7.22 fof(c_0_7051, plain, ![X8204, X8205]:(~c_Relation_Osym(X8205,X8204)|(~c_Relation_Otrans(X8205,X8204)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X8205,X8205),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X8205,X8205,X8205),hAPP(c_Relation_Oconverse(X8205,X8205),X8204)),X8204)),X8204)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sym__trans__comp__subset])])])). 6.97/7.22 fof(c_0_7052, plain, ![X1261, X1262, X1263]:(~c_Relation_Orefl__on(X1263,X1262,X1261)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1263,X1263),tc_HOL_Obool)),X1261),hAPP(hAPP(c_Relation_Orel__comp(X1263,X1263,X1263),hAPP(c_Relation_Oconverse(X1263,X1263),X1261)),X1261)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_refl__on__comp__subset])])])). 6.97/7.22 fof(c_0_7053, plain, ![X10051, X10052, X10053]:(~class_Int_Onumber__ring(X10053)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10053),hAPP(c_Int_Onumber__class_Onumber__of(X10053),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X10052))),X10051)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10053),hAPP(c_Groups_Ouminus__class_Ouminus(X10053),hAPP(c_Int_Onumber__class_Onumber__of(X10053),X10052))),X10051)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__number__of__mult])])])). 6.97/7.22 fof(c_0_7054, plain, ![X4646, X4647, X4648, X4649, X4650]:(~class_Groups_Oordered__cancel__ab__semigroup__add(X4650)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4650),X4649),X4648))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4650),X4647),X4646))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4650),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4650),X4649),X4647)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4650),X4648),X4646)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__strict__mono])])])). 6.97/7.22 fof(c_0_7055, plain, ![X8624, X8625, X8626, X8627, X8628]:(~class_Groups_Oordered__cancel__ab__semigroup__add(X8628)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8628),X8627),X8626))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8628),X8625),X8624))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8628),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8628),X8627),X8625)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8628),X8626),X8624)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__le__less__mono])])])). 6.97/7.22 fof(c_0_7056, plain, ![X12731, X12732, X12733, X12734, X12735]:(~class_Groups_Oordered__cancel__ab__semigroup__add(X12735)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12735),X12734),X12733))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12735),X12732),X12731))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12735),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12735),X12734),X12732)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12735),X12733),X12731)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__le__mono])])). 6.97/7.22 fof(c_0_7057, plain, ![X10107, X10108, X10109, X10110, X10111]:(~class_Groups_Oordered__ab__semigroup__add(X10111)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10111),X10110),X10109))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10111),X10108),X10107))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10111),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10111),X10110),X10108)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10111),X10109),X10107)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__mono])])])). 6.97/7.22 fof(c_0_7058, plain, ![X4870, X4871, X4872, X4873, X4874]:(~class_Lattices_Osemilattice__inf(X4874)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4874),X4873),X4872))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4874),X4871),X4870))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4874),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4874),X4873),X4871)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4874),X4872),X4870)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__mono])])])). 6.97/7.22 fof(c_0_7059, plain, ![X5856, X5857, X5858, X5859]:(~class_Rings_Olinordered__semidom(X5859)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5859),X5858),X5857))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5859),c_Groups_Ozero__class_Ozero(X5859)),X5858))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5859),hAPP(hAPP(c_Power_Opower__class_Opower(X5859),X5858),X5856)),hAPP(hAPP(c_Power_Opower__class_Opower(X5859),X5857),X5856)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__mono])])])). 6.97/7.22 fof(c_0_7060, plain, ![X6126, X6127, X6128, X6129]:(~class_Fields_Olinordered__field__inverse__zero(X6129)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6129),X6128),X6127))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6129),c_Groups_Ozero__class_Ozero(X6129)),X6126))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6129),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6129),X6128),X6126)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6129),X6127),X6126)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__right__mono])])). 6.97/7.22 fof(c_0_7061, plain, ![X691, X692, X693, X694, X695]:(~class_Lattices_Osemilattice__sup(X695)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X695),X694),X693))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X695),X692),X691))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X695),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X695),X694),X692)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X695),X693),X691)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__mono])])). 6.97/7.22 fof(c_0_7062, plain, ![X6606, X6607, X6608, X6609]:((hBOOL(hAPP(hAPP(c_member(X6609),X6608),X6607))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6609,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X6609),X6608),X6606)),X6607)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6609,tc_HOL_Obool)),X6606),X6607))&(~hBOOL(hAPP(hAPP(c_member(X6609),X6608),X6607))|hAPP(hAPP(c_Set_Oinsert(X6609),X6608),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6609,tc_HOL_Obool)),X6606),X6607))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6609,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X6609),X6608),X6606)),X6607))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__insert__left])])])). 6.97/7.22 fof(c_0_7063, plain, ![X9180, X9181, X9182]:(~class_Groups_Oab__semigroup__mult(X9182)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9182),X9181))|(hBOOL(hAPP(hAPP(c_member(X9182),X9180),X9181))|hAPP(hAPP(c_Finite__Set_Ofold(X9182,X9182,c_Groups_Otimes__class_Otimes(X9182)),X9180),X9181)=hAPP(c_Finite__Set_Ofold1(X9182,c_Groups_Otimes__class_Otimes(X9182)),hAPP(hAPP(c_Set_Oinsert(X9182),X9180),X9181))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__eq__fold])])])). 6.97/7.22 cnf(c_0_7064, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)=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),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_5102])). 6.97/7.22 fof(c_0_7065, plain, ![X12736, X12737, X12738, X12739]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12739),hAPP(hAPP(c_Power_Opower__class_Opower(X12739),X12738),X12737)),hAPP(hAPP(c_Power_Opower__class_Opower(X12739),X12738),X12736)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12737),X12736))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12739),c_Groups_Oone__class_Oone(X12739)),X12738))|~class_Rings_Olinordered__semidom(X12739))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12737),X12736))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12739),hAPP(hAPP(c_Power_Opower__class_Opower(X12739),X12738),X12737)),hAPP(hAPP(c_Power_Opower__class_Opower(X12739),X12738),X12736)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12739),c_Groups_Oone__class_Oone(X12739)),X12738))|~class_Rings_Olinordered__semidom(X12739))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff])])])). 6.97/7.22 fof(c_0_7066, plain, ![X6657, X6658, X6659, X6660]:(~class_Rings_Olinordered__semidom(X6660)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6659),X6658))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6660),c_Groups_Oone__class_Oone(X6660)),X6657))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6660),hAPP(hAPP(c_Power_Opower__class_Opower(X6660),X6657),X6659)),hAPP(hAPP(c_Power_Opower__class_Opower(X6660),X6657),X6658)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__increasing])])])). 6.97/7.22 fof(c_0_7067, plain, ![X11017, X11018, X11019, X11020]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11018),X11017))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11020),hAPP(hAPP(c_Power_Opower__class_Opower(X11020),X11019),X11018)),hAPP(hAPP(c_Power_Opower__class_Opower(X11020),X11019),X11017)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11020),c_Groups_Oone__class_Oone(X11020)),X11019))|~class_Rings_Olinordered__semidom(X11020))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11020),hAPP(hAPP(c_Power_Opower__class_Opower(X11020),X11019),X11018)),hAPP(hAPP(c_Power_Opower__class_Opower(X11020),X11019),X11017)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11018),X11017))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11020),c_Groups_Oone__class_Oone(X11020)),X11019))|~class_Rings_Olinordered__semidom(X11020))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing__iff])])])). 6.97/7.22 fof(c_0_7068, plain, ![X3017, X3018, X3019, X3020, X3022]:(((hBOOL(hAPP(X3017,esk99_4(X3017,X3018,X3019,X3020)))|~hBOOL(hAPP(X3018,X3022))|hBOOL(hAPP(X3018,esk98_4(X3017,X3018,X3019,X3020)))|~c_Equiv__Relations_Oequivp(X3020,X3019))&(hBOOL(hAPP(hAPP(c_member(X3020),esk99_4(X3017,X3018,X3019,X3020)),c_Quotient_ORespects(X3020,X3019)))|~hBOOL(hAPP(X3018,X3022))|hBOOL(hAPP(X3018,esk98_4(X3017,X3018,X3019,X3020)))|~c_Equiv__Relations_Oequivp(X3020,X3019)))&((hBOOL(hAPP(X3017,esk99_4(X3017,X3018,X3019,X3020)))|~hBOOL(hAPP(X3018,X3022))|~hBOOL(hAPP(X3017,esk98_4(X3017,X3018,X3019,X3020)))|~c_Equiv__Relations_Oequivp(X3020,X3019))&(hBOOL(hAPP(hAPP(c_member(X3020),esk99_4(X3017,X3018,X3019,X3020)),c_Quotient_ORespects(X3020,X3019)))|~hBOOL(hAPP(X3018,X3022))|~hBOOL(hAPP(X3017,esk98_4(X3017,X3018,X3019,X3020)))|~c_Equiv__Relations_Oequivp(X3020,X3019)))), 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_bex__reg__right])])])])])])). 6.97/7.22 cnf(c_0_7069, plain, (X6=hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3)),X6))|hAPP(c_Set_Oimage(X1,X2,X3),X4)!=X5|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X6),X5))), inference(split_conjunct,[status(thm)],[c_0_5158])). 6.97/7.22 fof(c_0_7070, plain, ![X10895, X10896, X10897]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10897),hAPP(c_Int_Onumber__class_Onumber__of(X10897),X10896)),hAPP(c_Int_Onumber__class_Onumber__of(X10897),X10895)))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X10897),hAPP(c_Int_Onumber__class_Onumber__of(X10897),X10896)),hAPP(c_Int_Onumber__class_Onumber__of(X10897),X10895))=hAPP(c_Int_Onumber__class_Onumber__of(X10897),X10895)|(~class_Int_Onumber(X10897)|~class_Orderings_Oord(X10897)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10897),hAPP(c_Int_Onumber__class_Onumber__of(X10897),X10896)),hAPP(c_Int_Onumber__class_Onumber__of(X10897),X10895)))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X10897),hAPP(c_Int_Onumber__class_Onumber__of(X10897),X10896)),hAPP(c_Int_Onumber__class_Onumber__of(X10897),X10895))=hAPP(c_Int_Onumber__class_Onumber__of(X10897),X10896)|(~class_Int_Onumber(X10897)|~class_Orderings_Oord(X10897)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_max__number__of])])])])). 6.97/7.22 fof(c_0_7071, plain, ![X11694, X11695, X11696, X11697]:(~class_Fields_Olinordered__field__inverse__zero(X11697)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11697),X11696),X11695))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11697),X11694),c_Groups_Ozero__class_Ozero(X11697)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11697),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11697),X11695),X11694)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11697),X11696),X11694)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__right__mono__neg])])). 6.97/7.22 fof(c_0_7072, plain, ![X9885, X9886, X9887, X9888]:(~class_Groups_Oordered__ab__semigroup__add__imp__le(X9888)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X9888),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9888),X9887),X9885)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9888),X9886),X9885))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9888),hAPP(hAPP(c_Orderings_Oord__class_Omax(X9888),X9887),X9886)),X9885)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__add__distrib__left])])). 6.97/7.22 fof(c_0_7073, plain, ![X6853, X6854, X6855, X6856]:(~class_Rings_Odivision__ring(X6856)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6856),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6856),X6855),X6853)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6856),X6854),X6853))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6856),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6856),X6855),X6854)),X6853)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__divide__distrib])])])). 6.97/7.22 cnf(c_0_7074, 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_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5159, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.22 cnf(c_0_7075, 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_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5160, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.22 cnf(c_0_7076, 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_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5161, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.22 cnf(c_0_7077, 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_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5162, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.22 fof(c_0_7078, plain, ![X11208, X11209, X11210]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11210),hAPP(c_Int_Onumber__class_Onumber__of(X11210),X11209)),hAPP(c_Int_Onumber__class_Onumber__of(X11210),X11208)))|hAPP(c_Int_Onumber__class_Onumber__of(X11210),X11209)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X11210),hAPP(c_Int_Onumber__class_Onumber__of(X11210),X11209)),hAPP(c_Int_Onumber__class_Onumber__of(X11210),X11208))|(~class_Orderings_Oord(X11210)|~class_Int_Onumber(X11210)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11210),hAPP(c_Int_Onumber__class_Onumber__of(X11210),X11209)),hAPP(c_Int_Onumber__class_Onumber__of(X11210),X11208)))|hAPP(c_Int_Onumber__class_Onumber__of(X11210),X11208)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X11210),hAPP(c_Int_Onumber__class_Onumber__of(X11210),X11209)),hAPP(c_Int_Onumber__class_Onumber__of(X11210),X11208))|(~class_Orderings_Oord(X11210)|~class_Int_Onumber(X11210)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__number__of])])])])). 6.97/7.22 fof(c_0_7079, plain, ![X17549, X17550, X17551, X17552]:(~class_Lattices_Odistrib__lattice(X17552)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17552),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17552),X17551),X17549)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17552),X17550),X17549))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17552),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17552),X17551),X17550)),X17549)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__inf__distrib2])])). 6.97/7.22 fof(c_0_7080, plain, ![X3410, X3411, X3412, X3413]:(~class_Groups_Oordered__ab__group__add(X3413)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3413),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3413),X3412),X3411)),X3410)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X3413),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3413),X3412),X3410)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3413),X3411),X3410))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__diff__distrib__left])])). 6.97/7.22 fof(c_0_7081, plain, ![X1073, X1074, X1075, X1076]:(~class_Groups_Oordered__ab__group__add(X1076)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1076),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1076),X1075),X1074)),X1073)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1076),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1076),X1075),X1073)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1076),X1074),X1073))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__diff__distrib__left])])). 6.97/7.22 fof(c_0_7082, plain, ![X5656, X5657, X5658, X5659]:(~class_Groups_Oordered__ab__semigroup__add__imp__le(X5659)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5659),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5659),X5658),X5657)),X5656)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X5659),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5659),X5658),X5656)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5659),X5657),X5656))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__add__distrib__left])])). 6.97/7.22 fof(c_0_7083, plain, ![X3293, X3294, X3295]:(~class_Divides_Osemiring__div(X3295)|(c_Groups_Ozero__class_Ozero(X3295)=X3294|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X3295),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3295),X3294),X3293)),X3294)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3295),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X3295),X3293),X3294)),c_Groups_Oone__class_Oone(X3295)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__add__self1])])])). 6.97/7.22 fof(c_0_7084, plain, ![X9253, X9254, X9255, X9256]:(~class_Lattices_Odistrib__lattice(X9256)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X9256),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X9256),X9255),X9254)),X9253)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X9256),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X9256),X9255),X9253)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X9256),X9254),X9253))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__sup__distrib2])])])). 6.97/7.22 fof(c_0_7085, plain, ![X12290, X12291, X12292, X12293]:(~class_Rings_Ocomm__semiring(X12293)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12293),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12293),X12292),X12291)),X12290)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12293),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12293),X12292),X12290)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12293),X12291),X12290))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__class_Odistrib])])). 6.97/7.22 fof(c_0_7086, plain, ![X3892, X3893, X3894, X3895]:(~class_Rings_Ocomm__semiring__1(X3895)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3895),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3895),X3894),X3892)),X3893)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3895),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3895),X3894),X3893)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3895),X3892),X3893))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J])])])). 6.97/7.22 fof(c_0_7087, plain, ![X12852, X12853, X12854, X12855]:(~class_Rings_Odivision__ring(X12855)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12855),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X12855),X12854),X12853)),X12852)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X12855),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12855),X12854),X12852)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12855),X12853),X12852))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__divide__distrib])])). 6.97/7.22 fof(c_0_7088, plain, ![X15593, X15594, X15595, X15596, X15597, X15598, X15599, X15601, X15602, X15603, X15604, X15605, X15606, X15607, X15608]:(((hBOOL(hAPP(hAPP(c_member(X15599),esk526_7(X15593,X15594,X15595,X15596,X15597,X15598,X15599)),X15596))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X15599,tc_fun(X15598,tc_fun(X15597,tc_HOL_Obool))),X15596),X15595),X15594),X15593)))&(~hBOOL(hAPP(hAPP(hAPP(X15595,esk526_7(X15593,X15594,X15595,X15596,X15597,X15598,X15599)),X15594),X15593))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X15599,tc_fun(X15598,tc_fun(X15597,tc_HOL_Obool))),X15596),X15595),X15594),X15593))))&(~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X15607,tc_fun(X15606,tc_fun(X15605,tc_HOL_Obool))),X15604),X15603),X15602),X15601))|(~hBOOL(hAPP(hAPP(c_member(X15607),X15608),X15604))|hBOOL(hAPP(hAPP(hAPP(X15603,X15608),X15602),X15601))))), 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_INF2__iff])])])])])])])). 6.97/7.22 fof(c_0_7089, plain, ![X1447, X1448, X1449, X1450, X1451, X1452]:(~hBOOL(hAPP(hAPP(c_member(X1452),X1451),X1450))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X1452,X1449)),hAPP(hAPP(c_Product__Type_OPair(X1452,X1449),X1451),X1448)),X1447))|hBOOL(hAPP(hAPP(c_member(X1449),X1448),hAPP(c_Relation_OImage(X1452,X1449,X1447),X1450))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__ImageI])])). 6.97/7.22 fof(c_0_7090, plain, ![X17482, X17483, X17484, X17485, X17486]:(~c_Finite__Set_Ofun__left__comm(X17486,X17485,X17484)|hAPP(c_Fun_Ocomp(X17485,X17485,X17485,hAPP(X17484,X17483)),hAPP(X17484,X17482))=hAPP(c_Fun_Ocomp(X17485,X17485,X17485,hAPP(X17484,X17482)),hAPP(X17484,X17483))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__comp__comm])])). 6.97/7.22 fof(c_0_7091, plain, ![X12321, X12322, X12323, X12324, X12325, X12326, X12327]:((hBOOL(hAPP(hAPP(c_member(X12327),esk409_7(X12321,X12322,X12323,X12324,X12325,X12326,X12327)),X12326))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12327,tc_fun(X12322,tc_fun(X12321,tc_HOL_Obool))),X12326),X12325),X12324),X12323)))&(~hBOOL(hAPP(hAPP(hAPP(X12325,esk409_7(X12321,X12322,X12323,X12324,X12325,X12326,X12327)),X12324),X12323))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12327,tc_fun(X12322,tc_fun(X12321,tc_HOL_Obool))),X12326),X12325),X12324),X12323)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF2__I])])])])). 6.97/7.22 fof(c_0_7092, plain, ![X13216, X13217, X13218]:(~class_Divides_Osemiring__div(X13218)|(X13217=c_Groups_Ozero__class_Ozero(X13218)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X13218),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13218),X13216),X13217)),X13217)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13218),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X13218),X13216),X13217)),c_Groups_Oone__class_Oone(X13218)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__add__self2])])])). 6.97/7.22 fof(c_0_7093, plain, ![X9079, X9080, X9081, X9082]:(~c_Fun_Oinj__on(X9082,X9081,X9080,c_Orderings_Otop__class_Otop(tc_fun(X9082,tc_HOL_Obool)))|c_Fun_Oinj__on(X9082,tc_fun(X9079,X9081),hAPP(hAPP(c_COMBB(X9081,tc_fun(X9079,X9081),X9082),c_COMBK(X9081,X9079)),X9080),c_Orderings_Otop__class_Otop(tc_fun(X9082,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__fun])])])). 6.97/7.22 fof(c_0_7094, plain, ![X13299, X13300, X13301, X13302, X13303]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk436_5(X13299,X13300,X13301,X13302,X13303)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13303)),X13302)))|c_List_Olist__all2(X13303,X13301,X13299,X13302,X13300)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13301)),X13300)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13303)),X13302))&(~hBOOL(hAPP(hAPP(X13299,hAPP(hAPP(c_List_Onth(X13303),X13302),esk436_5(X13299,X13300,X13301,X13302,X13303))),hAPP(hAPP(c_List_Onth(X13301),X13300),esk436_5(X13299,X13300,X13301,X13302,X13303))))|c_List_Olist__all2(X13303,X13301,X13299,X13302,X13300)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13301)),X13300)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13303)),X13302))), 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])])])])])). 6.97/7.22 fof(c_0_7095, plain, ![X859, X860, X861]:(~class_Rings_Olinordered__idom(X861)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X861),c_Groups_Ozero__class_Ozero(X861)),X860))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X861),c_Groups_Ozero__class_Ozero(X861)),X859))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X861),X859),c_Groups_Oone__class_Oone(X861)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X861),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X861),X860),X859)),X860)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__right__le__one__le])])])). 6.97/7.22 fof(c_0_7096, plain, ![X12342, X12343, X12344]:(~class_Rings_Olinordered__idom(X12344)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12344),c_Groups_Ozero__class_Ozero(X12344)),X12343))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12344),c_Groups_Ozero__class_Ozero(X12344)),X12342))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12344),X12342),c_Groups_Oone__class_Oone(X12344)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12344),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12344),X12342),X12343)),X12343)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__left__le__one__le])])])). 6.97/7.22 fof(c_0_7097, plain, ![X8998, X8999, X9000, X9001, X9002]:((hBOOL(hAPP(hAPP(c_member(X9002),esk295_5(X8998,X8999,X9000,X9001,X9002)),X8999))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X9002,X9001)),X9000),hAPP(hAPP(c_Product__Type_OSigma(X9002,X9001),X8999),X8998))))&((hBOOL(hAPP(hAPP(c_member(X9001),esk296_5(X8998,X8999,X9000,X9001,X9002)),hAPP(X8998,esk295_5(X8998,X8999,X9000,X9001,X9002))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X9002,X9001)),X9000),hAPP(hAPP(c_Product__Type_OSigma(X9002,X9001),X8999),X8998))))&(X9000=hAPP(hAPP(c_Product__Type_OPair(X9002,X9001),esk295_5(X8998,X8999,X9000,X9001,X9002)),esk296_5(X8998,X8999,X9000,X9001,X9002))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X9002,X9001)),X9000),hAPP(hAPP(c_Product__Type_OSigma(X9002,X9001),X8999),X8998)))))), 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])])])])])). 6.97/7.22 cnf(c_0_7098, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|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_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)))), inference(split_conjunct,[status(thm)],[c_0_5163])). 6.97/7.22 fof(c_0_7099, plain, ![X2778, X2779, X2780, X2781, X2782, X2784, X2785, X2786, X2787, X2788, X2789]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk89_5(X2778,X2779,X2780,X2781,X2782)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2782)),X2779)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2781)),X2778)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2782)),X2779)|c_List_Olist__all2(X2782,X2781,X2780,X2779,X2778))&(~hBOOL(hAPP(hAPP(X2780,hAPP(hAPP(c_List_Onth(X2782),X2779),esk89_5(X2778,X2779,X2780,X2781,X2782))),hAPP(hAPP(c_List_Onth(X2781),X2778),esk89_5(X2778,X2779,X2780,X2781,X2782))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2781)),X2778)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2782)),X2779)|c_List_Olist__all2(X2782,X2781,X2780,X2779,X2778)))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2789),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2788)),X2785)))|hBOOL(hAPP(hAPP(X2786,hAPP(hAPP(c_List_Onth(X2788),X2785),X2789)),hAPP(hAPP(c_List_Onth(X2787),X2784),X2789)))|~c_List_Olist__all2(X2788,X2787,X2786,X2785,X2784))&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2787)),X2784)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2788)),X2785)|~c_List_Olist__all2(X2788,X2787,X2786,X2785,X2784)))), 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])])])])])])])). 6.97/7.22 fof(c_0_7100, plain, ![X10610, X10611, X10612, X10613, X10614, X10616]:(((hBOOL(hAPP(hAPP(c_member(X10613),esk349_5(X10610,X10611,X10612,X10613,X10614)),X10612))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10614),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10613,X10614),X10612),X10611)),X10610))|(~class_Orderings_Olinorder(X10614)|~class_Complete__Lattice_Ocomplete__lattice(X10614)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10614),hAPP(X10611,esk349_5(X10610,X10611,X10612,X10613,X10614))),X10610))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10614),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10613,X10614),X10612),X10611)),X10610))|(~class_Orderings_Olinorder(X10614)|~class_Complete__Lattice_Ocomplete__lattice(X10614))))&(~hBOOL(hAPP(hAPP(c_member(X10613),X10616),X10612))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10614),hAPP(X10611,X10616)),X10610))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10614),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10613,X10614),X10612),X10611)),X10610))|(~class_Orderings_Olinorder(X10614)|~class_Complete__Lattice_Ocomplete__lattice(X10614)))), 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])])])])])). 6.97/7.22 fof(c_0_7101, plain, ![X3928, X3929, X3930, X3931, X3932, X3934]:(((hBOOL(hAPP(hAPP(c_member(X3930),esk133_5(X3928,X3929,X3930,X3931,X3932)),X3929))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3932),X3931),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3930,X3932),X3929),X3928)))|(~class_Complete__Lattice_Ocomplete__lattice(X3932)|~class_Orderings_Olinorder(X3932)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3932),X3931),hAPP(X3928,esk133_5(X3928,X3929,X3930,X3931,X3932))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3932),X3931),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3930,X3932),X3929),X3928)))|(~class_Complete__Lattice_Ocomplete__lattice(X3932)|~class_Orderings_Olinorder(X3932))))&(~hBOOL(hAPP(hAPP(c_member(X3930),X3934),X3929))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3932),X3931),hAPP(X3928,X3934)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3932),X3931),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3930,X3932),X3929),X3928)))|(~class_Complete__Lattice_Ocomplete__lattice(X3932)|~class_Orderings_Olinorder(X3932)))), 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_less__SUP__iff])])])])])])). 6.97/7.22 fof(c_0_7102, plain, ![X14399, X14400, X14401, X14402]:(~class_Orderings_Olinorder(X14402)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14402),X14401),X14400))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14402),X14400),X14399))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14402,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X14402,X14401,X14400)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X14402,X14400),X14399))=c_SetInterval_Oord__class_OgreaterThanLessThan(X14402,X14401,X14399)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I15_J])])])). 6.97/7.22 fof(c_0_7103, plain, ![X6701, X6702, X6703]:(~class_Rings_Olinordered__ring(X6703)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6703),c_Groups_Ozero__class_Ozero(X6703)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6703),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6703),X6702),X6702)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6703),X6701),X6701))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__ge__zero])])). 6.97/7.22 fof(c_0_7104, plain, ![X12999, X13000, X13001]:(~class_Rings_Ocomm__semiring__1(X13001)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13001),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13001),X13000),c_Groups_Oone__class_Oone(X13001))),X12999)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13001),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13001),X13000),X12999)),X12999)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J])])])). 6.97/7.22 fof(c_0_7105, plain, ![X15199, X15200, X15201, X15202, X15203]:(~class_Rings_Ocomm__semiring__1(X15203)|(~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X15203),X15202),X15201))|(~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X15203),X15200),X15199))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X15203),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15203),X15202),X15200)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15203),X15201),X15199)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__dvd__mono])])])). 6.97/7.22 fof(c_0_7106, plain, ![X14128, X14129, X14130, X14131]:(~class_Orderings_Olinorder(X14131)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14131),X14130),X14129))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14131),X14129),X14128))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14131,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X14131,X14130),X14129)),c_SetInterval_Oord__class_OatLeastAtMost(X14131,X14129,X14128))=c_SetInterval_Oord__class_OatLeastAtMost(X14131,X14130,X14128)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I21_J])])])). 6.97/7.22 fof(c_0_7107, plain, ![X5293, X5294, X5295, X5296, X5297, X5298, X5299]:(~c_Finite__Set_Ofolding__idem(X5299,X5298,X5297,X5296)|hAPP(c_Fun_Ocomp(X5298,X5298,X5295,hAPP(X5297,X5294)),hAPP(c_Fun_Ocomp(X5298,X5298,X5295,hAPP(X5297,X5294)),X5293))=hAPP(c_Fun_Ocomp(X5298,X5298,X5295,hAPP(X5297,X5294)),X5293)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oidem__left__comp])])). 6.97/7.22 cnf(c_0_7108, 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))|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__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X5,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_4980])). 6.97/7.22 fof(c_0_7109, plain, ![X12790, X12791, X12792, X12793, X12794]:(~class_Orderings_Olinorder(X12794)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12794),X12793),X12792))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12794),X12791),X12790))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12794),hAPP(hAPP(c_Orderings_Oord__class_Omax(X12794),X12793),X12791)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X12794),X12792),X12790)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup__mono])])])). 6.97/7.22 fof(c_0_7110, plain, ![X4712, X4713, X4714, X4715, X4716]:(~class_Orderings_Olinorder(X4716)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4716),X4715),X4714))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4716),X4713),X4712))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4716),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4716),X4715),X4713)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4716),X4714),X4712)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oinf__mono])])])). 6.97/7.22 fof(c_0_7111, plain, ![X16340, X16341, X16342, X16343]:(~class_Orderings_Olinorder(X16343)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X16343),hAPP(hAPP(c_Orderings_Oord__class_Omax(X16343),X16342),X16340)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X16343),X16341),X16340))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X16343),hAPP(hAPP(c_Orderings_Oord__class_Omin(X16343),X16342),X16341)),X16340)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup__inf__distrib2])])])). 6.97/7.22 fof(c_0_7112, plain, ![X13714, X13715, X13716, X13717]:(~class_Rings_Ocomm__semiring__1(X13717)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13717),hAPP(hAPP(c_Power_Opower__class_Opower(X13717),X13716),X13714)),hAPP(hAPP(c_Power_Opower__class_Opower(X13717),X13715),X13714))=hAPP(hAPP(c_Power_Opower__class_Opower(X13717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13717),X13716),X13715)),X13714)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J])])). 6.97/7.22 fof(c_0_7113, plain, ![X2733, X2734, X2735, X2736]:(~class_Orderings_Olinorder(X2736)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X2736),hAPP(hAPP(c_Orderings_Oord__class_Omax(X2736),X2735),X2734)),X2733)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X2736),hAPP(hAPP(c_Orderings_Oord__class_Omin(X2736),X2735),X2733)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X2736),X2734),X2733))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__distrib2])])). 6.97/7.22 cnf(c_0_7114, 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)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),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),X1),X3))|~hBOOL(hAPP(X5,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4,X1)))), inference(split_conjunct,[status(thm)],[c_0_4980])). 6.97/7.22 fof(c_0_7115, plain, ![X11180, X11181, X11182, X11183, X11184, X11185]:(~c_Fun_Oinj__on(X11185,X11184,X11183,X11182)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11184,tc_HOL_Obool)),hAPP(c_Set_Oimage(X11185,X11184,X11183),X11182)),X11181))|(~c_Fun_Oinj__on(X11184,X11185,X11180,X11181)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11185,tc_HOL_Obool)),hAPP(c_Set_Oimage(X11184,X11185,X11180),X11181)),X11182))|c_Fun_Obij__betw(X11185,X11184,esk372_6(X11180,X11181,X11182,X11183,X11184,X11185),X11182,X11181))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Cantor__Bernstein])])])])). 6.97/7.22 fof(c_0_7116, plain, ![X801, X802, X803, X804]:(~class_Groups_Ocomm__monoid__mult(X804)|hAPP(hAPP(c_Power_Opower__class_Opower(X804),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X804),X803),X802)),X801)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X804),hAPP(hAPP(c_Power_Opower__class_Opower(X804),X803),X801)),hAPP(hAPP(c_Power_Opower__class_Opower(X804),X802),X801))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__mult__distrib])])])). 6.97/7.22 fof(c_0_7117, plain, ![X6624, X6625, X6626, X6627]:(~class_Fields_Ofield__inverse__zero(X6627)|hAPP(hAPP(c_Power_Opower__class_Opower(X6627),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6627),X6626),X6625)),X6624)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6627),hAPP(hAPP(c_Power_Opower__class_Opower(X6627),X6626),X6624)),hAPP(hAPP(c_Power_Opower__class_Opower(X6627),X6625),X6624))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__divide])])). 6.97/7.22 fof(c_0_7118, plain, ![X5426, X5427, X5428]:((~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,X5428)),X5427)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X5428)),X5426)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5427),X5426)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5427),X5426))|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,X5428)),X5427)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X5428)),X5426))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__less__cancel1])])). 6.97/7.22 cnf(c_0_7119, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk360_3(X1,X2,X3))),esk361_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_5164])). 6.97/7.22 fof(c_0_7120, plain, ![X3602, X3603, X3604, X3605, X3606, X3608, X3609, X3610, X3611, X3612, X3613]:(((hBOOL(hAPP(hAPP(c_member(X3606),esk117_5(X3602,X3603,X3604,X3605,X3606)),hAPP(c_List_Oset(X3606),X3603)))|hAPP(hAPP(c_List_Omap(X3606,X3605),X3602),X3603)=hAPP(hAPP(c_List_Omap(X3606,X3605),X3604),X3603))&(hAPP(X3604,esk117_5(X3602,X3603,X3604,X3605,X3606))!=hAPP(X3602,esk117_5(X3602,X3603,X3604,X3605,X3606))|hAPP(hAPP(c_List_Omap(X3606,X3605),X3602),X3603)=hAPP(hAPP(c_List_Omap(X3606,X3605),X3604),X3603)))&(hAPP(hAPP(c_List_Omap(X3612,X3611),X3608),X3609)!=hAPP(hAPP(c_List_Omap(X3612,X3611),X3610),X3609)|(~hBOOL(hAPP(hAPP(c_member(X3612),X3613),hAPP(c_List_Oset(X3612),X3609)))|hAPP(X3610,X3613)=hAPP(X3608,X3613)))), 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])])])])])])). 6.97/7.22 fof(c_0_7121, plain, ![X10520, X10521, X10522, X10523, X10524, X10525]:(~c_Finite__Set_Ofolding__idem(X10525,X10524,X10523,X10522)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10525),X10521))|hAPP(X10522,hAPP(hAPP(c_Set_Oinsert(X10525),X10520),X10521))=hAPP(c_Fun_Ocomp(X10524,X10524,X10524,hAPP(X10522,X10521)),hAPP(X10523,X10520)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__idem_Oinsert__idem])])])). 6.97/7.22 fof(c_0_7122, plain, ![X9287, X9288, X9289, X9290]:(~class_Orderings_Olinorder(X9290)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X9290),hAPP(hAPP(c_Orderings_Oord__class_Omax(X9290),X9289),X9288)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X9290),X9289),X9287))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X9290),X9289),hAPP(hAPP(c_Orderings_Oord__class_Omin(X9290),X9288),X9287))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__distrib1])])). 6.97/7.22 fof(c_0_7123, plain, ![X14020, X14021, X14022, X14023, X14025, X14026, X14027, X14030]:(((~hBOOL(hAPP(hAPP(c_member(tc_prod(X14021,X14021)),hAPP(hAPP(c_Product__Type_OPair(X14021,X14021),X14025),esk472_3(X14020,X14021,X14022))),X14020))|~hBOOL(hAPP(hAPP(c_member(X14021),X14025),X14022))|~hBOOL(hAPP(hAPP(c_member(X14021),X14023),X14022))|~c_Wellfounded_Owf(X14021,X14020))&(hBOOL(hAPP(hAPP(c_member(X14021),esk472_3(X14020,X14021,X14022)),X14022))|~hBOOL(hAPP(hAPP(c_member(X14021),X14023),X14022))|~c_Wellfounded_Owf(X14021,X14020)))&((hBOOL(hAPP(hAPP(c_member(X14027),esk474_2(X14026,X14027)),esk473_2(X14026,X14027)))|c_Wellfounded_Owf(X14027,X14026))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X14027,X14027)),hAPP(hAPP(c_Product__Type_OPair(X14027,X14027),esk475_3(X14026,X14027,X14030)),X14030)),X14026))|~hBOOL(hAPP(hAPP(c_member(X14027),X14030),esk473_2(X14026,X14027)))|c_Wellfounded_Owf(X14027,X14026))&(hBOOL(hAPP(hAPP(c_member(X14027),esk475_3(X14026,X14027,X14030)),esk473_2(X14026,X14027)))|~hBOOL(hAPP(hAPP(c_member(X14027),X14030),esk473_2(X14026,X14027)))|c_Wellfounded_Owf(X14027,X14026))))), 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])])])])])])])). 6.97/7.22 fof(c_0_7124, plain, ![X11328, X11329, X11330, X11331]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11331,tc_HOL_Obool)),X11330),X11329))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11331,tc_HOL_Obool)),X11328),X11329))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11331,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11331,tc_HOL_Obool)),X11330),X11328)),X11329)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Un__least])])])). 6.97/7.22 fof(c_0_7125, plain, ![X5624, X5625, X5626, X5627]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5627,tc_HOL_Obool)),X5626),X5625))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5627,tc_HOL_Obool)),X5626),X5624))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5627,tc_HOL_Obool)),X5626),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5627,tc_HOL_Obool)),X5625),X5624))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__greatest])])])). 6.97/7.22 fof(c_0_7126, plain, ![X6832, X6833, X6834, X6835, X6836]:(~c_Fun_Oinj__on(X6836,X6835,X6834,c_Orderings_Otop__class_Otop(tc_fun(X6836,tc_HOL_Obool)))|X6832=hAPP(c_Fun_Ocomp(X6835,X6833,X6836,hAPP(c_Fun_Ocomp(X6836,X6833,X6835,X6832),c_Hilbert__Choice_Oinv__into(X6836,X6835,c_Orderings_Otop__class_Otop(tc_fun(X6836,tc_HOL_Obool)),X6834))),X6834)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_o__inv__o__cancel])])])). 6.97/7.22 fof(c_0_7127, plain, ![X8032, X8033, X8034, X8036, X8037]:((((hAPP(X8032,esk262_3(X8032,X8033,X8034))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8034,tc_Nat_Onat),X8032),X8033)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8034),X8033)))&(~hBOOL(hAPP(hAPP(c_member(X8034),X8036),X8033))|(X8036=esk262_3(X8032,X8033,X8034)|hAPP(X8032,X8036)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8034,tc_Nat_Onat),X8032),X8033)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8034),X8033))))&(hBOOL(hAPP(hAPP(c_member(X8034),esk262_3(X8032,X8033,X8034)),X8033))|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8034,tc_Nat_Onat),X8032),X8033)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8034),X8033))))&((hBOOL(hAPP(hAPP(c_member(X8034),esk263_4(X8032,X8033,X8034,X8037)),X8033))|hAPP(X8032,X8037)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X8034),X8037),X8033))|c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8034,tc_Nat_Onat),X8032),X8033)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8034),X8033)))&((esk263_4(X8032,X8033,X8034,X8037)!=X8037|hAPP(X8032,X8037)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X8034),X8037),X8033))|c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8034,tc_Nat_Onat),X8032),X8033)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8034),X8033)))&(hAPP(X8032,esk263_4(X8032,X8033,X8034,X8037))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(X8032,X8037)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X8034),X8037),X8033))|c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8034,tc_Nat_Onat),X8032),X8033)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8034),X8033)))))), 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])])])])])])). 6.97/7.22 fof(c_0_7128, plain, ![X5885, X5886, X5887, X5888, X5889]:((hBOOL(hAPP(hAPP(c_member(X5888),esk194_5(X5885,X5886,X5887,X5888,X5889)),X5887))|(c_Groups_Ozero__class_Ozero(X5889)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5888,X5889),X5886),X5887)|(~hBOOL(hAPP(hAPP(c_member(X5888),X5885),X5887))|c_Groups_Ozero__class_Ozero(X5889)=hAPP(X5886,X5885)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5888),X5887))|~class_Groups_Oordered__ab__group__add(X5889))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5889),c_Groups_Ozero__class_Ozero(X5889)),hAPP(X5886,esk194_5(X5885,X5886,X5887,X5888,X5889))))|(c_Groups_Ozero__class_Ozero(X5889)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5888,X5889),X5886),X5887)|(~hBOOL(hAPP(hAPP(c_member(X5888),X5885),X5887))|c_Groups_Ozero__class_Ozero(X5889)=hAPP(X5886,X5885)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5888),X5887))|~class_Groups_Oordered__ab__group__add(X5889))), 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])])])])])). 6.97/7.22 fof(c_0_7129, plain, ![X7052, X7053, X7054, X7055]:(~class_Lattices_Odistrib__lattice(X7055)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7055),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7055),X7054),X7053)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7055),X7054),X7052))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7055),X7054),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7055),X7053),X7052))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__distrib1])])). 6.97/7.22 cnf(c_0_7130, plain, (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))=X3|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X2),X1))), inference(split_conjunct,[status(thm)],[c_0_4953])). 6.97/7.22 fof(c_0_7131, plain, ![X14098, X14099, X14100, X14101, X14102]:(~class_Complete__Lattice_Ocomplete__lattice(X14102)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14101,tc_HOL_Obool)),X14100),X14099))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14102),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X14101,X14102),X14099),X14098)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X14101,X14102),X14100),X14098))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INF__subset])])])). 6.97/7.22 fof(c_0_7132, plain, ![X3335, X3336, X3337, X3338]:(~class_Orderings_Olinorder(X3338)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X3338),X3337),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3338),X3336),X3335))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X3338),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3338),X3337),X3336)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3338),X3337),X3335))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oinf__sup__distrib1])])])). 6.97/7.22 fof(c_0_7133, plain, ![X16142, X16143, X16144, X16145, X16146]:(~class_Complete__Lattice_Ocomplete__lattice(X16146)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16145,tc_HOL_Obool)),X16144),X16143))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16146),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16145,X16146),X16144),X16142)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16145,X16146),X16143),X16142))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SUP__subset])])])). 6.97/7.22 cnf(c_0_7134, 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_5165])). 6.97/7.22 cnf(c_0_7135, 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),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))|~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_5166])). 6.97/7.22 fof(c_0_7136, plain, ![X12261, X12262, X12263, X12264, X12265]:((hBOOL(hAPP(hAPP(c_member(X12264),esk408_5(X12261,X12262,X12263,X12264,X12265)),hAPP(c_List_Oset(X12264),X12263)))|hAPP(hAPP(c_List_Olist_OCons(X12264),X12261),X12263)=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X12264,X12265,X12262),X12261),X12263)|~class_Orderings_Olinorder(X12265))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12265),hAPP(X12262,X12261)),hAPP(X12262,esk408_5(X12261,X12262,X12263,X12264,X12265))))|hAPP(hAPP(c_List_Olist_OCons(X12264),X12261),X12263)=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X12264,X12265,X12262),X12261),X12263)|~class_Orderings_Olinorder(X12265))), 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])])])])])). 6.97/7.22 fof(c_0_7137, plain, ![X15268, X15269, X15270, X15271, X15272, X15273, X15274]:((~hBOOL(hAPP(hAPP(c_member(X15270),X15269),c_Wellfounded_Oacc(X15270,X15268)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X15270,X15270)),hAPP(hAPP(c_Product__Type_OPair(X15270,X15270),X15271),X15269)),X15268))|hBOOL(hAPP(hAPP(c_member(X15270),X15271),c_Wellfounded_Oacc(X15270,X15268)))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X15274,X15274)),hAPP(hAPP(c_Product__Type_OPair(X15274,X15274),esk515_3(X15272,X15273,X15274)),X15273)),X15272))|hBOOL(hAPP(hAPP(c_member(X15274),X15273),c_Wellfounded_Oacc(X15274,X15272))))&(~hBOOL(hAPP(hAPP(c_member(X15274),esk515_3(X15272,X15273,X15274)),c_Wellfounded_Oacc(X15274,X15272)))|hBOOL(hAPP(hAPP(c_member(X15274),X15273),c_Wellfounded_Oacc(X15274,X15272)))))), 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])])])])])])). 6.97/7.22 cnf(c_0_7138, 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_5077])). 6.97/7.22 fof(c_0_7139, plain, ![X8780, X8781, X8782, X8783]:(~hBOOL(hAPP(hAPP(c_member(X8783),X8782),hAPP(c_Relation_ORange(X8781,X8783),X8780)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X8781,X8783)),hAPP(hAPP(c_Product__Type_OPair(X8781,X8783),esk283_4(X8780,X8781,X8782,X8783)),X8782)),X8780))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_RangeE])])])])). 6.97/7.22 fof(c_0_7140, plain, ![X6156, X6157, X6158]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X6158,X6158)),hAPP(hAPP(c_Product__Type_OPair(X6158,X6158),esk203_3(X6156,X6157,X6158)),X6157)),X6156))|hBOOL(hAPP(hAPP(c_member(X6158),X6157),c_Wellfounded_Oacc(X6158,X6156))))&(~hBOOL(hAPP(hAPP(c_member(X6158),esk203_3(X6156,X6157,X6158)),c_Wellfounded_Oacc(X6158,X6156)))|hBOOL(hAPP(hAPP(c_member(X6158),X6157),c_Wellfounded_Oacc(X6158,X6156))))), 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])])])])])). 6.97/7.22 fof(c_0_7141, plain, ![X1002, X1003, X1004, X1005]:(~class_Rings_Ocomm__semiring__1(X1005)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1005),X1004),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1005),X1003),X1002))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1005),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1005),X1004),X1003)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1005),X1004),X1002))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J])])). 6.97/7.22 fof(c_0_7142, plain, ![X1882, X1883, X1884, X1885, X1886, X1887, X1888, X1889, X1890]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X1883,X1885)),hAPP(hAPP(c_Product__Type_OPair(X1883,X1885),X1886),X1884)),X1882))|hBOOL(hAPP(hAPP(c_member(X1885),X1884),hAPP(c_Relation_ORange(X1883,X1885),X1882))))&(~hBOOL(hAPP(hAPP(c_member(X1890),X1889),hAPP(c_Relation_ORange(X1888,X1890),X1887)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1888,X1890)),hAPP(hAPP(c_Product__Type_OPair(X1888,X1890),esk61_4(X1887,X1888,X1889,X1890)),X1889)),X1887)))), 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])])])])])). 6.97/7.22 fof(c_0_7143, plain, ![X15036, X15037, X15038, X15039]:(~hBOOL(hAPP(hAPP(c_member(X15039),X15038),hAPP(c_Relation_ODomain(X15039,X15037),X15036)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X15039,X15037)),hAPP(hAPP(c_Product__Type_OPair(X15039,X15037),X15038),esk507_4(X15036,X15037,X15038,X15039))),X15036))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_DomainE])])])])). 6.97/7.22 fof(c_0_7144, plain, ![X10195, X10196]:(~class_Groups_Oordered__ab__group__add__abs(X10196)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10196),hAPP(c_Groups_Oabs__class_Oabs(X10196),hAPP(c_List_Omonoid__add__class_Olistsum(X10196),X10195))),hAPP(c_List_Omonoid__add__class_Olistsum(X10196),hAPP(hAPP(c_List_Omap(X10196,X10196),c_Groups_Oabs__class_Oabs(X10196)),X10195))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__abs])])])). 6.97/7.22 cnf(c_0_7145, plain, (X2=hAPP(c_Set_Oimage(tc_Nat_Onat,X1,esk293_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)),esk292_2(X2,X1))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5167])). 6.97/7.22 fof(c_0_7146, plain, ![X1543, X1544, X1545]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X1545,X1545)),hAPP(hAPP(c_Product__Type_OPair(X1545,X1545),esk43_3(X1543,X1544,X1545)),X1544)),X1543))|hBOOL(hAPP(hAPP(c_member(X1545),X1544),c_Wellfounded_Oacc(X1545,X1543))))&(~hBOOL(hAPP(hAPP(c_member(X1545),esk43_3(X1543,X1544,X1545)),c_Wellfounded_Oacc(X1545,X1543)))|hBOOL(hAPP(hAPP(c_member(X1545),X1544),c_Wellfounded_Oacc(X1545,X1543))))), 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])])])])])). 6.97/7.22 fof(c_0_7147, plain, ![X4484, X4485, X4486, X4487, X4488, X4489, X4490, X4491, X4492]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X4487,X4485)),hAPP(hAPP(c_Product__Type_OPair(X4487,X4485),X4486),X4488)),X4484))|hBOOL(hAPP(hAPP(c_member(X4487),X4486),hAPP(c_Relation_ODomain(X4487,X4485),X4484))))&(~hBOOL(hAPP(hAPP(c_member(X4492),X4491),hAPP(c_Relation_ODomain(X4492,X4490),X4489)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X4492,X4490)),hAPP(hAPP(c_Product__Type_OPair(X4492,X4490),X4491),esk154_4(X4489,X4490,X4491,X4492))),X4489)))), 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])])])])])). 6.97/7.22 fof(c_0_7148, plain, ![X12740, X12741, X12742, X12743]:((~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X12743)),X12742),c_List_Olists(X12743,X12740)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X12743)),X12741),c_List_Olists(X12743,X12740)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X12743)),hAPP(hAPP(c_List_Oappend(X12743),X12742),X12741)),c_List_Olists(X12743,X12740))))&((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X12743)),X12742),c_List_Olists(X12743,X12740)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X12743)),hAPP(hAPP(c_List_Oappend(X12743),X12742),X12741)),c_List_Olists(X12743,X12740))))&(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X12743)),X12741),c_List_Olists(X12743,X12740)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X12743)),hAPP(hAPP(c_List_Oappend(X12743),X12742),X12741)),c_List_Olists(X12743,X12740)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__in__lists__conv])])])). 6.97/7.22 cnf(c_0_7149, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk360_3(X1,X2,X3))),esk361_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_5164])). 6.97/7.22 fof(c_0_7150, plain, ![X606, X607, X608, X609]:(~class_Lattices_Odistrib__lattice(X609)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X609),X608),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X609),X607),X606))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X609),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X609),X608),X607)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X609),X608),X606))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__inf__distrib1])])). 6.97/7.22 cnf(c_0_7151, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk315_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_5083])). 6.97/7.22 cnf(c_0_7152, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk249_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_5084])). 6.97/7.22 fof(c_0_7153, plain, ![X1417, X1418, X1419, X1420]:(c_Orderings_Otop__class_Otop(tc_fun(X1419,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X1420,X1419,X1418),c_Orderings_Otop__class_Otop(tc_fun(X1420,tc_HOL_Obool)))|hAPP(c_Set_Oimage(X1420,X1419,X1418),hAPP(c_Set_Oimage(X1419,X1420,c_Hilbert__Choice_Oinv__into(X1420,X1419,c_Orderings_Otop__class_Otop(tc_fun(X1420,tc_HOL_Obool)),X1418)),X1417))=X1417), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__surj__f__inv__f])])). 6.97/7.22 fof(c_0_7154, plain, ![X7755, X7756, X7757]:(~class_Groups_Oordered__ab__group__add__abs(X7757)|hAPP(c_Groups_Oabs__class_Oabs(X7757),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7757),hAPP(c_Groups_Oabs__class_Oabs(X7757),X7756)),hAPP(c_Groups_Oabs__class_Oabs(X7757),X7755)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7757),hAPP(c_Groups_Oabs__class_Oabs(X7757),X7756)),hAPP(c_Groups_Oabs__class_Oabs(X7757),X7755))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__add__abs])])])). 6.97/7.22 fof(c_0_7155, plain, ![X14125, X14126, X14127]:(~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),X14127),X14126)),X14125)),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)),X14125))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14127))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X14126),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])])])). 6.97/7.22 cnf(c_0_7156, 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_5168])). 6.97/7.22 fof(c_0_7157, plain, ![X8805, X8806, X8807]:(~class_Groups_Oab__semigroup__mult(X8807)|(c_Orderings_Obot__class_Obot(tc_fun(X8807,tc_HOL_Obool))=X8806|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8807),X8806))|(hBOOL(hAPP(hAPP(c_member(X8807),X8805),X8806))|hAPP(c_Finite__Set_Ofold1(X8807,c_Groups_Otimes__class_Otimes(X8807)),hAPP(hAPP(c_Set_Oinsert(X8807),X8805),X8806))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8807),X8805),hAPP(c_Finite__Set_Ofold1(X8807,c_Groups_Otimes__class_Otimes(X8807)),X8806)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__insert])])])). 6.97/7.22 fof(c_0_7158, plain, ![X337, X338, X339]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X339),X338))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X337))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X337),X339)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X337),X338))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmult__zless__mono2])])])). 6.97/7.22 fof(c_0_7159, plain, ![X4432, X4433, X4434, X4435]:((hBOOL(hAPP(hAPP(c_member(X4435),esk153_4(X4432,X4433,X4434,X4435)),hAPP(c_List_Oset(X4435),X4434)))|c_List_OtakeWhile(X4435,X4433,hAPP(hAPP(c_List_Oappend(X4435),X4434),X4432))=hAPP(hAPP(c_List_Oappend(X4435),X4434),c_List_OtakeWhile(X4435,X4433,X4432)))&(~hBOOL(hAPP(X4433,esk153_4(X4432,X4433,X4434,X4435)))|c_List_OtakeWhile(X4435,X4433,hAPP(hAPP(c_List_Oappend(X4435),X4434),X4432))=hAPP(hAPP(c_List_Oappend(X4435),X4434),c_List_OtakeWhile(X4435,X4433,X4432)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_takeWhile__append2])])])])). 6.97/7.22 fof(c_0_7160, plain, ![X10926, X10927, X10928, X10929]:(~class_Orderings_Olinorder(X10929)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10929),X10928),X10927))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10929),X10927),X10926))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10929,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10929,X10928,X10927)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10929,X10927,X10926))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10929,X10928),X10926)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I18_J])])). 6.97/7.22 cnf(c_0_7161, plain, (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))=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)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1))), inference(rw,[status(thm)],[c_0_5169, c_0_4565])). 6.97/7.22 fof(c_0_7162, plain, ![X10067, X10068, X10069]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10069),X10067))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10069),X10068)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10067),X10068))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10068))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10069),X10068)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10067),X10068)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10069),X10067))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10068))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10069),X10068)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10067),X10068))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2])])])). 6.97/7.22 fof(c_0_7163, plain, ![X14265, X14266, X14267]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14266),X14265))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14267),X14266)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14267),X14265)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14267)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14267),X14266)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14267),X14265)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14266),X14265))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14267)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__less__cancel1])])])). 6.97/7.22 fof(c_0_7164, plain, ![X1250, X1251, X1252, X1253, X1254]:((hAPP(hAPP(c_Set_Oinsert(X1254),X1252),X1251)=hAPP(hAPP(c_Set_Oinsert(X1254),esk38_5(X1250,X1251,X1252,X1253,X1254)),esk39_5(X1250,X1251,X1252,X1253,X1254))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1254,X1253,hAPP(hAPP(c_Set_Oinsert(X1254),X1252),X1251)),X1250)))&((hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1254,X1254,X1253,esk38_5(X1250,X1251,X1252,X1253,X1254),esk39_5(X1250,X1251,X1252,X1253,X1254)),X1250))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1254,X1253,hAPP(hAPP(c_Set_Oinsert(X1254),X1252),X1251)),X1250)))&(~hBOOL(hAPP(hAPP(c_member(X1254),esk38_5(X1250,X1251,X1252,X1253,X1254)),esk39_5(X1250,X1251,X1252,X1253,X1254)))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1254,X1253,hAPP(hAPP(c_Set_Oinsert(X1254),X1252),X1251)),X1250))))), 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])])])])])). 6.97/7.22 fof(c_0_7165, plain, ![X1052, X1053, X1054, X1055]:(~hBOOL(hAPP(hAPP(c_member(X1055),X1054),c_Wellfounded_Oacc(X1055,X1053)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X1055,X1055)),hAPP(hAPP(c_Product__Type_OPair(X1055,X1055),X1052),X1054)),c_Transitive__Closure_Ortrancl(X1055,X1053)))|hBOOL(hAPP(hAPP(c_member(X1055),X1052),c_Wellfounded_Oacc(X1055,X1053))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_acc__downwards])])])). 6.97/7.22 fof(c_0_7166, plain, ![X2879, X2880, X2881]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2881),X2880))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2879))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2881),X2879)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2880),X2879))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__mono1])])])). 6.97/7.22 fof(c_0_7167, plain, ![X3976, X3977, X3978]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3978))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3978),X3977))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3976),X3977)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3976),X3978))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__le__mono2])])). 6.97/7.22 fof(c_0_7168, plain, ![X2746, X2747, X2748]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2748),X2747))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2746),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),X2747),X2746)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2748),X2746))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono1__neg])])). 6.97/7.22 fof(c_0_7169, plain, ![X7035, X7036, X7037, X7038]:((hAPP(hAPP(c_List_Onth(X7038),X7037),X7035)!=hAPP(hAPP(c_List_Onth(X7038),X7037),X7036)|X7036=X7035|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7035),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7038)),X7037)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7036),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7038)),X7037)))|~hBOOL(hAPP(c_List_Odistinct(X7038),X7037)))&(X7036!=X7035|hAPP(hAPP(c_List_Onth(X7038),X7037),X7035)=hAPP(hAPP(c_List_Onth(X7038),X7037),X7036)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7035),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7038)),X7037)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7036),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7038)),X7037)))|~hBOOL(hAPP(c_List_Odistinct(X7038),X7037)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__eq__iff__index__eq])])])])). 6.97/7.22 fof(c_0_7170, plain, ![X15418, X15419, X15420, X15424, X15425, X15426, X15427, X15428, X15429]:(((hBOOL(hAPP(hAPP(c_member(tc_prod(X15420,X15419)),hAPP(hAPP(c_Product__Type_OPair(X15420,X15419),esk519_3(X15418,X15419,X15420)),esk520_3(X15418,X15419,X15420))),X15418))|c_Relation_Osingle__valued(X15420,X15419,X15418))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X15420,X15419)),hAPP(hAPP(c_Product__Type_OPair(X15420,X15419),esk519_3(X15418,X15419,X15420)),esk521_3(X15418,X15419,X15420))),X15418))|c_Relation_Osingle__valued(X15420,X15419,X15418))&(esk520_3(X15418,X15419,X15420)!=esk521_3(X15418,X15419,X15420)|c_Relation_Osingle__valued(X15420,X15419,X15418))))&(~c_Relation_Osingle__valued(X15426,X15425,X15424)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X15426,X15425)),hAPP(hAPP(c_Product__Type_OPair(X15426,X15425),X15427),X15428)),X15424))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X15426,X15425)),hAPP(hAPP(c_Product__Type_OPair(X15426,X15425),X15427),X15429)),X15424))|X15428=X15429)))), 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_single__valued__def])])])])])])). 6.97/7.22 fof(c_0_7171, plain, ![X13553, X13554, X13555, X13556]:(~class_Groups_Omonoid__mult(X13556)|hAPP(hAPP(c_Power_Opower__class_Opower(X13556),X13555),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13554),X13553))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13556),hAPP(hAPP(c_Power_Opower__class_Opower(X13556),X13555),X13554)),hAPP(hAPP(c_Power_Opower__class_Opower(X13556),X13555),X13553))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__add])])). 6.97/7.22 fof(c_0_7172, plain, ![X11897, X11898, X11899, X11900]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11900,tc_HOL_Obool)),X11899),X11898))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11900,tc_HOL_Obool)),X11898),X11897))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11900,tc_HOL_Obool)),X11898),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11900,tc_HOL_Obool)),X11897),X11899))=X11899)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_double__diff])])])). 6.97/7.22 fof(c_0_7173, plain, ![X7147, X7148]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7148))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7148),X7147))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X7147),X7148)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X7147),X7148)),X7148)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__div__geq])])])). 6.97/7.22 fof(c_0_7174, plain, ![X2329, X2330, X2331, X2332, X2334]:(((hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2331),X2329),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2331),esk73_3(X2329,X2330,X2331)),c_Groups_Ozero__class_Ozero(X2331))))|~hBOOL(hAPP(X2330,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2331),X2329),X2332)))|(~class_Rings_Osemiring__0(X2331)|~class_Rings_Odvd(X2331)))&(hBOOL(hAPP(X2330,esk73_3(X2329,X2330,X2331)))|~hBOOL(hAPP(X2330,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2331),X2329),X2332)))|(~class_Rings_Osemiring__0(X2331)|~class_Rings_Odvd(X2331))))&(~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2331),X2329),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2331),X2334),c_Groups_Ozero__class_Ozero(X2331))))|~hBOOL(hAPP(X2330,X2334))|hBOOL(hAPP(X2330,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2331),X2329),esk74_3(X2329,X2330,X2331))))|(~class_Rings_Osemiring__0(X2331)|~class_Rings_Odvd(X2331)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unity__coeff__ex])])])])])). 6.97/7.22 fof(c_0_7175, plain, ![X2444, X2445, X2446]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2446),X2445))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2446,X2446),tc_HOL_Obool)),X2444),hAPP(hAPP(c_Product__Type_OSigma(X2446,X2446),X2445),hAPP(c_COMBK(tc_fun(X2446,tc_HOL_Obool),X2446),X2445))))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X2446,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2446),X2445),X2444))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__quotient])])])). 6.97/7.22 fof(c_0_7176, plain, ![X499, X500, X501, X502]:((hBOOL(hAPP(hAPP(c_member(tc_fun(X501,tc_HOL_Obool)),esk8_4(X499,X500,X501,X502)),X502))|c_Fun_Oinj__on(X501,X500,X499,c_Complete__Lattice_OInf__class_OInf(tc_fun(X501,tc_HOL_Obool),X502))|c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X501,tc_HOL_Obool),tc_HOL_Obool))=X502)&(~c_Fun_Oinj__on(X501,X500,X499,esk8_4(X499,X500,X501,X502))|c_Fun_Oinj__on(X501,X500,X499,c_Complete__Lattice_OInf__class_OInf(tc_fun(X501,tc_HOL_Obool),X502))|c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X501,tc_HOL_Obool),tc_HOL_Obool))=X502)), 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])])])])])). 6.97/7.22 fof(c_0_7177, plain, ![X7133, X7134, X7135, X7136]:(~class_Rings_Ocomm__semiring__1(X7136)|hAPP(hAPP(c_Power_Opower__class_Opower(X7136),X7135),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7134),X7133))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7136),hAPP(hAPP(c_Power_Opower__class_Opower(X7136),X7135),X7134)),hAPP(hAPP(c_Power_Opower__class_Opower(X7136),X7135),X7133))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J])])])). 6.97/7.22 fof(c_0_7178, plain, ![X10508, X10509, X10510, X10511, X10512]:(~c_Relation_Orefl__on(X10512,X10511,X10510)|(~c_Relation_Orefl__on(X10512,X10509,X10508)|c_Relation_Orefl__on(X10512,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10512,tc_HOL_Obool)),X10511),X10509),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10512,X10512),tc_HOL_Obool)),X10510),X10508)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_refl__on__Int])])])). 6.97/7.22 fof(c_0_7179, plain, ![X12969, X12970, X12971, X12972, X12973]:(~c_Relation_Orefl__on(X12973,X12972,X12971)|(~c_Relation_Orefl__on(X12973,X12970,X12969)|c_Relation_Orefl__on(X12973,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12973,tc_HOL_Obool)),X12972),X12970),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X12973,X12973),tc_HOL_Obool)),X12971),X12969)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_refl__on__Un])])])). 6.97/7.22 fof(c_0_7180, plain, ![X6588, X6589, X6590]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6590))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X6589),X6588)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6590),X6589)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6590),X6588))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel1])])). 6.97/7.23 fof(c_0_7181, plain, ![X16225, X16226, X16227]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X16225),X16226))|hBOOL(hAPP(X16227,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X16226)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X16225))))|~hBOOL(hAPP(X16227,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16226),X16225)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16226),X16225))|hBOOL(hAPP(X16227,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X16227,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16226),X16225))))))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16226),X16225))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X16225),X16226))|hBOOL(hAPP(X16227,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16226),X16225)))))&(~hBOOL(hAPP(X16227,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X16225),X16226))|hBOOL(hAPP(X16227,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16226),X16225))))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16226),X16225))|~hBOOL(hAPP(X16227,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X16226)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X16225))))|hBOOL(hAPP(X16227,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16226),X16225)))))&(~hBOOL(hAPP(X16227,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X16227,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X16226)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X16225))))|hBOOL(hAPP(X16227,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16226),X16225)))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiff__int__split])])])])). 6.97/7.23 fof(c_0_7182, plain, ![X1860, X1861, X1862, X1865, X1866]:(((hBOOL(hAPP(hAPP(c_member(X1862),esk59_3(X1860,X1861,X1862)),hAPP(c_List_Oset(X1862),X1861)))|~c_List_Olinorder__class_Osorted(X1862,X1860)|~c_List_Olinorder__class_Osorted(X1862,X1861)|c_List_Olinorder__class_Osorted(X1862,hAPP(hAPP(c_List_Oappend(X1862),X1861),X1860))|~class_Orderings_Olinorder(X1862))&((hBOOL(hAPP(hAPP(c_member(X1862),esk60_3(X1860,X1861,X1862)),hAPP(c_List_Oset(X1862),X1860)))|~c_List_Olinorder__class_Osorted(X1862,X1860)|~c_List_Olinorder__class_Osorted(X1862,X1861)|c_List_Olinorder__class_Osorted(X1862,hAPP(hAPP(c_List_Oappend(X1862),X1861),X1860))|~class_Orderings_Olinorder(X1862))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1862),esk59_3(X1860,X1861,X1862)),esk60_3(X1860,X1861,X1862)))|~c_List_Olinorder__class_Osorted(X1862,X1860)|~c_List_Olinorder__class_Osorted(X1862,X1861)|c_List_Olinorder__class_Osorted(X1862,hAPP(hAPP(c_List_Oappend(X1862),X1861),X1860))|~class_Orderings_Olinorder(X1862))))&(((c_List_Olinorder__class_Osorted(X1862,X1860)|~c_List_Olinorder__class_Osorted(X1862,hAPP(hAPP(c_List_Oappend(X1862),X1861),X1860))|~class_Orderings_Olinorder(X1862))&(~hBOOL(hAPP(hAPP(c_member(X1862),X1865),hAPP(c_List_Oset(X1862),X1861)))|(~hBOOL(hAPP(hAPP(c_member(X1862),X1866),hAPP(c_List_Oset(X1862),X1860)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1862),X1865),X1866)))|~c_List_Olinorder__class_Osorted(X1862,hAPP(hAPP(c_List_Oappend(X1862),X1861),X1860))|~class_Orderings_Olinorder(X1862)))&(c_List_Olinorder__class_Osorted(X1862,X1861)|~c_List_Olinorder__class_Osorted(X1862,hAPP(hAPP(c_List_Oappend(X1862),X1861),X1860))|~class_Orderings_Olinorder(X1862)))), 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])])])])])])). 6.97/7.23 fof(c_0_7183, plain, ![X15457, X15458, X15459, X15460, X15461]:(~class_Orderings_Olinorder(X15461)|c_SetInterval_Oord__class_OgreaterThanAtMost(X15461,hAPP(hAPP(c_Orderings_Oord__class_Omax(X15461),X15460),X15458),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15461),X15459),X15457))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15461,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X15461,X15460,X15459)),c_SetInterval_Oord__class_OgreaterThanAtMost(X15461,X15458,X15457))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__greaterThanAtMost])])). 6.97/7.23 fof(c_0_7184, plain, ![X12775, X12776, X12777, X12778, X12779]:(~class_Orderings_Olinorder(X12779)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12779,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X12779,X12778,X12777)),c_SetInterval_Oord__class_OgreaterThanLessThan(X12779,X12776,X12775))=c_SetInterval_Oord__class_OgreaterThanLessThan(X12779,hAPP(hAPP(c_Orderings_Oord__class_Omax(X12779),X12778),X12776),hAPP(hAPP(c_Orderings_Oord__class_Omin(X12779),X12777),X12775))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__greaterThanLessThan])])). 6.97/7.23 fof(c_0_7185, plain, ![X12402, X12403, X12404, X12405, X12406]:(~class_Orderings_Olinorder(X12406)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12406,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X12406,X12405,X12404)),c_SetInterval_Oord__class_OatLeastAtMost(X12406,X12403,X12402))=c_SetInterval_Oord__class_OatLeastAtMost(X12406,hAPP(hAPP(c_Orderings_Oord__class_Omax(X12406),X12405),X12403),hAPP(hAPP(c_Orderings_Oord__class_Omin(X12406),X12404),X12402))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__atLeastAtMost])])])). 6.97/7.23 cnf(c_0_7186, 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_5170])). 6.97/7.23 fof(c_0_7187, plain, ![X3289, X3290, X3291, X3292]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3292),X3291))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3290),X3289))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X3292,X3290)),hAPP(hAPP(c_Product__Type_OSigma(X3292,X3290),X3291),hAPP(c_COMBK(tc_fun(X3290,tc_HOL_Obool),X3292),X3289)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__cartesian__product])])])). 6.97/7.23 fof(c_0_7188, plain, ![X15329, X15330, X15331, X15332]:(~class_Groups_Ocomm__monoid__mult(X15332)|~class_Rings_Oring__1(X15332)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X15331,X15332),hAPP(hAPP(c_COMBB(tc_Int_Oint,X15332,X15331),c_Int_Oring__1__class_Oof__int(X15332)),X15330)),X15329)=hAPP(c_Int_Oring__1__class_Oof__int(X15332),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X15331,tc_Int_Oint),X15330),X15329))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__setprod])])). 6.97/7.23 fof(c_0_7189, plain, ![X5119, X5120, X5121, X5122]:(~class_Rings_Osemiring__1(X5122)|~class_Groups_Ocomm__monoid__mult(X5122)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5122),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5121,tc_Nat_Onat),X5120),X5119))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5121,X5122),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5122,X5121),c_Nat_Osemiring__1__class_Oof__nat(X5122)),X5120)),X5119)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__setprod])])])). 6.97/7.23 fof(c_0_7190, plain, ![X8150, X8151, X8152, X8153, X8154, X8155, X8156, X8157]:(~c_Finite__Set_Ofolding__image__simple__idem(X8157,X8156,X8155,X8154,X8153,X8152)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8156),X8151))|hAPP(hAPP(X8155,hAPP(X8153,X8150)),hAPP(X8152,X8151))=hAPP(X8152,hAPP(hAPP(c_Set_Oinsert(X8156),X8150),X8151)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oinsert__idem])])). 6.97/7.23 cnf(c_0_7191, 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,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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))|~class_Groups_Ocomm__monoid__add(X1)|hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Ozero__class_Ozero(X1)), inference(split_conjunct,[status(thm)],[c_0_5171])). 6.97/7.23 cnf(c_0_7192, 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_5172])). 6.97/7.23 fof(c_0_7193, plain, ![X1502, X1503, X1504, X1505, X1506, X1507]:(~c_List_Olist__all2(X1507,X1506,X1505,X1504,X1503)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1502),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1506)),X1503)))|hBOOL(hAPP(hAPP(X1505,hAPP(hAPP(c_List_Onth(X1507),X1504),X1502)),hAPP(hAPP(c_List_Onth(X1506),X1503),X1502))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__all2__nthD2])])])). 6.97/7.23 cnf(c_0_7194, 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_5173, c_0_5174])). 6.97/7.23 fof(c_0_7195, plain, ![X8023, X8024, X8025, X8026]:(~class_Orderings_Olinorder(X8026)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8026),X8025),X8024))|hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X8026,X8024),X8023)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8026,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X8026,X8025),X8023)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X8026,X8025),X8024)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__diff])])). 6.97/7.23 fof(c_0_7196, plain, ![X602, X603, X604, X605]:(~class_Rings_Ocomm__semiring__1(X605)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X605),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X605),X604),X603)),X602)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X605),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X605),X604),X602)),X603)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])])). 6.97/7.23 fof(c_0_7197, plain, ![X13033, X13034, X13035, X13036]:(~class_Rings_Ocomm__semiring__1(X13036)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13036),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13036),X13035),X13034)),X13033)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13036),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13036),X13035),X13033)),X13034)), 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])])])). 6.97/7.23 fof(c_0_7198, plain, ![X7640, X7641, X7642, X7643]:(~class_Rings_Osemiring__1(X7643)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7643),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7643),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7642)),X7640))),X7641)=hAPP(c_List_Omonoid__add__class_Olistsum(X7643),hAPP(hAPP(c_List_Omap(X7642,X7643),hAPP(c_COMBK(X7643,X7642),X7641)),X7640))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__triv])])). 6.97/7.23 fof(c_0_7199, plain, ![X13171, X13172, X13173, X13174, X13175]:(~c_Finite__Set_Ofolding__one(X13175,X13174,X13173)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13175),X13172))|(hBOOL(hAPP(hAPP(c_member(X13175),X13171),X13172))|(X13172=c_Orderings_Obot__class_Obot(tc_fun(X13175,tc_HOL_Obool))|hAPP(X13173,hAPP(hAPP(c_Set_Oinsert(X13175),X13171),X13172))=hAPP(hAPP(X13174,X13171),hAPP(X13173,X13172)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one_Oinsert])])])). 6.97/7.23 fof(c_0_7200, plain, ![X5051, X5052, X5053, X5054]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5054),X5053))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5052),X5051))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5054),X5052)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5053),X5051))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zadd__zless__mono])])])). 6.97/7.23 fof(c_0_7201, plain, ![X11361, X11362, X11363]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11363),X11362))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11361),X11363))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11363),X11361)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11362),X11361))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__less__mono])])])). 6.97/7.23 fof(c_0_7202, plain, ![X14522, X14523, X14524]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14524),X14523))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14524),X14522))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14522),X14523)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14522),X14524))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono2])])). 6.97/7.23 fof(c_0_7203, plain, ![X3663, X3664, X3665, X3666]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3666),X3665))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3664),X3663))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3666),X3664)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3665),X3663))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__less__mono])])])). 6.97/7.23 fof(c_0_7204, plain, ![X8067, X8068, X8069, X8070, X8071, X8072]:(~c_Finite__Set_Ofolding__idem(X8072,X8071,X8070,X8069)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8072),X8068))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8072,tc_HOL_Obool)),X8067),X8068))|hAPP(c_Fun_Ocomp(X8071,X8071,X8071,hAPP(X8069,X8068)),hAPP(X8069,X8067))=hAPP(X8069,X8068)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__idem_Osubset__comp__idem])])])). 6.97/7.23 fof(c_0_7205, plain, ![X6872, X6873]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X6873),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))|c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)=c_Random_Olog(X6873,X6872))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X6872),X6873))|c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)=c_Random_Olog(X6873,X6872)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X6873),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X6872),X6873))|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(X6873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X6872),X6873)))=c_Random_Olog(X6873,X6872))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_log_Osimps])])])])). 6.97/7.23 fof(c_0_7206, plain, ![X7249, X7250, X7251, X7252]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7252),X7251))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7250),X7249))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7252),X7250)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7251),X7249))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__le__mono])])])). 6.97/7.23 fof(c_0_7207, plain, ![X10837, X10838, X10839, X10840]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10840),X10839))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10838),X10837))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10840),X10838)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10839),X10837))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__le__mono])])])). 6.97/7.23 fof(c_0_7208, plain, ![X4948, X4949, X4950, X4951]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4951,tc_HOL_Obool)),X4950),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4951,tc_HOL_Obool)),X4949),X4948)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4951,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4951,tc_HOL_Obool)),X4950),X4949)),X4948)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4951,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4951,tc_HOL_Obool)),X4950),X4949)),X4948))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4951,tc_HOL_Obool)),X4950),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4951,tc_HOL_Obool)),X4949),X4948))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__subset__conv])])). 6.97/7.23 fof(c_0_7209, plain, ![X11649, X11650, X11651, X11652]:(~class_Divides_Osemiring__div(X11652)|(~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X11652),X11651),X11650))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11652),X11649),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X11652),X11650),X11651))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X11652),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11652),X11649),X11650)),X11651))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__swap])])). 6.97/7.23 fof(c_0_7210, plain, ![X9677, X9678, X9679]:(~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),X9679),X9678)),X9677)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9677),X9679))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9679))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9678))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_q__pos__lemma])])). 6.97/7.23 fof(c_0_7211, plain, ![X13533, X13534]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13533))|c_Divides_OnegDivAlg(X13534,X13533)=c_Divides_Odivmod__int(X13534,X13533)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13534)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13533))|c_Divides_Odivmod__int(X13534,X13533)=hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X13534),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X13533)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13534))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13533))|c_Divides_OposDivAlg(X13534,X13533)=c_Divides_Odivmod__int(X13534,X13533)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13534)))&((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X13534|c_Divides_Odivmod__int(X13534,X13533)=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))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13533))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13534)))&(X13534=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X13534),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X13533)))=c_Divides_Odivmod__int(X13534,X13533)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13533))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13534)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__int__def])])])])). 6.97/7.23 fof(c_0_7212, plain, ![X14736, X14737]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X14737),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X14736),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14736),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X14737)))))|X14737=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X14736),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14736),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X14737)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_subset__card__intvl__is__intvl])])])). 6.97/7.23 fof(c_0_7213, plain, ![X15291, X15292, X15293]:(~class_Rings_Olinordered__semidom(X15293)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15293),c_Groups_Ozero__class_Ozero(X15293)),X15292))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15293),X15292),c_Groups_Oone__class_Oone(X15293)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15293),hAPP(hAPP(c_Power_Opower__class_Opower(X15293),X15292),hAPP(c_Nat_OSuc,X15291))),c_Groups_Oone__class_Oone(X15293)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less__one])])). 6.97/7.23 cnf(c_0_7214, 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_5175])). 6.97/7.23 fof(c_0_7215, plain, ![X13502, X13503, X13504, X13505, X13506]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13506,tc_HOL_Obool)),X13505),X13504))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13503,tc_HOL_Obool)),hAPP(c_Set_Oimage(X13506,X13503,X13502),X13505)),hAPP(c_Set_Oimage(X13506,X13503,X13502),X13504)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__mono])])])). 6.97/7.23 fof(c_0_7216, plain, ![X5113, X5114]:((X5113=c_List_Olist_ONil(tc_List_Olist(X5114))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5114))),c_List_Otranspose(X5114,X5113))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5114)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X5114)),X5113),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(X5114),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X5114))),X5113))))&(X5113!=c_List_Olist_ONil(tc_List_Olist(X5114))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5114))),c_List_Otranspose(X5114,X5113))|~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5114),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X5114))),X5113))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_length__transpose__sorted])])])])). 6.97/7.23 fof(c_0_7217, plain, ![X16885, X16886, X16887, X16888]:(~class_Orderings_Olinorder(X16888)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16888),X16887),X16886))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16888),X16886),X16885))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16888,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X16888,X16887,X16886)),c_SetInterval_Oord__class_OatLeastAtMost(X16888,X16886,X16885))=c_SetInterval_Oord__class_OgreaterThanAtMost(X16888,X16887,X16885)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I19_J])])])). 6.97/7.23 fof(c_0_7218, plain, ![X3196, X3197, X3198, X3199]:(~class_Orderings_Olinorder(X3199)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3199),X3198),X3197))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3199),X3197),X3196))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3199,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X3199,X3198,X3197)),c_SetInterval_Oord__class_OgreaterThanLessThan(X3199,X3197,X3196))=c_SetInterval_Oord__class_OgreaterThanLessThan(X3199,X3198,X3196)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I16_J])])])). 6.97/7.23 fof(c_0_7219, plain, ![X17002, X17003, X17004]:(~class_Rings_Ocomm__semiring__1(X17004)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17004),X17003),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17004),X17002),X17003))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17004),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17004),X17002),c_Groups_Oone__class_Oone(X17004))),X17003)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J])])])). 6.97/7.23 fof(c_0_7220, plain, ![X9540, X9541, X9542]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9542,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9542,tc_HOL_Obool)),X9541)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9542,tc_HOL_Obool)),X9540)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9542,tc_HOL_Obool)),X9540),X9541)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9542,tc_HOL_Obool)),X9540),X9541))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9542,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9542,tc_HOL_Obool)),X9541)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9542,tc_HOL_Obool)),X9540))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__subset__Compl__iff])])). 6.97/7.23 fof(c_0_7221, plain, ![X13017, X13018, X13019, X13020]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13020,tc_HOL_Obool)),X13019),X13018))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13020,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X13020),X13017),X13019)),hAPP(hAPP(c_Set_Oinsert(X13020),X13017),X13018)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__mono])])). 6.97/7.23 fof(c_0_7222, plain, ![X15453, X15454, X15455, X15456]:(~class_Orderings_Olinorder(X15456)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15456),X15455),X15454))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15456),X15454),X15453))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15456,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X15456,X15455,X15454)),c_SetInterval_Oord__class_OgreaterThanAtMost(X15456,X15454,X15453))=c_SetInterval_Oord__class_OatLeastAtMost(X15456,X15455,X15453)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I22_J])])])). 6.97/7.23 fof(c_0_7223, plain, ![X3700, X3701, X3702, X3703]:(~class_Orderings_Olinorder(X3703)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3703),X3702),X3701))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3703),X3701),X3700))|c_SetInterval_Oord__class_OgreaterThanAtMost(X3703,X3702,X3700)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3703,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X3703,X3702,X3701)),c_SetInterval_Oord__class_OgreaterThanAtMost(X3703,X3701,X3700))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I20_J])])])). 6.97/7.23 cnf(c_0_7224, plain, (hBOOL(hAPP(c_List_Odistinct(X2),c_List_Oconcat(X2,X1)))|esk289_2(X1,X2)!=esk288_2(X1,X2)|~hBOOL(hAPP(c_List_Odistinct(X2),esk287_2(X1,X2)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),X1))), inference(split_conjunct,[status(thm)],[c_0_4933])). 6.97/7.23 cnf(c_0_7225, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X2,tc_HOL_Obool)),X5),X3)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X2,tc_HOL_Obool)),X6),X1)|hAPP(X1,esk570_6(X2,X3,X1,X4,X5,X6))!=hAPP(X3,esk570_6(X2,X3,X1,X4,X5,X6))|X6!=X5), inference(split_conjunct,[status(thm)],[c_0_5136])). 6.97/7.23 cnf(c_0_7226, plain, (hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(c_Finite__Set_Ocard(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))))|~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_5176])). 6.97/7.23 fof(c_0_7227, plain, ![X12201, X12202, X12203, X12204]:(~class_Rings_Osemiring__1(X12204)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X12204),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12203,tc_Nat_Onat),X12202),X12201))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12203,X12204),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X12204,X12203),c_Nat_Osemiring__1__class_Oof__nat(X12204)),X12202)),X12201)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__setsum])])). 6.97/7.23 fof(c_0_7228, plain, ![X16201, X16202, X16203, X16204, X16205, X16206, X16207, X16208]:(~c_Finite__Set_Ofolding__image(X16208,X16207,X16206,X16205,X16204)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16207),X16203))|(~c_Fun_Oinj__on(X16207,X16207,X16202,X16203)|hAPP(hAPP(X16204,hAPP(c_Fun_Ocomp(X16207,X16208,X16207,X16201),X16202)),X16203)=hAPP(hAPP(X16204,X16201),hAPP(c_Set_Oimage(X16207,X16207,X16202),X16203))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image_Oreindex])])])). 6.97/7.23 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,esk165_6(X3,X4,X2,X5,X6,X1))))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,X1),X2),X5)!=X4|~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_5097])). 6.97/7.23 fof(c_0_7230, plain, ![X3476, X3477, X3478]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3478))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3477),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3478),X3476))!=X3478|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3477))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3476),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])])])). 6.97/7.23 fof(c_0_7231, plain, ![X8773, X8774, X8775, X8776]:(~class_Groups_Oordered__ab__group__add__abs(X8776)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8776),c_Groups_Ozero__class_Ozero(X8776)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8775,X8776),hAPP(hAPP(c_COMBB(X8776,X8776,X8775),c_Groups_Oabs__class_Oabs(X8776)),X8774)),X8773)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__abs__ge__zero])])])). 6.97/7.23 fof(c_0_7232, plain, ![X7123, X7124, X7125, X7126, X7127, X7128]:(hBOOL(hAPP(hAPP(c_member(X7128),X7127),hAPP(c_List_Oset(X7128),X7126)))|hAPP(hAPP(c_List_Omap(X7128,X7125),c_Fun_Ofun__upd(X7128,X7125,X7124,X7127,X7123)),X7126)=hAPP(hAPP(c_List_Omap(X7128,X7125),X7124),X7126)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__fun__upd])])])). 6.97/7.23 fof(c_0_7233, plain, ![X5992, X5993, X5994, X5995, X5996, X5997]:(~c_Finite__Set_Ofun__left__comm(X5997,X5996,X5995)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5997),X5994))|hAPP(hAPP(c_Finite__Set_Ofold(X5997,X5996,X5995),hAPP(hAPP(X5995,X5993),X5992)),X5994)=hAPP(hAPP(X5995,X5993),hAPP(hAPP(c_Finite__Set_Ofold(X5997,X5996,X5995),X5992),X5994)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__fun__comm])])])). 6.97/7.23 fof(c_0_7234, plain, ![X4964, X4965, X4966]:(~class_Orderings_Olinorder(X4966)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4966),X4965))|(X4965=c_Orderings_Obot__class_Obot(tc_fun(X4966,tc_HOL_Obool))|c_Big__Operators_Olattice_OSup__fin(X4966,c_Orderings_Oord__class_Omax(X4966),hAPP(hAPP(c_Set_Oinsert(X4966),X4964),X4965))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4966),X4964),c_Big__Operators_Olattice_OSup__fin(X4966,c_Orderings_Oord__class_Omax(X4966),X4965))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Oinsert__idem])])])). 6.97/7.23 fof(c_0_7235, plain, ![X10156, X10157]:(~class_Lattices_Oab__semigroup__idem__mult(X10157)|(c_List_Olist_ONil(X10157)=X10156|hAPP(c_Finite__Set_Ofold1(X10157,c_Groups_Otimes__class_Otimes(X10157)),hAPP(c_List_Oset(X10157),X10156))=hAPP(c_List_Ofoldl(X10157,X10157,c_Groups_Otimes__class_Otimes(X10157),hAPP(c_List_Ohd(X10157),X10156)),hAPP(c_List_Otl(X10157),X10156)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__set])])])). 6.97/7.23 fof(c_0_7236, plain, ![X671, X672, X674, X675, X676, X678]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk13_2(X671,X672)),X672))|(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X674),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X672)))|hBOOL(hAPP(X671,X674))))&(~hBOOL(hAPP(X671,esk13_2(X671,X672)))|(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X674),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X672)))|hBOOL(hAPP(X671,X674)))))&((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk14_2(X675,X676)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X676)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X678),X676))|hBOOL(hAPP(X675,X678))))&(~hBOOL(hAPP(X675,esk14_2(X675,X676)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X678),X676))|hBOOL(hAPP(X675,X678)))))), 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__eq])])])])])])])). 6.97/7.23 fof(c_0_7237, plain, ![X7895, X7896, X7897, X7898]:(~hBOOL(hAPP(hAPP(c_member(X7898),X7897),c_Wellfounded_Oacc(X7898,X7896)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X7898,X7898)),hAPP(hAPP(c_Product__Type_OPair(X7898,X7898),X7895),X7897)),X7896))|hBOOL(hAPP(hAPP(c_member(X7898),X7895),c_Wellfounded_Oacc(X7898,X7896))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_acc__downward])])])). 6.97/7.23 fof(c_0_7238, plain, ![X12483, X12484, X12485, X12486]:(~class_Groups_Oab__group__add(X12486)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12485,X12486),hAPP(hAPP(c_COMBB(X12486,X12486,X12485),c_Groups_Ouminus__class_Ouminus(X12486)),X12484)),X12483)=hAPP(c_Groups_Ouminus__class_Ouminus(X12486),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12485,X12486),X12484),X12483))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__negf])])])). 6.97/7.23 fof(c_0_7239, plain, ![X2888, X2889, X2890]:(~class_Orderings_Olinorder(X2890)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2890),X2889))|(X2889=c_Orderings_Obot__class_Obot(tc_fun(X2890,tc_HOL_Obool))|c_Big__Operators_Olattice_OInf__fin(X2890,c_Orderings_Oord__class_Omin(X2890),hAPP(hAPP(c_Set_Oinsert(X2890),X2888),X2889))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X2890),X2888),c_Big__Operators_Olattice_OInf__fin(X2890,c_Orderings_Oord__class_Omin(X2890),X2889))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Oinsert__idem])])])). 6.97/7.23 fof(c_0_7240, plain, ![X14179, X14180, X14181, X14182, X14183, X14184, X14185]:(X14185=X14184|c_Fun_Ofun__upd(X14183,X14182,c_Fun_Ofun__upd(X14183,X14182,X14181,X14184,X14179),X14185,X14180)=c_Fun_Ofun__upd(X14183,X14182,c_Fun_Ofun__upd(X14183,X14182,X14181,X14185,X14180),X14184,X14179)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__upd__twist])])])). 6.97/7.23 fof(c_0_7241, plain, ![X1214, X1215, X1216, X1217]:((X1216!=X1214|hBOOL(hAPP(hAPP(c_member(tc_prod(X1217,X1217)),hAPP(hAPP(c_Product__Type_OPair(X1217,X1217),X1216),X1214)),c_Transitive__Closure_Ortrancl(X1217,X1215)))|hBOOL(hAPP(hAPP(c_member(X1217),X1216),hAPP(c_Relation_ODomain(X1217,X1217),X1215))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X1217,X1217)),hAPP(hAPP(c_Product__Type_OPair(X1217,X1217),X1216),X1214)),c_Transitive__Closure_Ortrancl(X1217,X1215)))|X1216=X1214|hBOOL(hAPP(hAPP(c_member(X1217),X1216),hAPP(c_Relation_ODomain(X1217,X1217),X1215))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Not__Domain__rtrancl])])])])). 6.97/7.23 cnf(c_0_7242, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))|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))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_5177])). 6.97/7.23 cnf(c_0_7243, 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_5178])). 6.97/7.23 fof(c_0_7244, plain, ![X17199, X17200, X17201, X17202]:((~hBOOL(hAPP(hAPP(c_member(X17202),X17201),X17199))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X17202)),X17200),c_List_Olists(X17202,X17199)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X17202)),hAPP(hAPP(c_List_Olist_OCons(X17202),X17201),X17200)),c_List_Olists(X17202,X17199))))&((hBOOL(hAPP(hAPP(c_member(X17202),X17201),X17199))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X17202)),hAPP(hAPP(c_List_Olist_OCons(X17202),X17201),X17200)),c_List_Olists(X17202,X17199))))&(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X17202)),X17200),c_List_Olists(X17202,X17199)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X17202)),hAPP(hAPP(c_List_Olist_OCons(X17202),X17201),X17200)),c_List_Olists(X17202,X17199)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__in__lists__iff])])])). 6.97/7.23 cnf(c_0_7245, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X2),X1))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)|X2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|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))!=X3), inference(split_conjunct,[status(thm)],[c_0_4953])). 6.97/7.23 cnf(c_0_7246, 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_5179]), ['final']). 6.97/7.23 cnf(c_0_7247, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_5180]), ['final']). 6.97/7.23 fof(c_0_7248, plain, ![X15701, X15702, X15703, X15704, X15705, X15707, X15708, X15709, X15710, X15711, X15712]:(((X15704=hAPP(c_Set_Oimage(X15703,X15705,X15702),esk530_5(X15701,X15702,X15703,X15704,X15705))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15705,tc_HOL_Obool)),X15704),hAPP(c_Set_Oimage(X15703,X15705,X15702),X15701))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15703,tc_HOL_Obool)),esk530_5(X15701,X15702,X15703,X15704,X15705)),X15701))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15705,tc_HOL_Obool)),X15704),hAPP(c_Set_Oimage(X15703,X15705,X15702),X15701)))))&(X15710!=hAPP(c_Set_Oimage(X15709,X15711,X15708),X15712)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15709,tc_HOL_Obool)),X15712),X15707))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15711,tc_HOL_Obool)),X15710),hAPP(c_Set_Oimage(X15709,X15711,X15708),X15707))))), 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])])])])])])). 6.97/7.23 cnf(c_0_7249, 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))|hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X4),X1)!=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5181, c_0_4471]), c_0_4471])). 6.97/7.23 cnf(c_0_7250, 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_5182])). 6.97/7.23 fof(c_0_7251, plain, ![X16295, X16296, X16297, X16298, X16299, X16300, X16301, X16302]:(~c_Finite__Set_Ofolding__image__simple__idem(X16302,X16301,X16300,X16299,X16298,X16297)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16301),X16296))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16301,tc_HOL_Obool)),X16295),X16296))|hAPP(X16297,X16296)=hAPP(hAPP(X16300,hAPP(X16297,X16295)),hAPP(X16297,X16296))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image__simple__idem_Osubset__idem])])])). 6.97/7.23 fof(c_0_7252, plain, ![X15625, X15626, X15627, X15628, X15630, X15631, X15632, X15634]:((((hBOOL(hAPP(hAPP(c_member(X15627),esk527_4(X15625,X15626,X15627,X15628)),hAPP(c_List_Oset(X15627),X15625)))|~hBOOL(hAPP(hAPP(c_member(X15627),X15628),hAPP(c_List_Oset(X15627),X15625)))|~hBOOL(hAPP(X15626,X15628))|c_List_Olist__ex1(X15627,X15626,X15625))&(hBOOL(hAPP(X15626,esk527_4(X15625,X15626,X15627,X15628)))|~hBOOL(hAPP(hAPP(c_member(X15627),X15628),hAPP(c_List_Oset(X15627),X15625)))|~hBOOL(hAPP(X15626,X15628))|c_List_Olist__ex1(X15627,X15626,X15625)))&(X15628!=esk527_4(X15625,X15626,X15627,X15628)|~hBOOL(hAPP(hAPP(c_member(X15627),X15628),hAPP(c_List_Oset(X15627),X15625)))|~hBOOL(hAPP(X15626,X15628))|c_List_Olist__ex1(X15627,X15626,X15625)))&(((hBOOL(hAPP(hAPP(c_member(X15632),esk528_3(X15630,X15631,X15632)),hAPP(c_List_Oset(X15632),X15630)))|~c_List_Olist__ex1(X15632,X15631,X15630))&(~hBOOL(hAPP(hAPP(c_member(X15632),X15634),hAPP(c_List_Oset(X15632),X15630)))|~hBOOL(hAPP(X15631,X15634))|esk528_3(X15630,X15631,X15632)=X15634|~c_List_Olist__ex1(X15632,X15631,X15630)))&(hBOOL(hAPP(X15631,esk528_3(X15630,X15631,X15632)))|~c_List_Olist__ex1(X15632,X15631,X15630)))), 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])])])])])])). 6.97/7.23 fof(c_0_7253, plain, ![X7476, X7477, X7478, X7480, X7481, X7482, X7483, X7484]:((((~hBOOL(hAPP(X7477,X7480))|~hBOOL(hAPP(hAPP(c_member(X7478),X7480),hAPP(c_List_Oset(X7478),X7476)))|esk241_3(X7476,X7477,X7478)=X7480|~c_List_Olist__ex1(X7478,X7477,X7476))&(hBOOL(hAPP(X7477,esk241_3(X7476,X7477,X7478)))|~c_List_Olist__ex1(X7478,X7477,X7476)))&(hBOOL(hAPP(hAPP(c_member(X7478),esk241_3(X7476,X7477,X7478)),hAPP(c_List_Oset(X7478),X7476)))|~c_List_Olist__ex1(X7478,X7477,X7476)))&(((hBOOL(hAPP(X7482,esk242_4(X7481,X7482,X7483,X7484)))|~hBOOL(hAPP(X7482,X7484))|~hBOOL(hAPP(hAPP(c_member(X7483),X7484),hAPP(c_List_Oset(X7483),X7481)))|c_List_Olist__ex1(X7483,X7482,X7481))&(hBOOL(hAPP(hAPP(c_member(X7483),esk242_4(X7481,X7482,X7483,X7484)),hAPP(c_List_Oset(X7483),X7481)))|~hBOOL(hAPP(X7482,X7484))|~hBOOL(hAPP(hAPP(c_member(X7483),X7484),hAPP(c_List_Oset(X7483),X7481)))|c_List_Olist__ex1(X7483,X7482,X7481)))&(X7484!=esk242_4(X7481,X7482,X7483,X7484)|~hBOOL(hAPP(X7482,X7484))|~hBOOL(hAPP(hAPP(c_member(X7483),X7484),hAPP(c_List_Oset(X7483),X7481)))|c_List_Olist__ex1(X7483,X7482,X7481)))), 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])])])])])])). 6.97/7.23 cnf(c_0_7254, 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,X1)),X2)=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))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5183, c_0_5184]), c_0_5184])). 6.97/7.23 cnf(c_0_7255, 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_5185, c_0_5186]), ['final']). 6.97/7.23 fof(c_0_7256, plain, ![X1434, X1435, X1436]:(~class_Rings_Olinordered__semidom(X1436)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1436),c_Groups_Oone__class_Oone(X1436)),X1435))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1436),c_Groups_Oone__class_Oone(X1436)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1436),X1435),hAPP(hAPP(c_Power_Opower__class_Opower(X1436),X1435),X1434)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1__lemma])])). 6.97/7.23 fof(c_0_7257, plain, ![X14876, X14877, X14878]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14878))|(X14878!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X14877),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14878),X14876))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14877),X14878))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X14876))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_self__quotient__aux1])])])). 6.97/7.23 fof(c_0_7258, plain, ![X13423, X13424, X13425]:(~class_Lattices_Olattice(X13425)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13425),X13424))|(c_Orderings_Obot__class_Obot(tc_fun(X13425,tc_HOL_Obool))=X13423|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13425,tc_HOL_Obool)),X13423),X13424))|c_Big__Operators_Olattice__class_OSup__fin(X13425,X13424)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X13425),c_Big__Operators_Olattice__class_OSup__fin(X13425,X13423)),c_Big__Operators_Olattice__class_OSup__fin(X13425,X13424)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Osubset__idem])])])). 6.97/7.23 fof(c_0_7259, plain, ![X625, X626, X627]:(~class_Orderings_Olinorder(X627)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X627),X626))|(c_Orderings_Obot__class_Obot(tc_fun(X627,tc_HOL_Obool))=X625|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X627,tc_HOL_Obool)),X625),X626))|c_Big__Operators_Olinorder__class_OMin(X627,X626)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X627),c_Big__Operators_Olinorder__class_OMin(X627,X625)),c_Big__Operators_Olinorder__class_OMin(X627,X626)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min_Osubset__idem])])])). 6.97/7.23 fof(c_0_7260, plain, ![X10173, X10174, X10175]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X10175),esk332_3(X10173,X10174,X10175)))|hBOOL(hAPP(X10173,c_Orderings_Obot__class_Obot(tc_fun(X10175,tc_HOL_Obool))))|~hBOOL(hAPP(X10173,X10174))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10175),X10174)))&((hBOOL(hAPP(hAPP(c_member(X10175),esk331_3(X10173,X10174,X10175)),esk332_3(X10173,X10174,X10175)))|hBOOL(hAPP(X10173,c_Orderings_Obot__class_Obot(tc_fun(X10175,tc_HOL_Obool))))|~hBOOL(hAPP(X10173,X10174))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10175),X10174)))&((hBOOL(hAPP(X10173,esk332_3(X10173,X10174,X10175)))|hBOOL(hAPP(X10173,c_Orderings_Obot__class_Obot(tc_fun(X10175,tc_HOL_Obool))))|~hBOOL(hAPP(X10173,X10174))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10175),X10174)))&(~hBOOL(hAPP(X10173,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10175,tc_HOL_Obool)),esk332_3(X10173,X10174,X10175)),hAPP(hAPP(c_Set_Oinsert(X10175),esk331_3(X10173,X10174,X10175)),c_Orderings_Obot__class_Obot(tc_fun(X10175,tc_HOL_Obool))))))|hBOOL(hAPP(X10173,c_Orderings_Obot__class_Obot(tc_fun(X10175,tc_HOL_Obool))))|~hBOOL(hAPP(X10173,X10174))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10175),X10174)))))), 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])])])])])). 6.97/7.23 fof(c_0_7261, plain, ![X943, X944, X945]:((hBOOL(hAPP(hAPP(c_member(X945),esk26_3(X943,X944,X945)),X943))|c_Relation_Orefl__on(X945,X943,X944)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X945,X945),tc_HOL_Obool)),X944),hAPP(hAPP(c_Product__Type_OSigma(X945,X945),X943),hAPP(c_COMBK(tc_fun(X945,tc_HOL_Obool),X945),X943)))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X945,X945)),hAPP(hAPP(c_Product__Type_OPair(X945,X945),esk26_3(X943,X944,X945)),esk26_3(X943,X944,X945))),X944))|c_Relation_Orefl__on(X945,X943,X944)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X945,X945),tc_HOL_Obool)),X944),hAPP(hAPP(c_Product__Type_OSigma(X945,X945),X943),hAPP(c_COMBK(tc_fun(X945,tc_HOL_Obool),X945),X943)))))), 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])])])])])). 6.97/7.23 fof(c_0_7262, plain, ![X5882, X5883, X5884]:(~class_Lattices_Olattice(X5884)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5884),X5883))|(c_Orderings_Obot__class_Obot(tc_fun(X5884,tc_HOL_Obool))=X5882|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5884,tc_HOL_Obool)),X5882),X5883))|c_Big__Operators_Olattice__class_OInf__fin(X5884,X5883)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5884),c_Big__Operators_Olattice__class_OInf__fin(X5884,X5882)),c_Big__Operators_Olattice__class_OInf__fin(X5884,X5883)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Osubset__idem])])])). 6.97/7.23 fof(c_0_7263, plain, ![X6839, X6840, X6841]:(~class_Orderings_Olinorder(X6841)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6841),X6840))|(X6839=c_Orderings_Obot__class_Obot(tc_fun(X6841,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6841,tc_HOL_Obool)),X6839),X6840))|c_Big__Operators_Olinorder__class_OMax(X6841,X6840)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X6841),c_Big__Operators_Olinorder__class_OMax(X6841,X6839)),c_Big__Operators_Olinorder__class_OMax(X6841,X6840)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max_Osubset__idem])])])). 6.97/7.23 fof(c_0_7264, plain, ![X15077, X15078, X15079]:(~class_Rings_Oring__1(X15079)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15078),X15077))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15079),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X15077),X15078))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15079),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15079),X15077)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15079),X15078)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__diff])])). 6.97/7.23 cnf(c_0_7265, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk451_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_5027])). 6.97/7.23 fof(c_0_7266, plain, ![X14069, X14070, X14071, X14072]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14072),X14070),X14069))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14072),X14071),c_Groups_Ozero__class_Ozero(X14072)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14072),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14072),X14071),X14070)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14072),X14071),X14069)))|~class_Rings_Olinordered__ring__strict(X14072))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14072),c_Groups_Ozero__class_Ozero(X14072)),X14071))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14072),X14071),c_Groups_Ozero__class_Ozero(X14072)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14072),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14072),X14071),X14070)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14072),X14071),X14069)))|~class_Rings_Olinordered__ring__strict(X14072)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14072),X14070),X14069))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14072),X14069),X14070))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14072),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14072),X14071),X14070)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14072),X14071),X14069)))|~class_Rings_Olinordered__ring__strict(X14072))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14072),c_Groups_Ozero__class_Ozero(X14072)),X14071))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14072),X14069),X14070))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14072),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14072),X14071),X14070)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14072),X14071),X14069)))|~class_Rings_Olinordered__ring__strict(X14072))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14072),X14071),c_Groups_Ozero__class_Ozero(X14072)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14072),X14069),X14070))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14072),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14072),X14071),X14070)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14072),X14071),X14069)))|~class_Rings_Olinordered__ring__strict(X14072))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14072),X14070),X14069))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14072),c_Groups_Ozero__class_Ozero(X14072)),X14071))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14072),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14072),X14071),X14070)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14072),X14071),X14069)))|~class_Rings_Olinordered__ring__strict(X14072)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__less__cancel__left__disj])])])])). 6.97/7.23 fof(c_0_7267, plain, ![X11221, X11222, X11223, X11224]:(~class_Fields_Ofield__inverse__zero(X11224)|(c_Groups_Ozero__class_Ozero(X11224)=X11223|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11224),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11224),X11223),X11222)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11224),X11223),X11221))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11224),X11222),X11221))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__divide__mult__cancel__left])])])). 6.97/7.23 cnf(c_0_7268, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2))=hAPP(c_Int_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)),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_5187])). 6.97/7.23 fof(c_0_7269, plain, ![X13414, X13415, X13416, X13417]:(~hBOOL(hAPP(hAPP(c_member(X13417),X13416),X13415))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13417,tc_HOL_Obool)),X13415),hAPP(X13414,X13415)))|hBOOL(hAPP(hAPP(c_member(X13417),X13416),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X13417,tc_HOL_Obool),X13414))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_weak__coinduct])])])). 6.97/7.23 fof(c_0_7270, plain, ![X14105, X14106, X14107, X14108]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X14108),esk481_4(X14105,X14106,X14107,X14108)))|hBOOL(hAPP(X14105,X14107))|~hBOOL(hAPP(X14105,c_Orderings_Obot__class_Obot(tc_fun(X14108,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14108,tc_HOL_Obool)),X14107),X14106))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14108),X14107)))&((hBOOL(hAPP(hAPP(c_member(X14108),esk480_4(X14105,X14106,X14107,X14108)),X14106))|hBOOL(hAPP(X14105,X14107))|~hBOOL(hAPP(X14105,c_Orderings_Obot__class_Obot(tc_fun(X14108,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14108,tc_HOL_Obool)),X14107),X14106))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14108),X14107)))&((~hBOOL(hAPP(hAPP(c_member(X14108),esk480_4(X14105,X14106,X14107,X14108)),esk481_4(X14105,X14106,X14107,X14108)))|hBOOL(hAPP(X14105,X14107))|~hBOOL(hAPP(X14105,c_Orderings_Obot__class_Obot(tc_fun(X14108,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14108,tc_HOL_Obool)),X14107),X14106))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14108),X14107)))&((hBOOL(hAPP(X14105,esk481_4(X14105,X14106,X14107,X14108)))|hBOOL(hAPP(X14105,X14107))|~hBOOL(hAPP(X14105,c_Orderings_Obot__class_Obot(tc_fun(X14108,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14108,tc_HOL_Obool)),X14107),X14106))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14108),X14107)))&(~hBOOL(hAPP(X14105,hAPP(hAPP(c_Set_Oinsert(X14108),esk480_4(X14105,X14106,X14107,X14108)),esk481_4(X14105,X14106,X14107,X14108))))|hBOOL(hAPP(X14105,X14107))|~hBOOL(hAPP(X14105,c_Orderings_Obot__class_Obot(tc_fun(X14108,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14108,tc_HOL_Obool)),X14107),X14106))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14108),X14107))))))), 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])])])])])). 6.97/7.23 fof(c_0_7271, plain, ![X4986, X4987, X4988, X4989]:(~class_Divides_Osemiring__div(X4989)|(X4988=c_Groups_Ozero__class_Ozero(X4989)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4989),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4989),X4988),X4987)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4989),X4988),X4986))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4989),X4987),X4986))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult1])])). 6.97/7.23 fof(c_0_7272, plain, ![X8262, X8263, X8264, X8265]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X8265),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8265,tc_HOL_Obool)),X8264),hAPP(hAPP(c_Set_Oinsert(X8265),X8263),X8262))))|hBOOL(hAPP(c_Finite__Set_Ofinite(X8265),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8265,tc_HOL_Obool)),X8264),X8262))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8265),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8265,tc_HOL_Obool)),X8264),X8262)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X8265),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8265,tc_HOL_Obool)),X8264),hAPP(hAPP(c_Set_Oinsert(X8265),X8263),X8262)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Diff__insert])])). 6.97/7.23 fof(c_0_7273, plain, ![X8220, X8221, X8222, X8223]:((~hBOOL(hAPP(hAPP(c_member(X8223),X8222),hAPP(c_List_Oset(X8223),c_List_Obutlast(X8223,X8221))))|hBOOL(hAPP(hAPP(c_member(X8223),X8222),hAPP(c_List_Oset(X8223),c_List_Obutlast(X8223,hAPP(hAPP(c_List_Oappend(X8223),X8221),X8220))))))&(~hBOOL(hAPP(hAPP(c_member(X8223),X8222),hAPP(c_List_Oset(X8223),c_List_Obutlast(X8223,X8220))))|hBOOL(hAPP(hAPP(c_member(X8223),X8222),hAPP(c_List_Oset(X8223),c_List_Obutlast(X8223,hAPP(hAPP(c_List_Oappend(X8223),X8221),X8220))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_in__set__butlast__appendI])])])])). 6.97/7.23 fof(c_0_7274, plain, ![X10415, X10416, X10417, X10418]:(~class_Fields_Ofield__inverse__zero(X10418)|(X10417=c_Groups_Ozero__class_Ozero(X10418)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10418),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10418),X10416),X10417)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10418),X10415),X10417))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10418),X10416),X10415))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__right])])). 6.97/7.23 fof(c_0_7275, plain, ![X7506, X7507, X7508, X7509, X7510, X7512, X7513, X7514, X7515, X7517]:(((((hBOOL(hAPP(c_Finite__Set_Ofinite(X7509),X7506))|~c_Wellfounded_Omax__extp(X7509,X7508,X7507,X7506))&(c_Orderings_Obot__class_Obot(tc_fun(X7509,tc_HOL_Obool))!=X7506|~c_Wellfounded_Omax__extp(X7509,X7508,X7507,X7506)))&((hBOOL(hAPP(hAPP(X7508,X7510),esk245_5(X7506,X7507,X7508,X7509,X7510)))|~hBOOL(hAPP(hAPP(c_member(X7509),X7510),X7507))|~c_Wellfounded_Omax__extp(X7509,X7508,X7507,X7506))&(hBOOL(hAPP(hAPP(c_member(X7509),esk245_5(X7506,X7507,X7508,X7509,X7510)),X7506))|~hBOOL(hAPP(hAPP(c_member(X7509),X7510),X7507))|~c_Wellfounded_Omax__extp(X7509,X7508,X7507,X7506))))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X7509),X7507))|~c_Wellfounded_Omax__extp(X7509,X7508,X7507,X7506)))&((hBOOL(hAPP(hAPP(c_member(X7515),esk246_4(X7512,X7513,X7514,X7515)),X7513))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7515),X7512))|c_Orderings_Obot__class_Obot(tc_fun(X7515,tc_HOL_Obool))=X7512)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7515),X7513))|c_Wellfounded_Omax__extp(X7515,X7514,X7513,X7512))&(~hBOOL(hAPP(hAPP(X7514,esk246_4(X7512,X7513,X7514,X7515)),X7517))|~hBOOL(hAPP(hAPP(c_member(X7515),X7517),X7512))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7515),X7512))|c_Orderings_Obot__class_Obot(tc_fun(X7515,tc_HOL_Obool))=X7512)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7515),X7513))|c_Wellfounded_Omax__extp(X7515,X7514,X7513,X7512)))), 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_Osimps])])])])])])])). 6.97/7.23 fof(c_0_7276, plain, ![X11790, X11791, X11792, X11793]:(~class_Groups_Osemigroup__add(X11793)|hAPP(c_List_Ofoldl(X11793,X11793,c_Groups_Oplus__class_Oplus(X11793),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11793),X11792),X11791)),X11790)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11793),X11792),hAPP(c_List_Ofoldl(X11793,X11793,c_Groups_Oplus__class_Oplus(X11793),X11791),X11790))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_foldl__assoc])])])). 6.97/7.23 fof(c_0_7277, plain, ![X5151, X5152, X5153, X5154, X5155, X5156]:(~c_Finite__Set_Ofolding__idem(X5156,X5155,X5154,X5153)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5156),X5152))|(~hBOOL(hAPP(hAPP(c_member(X5156),X5151),X5152))|hAPP(c_Fun_Ocomp(X5155,X5155,X5155,hAPP(X5153,X5152)),hAPP(X5154,X5151))=hAPP(X5153,X5152)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__idem_Oin__comp__idem])])])). 6.97/7.23 fof(c_0_7278, plain, ![X17582, X17583, X17584, X17585, X17586]:(~hBOOL(hAPP(hAPP(c_member(X17585),X17586),X17584))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X17583),hAPP(X17582,X17586)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X17583),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17585,tc_fun(X17583,tc_HOL_Obool)),X17584),X17582)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__INT])])])])). 6.97/7.23 cnf(c_0_7279, plain, (hBOOL(hAPP(X1,esk120_2(X1,X2)))|~hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(X1,esk118_2(X1,X2)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk118_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk119_2(X1,X2)),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_4950])). 6.97/7.23 cnf(c_0_7280, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk339_4(X1,X2,X3,X4)),X1))|X4=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_5122])). 6.97/7.23 fof(c_0_7281, plain, ![X8578, X8579, X8580, X8581, X8583]:((hBOOL(hAPP(hAPP(c_member(X8581),esk280_4(X8578,X8579,X8580,X8581)),X8580))|c_Wellfounded_Omax__extp(X8581,X8578,X8580,X8579)|X8579=c_Orderings_Obot__class_Obot(tc_fun(X8581,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8581),X8579))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8581),X8580)))&(~hBOOL(hAPP(hAPP(X8578,esk280_4(X8578,X8579,X8580,X8581)),X8583))|~hBOOL(hAPP(hAPP(c_member(X8581),X8583),X8579))|c_Wellfounded_Omax__extp(X8581,X8578,X8580,X8579)|X8579=c_Orderings_Obot__class_Obot(tc_fun(X8581,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8581),X8579))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8581),X8580)))), 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__extp_Ointros])])])])])])). 6.97/7.23 fof(c_0_7282, plain, ![X10495, X10496, X10497, X10498, X10499]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10499),X10496),X10498))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10499),X10498),X10497))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10499,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10499,X10498,X10497)),c_SetInterval_Oord__class_OatLeastAtMost(X10499,X10496,X10495)))|~class_Orderings_Oorder(X10499))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10499),X10497),X10495))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10499),X10498),X10497))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10499,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10499,X10498,X10497)),c_SetInterval_Oord__class_OatLeastAtMost(X10499,X10496,X10495)))|~class_Orderings_Oorder(X10499)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10499),X10498),X10497))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10499,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10499,X10498,X10497)),c_SetInterval_Oord__class_OatLeastAtMost(X10499,X10496,X10495)))|~class_Orderings_Oorder(X10499))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10499),X10496),X10498))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10499),X10497),X10495))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10499,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10499,X10498,X10497)),c_SetInterval_Oord__class_OatLeastAtMost(X10499,X10496,X10495)))|~class_Orderings_Oorder(X10499)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastatMost__subset__iff])])])])). 6.97/7.23 fof(c_0_7283, plain, ![X14676, X14677, X14678, X14679]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk499_4(X14676,X14677,X14678,X14679)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14679)),X14678)))|(~hBOOL(hAPP(hAPP(c_member(X14679),X14676),hAPP(c_List_Oset(X14679),X14678)))|hBOOL(hAPP(X14677,X14676))))&(~hBOOL(hAPP(X14677,hAPP(hAPP(c_List_Onth(X14679),X14678),esk499_4(X14676,X14677,X14678,X14679))))|(~hBOOL(hAPP(hAPP(c_member(X14679),X14676),hAPP(c_List_Oset(X14679),X14678)))|hBOOL(hAPP(X14677,X14676))))), 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])])])])])). 6.97/7.23 cnf(c_0_7284, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk126_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_5126])). 6.97/7.23 fof(c_0_7285, plain, ![X4324, X4325, X4326, X4327]:(~c_Fun_Oinj__on(X4327,X4326,X4325,c_Orderings_Otop__class_Otop(tc_fun(X4327,tc_HOL_Obool)))|X4324=hAPP(c_Set_Oimage(X4326,X4327,c_Hilbert__Choice_Oinv__into(X4327,X4326,c_Orderings_Otop__class_Otop(tc_fun(X4327,tc_HOL_Obool)),X4325)),hAPP(c_Set_Oimage(X4327,X4326,X4325),X4324))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inv__image__comp])])])). 6.97/7.23 fof(c_0_7286, plain, ![X5917, X5918, X5919]:(~c_Fun_Oinj__on(X5919,X5918,X5917,c_Orderings_Otop__class_Otop(tc_fun(X5919,tc_HOL_Obool)))|hAPP(c_Set_Oimage(X5918,X5919,c_Hilbert__Choice_Oinv__into(X5919,X5918,c_Orderings_Otop__class_Otop(tc_fun(X5919,tc_HOL_Obool)),X5917)),c_Orderings_Otop__class_Otop(tc_fun(X5918,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X5919,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__imp__surj__inv])])). 6.97/7.23 fof(c_0_7287, plain, ![X368, X369, X370, X371]:(~c_Relation_Orefl__on(X371,X370,X369)|(~hBOOL(hAPP(hAPP(c_member(X371),X368),X370))|hBOOL(hAPP(hAPP(c_member(tc_prod(X371,X371)),hAPP(hAPP(c_Product__Type_OPair(X371,X371),X368),X368)),X369)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_refl__onD])])])). 6.97/7.23 fof(c_0_7288, plain, ![X1292, X1293, X1294, X1295]:(~class_Fields_Olinordered__field(X1295)|hAPP(c_Groups_Oabs__class_Oabs(X1295),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1294,X1295),X1293),X1292))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1294,X1295),hAPP(hAPP(c_COMBB(X1295,X1295,X1294),c_Groups_Oabs__class_Oabs(X1295)),X1293)),X1292)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__setprod])])])). 6.97/7.23 fof(c_0_7289, plain, ![X14738, X14739, X14740, X14741, X14742, X14743]:(~class_Complete__Lattice_Ocomplete__lattice(X14743)|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14742,X14743),X14740),hAPP(hAPP(c_COMBC(X14742,X14741,X14743),X14739),X14738))=hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14742,tc_fun(X14741,X14743)),X14740),X14739),X14738)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SUPR__apply])])])). 6.97/7.23 fof(c_0_7290, plain, ![X12176, X12177, X12178, X12179, X12180]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12180),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12179)),X12178)))|hAPP(hAPP(c_List_Onth(X12177),hAPP(hAPP(c_List_Omap(X12179,X12177),X12176),X12178)),X12180)=hAPP(X12176,hAPP(hAPP(c_List_Onth(X12179),X12178),X12180))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__map])])). 6.97/7.23 fof(c_0_7291, plain, ![X9265, X9266, X9267, X9268]:(~class_Rings_Oring__1(X9268)|hAPP(c_Int_Oring__1__class_Oof__int(X9268),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9267,tc_Int_Oint),X9266),X9265))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9267,X9268),hAPP(hAPP(c_COMBB(tc_Int_Oint,X9268,X9267),c_Int_Oring__1__class_Oof__int(X9268)),X9266)),X9265)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__setsum])])])). 6.97/7.23 fof(c_0_7292, plain, ![X5254, X5255, X5256, X5257]:(~class_Divides_Osemiring__div(X5257)|(X5256=c_Groups_Ozero__class_Ozero(X5257)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X5257),X5255),X5254)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X5257),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5257),X5255),X5256)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5257),X5254),X5256)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__mult__mult2])])])). 6.97/7.23 fof(c_0_7293, plain, ![X17111, X17112, X17113, X17114, X17115]:(~hBOOL(hAPP(hAPP(c_member(X17115),X17114),X17113))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17112,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17115,tc_fun(X17112,tc_HOL_Obool)),X17113),X17111)),hAPP(X17111,X17114)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__lower])])). 6.97/7.23 fof(c_0_7294, plain, ![X1018, X1019, X1020, X1021, X1022]:(~hBOOL(hAPP(hAPP(c_member(X1022),X1021),X1020))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1019,tc_HOL_Obool)),hAPP(X1018,X1021)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1022,tc_fun(X1019,tc_HOL_Obool)),X1020),X1018)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__upper])])])). 6.97/7.23 fof(c_0_7295, plain, ![X13118, X13119, X13120, X13123, X13124, X13125, X13126, X13127]:(((hAPP(hAPP(c_List_Oappend(X13120),esk428_3(X13118,X13119,X13120)),hAPP(hAPP(c_List_Olist_OCons(X13120),X13119),esk429_3(X13118,X13119,X13120)))=X13118|~hBOOL(hAPP(hAPP(c_member(X13120),X13119),hAPP(c_List_Oset(X13120),X13118))))&(~hBOOL(hAPP(hAPP(c_member(X13120),X13119),hAPP(c_List_Oset(X13120),esk429_3(X13118,X13119,X13120))))|~hBOOL(hAPP(hAPP(c_member(X13120),X13119),hAPP(c_List_Oset(X13120),X13118)))))&(hAPP(hAPP(c_List_Oappend(X13125),X13126),hAPP(hAPP(c_List_Olist_OCons(X13125),X13124),X13127))!=X13123|hBOOL(hAPP(hAPP(c_member(X13125),X13124),hAPP(c_List_Oset(X13125),X13127)))|hBOOL(hAPP(hAPP(c_member(X13125),X13124),hAPP(c_List_Oset(X13125),X13123))))), 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])])])])])])])). 6.97/7.23 fof(c_0_7296, plain, ![X6338, X6339, X6340, X6341, X6342, X6343, X6344, X6345]:((hBOOL(hAPP(hAPP(c_member(X6340),X6339),hAPP(c_List_Oset(X6340),X6341)))|X6338!=hAPP(hAPP(c_List_Oappend(X6340),X6341),hAPP(hAPP(c_List_Olist_OCons(X6340),X6339),X6342))|hBOOL(hAPP(hAPP(c_member(X6340),X6339),hAPP(c_List_Oset(X6340),X6338))))&((~hBOOL(hAPP(hAPP(c_member(X6345),X6344),hAPP(c_List_Oset(X6345),esk210_3(X6343,X6344,X6345))))|~hBOOL(hAPP(hAPP(c_member(X6345),X6344),hAPP(c_List_Oset(X6345),X6343))))&(X6343=hAPP(hAPP(c_List_Oappend(X6345),esk210_3(X6343,X6344,X6345)),hAPP(hAPP(c_List_Olist_OCons(X6345),X6344),esk211_3(X6343,X6344,X6345)))|~hBOOL(hAPP(hAPP(c_member(X6345),X6344),hAPP(c_List_Oset(X6345),X6343)))))), 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])])])])])])])). 6.97/7.23 cnf(c_0_7297, 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_5188])). 6.97/7.23 cnf(c_0_7298, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X5,X3))|~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,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X4),X1)))), inference(split_conjunct,[status(thm)],[c_0_5135])). 6.97/7.23 fof(c_0_7299, plain, ![X9961, X9962, X9963]:(~class_Lattices_Oab__semigroup__idem__mult(X9963)|(X9962=c_Orderings_Obot__class_Obot(tc_fun(X9963,tc_HOL_Obool))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9963),X9962))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9963),X9961),hAPP(c_Finite__Set_Ofold1(X9963,c_Groups_Otimes__class_Otimes(X9963)),X9962))=hAPP(c_Finite__Set_Ofold1(X9963,c_Groups_Otimes__class_Otimes(X9963)),hAPP(hAPP(c_Set_Oinsert(X9963),X9961),X9962))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__insert__idem])])])). 6.97/7.23 cnf(c_0_7300, 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_5189])). 6.97/7.23 cnf(c_0_7301, 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_5041])). 6.97/7.23 cnf(c_0_7302, 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_5044])). 6.97/7.23 fof(c_0_7303, plain, ![X16627, X16628, X16629]:(c_List_Olist_ONil(X16628)=X16629|hAPP(hAPP(c_List_Otake(X16628),hAPP(c_Nat_OSuc,X16627)),X16629)=hAPP(hAPP(c_List_Olist_OCons(X16628),hAPP(c_List_Ohd(X16628),X16629)),hAPP(hAPP(c_List_Otake(X16628),X16627),hAPP(c_List_Otl(X16628),X16629)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__Suc])])). 6.97/7.23 fof(c_0_7304, plain, ![X8725, X8726, X8727, X8728]:(~c_Wellfounded_Owf(X8728,X8727)|(~c_Fun_Oinj__on(X8728,X8726,X8725,c_Orderings_Otop__class_Otop(tc_fun(X8728,tc_HOL_Obool)))|c_Wellfounded_Owf(X8726,hAPP(c_Set_Oimage(tc_prod(X8728,X8728),tc_prod(X8726,X8726),c_Product__Type_Omap__pair(X8728,X8726,X8728,X8726,X8725,X8725)),X8727)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__map__pair__image])])])). 6.97/7.23 fof(c_0_7305, plain, ![X4690, X4691, X4692, X4693, X4694, X4695, X4696, X4697]:((~c_Fun_Obij__betw(X4692,X4696,hAPP(c_Fun_Ocomp(X4697,X4696,X4692,X4695),X4691),X4690,X4693)|c_Fun_Obij__betw(X4692,X4697,X4691,X4690,X4694)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4697,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4692,X4697,X4691),X4690)),X4694))|~c_Fun_Obij__betw(X4697,X4696,X4695,X4694,X4693))&(~c_Fun_Obij__betw(X4692,X4697,X4691,X4690,X4694)|c_Fun_Obij__betw(X4692,X4696,hAPP(c_Fun_Ocomp(X4697,X4696,X4692,X4695),X4691),X4690,X4693)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4697,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4692,X4697,X4691),X4690)),X4694))|~c_Fun_Obij__betw(X4697,X4696,X4695,X4694,X4693))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bij__betw__comp__iff2])])])])). 6.97/7.23 fof(c_0_7306, plain, ![X15520, X15521, X15522, X15523]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X15523|hAPP(hAPP(c_List_Onth(X15522),X15520),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X15523),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_List_Onth(X15522),hAPP(hAPP(c_List_Olist_OCons(X15522),X15521),X15520)),X15523))&(X15523!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X15521=hAPP(hAPP(c_List_Onth(X15522),hAPP(hAPP(c_List_Olist_OCons(X15522),X15521),X15520)),X15523))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__Cons_H])])])). 6.97/7.23 cnf(c_0_7307, 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_5190])). 6.97/7.23 cnf(c_0_7308, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(c_Set_OCollect(X1),X4))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(X4,X2))), inference(split_conjunct,[status(thm)],[c_0_5191])). 6.97/7.23 fof(c_0_7309, plain, ![X14884, X14885, X14886, X14887, X14888]:(~c_Finite__Set_Ofun__left__comm(X14888,X14887,X14886)|hAPP(c_List_Ofoldl(X14887,X14888,hAPP(c_COMBC(X14888,X14887,X14887),X14886),X14885),c_List_Oremdups(X14888,X14884))=hAPP(hAPP(c_Finite__Set_Ofold(X14888,X14887,X14886),X14885),hAPP(c_List_Oset(X14888),X14884))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__set__remdups])])])). 6.97/7.23 fof(c_0_7310, plain, ![X11888, X11889, X11890, X11891]:(~class_Divides_Oring__div(X11891)|c_Divides_Odiv__class_Omod(X11891,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X11891),c_Divides_Odiv__class_Omod(X11891,X11890,X11888)),c_Divides_Odiv__class_Omod(X11891,X11889,X11888)),X11888)=c_Divides_Odiv__class_Omod(X11891,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X11891),X11890),X11889),X11888)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__diff__eq])])])). 6.97/7.23 fof(c_0_7311, plain, ![X5673, X5674, X5675, X5676]:(~class_Groups_Ocomm__monoid__add(X5676)|(~hBOOL(hAPP(c_List_Odistinct(X5675),X5674))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5675,X5676),X5673),hAPP(c_List_Oset(X5675),X5674))=hAPP(c_List_Omonoid__add__class_Olistsum(X5676),hAPP(hAPP(c_List_Omap(X5675,X5676),X5673),X5674)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__distinct__conv__setsum__set])])])). 6.97/7.23 fof(c_0_7312, plain, ![X2148, X2149, X2150]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2150,X2150),tc_HOL_Obool)),X2149),X2148))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X2150),tc_List_Olist(X2150)),tc_HOL_Obool)),c_List_Olistrel1(X2150,X2149)),c_List_Olistrel1(X2150,X2148)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__mono])])). 6.97/7.23 fof(c_0_7313, plain, ![X10783, X10784, X10785]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10785,X10785),tc_HOL_Obool)),X10784),X10783))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X10785),tc_List_Olist(X10785)),tc_HOL_Obool)),c_List_Olistrel(X10785,X10784)),c_List_Olistrel(X10785,X10783)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__mono])])). 6.97/7.23 fof(c_0_7314, plain, ![X6955, X6956, X6957, X6958]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6958,X6957),tc_HOL_Obool)),X6956),X6955))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6958,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X6958,X6957),X6956)),hAPP(c_Relation_ODomain(X6958,X6957),X6955)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Domain__mono])])). 6.97/7.23 fof(c_0_7315, plain, ![X4888, X4889, X4890]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X4890,tc_HOL_Obool),tc_HOL_Obool)),X4889),X4888))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4890,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4890,tc_HOL_Obool),X4889)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4890,tc_HOL_Obool),X4888)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Union__mono])])). 6.97/7.23 fof(c_0_7316, plain, ![X15515, X15516, X15517, X15518, X15519]:(~hBOOL(hAPP(hAPP(c_member(X15519),X15518),hAPP(c_List_Oset(X15519),X15517)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15516),hAPP(X15515,X15518)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15516),c_List_Olist_Olist__size(X15519,X15515,X15517))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__size__estimation])])])). 6.97/7.23 fof(c_0_7317, plain, ![X10691, X10692, X10693, X10694, X10695]:(~hBOOL(hAPP(hAPP(c_member(X10695),X10694),hAPP(c_List_Oset(X10695),X10693)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10692),hAPP(X10691,X10694)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10692),c_List_Olist_Olist__size(X10695,X10691,X10693))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__size__estimation_H])])). 6.97/7.23 fof(c_0_7318, plain, ![X7829, X7830, X7831, X7832, X7833]:(~hBOOL(hAPP(hAPP(c_member(X7833),X7832),hAPP(c_List_Oset(X7833),X7831)))|(hBOOL(hAPP(X7830,X7832))|c_List_OtakeWhile(X7833,X7830,hAPP(hAPP(c_List_Oappend(X7833),X7831),X7829))=c_List_OtakeWhile(X7833,X7830,X7831))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_takeWhile__append1])])])). 6.97/7.23 fof(c_0_7319, plain, ![X313, X314, X315]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X315,tc_HOL_Obool),tc_HOL_Obool)),X314),X313))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X315,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X315,tc_HOL_Obool),X313)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X315,tc_HOL_Obool),X314)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inter__anti__mono])])])). 6.97/7.23 fof(c_0_7320, plain, ![X13002, X13003, X13004, X13005, X13006]:((hBOOL(hAPP(hAPP(c_member(X13005),X13003),hAPP(c_List_Oset(X13005),X13002)))|~hBOOL(hAPP(c_List_Odistinct(X13005),X13002))|hBOOL(hAPP(c_List_Odistinct(X13005),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13005,X13006,X13004),X13003),X13002)))|~class_Orderings_Olinorder(X13006))&((~hBOOL(hAPP(hAPP(c_member(X13005),X13003),hAPP(c_List_Oset(X13005),X13002)))|~hBOOL(hAPP(c_List_Odistinct(X13005),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13005,X13006,X13004),X13003),X13002)))|~class_Orderings_Olinorder(X13006))&(hBOOL(hAPP(c_List_Odistinct(X13005),X13002))|~hBOOL(hAPP(c_List_Odistinct(X13005),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13005,X13006,X13004),X13003),X13002)))|~class_Orderings_Olinorder(X13006)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__insort])])])])). 6.97/7.23 fof(c_0_7321, plain, ![X7519, X7520]:((X7520=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7520),X7519)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7519),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X7520),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X7519)))&(X7520!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7520),X7519)=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__if])])])). 6.97/7.23 cnf(c_0_7322, plain, (hAPP(c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3)),X4)=hAPP(c_Set_Ovimage(X1,X2,X3),X4)|~c_Fun_Obij__betw(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_5192])). 6.97/7.23 fof(c_0_7323, plain, ![X17340, X17341, X17342, X17343]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17343),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17343),X17340),X17342)),X17341))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17343),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17343),X17341),X17342)),X17340))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17343),X17342),c_Groups_Ozero__class_Ozero(X17343)))|~class_Fields_Olinordered__field(X17343))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17343),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17343),X17341),X17342)),X17340))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17343),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17343),X17340),X17342)),X17341))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17343),X17342),c_Groups_Ozero__class_Ozero(X17343)))|~class_Fields_Olinordered__field(X17343))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__divide__less__eq])])])). 6.97/7.23 fof(c_0_7324, plain, ![X15344, X15345, X15346, X15347]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15347),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15347),X15344),X15346)),X15345))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15347),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15347),X15345),X15346)),X15344))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15347),X15346),c_Groups_Ozero__class_Ozero(X15347)))|~class_Fields_Olinordered__field(X15347))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15347),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15347),X15345),X15346)),X15344))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15347),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15347),X15344),X15346)),X15345))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15347),X15346),c_Groups_Ozero__class_Ozero(X15347)))|~class_Fields_Olinordered__field(X15347))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__divide__le__eq])])])])). 6.97/7.23 fof(c_0_7325, plain, ![X4616, X4617, X4618, X4619]:(((hBOOL(hAPP(hAPP(c_member(X4619),X4618),X4617))|~hBOOL(hAPP(hAPP(c_member(X4619),X4618),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4619,tc_HOL_Obool)),X4617),X4616))))&(~hBOOL(hAPP(hAPP(c_member(X4619),X4618),X4616))|~hBOOL(hAPP(hAPP(c_member(X4619),X4618),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4619,tc_HOL_Obool)),X4617),X4616)))))&(~hBOOL(hAPP(hAPP(c_member(X4619),X4618),X4617))|hBOOL(hAPP(hAPP(c_member(X4619),X4618),X4616))|hBOOL(hAPP(hAPP(c_member(X4619),X4618),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4619,tc_HOL_Obool)),X4617),X4616))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Diff__iff])])])])). 6.97/7.23 fof(c_0_7326, plain, ![X6035, X6036, X6037, X6038]:(~class_Fields_Olinordered__field(X6038)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6038),c_Groups_Ozero__class_Ozero(X6038)),X6037))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6038),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6038),X6036),X6037)),X6035))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6038),X6036),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6038),X6035),X6037)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__imp__less__div__pos])])])). 6.97/7.23 fof(c_0_7327, plain, ![X12540, X12541, X12542, X12543]:(~class_Fields_Olinordered__field(X12543)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12543),c_Groups_Ozero__class_Ozero(X12543)),X12542))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12543),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12543),X12541),X12542)),X12540))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12543),X12541),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12543),X12540),X12542)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__imp__le__div__pos])])])). 6.97/7.23 fof(c_0_7328, plain, ![X1703, X1704, X1705]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1705))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1704),X1703)),X1705)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1704),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1703),X1705))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__zmult2__eq])])])). 6.97/7.23 cnf(c_0_7329, 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_5193])). 6.97/7.23 cnf(c_0_7330, 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_5194])). 6.97/7.23 fof(c_0_7331, plain, ![X15578, X15579, X15580, X15581]:(~class_Fields_Olinordered__field(X15581)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15581),c_Groups_Ozero__class_Ozero(X15581)),X15580))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15581),X15579),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15581),X15578),X15580)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15581),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15581),X15579),X15580)),X15578))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__imp__div__pos__less])])])). 6.97/7.23 fof(c_0_7332, plain, ![X2487, X2488, X2489, X2490]:(~class_Fields_Olinordered__field(X2490)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2490),c_Groups_Ozero__class_Ozero(X2490)),X2489))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2490),X2488),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2490),X2487),X2489)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2490),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2490),X2488),X2489)),X2487))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__imp__div__pos__le])])])). 6.97/7.23 fof(c_0_7333, plain, ![X15618, X15619, X15620, X15621]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15621),X15619),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15621),X15618),X15620)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15621),X15618),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15621),X15619),X15620)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15621),X15620),c_Groups_Ozero__class_Ozero(X15621)))|~class_Fields_Olinordered__field(X15621))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15621),X15618),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15621),X15619),X15620)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15621),X15619),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15621),X15618),X15620)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15621),X15620),c_Groups_Ozero__class_Ozero(X15621)))|~class_Fields_Olinordered__field(X15621))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__divide__eq])])])). 6.97/7.23 cnf(c_0_7334, 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_5195])). 6.97/7.23 fof(c_0_7335, plain, ![X11243, X11244, X11246, X11247, X11248, X11250]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk373_2(X11243,X11244)),X11244))|(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X11246),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X11244)))|hBOOL(hAPP(X11243,X11246))))&(~hBOOL(hAPP(X11243,esk373_2(X11243,X11244)))|(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X11246),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X11244)))|hBOOL(hAPP(X11243,X11246)))))&((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk374_2(X11247,X11248)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X11248)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11250),X11248))|hBOOL(hAPP(X11247,X11250))))&(~hBOOL(hAPP(X11247,esk374_2(X11247,X11248)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11250),X11248))|hBOOL(hAPP(X11247,X11250)))))), 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])])])])])])])). 6.97/7.23 cnf(c_0_7336, 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_5196])). 6.97/7.23 cnf(c_0_7337, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk27_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_5197])). 6.97/7.23 fof(c_0_7338, plain, ![X16663, X16664, X16665, X16666]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16666),X16663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16666),X16664),X16665)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16666),X16664),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16666),X16663),X16665)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16666),X16665),c_Groups_Ozero__class_Ozero(X16666)))|~class_Fields_Olinordered__field(X16666))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16666),X16664),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16666),X16663),X16665)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16666),X16663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16666),X16664),X16665)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16666),X16665),c_Groups_Ozero__class_Ozero(X16666)))|~class_Fields_Olinordered__field(X16666))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__divide__eq])])])). 6.97/7.23 fof(c_0_7339, plain, ![X5923, X5924, X5925, X5926, X5927]:(~c_Fun_Oinj__on(X5927,X5926,X5925,c_Orderings_Otop__class_Otop(tc_fun(X5927,tc_HOL_Obool)))|(~c_Fun_Oinj__on(X5924,X5927,X5923,c_Orderings_Otop__class_Otop(tc_fun(X5924,tc_HOL_Obool)))|c_Fun_Oinj__on(X5924,X5926,hAPP(c_Fun_Ocomp(X5927,X5926,X5924,X5925),X5923),c_Orderings_Otop__class_Otop(tc_fun(X5924,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__comp])])). 6.97/7.23 fof(c_0_7340, plain, ![X1378, X1379, X1380]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1380),X1379)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1380),X1378)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1380))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1379),X1378))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1380))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1380),X1379)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1380),X1378))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1379),X1378))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1380),X1379)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1380),X1378)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__le__cancel1])])])])). 6.97/7.23 cnf(c_0_7341, plain, (c_Relation_Otrans(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1)))|~c_Relation_Otrans(X1,X2)|~c_Relation_Oantisym(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5198])). 6.97/7.23 fof(c_0_7342, plain, ![X5388, X5389, X5390]:(~class_Orderings_Olinorder(X5390)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5390),X5389),X5388))|hAPP(c_SetInterval_Oord__class_OatLeast(X5390),X5389)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5390,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5390,X5389),X5388)),hAPP(c_SetInterval_Oord__class_OatLeast(X5390),X5388)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I14_J])])). 6.97/7.23 fof(c_0_7343, plain, ![X1724, X1725, X1726]:(~class_Orderings_Olinorder(X1726)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1726),X1725),X1724))|hAPP(c_SetInterval_Oord__class_OlessThan(X1726),X1724)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1726,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1726),X1725)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1726,X1725),X1724)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I8_J])])])). 6.97/7.23 fof(c_0_7344, plain, ![X2426, X2427, X2428]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2427))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2428),X2427)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2426),X2427))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2428),X2426))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2428),X2427)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2426),X2427)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2428),X2427)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2426),X2427)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2427))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2428),X2426))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__le__cancel2])])])])). 6.97/7.23 fof(c_0_7345, plain, ![X16130, X16131, X16132, X16133, X16134, X16135]:(~class_Complete__Lattice_Ocomplete__lattice(X16135)|hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16134,tc_fun(X16133,X16135)),X16132),X16131),X16130)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16134,X16135),X16132),hAPP(hAPP(c_COMBC(X16134,X16133,X16135),X16131),X16130))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INFI__apply])])). 6.97/7.23 cnf(c_0_7346, 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,esk529_5(X2,X1,X3,X4,X5))!=hAPP(X2,esk529_5(X2,X1,X3,X4,X5))|~c_Nat__Transfer_Onat__set(X3)|X3!=X4|~class_Groups_Ocomm__monoid__add(X5)|~class_Groups_Ocomm__monoid__mult(X5)), inference(split_conjunct,[status(thm)],[c_0_5131])). 6.97/7.23 fof(c_0_7347, plain, ![X9715, X9716, X9717, X9718]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X9718|hAPP(hAPP(c_List_Odrop(X9717),X9718),hAPP(hAPP(c_List_Olist_OCons(X9717),X9716),X9715))=hAPP(hAPP(c_List_Olist_OCons(X9717),X9716),X9715))&(X9718=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_List_Odrop(X9717),X9718),hAPP(hAPP(c_List_Olist_OCons(X9717),X9716),X9715))=hAPP(hAPP(c_List_Odrop(X9717),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X9718),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X9715))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_drop__Cons_H])])])). 6.97/7.23 fof(c_0_7348, plain, ![X5267, X5268, X5269]:((hBOOL(hAPP(hAPP(c_member(X5269),esk170_3(X5267,X5268,X5269)),X5268))|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(X5269,tc_Nat_Onat),X5267),X5268)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5269),X5268)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X5267,esk170_3(X5267,X5268,X5269))))|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(X5269,tc_Nat_Onat),X5267),X5268)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5269),X5268)))), 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])])])])])). 6.97/7.23 fof(c_0_7349, plain, ![X14504, X14505, X14506, X14507, X14508, X14509, X14510, X14511, X14512, X14513, X14514]:(((X14504!=hAPP(hAPP(c_List_Oappend(X14508),X14509),X14506)|X14507!=hAPP(hAPP(c_List_Olist_OCons(X14508),X14505),X14509)|hAPP(hAPP(c_List_Oappend(X14508),X14507),X14506)=hAPP(hAPP(c_List_Olist_OCons(X14508),X14505),X14504))&(X14506!=hAPP(hAPP(c_List_Olist_OCons(X14508),X14505),X14504)|X14507!=c_List_Olist_ONil(X14508)|hAPP(hAPP(c_List_Oappend(X14508),X14507),X14506)=hAPP(hAPP(c_List_Olist_OCons(X14508),X14505),X14504)))&(((X14512=hAPP(hAPP(c_List_Olist_OCons(X14514),X14511),X14510)|X14510=hAPP(hAPP(c_List_Oappend(X14514),esk490_5(X14510,X14511,X14512,X14513,X14514)),X14512)|hAPP(hAPP(c_List_Oappend(X14514),X14513),X14512)!=hAPP(hAPP(c_List_Olist_OCons(X14514),X14511),X14510))&(X14513=c_List_Olist_ONil(X14514)|X14510=hAPP(hAPP(c_List_Oappend(X14514),esk490_5(X14510,X14511,X14512,X14513,X14514)),X14512)|hAPP(hAPP(c_List_Oappend(X14514),X14513),X14512)!=hAPP(hAPP(c_List_Olist_OCons(X14514),X14511),X14510)))&((X14512=hAPP(hAPP(c_List_Olist_OCons(X14514),X14511),X14510)|X14513=hAPP(hAPP(c_List_Olist_OCons(X14514),X14511),esk490_5(X14510,X14511,X14512,X14513,X14514))|hAPP(hAPP(c_List_Oappend(X14514),X14513),X14512)!=hAPP(hAPP(c_List_Olist_OCons(X14514),X14511),X14510))&(X14513=c_List_Olist_ONil(X14514)|X14513=hAPP(hAPP(c_List_Olist_OCons(X14514),X14511),esk490_5(X14510,X14511,X14512,X14513,X14514))|hAPP(hAPP(c_List_Oappend(X14514),X14513),X14512)!=hAPP(hAPP(c_List_Olist_OCons(X14514),X14511),X14510))))), 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])])])])])])). 6.97/7.23 cnf(c_0_7350, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X1),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X2),X4)|hAPP(X1,esk561_5(X1,X2,X3,X4,X5))!=hAPP(X2,esk561_5(X1,X2,X3,X4,X5))|~c_Nat__Transfer_Onat__set(X3)|X4!=X3|~class_Groups_Ocomm__monoid__mult(X5)|~class_Groups_Ocomm__monoid__add(X5)), inference(split_conjunct,[status(thm)],[c_0_5133])). 6.97/7.23 fof(c_0_7351, plain, ![X6122, X6123, X6124, X6125]:(~class_Rings_Olinordered__semidom(X6125)|(hAPP(hAPP(c_Power_Opower__class_Opower(X6125),X6124),X6123)!=hAPP(hAPP(c_Power_Opower__class_Opower(X6125),X6122),X6123)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6125),c_Groups_Ozero__class_Ozero(X6125)),X6124))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6125),c_Groups_Ozero__class_Ozero(X6125)),X6122))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6123))|X6124=X6122))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__eq__imp__eq__base])])])). 6.97/7.23 cnf(c_0_7352, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk229_2(X2,X1)),esk229_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_5199])). 6.97/7.23 fof(c_0_7353, plain, ![X8396, X8397]:(~class_Groups_Ocomm__monoid__add(X8397)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X8397),hAPP(c_List_Onth(X8397),X8396)),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(X8397)),X8396)))=hAPP(c_List_Omonoid__add__class_Olistsum(X8397),X8396)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__setsum__nth])])])). 6.97/7.23 cnf(c_0_7354, 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_5177])). 6.97/7.23 fof(c_0_7355, plain, ![X17612, X17613, X17614]:(~class_Rings_Olinordered__semiring__strict(X17614)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17614),c_Groups_Ozero__class_Ozero(X17614)),X17613))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17614),X17612),c_Groups_Ozero__class_Ozero(X17614)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17614),X17613),X17612)),c_Groups_Ozero__class_Ozero(X17614)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__pos__neg])])])). 6.97/7.23 fof(c_0_7356, plain, ![X17116, X17117, X17118]:(~class_Rings_Olinordered__semiring__strict(X17118)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17118),c_Groups_Ozero__class_Ozero(X17118)),X17117))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17118),X17116),c_Groups_Ozero__class_Ozero(X17118)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17118),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17118),X17116),X17117)),c_Groups_Ozero__class_Ozero(X17118)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__pos__neg2])])])). 6.97/7.23 fof(c_0_7357, plain, ![X4880, X4881, X4882]:(~class_Fields_Olinordered__field(X4882)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4882),X4881),c_Groups_Ozero__class_Ozero(X4882)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4882),c_Groups_Ozero__class_Ozero(X4882)),X4880))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4882),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4882),X4881),X4880)),c_Groups_Ozero__class_Ozero(X4882)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__neg__pos])])). 6.97/7.23 cnf(c_0_7358, 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_5200])). 6.97/7.23 cnf(c_0_7359, 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_5201, c_0_5202]), ['final']). 6.97/7.23 fof(c_0_7360, plain, ![X4347, X4348, X4349]:(~class_Fields_Olinordered__field(X4349)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4349),c_Groups_Ozero__class_Ozero(X4349)),X4348))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4349),X4347),c_Groups_Ozero__class_Ozero(X4349)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4349),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4349),X4348),X4347)),c_Groups_Ozero__class_Ozero(X4349)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__pos__neg])])])). 6.97/7.23 fof(c_0_7361, plain, ![X11103, X11104, X11105]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11105),c_Groups_Ozero__class_Ozero(X11105)),X11104))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11105),X11103),c_Groups_Ozero__class_Ozero(X11105)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11105),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11105),X11104),X11103)),c_Groups_Ozero__class_Ozero(X11105)))|~class_Rings_Oordered__cancel__semiring(X11105))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11105),c_Groups_Ozero__class_Ozero(X11105)),X11103))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11105),X11104),c_Groups_Ozero__class_Ozero(X11105)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11105),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11105),X11104),X11103)),c_Groups_Ozero__class_Ozero(X11105)))|~class_Rings_Oordered__cancel__semiring(X11105))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__neg__le])])])). 6.97/7.23 fof(c_0_7362, plain, ![X7733, X7734, X7735]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7735),X7733),c_Groups_Ozero__class_Ozero(X7735)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7735),c_Groups_Ozero__class_Ozero(X7735)),X7734))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7735),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7735),X7734),X7733)),c_Groups_Ozero__class_Ozero(X7735)))|~class_Rings_Olinordered__ring__strict(X7735))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7735),X7734),c_Groups_Ozero__class_Ozero(X7735)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7735),c_Groups_Ozero__class_Ozero(X7735)),X7733))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7735),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7735),X7734),X7733)),c_Groups_Ozero__class_Ozero(X7735)))|~class_Rings_Olinordered__ring__strict(X7735)))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7735),X7734),c_Groups_Ozero__class_Ozero(X7735)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7735),X7733),c_Groups_Ozero__class_Ozero(X7735)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7735),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7735),X7734),X7733)),c_Groups_Ozero__class_Ozero(X7735)))|~class_Rings_Olinordered__ring__strict(X7735))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7735),c_Groups_Ozero__class_Ozero(X7735)),X7733))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7735),X7733),c_Groups_Ozero__class_Ozero(X7735)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7735),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7735),X7734),X7733)),c_Groups_Ozero__class_Ozero(X7735)))|~class_Rings_Olinordered__ring__strict(X7735)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7735),X7734),c_Groups_Ozero__class_Ozero(X7735)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7735),c_Groups_Ozero__class_Ozero(X7735)),X7734))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7735),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7735),X7734),X7733)),c_Groups_Ozero__class_Ozero(X7735)))|~class_Rings_Olinordered__ring__strict(X7735))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7735),c_Groups_Ozero__class_Ozero(X7735)),X7733))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7735),c_Groups_Ozero__class_Ozero(X7735)),X7734))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7735),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7735),X7734),X7733)),c_Groups_Ozero__class_Ozero(X7735)))|~class_Rings_Olinordered__ring__strict(X7735))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__0__iff])])])). 6.97/7.23 fof(c_0_7363, plain, ![X1875, X1876, X1877]:(~class_Fields_Olinordered__field(X1877)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1877),c_Groups_Ozero__class_Ozero(X1877)),X1876))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1877),X1875),c_Groups_Ozero__class_Ozero(X1877)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1877),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1877),X1876),X1875)),c_Groups_Ozero__class_Ozero(X1877)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__nonneg__neg])])])). 6.97/7.23 fof(c_0_7364, plain, ![X4928, X4929, X4930]:(~class_Fields_Olinordered__field(X4930)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4930),X4929),c_Groups_Ozero__class_Ozero(X4930)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4930),c_Groups_Ozero__class_Ozero(X4930)),X4928))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4930),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4930),X4929),X4928)),c_Groups_Ozero__class_Ozero(X4930)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonpos__pos])])). 6.97/7.23 fof(c_0_7365, plain, ![X9824, X9825, X9826]:(~class_Groups_Oordered__comm__monoid__add(X9826)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9826),X9825),c_Groups_Ozero__class_Ozero(X9826)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9826),X9824),c_Groups_Ozero__class_Ozero(X9826)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9826),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9826),X9825),X9824)),c_Groups_Ozero__class_Ozero(X9826)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__neg__neg])])])). 6.97/7.23 fof(c_0_7366, plain, ![X14564, X14565, X14566]:(~class_Groups_Oordered__comm__monoid__add(X14566)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14566),X14565),c_Groups_Ozero__class_Ozero(X14566)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14566),X14564),c_Groups_Ozero__class_Ozero(X14566)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14566),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14566),X14565),X14564)),c_Groups_Ozero__class_Ozero(X14566)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__nonpos__neg])])])). 6.97/7.23 fof(c_0_7367, plain, ![X4231, X4232]:(c_List_Olist_ONil(X4231)=X4232|hAPP(c_List_Orotate1(X4231),X4232)=hAPP(hAPP(c_List_Oappend(X4231),hAPP(c_List_Otl(X4231),X4232)),hAPP(hAPP(c_List_Olist_OCons(X4231),hAPP(c_List_Ohd(X4231),X4232)),c_List_Olist_ONil(X4231)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rotate1__hd__tl])])])). 6.97/7.23 fof(c_0_7368, plain, ![X2617, X2618, X2619]:(~class_Groups_Oordered__comm__monoid__add(X2619)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2619),X2618),c_Groups_Ozero__class_Ozero(X2619)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2619),X2617),c_Groups_Ozero__class_Ozero(X2619)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2619),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2619),X2618),X2617)),c_Groups_Ozero__class_Ozero(X2619)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__neg__nonpos])])])). 6.97/7.23 fof(c_0_7369, plain, ![X1283, X1284, X1285]:(~class_Groups_Oordered__comm__monoid__add(X1285)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1285),X1284),c_Groups_Ozero__class_Ozero(X1285)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1285),X1283),c_Groups_Ozero__class_Ozero(X1285)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1285),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1285),X1284),X1283)),c_Groups_Ozero__class_Ozero(X1285)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__nonpos__nonpos])])])). 6.97/7.23 fof(c_0_7370, plain, ![X9103, X9104, X9105]:(~class_Rings_Olinordered__semidom(X9105)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9105),c_Groups_Oone__class_Oone(X9105)),X9104))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9105),c_Groups_Oone__class_Oone(X9105)),X9103))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9105),c_Groups_Oone__class_Oone(X9105)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9105),X9104),X9103)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__1__mult])])). 6.97/7.23 fof(c_0_7371, plain, ![X6943, X6944, X6945]:(~class_Groups_Oordered__comm__monoid__add(X6945)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6945),c_Groups_Ozero__class_Ozero(X6945)),X6944))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6945),c_Groups_Ozero__class_Ozero(X6945)),X6943))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6945),c_Groups_Ozero__class_Ozero(X6945)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6945),X6944),X6943)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__pos__pos])])])). 6.97/7.23 cnf(c_0_7372, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X2,X1)=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))), inference(split_conjunct,[status(thm)],[c_0_5203])). 6.97/7.23 fof(c_0_7373, plain, ![X7063, X7064, X7065]:(~class_Rings_Olinordered__semiring__strict(X7065)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7065),c_Groups_Ozero__class_Ozero(X7065)),X7064))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7065),c_Groups_Ozero__class_Ozero(X7065)),X7063))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7065),c_Groups_Ozero__class_Ozero(X7065)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7065),X7064),X7063)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__pos__pos])])])). 6.97/7.23 fof(c_0_7374, plain, ![X14153, X14154, X14155]:(~class_Fields_Olinordered__field(X14155)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14155),c_Groups_Ozero__class_Ozero(X14155)),X14154))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14155),c_Groups_Ozero__class_Ozero(X14155)),X14153))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14155),c_Groups_Ozero__class_Ozero(X14155)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14155),X14154),X14153)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__pos__pos])])])). 6.97/7.23 fof(c_0_7375, plain, ![X14041, X14042, X14043]:(~class_Rings_Oordered__cancel__semiring(X14043)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14043),c_Groups_Ozero__class_Ozero(X14043)),X14042))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14043),c_Groups_Ozero__class_Ozero(X14043)),X14041))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14043),c_Groups_Ozero__class_Ozero(X14043)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14043),X14042),X14041)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__nonneg__nonneg])])])). 6.97/7.23 fof(c_0_7376, plain, ![X15294, X15295, X15296]:(~class_Rings_Olinordered__semidom(X15296)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15296),c_Groups_Oone__class_Oone(X15296)),X15295))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X15294))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15296),c_Groups_Oone__class_Oone(X15296)),hAPP(hAPP(c_Power_Opower__class_Opower(X15296),X15295),X15294)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_one__less__power])])])). 6.97/7.23 fof(c_0_7377, plain, ![X16554, X16555, X16556]:(~class_Orderings_Olinorder(X16556)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16556,tc_HOL_Obool)),X16555),X16554))|(c_Orderings_Obot__class_Obot(tc_fun(X16556,tc_HOL_Obool))=X16555|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16556),X16554))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16556),c_Big__Operators_Olinorder__class_OMin(X16556,X16554)),c_Big__Operators_Olinorder__class_OMin(X16556,X16555))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min__antimono])])])). 6.97/7.23 fof(c_0_7378, plain, ![X4831, X4832, X4833]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4833),X4832),c_Groups_Ozero__class_Ozero(X4833)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4833),X4831),c_Groups_Ozero__class_Ozero(X4833)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4833),c_Groups_Ozero__class_Ozero(X4833)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4833),X4832),X4831)))|~class_Rings_Olinordered__ring__strict(X4833))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4833),c_Groups_Ozero__class_Ozero(X4833)),X4832))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4833),c_Groups_Ozero__class_Ozero(X4833)),X4831))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4833),c_Groups_Ozero__class_Ozero(X4833)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4833),X4832),X4831)))|~class_Rings_Olinordered__ring__strict(X4833)))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4833),c_Groups_Ozero__class_Ozero(X4833)),X4832))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4833),X4832),c_Groups_Ozero__class_Ozero(X4833)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4833),c_Groups_Ozero__class_Ozero(X4833)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4833),X4832),X4831)))|~class_Rings_Olinordered__ring__strict(X4833))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4833),c_Groups_Ozero__class_Ozero(X4833)),X4831))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4833),X4832),c_Groups_Ozero__class_Ozero(X4833)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4833),c_Groups_Ozero__class_Ozero(X4833)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4833),X4832),X4831)))|~class_Rings_Olinordered__ring__strict(X4833)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4833),c_Groups_Ozero__class_Ozero(X4833)),X4832))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4833),X4831),c_Groups_Ozero__class_Ozero(X4833)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4833),c_Groups_Ozero__class_Ozero(X4833)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4833),X4832),X4831)))|~class_Rings_Olinordered__ring__strict(X4833))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4833),c_Groups_Ozero__class_Ozero(X4833)),X4831))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4833),X4831),c_Groups_Ozero__class_Ozero(X4833)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4833),c_Groups_Ozero__class_Ozero(X4833)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4833),X4832),X4831)))|~class_Rings_Olinordered__ring__strict(X4833))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff])])])). 6.97/7.23 fof(c_0_7379, plain, ![X15903, X15904, X15905]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15905),X15903),c_Groups_Ozero__class_Ozero(X15905)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15905),X15904),c_Groups_Ozero__class_Ozero(X15905)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15905),c_Groups_Ozero__class_Ozero(X15905)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15905),X15904),X15903)))|~class_Rings_Oordered__ring(X15905))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15905),c_Groups_Ozero__class_Ozero(X15905)),X15904))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15905),c_Groups_Ozero__class_Ozero(X15905)),X15903))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15905),c_Groups_Ozero__class_Ozero(X15905)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15905),X15904),X15903)))|~class_Rings_Oordered__ring(X15905))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_split__mult__pos__le])])])])). 6.97/7.23 fof(c_0_7380, plain, ![X16320, X16321, X16322]:(~class_Fields_Olinordered__field(X16322)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16322),c_Groups_Ozero__class_Ozero(X16322)),X16321))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16322),c_Groups_Ozero__class_Ozero(X16322)),X16320))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16322),c_Groups_Ozero__class_Ozero(X16322)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16322),X16321),X16320)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__nonneg__pos])])])). 6.97/7.23 fof(c_0_7381, plain, ![X8506, X8507, X8508]:(~class_Rings_Olinordered__ring__strict(X8508)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8508),X8507),c_Groups_Ozero__class_Ozero(X8508)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8508),X8506),c_Groups_Ozero__class_Ozero(X8508)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8508),c_Groups_Ozero__class_Ozero(X8508)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8508),X8507),X8506)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__neg__neg])])])). 6.97/7.23 fof(c_0_7382, plain, ![X10334, X10335, X10336]:(~class_Orderings_Olinorder(X10336)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10336,tc_HOL_Obool)),X10335),X10334))|(X10335=c_Orderings_Obot__class_Obot(tc_fun(X10336,tc_HOL_Obool))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10336),X10334))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10336),c_Big__Operators_Olinorder__class_OMax(X10336,X10335)),c_Big__Operators_Olinorder__class_OMax(X10336,X10334))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max__mono])])])). 6.97/7.23 fof(c_0_7383, plain, ![X9258, X9259, X9260, X9261]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9261),X9260),X9258))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9261),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9261),X9260),X9259)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9261),X9258),X9259)))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X9261))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9261),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9261),X9260),X9259)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9261),X9258),X9259)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9261),X9260),X9258))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X9261))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__less__cancel__right])])])])). 6.97/7.23 fof(c_0_7384, plain, ![X10039, X10040]:(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X10040|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X10039,X10040),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X10039),X10040)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X10039,X10040))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__div__mod])])])). 6.97/7.23 fof(c_0_7385, plain, ![X1660, X1661, X1662]:(~class_Fields_Olinordered__field(X1662)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1662),X1661),c_Groups_Ozero__class_Ozero(X1662)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1662),X1660),c_Groups_Ozero__class_Ozero(X1662)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1662),c_Groups_Ozero__class_Ozero(X1662)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1662),X1661),X1660)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__neg__neg])])])). 6.97/7.23 fof(c_0_7386, plain, ![X4729, X4730, X4731]:(X4731=c_List_Olist_ONil(X4730)|hBOOL(hAPP(hAPP(c_member(X4730),hAPP(c_Product__Type_Ofst(X4730,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(X4730,X4731),X4729))),hAPP(c_List_Oset(X4730),X4731)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_select])])). 6.97/7.23 cnf(c_0_7387, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)=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)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_5157])). 6.97/7.23 fof(c_0_7388, plain, ![X2708, X2709, X2710, X2711]:(~class_Groups_Oordered__cancel__ab__semigroup__add(X2711)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2711),X2710),X2709))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2711),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2711),X2710),X2708)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2711),X2709),X2708))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__strict__right__mono])])])). 6.97/7.23 fof(c_0_7389, plain, ![X7923, X7924, X7925, X7926]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7926),X7924),X7923))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7926),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7926),X7925),X7924)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7926),X7925),X7923)))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X7926))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7926),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7926),X7925),X7924)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7926),X7925),X7923)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7926),X7924),X7923))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X7926))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__less__cancel__left])])])])). 6.97/7.23 fof(c_0_7390, plain, ![X914, X915, X916, X917]:(~class_Groups_Oordered__cancel__ab__semigroup__add(X917)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X917),X916),X915))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X917),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X917),X914),X916)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X917),X914),X915))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__strict__left__mono])])])). 6.97/7.23 fof(c_0_7391, plain, ![X879, X880, X881, X882]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X882),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X882),X881),X880)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X882),X879),X880)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X882),X881),X879))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X882))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X882),X881),X879))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X882),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X882),X881),X880)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X882),X879),X880)))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X882))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__le__cancel__right])])])])). 6.97/7.23 fof(c_0_7392, plain, ![X14420, X14421, X14422]:(~class_Fields_Olinordered__field(X14422)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14422),X14421),c_Groups_Ozero__class_Ozero(X14422)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14422),X14420),c_Groups_Ozero__class_Ozero(X14422)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14422),c_Groups_Ozero__class_Ozero(X14422)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14422),X14421),X14420)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__nonpos__neg])])])). 6.97/7.23 fof(c_0_7393, plain, ![X17099, X17100, X17101, X17102, X17103, X17104]:(hAPP(c_Hilbert__Choice_Oinv__into(X17104,X17103,X17102,X17101),X17099)!=hAPP(c_Hilbert__Choice_Oinv__into(X17104,X17103,X17102,X17101),X17100)|(~hBOOL(hAPP(hAPP(c_member(X17103),X17100),hAPP(c_Set_Oimage(X17104,X17103,X17101),X17102)))|(~hBOOL(hAPP(hAPP(c_member(X17103),X17099),hAPP(c_Set_Oimage(X17104,X17103,X17101),X17102)))|X17099=X17100))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inv__into__injective])])])). 6.97/7.23 fof(c_0_7394, plain, ![X4059, X4060]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4060),hAPP(c_Int_Onumber__class_Onumber__of(X4060),X4059)),c_Groups_Ozero__class_Ozero(X4060)))|hAPP(c_Groups_Oabs__class_Oabs(X4060),hAPP(c_Int_Onumber__class_Onumber__of(X4060),X4059))=hAPP(c_Groups_Ouminus__class_Ouminus(X4060),hAPP(c_Int_Onumber__class_Onumber__of(X4060),X4059))|(~class_Int_Onumber__ring(X4060)|~class_Rings_Olinordered__idom(X4060)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4060),hAPP(c_Int_Onumber__class_Onumber__of(X4060),X4059)),c_Groups_Ozero__class_Ozero(X4060)))|hAPP(c_Groups_Oabs__class_Oabs(X4060),hAPP(c_Int_Onumber__class_Onumber__of(X4060),X4059))=hAPP(c_Int_Onumber__class_Onumber__of(X4060),X4059)|(~class_Int_Onumber__ring(X4060)|~class_Rings_Olinordered__idom(X4060)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__number__of])])])])). 6.97/7.23 fof(c_0_7395, plain, ![X10934, X10935, X10936, X10937]:(~class_Groups_Oordered__ab__semigroup__add(X10937)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10937),X10936),X10935))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10937),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10937),X10936),X10934)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10937),X10935),X10934))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__right__mono])])])). 6.97/7.23 fof(c_0_7396, plain, ![X15721, X15722, X15723, X15724]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15724),X15722),X15721))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15724),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15724),X15723),X15722)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15724),X15723),X15721)))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X15724))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15724),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15724),X15723),X15722)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15724),X15723),X15721)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15724),X15722),X15721))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X15724))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__le__cancel__left])])])])). 6.97/7.23 fof(c_0_7397, plain, ![X818, X819, X820, X821]:(~class_Groups_Oordered__ab__semigroup__add(X821)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X821),X820),X819))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X821),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X821),X818),X820)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X821),X818),X819))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__left__mono])])])). 6.97/7.23 fof(c_0_7398, plain, ![X2074, X2075]:(~class_Orderings_Olinorder(X2075)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2075),X2074))|(X2074=c_Orderings_Obot__class_Obot(tc_fun(X2075,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2075),c_Big__Operators_Olattice_OInf__fin(X2075,c_Orderings_Oord__class_Omin(X2075),X2074)),c_Big__Operators_Olattice_OSup__fin(X2075,c_Orderings_Oord__class_Omax(X2075),X2074)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__le__Sup])])])). 6.97/7.23 fof(c_0_7399, plain, ![X15399, X15400, X15401, X15402, X15403, X15404]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X15404,X15403)),hAPP(hAPP(c_Product__Type_OPair(X15404,X15403),X15402),X15401)),hAPP(c_List_Oset(tc_prod(X15404,X15403)),hAPP(hAPP(c_List_Ozip(X15404,X15403),X15400),X15399))))|hBOOL(hAPP(hAPP(c_member(X15404),X15402),hAPP(c_List_Oset(X15404),X15400)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_set__zip__leftD])])])). 6.97/7.23 fof(c_0_7400, plain, ![X12747, X12748, X12749, X12750, X12751, X12752]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X12752,X12751)),hAPP(hAPP(c_Product__Type_OPair(X12752,X12751),X12750),X12749)),hAPP(c_List_Oset(tc_prod(X12752,X12751)),hAPP(hAPP(c_List_Ozip(X12752,X12751),X12748),X12747))))|hBOOL(hAPP(hAPP(c_member(X12751),X12749),hAPP(c_List_Oset(X12751),X12747)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_set__zip__rightD])])])). 6.97/7.23 fof(c_0_7401, plain, ![X12630, X12631, X12632, X12633, X12634, X12635, X12636, X12637, X12638]:(((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X12632|(~hBOOL(hAPP(hAPP(c_member(X12633),X12634),hAPP(c_List_Oset(X12633),c_List_Oreplicate(X12633,X12632,X12631))))|hBOOL(hAPP(X12630,X12634))))&(~hBOOL(hAPP(X12630,X12631))|(~hBOOL(hAPP(hAPP(c_member(X12633),X12634),hAPP(c_List_Oset(X12633),c_List_Oreplicate(X12633,X12632,X12631))))|hBOOL(hAPP(X12630,X12634)))))&((hBOOL(hAPP(hAPP(c_member(X12638),esk414_4(X12635,X12636,X12637,X12638)),hAPP(c_List_Oset(X12638),c_List_Oreplicate(X12638,X12637,X12636))))|(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X12637|hBOOL(hAPP(X12635,X12636))))&(~hBOOL(hAPP(X12635,esk414_4(X12635,X12636,X12637,X12638)))|(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X12637|hBOOL(hAPP(X12635,X12636)))))), 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__set__replicate])])])])])])])). 6.97/7.23 fof(c_0_7402, plain, ![X3405, X3406, X3407, X3408, X3409]:(~c_Finite__Set_Ofolding__one__idem(X3409,X3408,X3407)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3409),X3406))|(c_Orderings_Obot__class_Obot(tc_fun(X3409,tc_HOL_Obool))=X3406|hAPP(X3407,hAPP(hAPP(c_Set_Oinsert(X3409),X3405),X3406))=hAPP(hAPP(X3408,X3405),hAPP(X3407,X3406))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one__idem_Oinsert__idem])])])). 6.97/7.23 cnf(c_0_7403, plain, (X2=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))|~class_Fields_Ofield(X1)|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5204, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.23 fof(c_0_7404, plain, ![X7384, X7385, X7386, X7387]:(~class_Divides_Osemiring__div(X7387)|c_Divides_Odiv__class_Omod(X7387,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7387),X7386),X7385),X7384)=c_Divides_Odiv__class_Omod(X7387,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7387),c_Divides_Odiv__class_Omod(X7387,X7386,X7384)),c_Divides_Odiv__class_Omod(X7387,X7385,X7384)),X7384)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__add__eq])])])). 6.97/7.23 fof(c_0_7405, plain, ![X16179, X16180, X16181, X16182]:(~class_Divides_Osemiring__div(X16182)|c_Divides_Odiv__class_Omod(X16182,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16182),X16181),X16180),X16179)=c_Divides_Odiv__class_Omod(X16182,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16182),c_Divides_Odiv__class_Omod(X16182,X16181,X16179)),c_Divides_Odiv__class_Omod(X16182,X16180,X16179)),X16179)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__mult__eq])])])). 6.97/7.23 cnf(c_0_7406, 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_5205])). 6.97/7.23 cnf(c_0_7407, 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))), inference(split_conjunct,[status(thm)],[c_0_5206]), ['final']). 6.97/7.23 fof(c_0_7408, plain, ![X10632, X10633, X10634, X10636, X10637, X10638]:(((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk350_2(X10632,X10633)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10633)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10634),X10633))|~hBOOL(hAPP(X10632,X10634))))&(hBOOL(hAPP(X10632,esk350_2(X10632,X10633)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10634),X10633))|~hBOOL(hAPP(X10632,X10634)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk351_2(X10636,X10637)),X10637))|(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X10638),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10637)))|~hBOOL(hAPP(X10636,X10638))))&(hBOOL(hAPP(X10636,esk351_2(X10636,X10637)))|(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X10638),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10637)))|~hBOOL(hAPP(X10636,X10638)))))), 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])])])])])])). 6.97/7.23 fof(c_0_7409, plain, ![X5261, X5262, X5263, X5264]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X5264),X5263))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5262),X5261))|hAPP(c_Finite__Set_Ocard(tc_sum(X5264,X5262)),c_Sum__Type_OPlus(X5264,X5262,X5263,X5261))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5264),X5263)),hAPP(c_Finite__Set_Ocard(X5262),X5261)))&((hBOOL(hAPP(c_Finite__Set_Ofinite(X5264),X5263))|hAPP(c_Finite__Set_Ocard(tc_sum(X5264,X5262)),c_Sum__Type_OPlus(X5264,X5262,X5263,X5261))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X5262),X5261))|hAPP(c_Finite__Set_Ocard(tc_sum(X5264,X5262)),c_Sum__Type_OPlus(X5264,X5262,X5263,X5261))=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_card__Plus__conv__if])])])])). 6.97/7.23 fof(c_0_7410, plain, ![X10629, X10630, X10631]:(~class_Groups_Oordered__ab__group__add(X10631)|c_SetInterval_Oord__class_OgreaterThanAtMost(X10631,hAPP(c_Groups_Ouminus__class_Ouminus(X10631),X10629),hAPP(c_Groups_Ouminus__class_Ouminus(X10631),X10630))=hAPP(c_Set_Oimage(X10631,X10631,c_Groups_Ouminus__class_Ouminus(X10631)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10631,X10630),X10629))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__uminus__atLeastLessThan])])])). 6.97/7.23 fof(c_0_7411, plain, ![X11537, X11538, X11539]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11539),X11538))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11537),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11538),X11539))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11537),X11539)),X11538)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__diff__right])])])). 6.97/7.23 fof(c_0_7412, plain, ![X4295, X4296, X4297]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4297),X4296))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4295),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4296),X4297))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4295),X4296)),X4297)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc])])). 6.97/7.23 cnf(c_0_7413, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3)=X4|X3!=hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5)|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_5207])). 6.97/7.23 cnf(c_0_7414, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=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))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_5043])). 6.97/7.23 cnf(c_0_7415, 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_5208])). 6.97/7.23 fof(c_0_7416, plain, ![X11758, X11759, X11760, X11761, X11762, X11763, X11764, X11765]:(~c_Finite__Set_Ofolding__image__simple__idem(X11765,X11764,X11763,X11762,X11761,X11760)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11764),X11759))|(~hBOOL(hAPP(hAPP(c_member(X11764),X11758),X11759))|hAPP(X11760,X11759)=hAPP(hAPP(X11763,hAPP(X11761,X11758)),hAPP(X11760,X11759))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image__simple__idem_Oin__idem])])])). 6.97/7.23 fof(c_0_7417, plain, ![X3755, X3756, X3757, X3758, X3759, X3760, X3761]:((~c_List_Olist__all2(X3758,X3760,hAPP(hAPP(c_COMBB(X3761,tc_fun(X3760,tc_HOL_Obool),X3758),X3759),X3757),X3756,X3755)|c_List_Olist__all2(X3761,X3760,X3759,hAPP(hAPP(c_List_Omap(X3758,X3761),X3757),X3756),X3755))&(~c_List_Olist__all2(X3761,X3760,X3759,hAPP(hAPP(c_List_Omap(X3758,X3761),X3757),X3756),X3755)|c_List_Olist__all2(X3758,X3760,hAPP(hAPP(c_COMBB(X3761,tc_fun(X3760,tc_HOL_Obool),X3758),X3759),X3757),X3756,X3755))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__map1])])). 6.97/7.23 cnf(c_0_7418, 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_5209])). 6.97/7.23 cnf(c_0_7419, 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_5210]), ['final']). 6.97/7.23 cnf(c_0_7420, plain, (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))|X1!=c_Groups_Ozero__class_Ozero(X2)|X3!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__ring__strict(X2)), inference(split_conjunct,[status(thm)],[c_0_5211])). 6.97/7.23 fof(c_0_7421, plain, ![X5102, X5103, X5104]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5104,tc_HOL_Obool)),X5103),hAPP(hAPP(c_Set_Oinsert(X5104),X5102),c_Orderings_Obot__class_Obot(tc_fun(X5104,tc_HOL_Obool)))))|(c_Orderings_Obot__class_Obot(tc_fun(X5104,tc_HOL_Obool))=X5103|X5103=hAPP(hAPP(c_Set_Oinsert(X5104),X5102),c_Orderings_Obot__class_Obot(tc_fun(X5104,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_subset__singletonD])])])). 6.97/7.23 cnf(c_0_7422, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X2),c_Product__Type_Osnd(X1,X2)),X3)=X4|X3!=hAPP(hAPP(c_List_Ozip(X1,X2),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_5207])). 6.97/7.23 fof(c_0_7423, plain, ![X12309, X12310, X12311, X12312, X12313]:(~class_Groups_Ominus(X12313)|hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12312,X12313)),X12311),X12310),X12309)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X12313),hAPP(X12311,X12309)),hAPP(X12310,X12309))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__apply])])). 6.97/7.23 fof(c_0_7424, plain, ![X3837, X3838, X3839, X3840, X3841]:(~class_Lattices_Olattice(X3841)|hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3840,X3841)),X3839),X3838),X3837)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3841),hAPP(X3839,X3837)),hAPP(X3838,X3837))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__apply])])])). 6.97/7.23 fof(c_0_7425, plain, ![X8648, X8649, X8650, X8651]:(~hBOOL(hAPP(hAPP(c_member(tc_fun(X8651,tc_HOL_Obool)),X8650),X8649))|(~hBOOL(hAPP(hAPP(c_member(X8651),X8648),X8650))|hBOOL(hAPP(hAPP(c_member(X8651),X8648),c_Complete__Lattice_OSup__class_OSup(tc_fun(X8651,tc_HOL_Obool),X8649))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UnionI])])). 6.97/7.23 fof(c_0_7426, plain, ![X13795, X13796, X13797, X13798]:(~class_Divides_Osemiring__div(X13798)|c_Divides_Odiv__class_Omod(X13798,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13798),X13797),X13796),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13798),X13795),X13796))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13798),c_Divides_Odiv__class_Omod(X13798,X13797,X13795)),X13796)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__mult__mult2])])])). 6.97/7.23 cnf(c_0_7427, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk454_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_5212])). 6.97/7.23 fof(c_0_7428, plain, ![X8052, X8053, X8054, X8055, X8056]:(~class_Lattices_Olattice(X8056)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8056),hAPP(X8054,X8052)),hAPP(X8053,X8052))=hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8055,X8056)),X8054),X8053),X8052)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__fun__def])])). 6.97/7.23 fof(c_0_7429, plain, ![X15261, X15262, X15263, X15264]:(~class_Divides_Osemiring__div(X15264)|c_Divides_Odiv__class_Omod(X15264,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15264),X15263),X15262),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15264),X15263),X15261))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15264),X15263),c_Divides_Odiv__class_Omod(X15264,X15262,X15261))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__mult__mult1])])])). 6.97/7.23 cnf(c_0_7430, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)=hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(X1,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_5213])). 6.97/7.23 fof(c_0_7431, plain, ![X15661, X15662, X15663, X15664]:((~hBOOL(hAPP(hAPP(c_member(X15664),X15663),hAPP(c_List_Oset(X15664),X15662)))|hAPP(hAPP(c_List_Oappend(X15664),c_List_Oremove1(X15664,X15663,X15662)),X15661)=c_List_Oremove1(X15664,X15663,hAPP(hAPP(c_List_Oappend(X15664),X15662),X15661)))&(hBOOL(hAPP(hAPP(c_member(X15664),X15663),hAPP(c_List_Oset(X15664),X15662)))|c_List_Oremove1(X15664,X15663,hAPP(hAPP(c_List_Oappend(X15664),X15662),X15661))=hAPP(hAPP(c_List_Oappend(X15664),X15662),c_List_Oremove1(X15664,X15663,X15661)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_remove1__append])])])). 6.97/7.23 fof(c_0_7432, plain, ![X4514, X4515, X4516, X4517]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4517),tc_List_Olist(X4517))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4517),tc_List_Olist(X4517)),X4516),X4515)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X4517),c_List_Olistrel1(X4517,X4514))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4517)),X4516)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4517)),X4515)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rtrancl__listrel1__eq__len])])])). 6.97/7.23 cnf(c_0_7433, 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_5214])). 6.97/7.23 fof(c_0_7434, plain, ![X13729, X13730, X13731]:(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X13731,X13730)!=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X13729,X13730)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13729),X13731))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13729),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13730),esk458_3(X13729,X13730,X13731)))=X13731)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mod__eq__lemma])])])). 6.97/7.23 fof(c_0_7435, plain, ![X11345, X11346]:(~hBOOL(hAPP(c_List_Odistinct(X11346),X11345))|hBOOL(hAPP(c_List_Odistinct(tc_fun(X11346,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X11346),tc_fun(X11346,tc_HOL_Obool)),c_List_Oset(X11346)),c_Enum_Osublists(X11346,X11345))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__set__sublists])])])). 6.97/7.23 cnf(c_0_7436, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|c_Lazy__Sequence_Osmall__lazy_H(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))))), inference(split_conjunct,[status(thm)],[c_0_5215])). 6.97/7.23 fof(c_0_7437, plain, ![X2307, X2308, X2309, X2310, X2311, X2312, X2313, X2314]:(~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2314,tc_fun(X2313,tc_fun(X2312,tc_HOL_Obool))),X2311),X2310),X2309),X2308))|(hBOOL(hAPP(hAPP(hAPP(X2310,X2307),X2309),X2308))|~hBOOL(hAPP(hAPP(c_member(X2314),X2307),X2311)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INF2__E])])])). 6.97/7.23 fof(c_0_7438, plain, ![X14793, X14794, X14795, X14796, X14797]:(~class_Orderings_Olinorder(X14796)|~class_Orderings_Olinorder(X14797)|(~c_Orderings_Oorder__class_Omono(X14796,X14797,X14795)|hAPP(X14795,hAPP(hAPP(c_Orderings_Oord__class_Omax(X14796),X14794),X14793))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X14797),hAPP(X14795,X14794)),hAPP(X14795,X14793)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__of__mono])])). 6.97/7.23 cnf(c_0_7439, 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_5216])). 6.97/7.23 fof(c_0_7440, plain, ![X8002, X8003, X8004, X8005]:(((hBOOL(hAPP(hAPP(c_member(X8005),X8004),X8002))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8005,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X8005),X8004),X8003)),X8002)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8005,tc_HOL_Obool)),X8003),X8002))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8005,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X8005),X8004),X8003)),X8002))))&(~hBOOL(hAPP(hAPP(c_member(X8005),X8004),X8002))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8005,tc_HOL_Obool)),X8003),X8002))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8005,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X8005),X8004),X8003)),X8002)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__subset])])])). 6.97/7.23 fof(c_0_7441, plain, ![X16036, X16037, X16038]:(~c_Wellfounded_Owf(X16038,X16037)|(~c_Wellfounded_Owf(X16038,X16036)|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16038,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X16038,X16038),X16037)),hAPP(c_Relation_ORange(X16038,X16038),X16036))!=c_Orderings_Obot__class_Obot(tc_fun(X16038,tc_HOL_Obool))|c_Wellfounded_Owf(X16038,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X16038,X16038),tc_HOL_Obool)),X16037),X16036))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__Un])])])). 6.97/7.23 cnf(c_0_7442, plain, (c_List_OdropWhile(X1,X2,X3)=c_List_Olist_ONil(X1)|~hBOOL(hAPP(X2,hAPP(c_List_Ohd(X1),c_List_OdropWhile(X1,X2,X3))))), inference(split_conjunct,[status(thm)],[c_0_5217])). 6.97/7.23 fof(c_0_7443, plain, ![X7868, X7869, X7870, X7871, X7872]:(~class_Orderings_Olinorder(X7871)|~class_Orderings_Olinorder(X7872)|(~c_Orderings_Oorder__class_Omono(X7871,X7872,X7870)|hAPP(X7870,hAPP(hAPP(c_Orderings_Oord__class_Omin(X7871),X7869),X7868))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X7872),hAPP(X7870,X7869)),hAPP(X7870,X7868)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__of__mono])])])). 6.97/7.23 fof(c_0_7444, plain, ![X13757, X13758, X13759]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13759),c_Groups_Ozero__class_Ozero(X13759)),X13758))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13759),X13757),c_Groups_Ozero__class_Ozero(X13759)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13759),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13759),X13758),X13757)),c_Groups_Ozero__class_Ozero(X13759)))|~class_Fields_Olinordered__field__inverse__zero(X13759))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13759),X13758),c_Groups_Ozero__class_Ozero(X13759)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13759),c_Groups_Ozero__class_Ozero(X13759)),X13757))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13759),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13759),X13758),X13757)),c_Groups_Ozero__class_Ozero(X13759)))|~class_Fields_Olinordered__field__inverse__zero(X13759)))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13759),X13758),c_Groups_Ozero__class_Ozero(X13759)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13759),c_Groups_Ozero__class_Ozero(X13759)),X13758))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13759),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13759),X13758),X13757)),c_Groups_Ozero__class_Ozero(X13759)))|~class_Fields_Olinordered__field__inverse__zero(X13759))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13759),c_Groups_Ozero__class_Ozero(X13759)),X13757))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13759),c_Groups_Ozero__class_Ozero(X13759)),X13758))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13759),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13759),X13758),X13757)),c_Groups_Ozero__class_Ozero(X13759)))|~class_Fields_Olinordered__field__inverse__zero(X13759)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13759),X13758),c_Groups_Ozero__class_Ozero(X13759)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13759),X13757),c_Groups_Ozero__class_Ozero(X13759)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13759),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13759),X13758),X13757)),c_Groups_Ozero__class_Ozero(X13759)))|~class_Fields_Olinordered__field__inverse__zero(X13759))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13759),c_Groups_Ozero__class_Ozero(X13759)),X13757))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13759),X13757),c_Groups_Ozero__class_Ozero(X13759)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13759),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13759),X13758),X13757)),c_Groups_Ozero__class_Ozero(X13759)))|~class_Fields_Olinordered__field__inverse__zero(X13759))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__less__0__iff])])])])). 6.97/7.23 fof(c_0_7445, plain, ![X2697, X2698, X2699]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2699),X2697),c_Groups_Ozero__class_Ozero(X2699)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2699),c_Groups_Ozero__class_Ozero(X2699)),X2698))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2699),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2699),X2698),X2697)),c_Groups_Ozero__class_Ozero(X2699)))|~class_Fields_Olinordered__field__inverse__zero(X2699))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2699),X2698),c_Groups_Ozero__class_Ozero(X2699)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2699),c_Groups_Ozero__class_Ozero(X2699)),X2697))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2699),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2699),X2698),X2697)),c_Groups_Ozero__class_Ozero(X2699)))|~class_Fields_Olinordered__field__inverse__zero(X2699)))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2699),X2698),c_Groups_Ozero__class_Ozero(X2699)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2699),X2697),c_Groups_Ozero__class_Ozero(X2699)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2699),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2699),X2698),X2697)),c_Groups_Ozero__class_Ozero(X2699)))|~class_Fields_Olinordered__field__inverse__zero(X2699))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2699),c_Groups_Ozero__class_Ozero(X2699)),X2697))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2699),X2697),c_Groups_Ozero__class_Ozero(X2699)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2699),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2699),X2698),X2697)),c_Groups_Ozero__class_Ozero(X2699)))|~class_Fields_Olinordered__field__inverse__zero(X2699)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2699),X2698),c_Groups_Ozero__class_Ozero(X2699)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2699),c_Groups_Ozero__class_Ozero(X2699)),X2698))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2699),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2699),X2698),X2697)),c_Groups_Ozero__class_Ozero(X2699)))|~class_Fields_Olinordered__field__inverse__zero(X2699))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2699),c_Groups_Ozero__class_Ozero(X2699)),X2697))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2699),c_Groups_Ozero__class_Ozero(X2699)),X2698))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2699),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2699),X2698),X2697)),c_Groups_Ozero__class_Ozero(X2699)))|~class_Fields_Olinordered__field__inverse__zero(X2699))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__le__0__iff])])])). 6.97/7.23 fof(c_0_7446, plain, ![X16649, X16650, X16651, X16652, X16653]:(~c_Fun_Oinj__on(X16653,X16652,X16651,X16650)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16653,tc_HOL_Obool)),X16649),X16650))|hAPP(c_Set_Oimage(X16652,X16653,c_Hilbert__Choice_Oinv__into(X16653,X16652,X16650,X16651)),hAPP(c_Set_Oimage(X16653,X16652,X16651),X16649))=X16649)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inv__into__image__cancel])])])). 6.97/7.23 fof(c_0_7447, plain, ![X10145, X10146, X10147, X10148]:(~class_Rings_Olinordered__semidom(X10148)|(hAPP(hAPP(c_Power_Opower__class_Opower(X10148),X10147),hAPP(c_Nat_OSuc,X10146))!=hAPP(hAPP(c_Power_Opower__class_Opower(X10148),X10145),hAPP(c_Nat_OSuc,X10146))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10148),c_Groups_Ozero__class_Ozero(X10148)),X10147))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10148),c_Groups_Ozero__class_Ozero(X10148)),X10145))|X10145=X10147)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__inject__base])])])). 6.97/7.23 cnf(c_0_7448, 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_Otimes__class_Otimes(tc_Int_Oint),X1),X2))=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))), inference(split_conjunct,[status(thm)],[c_0_5218])). 6.97/7.23 fof(c_0_7449, plain, ![X13294, X13295, X13296]:(~class_Rings_Oring__1(X13296)|(~hBOOL(hAPP(hAPP(c_member(X13296),X13295),c_Int_Oring__1__class_OInts(X13296)))|(~hBOOL(hAPP(hAPP(c_member(X13296),X13294),c_Int_Oring__1__class_OInts(X13296)))|hBOOL(hAPP(hAPP(c_member(X13296),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13296),X13295),X13294)),c_Int_Oring__1__class_OInts(X13296)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Ints__diff])])])). 6.97/7.23 fof(c_0_7450, plain, ![X4541, X4542, X4543]:(~class_Rings_Osemiring__1(X4543)|(~hBOOL(hAPP(hAPP(c_member(X4543),X4542),c_Nat_Osemiring__1__class_ONats(X4543)))|(~hBOOL(hAPP(hAPP(c_member(X4543),X4541),c_Nat_Osemiring__1__class_ONats(X4543)))|hBOOL(hAPP(hAPP(c_member(X4543),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4543),X4542),X4541)),c_Nat_Osemiring__1__class_ONats(X4543)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nats__add])])])). 6.97/7.23 fof(c_0_7451, plain, ![X8765, X8766, X8767]:(~class_Rings_Oring__1(X8767)|(~hBOOL(hAPP(hAPP(c_member(X8767),X8766),c_Int_Oring__1__class_OInts(X8767)))|(~hBOOL(hAPP(hAPP(c_member(X8767),X8765),c_Int_Oring__1__class_OInts(X8767)))|hBOOL(hAPP(hAPP(c_member(X8767),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8767),X8766),X8765)),c_Int_Oring__1__class_OInts(X8767)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Ints__add])])])). 6.97/7.23 fof(c_0_7452, plain, ![X12282, X12283, X12284]:(~class_Rings_Osemiring__1(X12284)|(~hBOOL(hAPP(hAPP(c_member(X12284),X12283),c_Nat_Osemiring__1__class_ONats(X12284)))|(~hBOOL(hAPP(hAPP(c_member(X12284),X12282),c_Nat_Osemiring__1__class_ONats(X12284)))|hBOOL(hAPP(hAPP(c_member(X12284),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12284),X12283),X12282)),c_Nat_Osemiring__1__class_ONats(X12284)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nats__mult])])])). 6.97/7.23 fof(c_0_7453, plain, ![X10850, X10851, X10852]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10851),X10850))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X10851),X10852)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X10850),X10852)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10852),X10850))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10852),X10851)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X10851),X10852)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X10850),X10852)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10851),X10850))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10852),X10850))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10852),X10851)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__diff__iff])])])])). 6.97/7.23 fof(c_0_7454, plain, ![X11312, X11313, X11314]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11313),X11312))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11313),X11314)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11312),X11314)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11314),X11312))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11314),X11313)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11313),X11314)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11312),X11314)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11313),X11312))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11314),X11312))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11314),X11313)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__diff__iff])])])])). 6.97/7.23 fof(c_0_7455, plain, ![X6995, X6996, X6997]:(~class_Rings_Oring__1(X6997)|(~hBOOL(hAPP(hAPP(c_member(X6997),X6996),c_Int_Oring__1__class_OInts(X6997)))|(~hBOOL(hAPP(hAPP(c_member(X6997),X6995),c_Int_Oring__1__class_OInts(X6997)))|hBOOL(hAPP(hAPP(c_member(X6997),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6997),X6996),X6995)),c_Int_Oring__1__class_OInts(X6997)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Ints__mult])])])). 6.97/7.23 fof(c_0_7456, plain, ![X4846, X4847, X4848]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4848),X4846),c_Groups_Ozero__class_Ozero(X4848)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4848),X4847),c_Groups_Ozero__class_Ozero(X4848)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4848),c_Groups_Ozero__class_Ozero(X4848)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4848),X4847),X4846)))|~class_Fields_Olinordered__field__inverse__zero(X4848))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4848),c_Groups_Ozero__class_Ozero(X4848)),X4846))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4848),c_Groups_Ozero__class_Ozero(X4848)),X4847))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4848),c_Groups_Ozero__class_Ozero(X4848)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4848),X4847),X4846)))|~class_Fields_Olinordered__field__inverse__zero(X4848)))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4848),c_Groups_Ozero__class_Ozero(X4848)),X4846))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4848),X4846),c_Groups_Ozero__class_Ozero(X4848)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4848),c_Groups_Ozero__class_Ozero(X4848)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4848),X4847),X4846)))|~class_Fields_Olinordered__field__inverse__zero(X4848))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4848),c_Groups_Ozero__class_Ozero(X4848)),X4847))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4848),X4846),c_Groups_Ozero__class_Ozero(X4848)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4848),c_Groups_Ozero__class_Ozero(X4848)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4848),X4847),X4846)))|~class_Fields_Olinordered__field__inverse__zero(X4848)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4848),c_Groups_Ozero__class_Ozero(X4848)),X4846))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4848),X4847),c_Groups_Ozero__class_Ozero(X4848)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4848),c_Groups_Ozero__class_Ozero(X4848)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4848),X4847),X4846)))|~class_Fields_Olinordered__field__inverse__zero(X4848))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4848),c_Groups_Ozero__class_Ozero(X4848)),X4847))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4848),X4847),c_Groups_Ozero__class_Ozero(X4848)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4848),c_Groups_Ozero__class_Ozero(X4848)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4848),X4847),X4846)))|~class_Fields_Olinordered__field__inverse__zero(X4848))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__divide__iff])])])). 6.97/7.23 fof(c_0_7457, plain, ![X6359, X6360, X6361]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6361),X6360),c_Groups_Ozero__class_Ozero(X6361)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6361),c_Groups_Ozero__class_Ozero(X6361)),X6359))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6361),c_Groups_Ozero__class_Ozero(X6361)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6361),X6360),X6359)))|~class_Fields_Olinordered__field__inverse__zero(X6361))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6361),X6359),c_Groups_Ozero__class_Ozero(X6361)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6361),c_Groups_Ozero__class_Ozero(X6361)),X6359))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6361),c_Groups_Ozero__class_Ozero(X6361)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6361),X6360),X6359)))|~class_Fields_Olinordered__field__inverse__zero(X6361)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6361),X6360),c_Groups_Ozero__class_Ozero(X6361)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6361),c_Groups_Ozero__class_Ozero(X6361)),X6360))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6361),c_Groups_Ozero__class_Ozero(X6361)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6361),X6360),X6359)))|~class_Fields_Olinordered__field__inverse__zero(X6361))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6361),X6359),c_Groups_Ozero__class_Ozero(X6361)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6361),c_Groups_Ozero__class_Ozero(X6361)),X6360))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6361),c_Groups_Ozero__class_Ozero(X6361)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6361),X6360),X6359)))|~class_Fields_Olinordered__field__inverse__zero(X6361))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6361),c_Groups_Ozero__class_Ozero(X6361)),X6359))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6361),c_Groups_Ozero__class_Ozero(X6361)),X6360))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6361),c_Groups_Ozero__class_Ozero(X6361)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6361),X6360),X6359)))|~class_Fields_Olinordered__field__inverse__zero(X6361))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6361),X6360),c_Groups_Ozero__class_Ozero(X6361)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6361),X6359),c_Groups_Ozero__class_Ozero(X6361)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6361),c_Groups_Ozero__class_Ozero(X6361)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6361),X6360),X6359)))|~class_Fields_Olinordered__field__inverse__zero(X6361)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__le__divide__iff])])])])). 6.97/7.23 cnf(c_0_7458, plain, (X2=esk231_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_5134])). 6.97/7.23 fof(c_0_7459, plain, ![X2835, X2836, X2837, X2838, X2839, X2840, X2841]:((hBOOL(hAPP(hAPP(c_member(X2841),esk90_7(X2835,X2836,X2837,X2838,X2839,X2840,X2841)),X2838))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2841,tc_fun(X2840,tc_fun(X2839,tc_HOL_Obool))),X2838),X2837),X2836),X2835)))&(hBOOL(hAPP(hAPP(hAPP(X2837,esk90_7(X2835,X2836,X2837,X2838,X2839,X2840,X2841)),X2836),X2835))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2841,tc_fun(X2840,tc_fun(X2839,tc_HOL_Obool))),X2838),X2837),X2836),X2835)))), 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])])])])])). 6.97/7.23 fof(c_0_7460, plain, ![X13351, X13352, X13353]:((((hBOOL(hAPP(c_List_Odistinct(X13353),X13352))|~hBOOL(hAPP(c_List_Odistinct(X13353),hAPP(hAPP(c_List_Oappend(X13353),X13352),X13351))))&(hBOOL(hAPP(c_List_Odistinct(X13353),X13351))|~hBOOL(hAPP(c_List_Odistinct(X13353),hAPP(hAPP(c_List_Oappend(X13353),X13352),X13351)))))&(c_Orderings_Obot__class_Obot(tc_fun(X13353,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13353,tc_HOL_Obool)),hAPP(c_List_Oset(X13353),X13352)),hAPP(c_List_Oset(X13353),X13351))|~hBOOL(hAPP(c_List_Odistinct(X13353),hAPP(hAPP(c_List_Oappend(X13353),X13352),X13351)))))&(~hBOOL(hAPP(c_List_Odistinct(X13353),X13352))|~hBOOL(hAPP(c_List_Odistinct(X13353),X13351))|c_Orderings_Obot__class_Obot(tc_fun(X13353,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13353,tc_HOL_Obool)),hAPP(c_List_Oset(X13353),X13352)),hAPP(c_List_Oset(X13353),X13351))|hBOOL(hAPP(c_List_Odistinct(X13353),hAPP(hAPP(c_List_Oappend(X13353),X13352),X13351))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__append])])])). 6.97/7.23 fof(c_0_7461, plain, ![X1128, X1129]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1129),X1128))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1128)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1129))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1128),X1129))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiff__int])])). 6.97/7.23 fof(c_0_7462, plain, ![X4732, X4733, X4734, X4735, X4736]:((~hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X4736,X4735,X4734),X4733),X4732))|hBOOL(hAPP(hAPP(c_member(tc_prod(X4736,X4735)),hAPP(hAPP(c_Product__Type_OPair(X4736,X4735),X4733),X4732)),X4734)))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X4736,X4735)),hAPP(hAPP(c_Product__Type_OPair(X4736,X4735),X4733),X4732)),X4734))|hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X4736,X4735,X4734),X4733),X4732)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])])). 6.97/7.23 fof(c_0_7463, plain, ![X12520, X12521, X12522, X12523, X12524]:((~c_Relation_Oirrefl(X12521,X12520)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X12521,X12521)),hAPP(hAPP(c_Product__Type_OPair(X12521,X12521),X12522),X12522)),X12520)))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X12524,X12524)),hAPP(hAPP(c_Product__Type_OPair(X12524,X12524),esk412_2(X12523,X12524)),esk412_2(X12523,X12524))),X12523))|c_Relation_Oirrefl(X12524,X12523))), 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])])])])])])). 6.97/7.23 fof(c_0_7464, plain, ![X16442, X16443, X16444, X16445]:(~class_Rings_Olinordered__semidom(X16445)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16445),hAPP(hAPP(c_Power_Opower__class_Opower(X16445),X16444),hAPP(c_Nat_OSuc,X16443))),hAPP(hAPP(c_Power_Opower__class_Opower(X16445),X16442),hAPP(c_Nat_OSuc,X16443))))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16445),c_Groups_Ozero__class_Ozero(X16445)),X16442))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16445),X16444),X16442))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__le__imp__le__base])])])). 6.97/7.23 fof(c_0_7465, plain, ![X17525, X17526, X17527, X17528, X17529, X17530]:((~c_Relation_Oantisym(X17526,X17525)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X17526,X17526)),hAPP(hAPP(c_Product__Type_OPair(X17526,X17526),X17527),X17528)),X17525))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X17526,X17526)),hAPP(hAPP(c_Product__Type_OPair(X17526,X17526),X17528),X17527)),X17525))|X17528=X17527)))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X17530,X17530)),hAPP(hAPP(c_Product__Type_OPair(X17530,X17530),esk596_2(X17529,X17530)),esk597_2(X17529,X17530))),X17529))|c_Relation_Oantisym(X17530,X17529))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X17530,X17530)),hAPP(hAPP(c_Product__Type_OPair(X17530,X17530),esk597_2(X17529,X17530)),esk596_2(X17529,X17530))),X17529))|c_Relation_Oantisym(X17530,X17529))&(esk597_2(X17529,X17530)!=esk596_2(X17529,X17530)|c_Relation_Oantisym(X17530,X17529))))), 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_antisym__def])])])])])])])). 6.97/7.23 cnf(c_0_7466, 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),X1)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)), inference(split_conjunct,[status(thm)],[c_0_5219])). 6.97/7.23 fof(c_0_7467, plain, ![X1238, X1239, X1240]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1240,tc_HOL_Obool)),X1239),X1238))|hBOOL(hAPP(hAPP(c_member(X1240),esk37_3(X1238,X1239,X1240)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1240,tc_HOL_Obool)),X1238),X1239)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_psubset__imp__ex__mem])])])])). 6.97/7.23 fof(c_0_7468, plain, ![X7489, X7490, X7491]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7491,tc_HOL_Obool)),X7490),X7489))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X7491,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X7491),X7490)),hAPP(c_Set_OPow(X7491),X7489)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pow__mono])])). 6.97/7.23 fof(c_0_7469, plain, ![X15749, X15750, X15751, X15752, X15753, X15755, X15756, X15757, X15758, X15759, X15760]:(((hBOOL(hAPP(hAPP(c_member(X15751),esk531_5(X15749,X15750,X15751,X15752,X15753)),X15750))|~hBOOL(hAPP(hAPP(c_member(X15753),X15752),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15751,tc_fun(X15753,tc_HOL_Obool)),X15750),X15749))))&(hBOOL(hAPP(hAPP(c_member(X15753),X15752),hAPP(X15749,esk531_5(X15749,X15750,X15751,X15752,X15753))))|~hBOOL(hAPP(hAPP(c_member(X15753),X15752),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15751,tc_fun(X15753,tc_HOL_Obool)),X15750),X15749)))))&(~hBOOL(hAPP(hAPP(c_member(X15757),X15760),X15756))|~hBOOL(hAPP(hAPP(c_member(X15759),X15758),hAPP(X15755,X15760)))|hBOOL(hAPP(hAPP(c_member(X15759),X15758),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15757,tc_fun(X15759,tc_HOL_Obool)),X15756),X15755))))), 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])])])])])])). 6.97/7.23 fof(c_0_7470, plain, ![X14798, X14799, X14800, X14801, X14802]:((hBOOL(hAPP(hAPP(c_member(X14800),esk500_5(X14798,X14799,X14800,X14801,X14802)),X14799))|~hBOOL(hAPP(hAPP(c_member(X14802),X14801),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14800,tc_fun(X14802,tc_HOL_Obool)),X14799),X14798))))&(hBOOL(hAPP(hAPP(c_member(X14802),X14801),hAPP(X14798,esk500_5(X14798,X14799,X14800,X14801,X14802))))|~hBOOL(hAPP(hAPP(c_member(X14802),X14801),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14800,tc_fun(X14802,tc_HOL_Obool)),X14799),X14798))))), 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__E])])])])])). 6.97/7.23 fof(c_0_7471, plain, ![X16783, X16784, X16785, X16786, X16787, X16788, X16789]:((~c_Relation_Otrans(X16784,X16783)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X16784,X16784)),hAPP(hAPP(c_Product__Type_OPair(X16784,X16784),X16785),X16786)),X16783))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X16784,X16784)),hAPP(hAPP(c_Product__Type_OPair(X16784,X16784),X16786),X16787)),X16783))|hBOOL(hAPP(hAPP(c_member(tc_prod(X16784,X16784)),hAPP(hAPP(c_Product__Type_OPair(X16784,X16784),X16785),X16787)),X16783)))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X16789,X16789)),hAPP(hAPP(c_Product__Type_OPair(X16789,X16789),esk562_2(X16788,X16789)),esk563_2(X16788,X16789))),X16788))|c_Relation_Otrans(X16789,X16788))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X16789,X16789)),hAPP(hAPP(c_Product__Type_OPair(X16789,X16789),esk563_2(X16788,X16789)),esk564_2(X16788,X16789))),X16788))|c_Relation_Otrans(X16789,X16788))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X16789,X16789)),hAPP(hAPP(c_Product__Type_OPair(X16789,X16789),esk562_2(X16788,X16789)),esk564_2(X16788,X16789))),X16788))|c_Relation_Otrans(X16789,X16788))))), 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_trans__def])])])])])])])). 6.97/7.23 cnf(c_0_7472, 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_5220])). 6.97/7.23 fof(c_0_7473, plain, ![X1922, X1923, X1924]:(~c_Fun_Obij__betw(X1924,X1923,X1922,c_Orderings_Otop__class_Otop(tc_fun(X1924,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1923,tc_HOL_Obool)))|c_Hilbert__Choice_Oinv__into(X1923,X1924,c_Orderings_Otop__class_Otop(tc_fun(X1923,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(X1924,X1923,c_Orderings_Otop__class_Otop(tc_fun(X1924,tc_HOL_Obool)),X1922))=X1922), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inv__inv__eq])])])). 6.97/7.23 cnf(c_0_7474, 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))))|X3!=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(split_conjunct,[status(thm)],[c_0_5221])). 6.97/7.23 fof(c_0_7475, plain, ![X1112, X1113, X1114, X1115]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1115),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1114)),X1113)))|hBOOL(hAPP(hAPP(c_member(X1114),X1112),hAPP(c_List_Oset(X1114),hAPP(hAPP(c_List_Olist__update(X1114,X1113),X1115),X1112))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_set__update__memI])])])). 6.97/7.23 fof(c_0_7476, plain, ![X2356, X2357, X2358, X2359, X2360]:(~c_Finite__Set_Ofolding__one__idem(X2360,X2359,X2358)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2360),X2357))|hAPP(X2358,hAPP(hAPP(c_Set_Oinsert(X2360),X2356),X2357))=hAPP(hAPP(c_Finite__Set_Ofold(X2360,X2360,X2359),X2356),X2357))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one__idem_Oeq__fold__idem_H])])])). 6.97/7.23 fof(c_0_7477, plain, ![X2454, X2455, X2456, X2457, X2459, X2460, X2461, X2462, X2463]:(((hBOOL(hAPP(hAPP(c_member(X2457),esk82_4(X2454,X2455,X2456,X2457)),hAPP(c_List_Oset(X2457),c_List_Oreplicate(X2457,X2456,X2455))))|(X2456=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(X2454,X2455))))&(hBOOL(hAPP(X2454,esk82_4(X2454,X2455,X2456,X2457)))|(X2456=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(X2454,X2455)))))&((X2461!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|(~hBOOL(hAPP(hAPP(c_member(X2462),X2463),hAPP(c_List_Oset(X2462),c_List_Oreplicate(X2462,X2461,X2460))))|~hBOOL(hAPP(X2459,X2463))))&(hBOOL(hAPP(X2459,X2460))|(~hBOOL(hAPP(hAPP(c_member(X2462),X2463),hAPP(c_List_Oset(X2462),c_List_Oreplicate(X2462,X2461,X2460))))|~hBOOL(hAPP(X2459,X2463)))))), 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])])])])])])). 6.97/7.23 cnf(c_0_7478, plain, (hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),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_5222, c_0_4573])). 6.97/7.23 cnf(c_0_7479, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|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_5164])). 6.97/7.23 fof(c_0_7480, plain, ![X4967, X4968, X4969]:(~class_Complete__Lattice_Ocomplete__lattice(X4969)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4969),X4968),X4967)=c_Complete__Lattice_OInf__class_OInf(X4969,hAPP(hAPP(c_Set_Oinsert(X4969),X4968),hAPP(hAPP(c_Set_Oinsert(X4969),X4967),c_Orderings_Obot__class_Obot(tc_fun(X4969,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__binary])])])). 6.97/7.23 cnf(c_0_7481, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X4)=hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)|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)!=hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)|~class_Fields_Ofield__inverse__zero(X2)|~class_Int_Onumber(X2)), inference(split_conjunct,[status(thm)],[c_0_5223])). 6.97/7.23 fof(c_0_7482, plain, ![X12937, X12938, X12939]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X12939,X12939),tc_HOL_Obool)),X12938),c_Transitive__Closure_Ortrancl(X12939,X12937)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X12939,X12939),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X12939,X12938)),c_Transitive__Closure_Ortrancl(X12939,X12937)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rtrancl__subset__rtrancl])])])). 6.97/7.23 fof(c_0_7483, plain, ![X1264, X1265, X1266, X1267, X1268]:(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1268,X1268,X1267,X1266,X1265),X1264))|(hBOOL(hAPP(hAPP(c_member(X1268),X1266),X1265))|hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1268,X1267,hAPP(hAPP(c_Set_Oinsert(X1268),X1266),X1265)),X1264)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1Set_Ointros])])])). 6.97/7.23 fof(c_0_7484, plain, ![X10293, X10294, X10295]:((hBOOL(hAPP(hAPP(c_member(X10295),esk340_3(X10293,X10294,X10295)),hAPP(c_List_Oset(X10295),X10294)))|(~c_List_Olinorder__class_Osorted(X10295,X10294)|c_List_Olinorder__class_Osorted(X10295,hAPP(hAPP(c_List_Olist_OCons(X10295),X10293),X10294)))|~class_Orderings_Olinorder(X10295))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10295),X10293),esk340_3(X10293,X10294,X10295)))|(~c_List_Olinorder__class_Osorted(X10295,X10294)|c_List_Olinorder__class_Osorted(X10295,hAPP(hAPP(c_List_Olist_OCons(X10295),X10293),X10294)))|~class_Orderings_Olinorder(X10295))), 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])])])])])). 6.97/7.23 fof(c_0_7485, plain, ![X11525, X11526, X11527]:(~class_Complete__Lattice_Ocomplete__lattice(X11527)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X11527),X11526),X11525)=c_Complete__Lattice_OSup__class_OSup(X11527,hAPP(hAPP(c_Set_Oinsert(X11527),X11526),hAPP(hAPP(c_Set_Oinsert(X11527),X11525),c_Orderings_Obot__class_Obot(tc_fun(X11527,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__binary])])])). 6.97/7.23 fof(c_0_7486, plain, ![X2932, X2933, X2934, X2935, X2936, X2937, X2938]:(((c_List_Olist__all2(X2938,X2937,X2936,X2934,X2932)|~c_List_Olist__all2(X2938,X2937,X2936,hAPP(hAPP(c_List_Olist_OCons(X2938),X2935),X2934),hAPP(hAPP(c_List_Olist_OCons(X2937),X2933),X2932)))&(hBOOL(hAPP(hAPP(X2936,X2935),X2933))|~c_List_Olist__all2(X2938,X2937,X2936,hAPP(hAPP(c_List_Olist_OCons(X2938),X2935),X2934),hAPP(hAPP(c_List_Olist_OCons(X2937),X2933),X2932))))&(~c_List_Olist__all2(X2938,X2937,X2936,X2934,X2932)|~hBOOL(hAPP(hAPP(X2936,X2935),X2933))|c_List_Olist__all2(X2938,X2937,X2936,hAPP(hAPP(c_List_Olist_OCons(X2938),X2935),X2934),hAPP(hAPP(c_List_Olist_OCons(X2937),X2933),X2932)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__Cons])])])). 6.97/7.23 fof(c_0_7487, plain, ![X11062, X11063, X11064, X11065, X11066, X11067, X11068]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X11067),X11063))|hAPP(hAPP(X11064,X11062),X11063)=X11065|~c_Big__Operators_Ocomm__monoid__big(X11068,X11067,X11066,X11065,X11064))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11067),X11063))|hAPP(hAPP(X11064,X11062),X11063)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X11068,X11067,X11066),X11062),X11065),X11063)|~c_Big__Operators_Ocomm__monoid__big(X11068,X11067,X11066,X11065,X11064))), 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])])])])). 6.97/7.23 fof(c_0_7488, plain, ![X6480, X6481, X6482, X6483, X6484, X6485, X6486]:(~c_Finite__Set_Ofolding__image(X6486,X6485,X6484,X6483,X6482)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6485),X6481))|hAPP(hAPP(X6482,X6480),X6481)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6486,X6485,X6484),X6480),X6483),X6481))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image_Oeq__fold])])). 6.97/7.23 fof(c_0_7489, plain, ![X9626, X9627, X9628, X9629]:(~class_Orderings_Olinorder(X9629)|c_SetInterval_Oord__class_OatLeastAtMost(X9629,hAPP(hAPP(c_Orderings_Oord__class_Omax(X9629),X9628),X9626),X9627)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9629,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X9629,X9628,X9627)),hAPP(c_SetInterval_Oord__class_OatLeast(X9629),X9626))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__atLeastAtMostL2])])])). 6.97/7.23 fof(c_0_7490, plain, ![X15977, X15978, X15979, X15981]:(((hBOOL(hAPP(hAPP(c_member(X15979),esk540_3(X15977,X15978,X15979)),hAPP(c_List_Oset(X15979),X15977)))|~c_List_Olinorder__class_Osorted(X15979,X15977)|c_List_Olinorder__class_Osorted(X15979,hAPP(hAPP(c_List_Olist_OCons(X15979),X15978),X15977))|~class_Orderings_Olinorder(X15979))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15979),X15978),esk540_3(X15977,X15978,X15979)))|~c_List_Olinorder__class_Osorted(X15979,X15977)|c_List_Olinorder__class_Osorted(X15979,hAPP(hAPP(c_List_Olist_OCons(X15979),X15978),X15977))|~class_Orderings_Olinorder(X15979)))&((~hBOOL(hAPP(hAPP(c_member(X15979),X15981),hAPP(c_List_Oset(X15979),X15977)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15979),X15978),X15981))|~c_List_Olinorder__class_Osorted(X15979,hAPP(hAPP(c_List_Olist_OCons(X15979),X15978),X15977))|~class_Orderings_Olinorder(X15979))&(c_List_Olinorder__class_Osorted(X15979,X15977)|~c_List_Olinorder__class_Osorted(X15979,hAPP(hAPP(c_List_Olist_OCons(X15979),X15978),X15977))|~class_Orderings_Olinorder(X15979)))), 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])])])])])])). 6.97/7.23 fof(c_0_7491, plain, ![X4046, X4047, X4048, X4050]:(((hBOOL(hAPP(hAPP(c_member(X4048),esk139_3(X4046,X4047,X4048)),hAPP(c_List_Oset(X4048),X4046)))|~c_List_Olinorder__class_Osorted(X4048,X4046)|c_List_Olinorder__class_Osorted(X4048,hAPP(hAPP(c_List_Olist_OCons(X4048),X4047),X4046))|~class_Orderings_Olinorder(X4048))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4048),X4047),esk139_3(X4046,X4047,X4048)))|~c_List_Olinorder__class_Osorted(X4048,X4046)|c_List_Olinorder__class_Osorted(X4048,hAPP(hAPP(c_List_Olist_OCons(X4048),X4047),X4046))|~class_Orderings_Olinorder(X4048)))&((~hBOOL(hAPP(hAPP(c_member(X4048),X4050),hAPP(c_List_Oset(X4048),X4046)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4048),X4047),X4050))|~c_List_Olinorder__class_Osorted(X4048,hAPP(hAPP(c_List_Olist_OCons(X4048),X4047),X4046))|~class_Orderings_Olinorder(X4048))&(c_List_Olinorder__class_Osorted(X4048,X4046)|~c_List_Olinorder__class_Osorted(X4048,hAPP(hAPP(c_List_Olist_OCons(X4048),X4047),X4046))|~class_Orderings_Olinorder(X4048)))), 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])])])])])])). 6.97/7.23 fof(c_0_7492, plain, ![X4750, X4751, X4752]:(~class_Orderings_Olinorder(X4752)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4752),X4751),X4750))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4752,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4752,X4751,X4750)),hAPP(c_SetInterval_Oord__class_OatLeast(X4752),X4750))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X4752),X4751))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I12_J])])])). 6.97/7.23 fof(c_0_7493, plain, ![X1663, X1664, X1665]:(~class_Orderings_Olinorder(X1665)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1665),X1664),X1663))|hAPP(c_SetInterval_Oord__class_OgreaterThan(X1665),X1664)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1665,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1665,X1664,X1663)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1665),X1663)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I11_J])])). 6.97/7.23 fof(c_0_7494, plain, ![X9110, X9111, X9112, X9113]:(~class_Orderings_Olinorder(X9113)|c_SetInterval_Oord__class_OatLeastAtMost(X9113,X9112,hAPP(hAPP(c_Orderings_Oord__class_Omin(X9113),X9111),X9110))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9113,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X9113,X9112,X9111)),hAPP(c_SetInterval_Oord__class_OatMost(X9113),X9110))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__atLeastAtMostL1])])])). 6.97/7.23 cnf(c_0_7495, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3)=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ozero__class_Ozero(X2)|c_Groups_Ozero__class_Ozero(X2)!=X3|~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_5224])). 6.97/7.23 fof(c_0_7496, plain, ![X14132, X14133, X14134, X14135]:(~class_Orderings_Olinorder(X14135)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14135,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X14135),X14134)),c_SetInterval_Oord__class_OatLeastAtMost(X14135,X14133,X14132))=c_SetInterval_Oord__class_OatLeastAtMost(X14135,hAPP(hAPP(c_Orderings_Oord__class_Omax(X14135),X14134),X14133),X14132)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__atLeastAtMostR2])])])). 6.97/7.23 fof(c_0_7497, plain, ![X11211, X11212, X11213, X11214]:((~hBOOL(hAPP(X11214,X11213))|hAPP(hAPP(c_List_Olist_OCons(X11212),X11213),hAPP(c_List_Ofilter(X11212,X11214),X11211))=hAPP(c_List_Ofilter(X11212,X11214),hAPP(hAPP(c_List_Olist_OCons(X11212),X11213),X11211)))&(hBOOL(hAPP(X11214,X11213))|hAPP(c_List_Ofilter(X11212,X11214),X11211)=hAPP(c_List_Ofilter(X11212,X11214),hAPP(hAPP(c_List_Olist_OCons(X11212),X11213),X11211)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_filter_Osimps_I2_J])])])). 6.97/7.23 fof(c_0_7498, plain, ![X15791, X15792, X15793]:(~class_Orderings_Olinorder(X15793)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15793),X15792),X15791))|hAPP(c_SetInterval_Oord__class_OatLeast(X15793),X15792)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15793,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X15793,X15792,X15791)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X15793),X15791)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I13_J])])])). 6.97/7.23 fof(c_0_7499, plain, ![X10382, X10383, X10384]:(~class_Orderings_Olinorder(X10384)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10384),X10383),X10382))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10384,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X10384),X10383)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10384,X10383,X10382))=hAPP(c_SetInterval_Oord__class_OlessThan(X10384),X10382))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I7_J])])). 6.97/7.23 fof(c_0_7500, plain, ![X6252, X6253, X6254]:(~class_Orderings_Olinorder(X6254)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6254),X6253),X6252))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6254,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X6254),X6253)),c_SetInterval_Oord__class_OgreaterThanAtMost(X6254,X6253,X6252))=hAPP(c_SetInterval_Oord__class_OatMost(X6254),X6252))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I9_J])])])). 6.97/7.23 fof(c_0_7501, plain, ![X17479, X17480, X17481]:(~class_Orderings_Olinorder(X17481)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17481),X17480),X17479))|hAPP(c_SetInterval_Oord__class_OatMost(X17481),X17479)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17481,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X17481),X17480)),c_SetInterval_Oord__class_OatLeastAtMost(X17481,X17480,X17479)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I10_J])])])). 6.97/7.23 fof(c_0_7502, plain, ![X15080, X15081, X15082, X15083]:(~class_Orderings_Olinorder(X15083)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15083,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X15083),X15082)),c_SetInterval_Oord__class_OatLeastAtMost(X15083,X15081,X15080))=c_SetInterval_Oord__class_OatLeastAtMost(X15083,X15081,hAPP(hAPP(c_Orderings_Oord__class_Omin(X15083),X15082),X15080))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR1])])). 6.97/7.23 fof(c_0_7503, plain, ![X2223, X2224, X2225, X2226, X2227, X2228]:(~c_Relation_Osingle__valued(X2228,X2227,X2226)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X2228,X2227)),hAPP(hAPP(c_Product__Type_OPair(X2228,X2227),X2225),X2224)),X2226))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X2228,X2227)),hAPP(hAPP(c_Product__Type_OPair(X2228,X2227),X2225),X2223)),X2226))|X2224=X2223))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_single__valuedD])])])). 6.97/7.23 fof(c_0_7504, plain, ![X2069, X2070, X2071, X2072, X2073]:((~c_List_Olinorder__class_Osorted(X2073,hAPP(hAPP(c_List_Omap(X2072,X2073),X2071),X2069))|c_List_Olinorder__class_Osorted(X2073,hAPP(hAPP(c_List_Omap(X2072,X2073),X2071),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2072,X2073,X2071),X2070),X2069)))|~class_Orderings_Olinorder(X2073))&(~c_List_Olinorder__class_Osorted(X2073,hAPP(hAPP(c_List_Omap(X2072,X2073),X2071),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2072,X2073,X2071),X2070),X2069)))|c_List_Olinorder__class_Osorted(X2073,hAPP(hAPP(c_List_Omap(X2072,X2073),X2071),X2069))|~class_Orderings_Olinorder(X2073))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__insort__key])])])])). 6.97/7.23 fof(c_0_7505, plain, ![X4561, X4562, X4563]:(~class_Fields_Ofield__inverse__zero(X4563)|hAPP(hAPP(c_Power_Opower__class_Opower(X4563),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4563),c_Groups_Oone__class_Oone(X4563)),X4562)),X4561)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4563),c_Groups_Oone__class_Oone(X4563)),hAPP(hAPP(c_Power_Opower__class_Opower(X4563),X4562),X4561))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__over])])). 6.97/7.23 fof(c_0_7506, plain, ![X7004, X7005, X7006]:(~class_Groups_Omonoid__add(X7006)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7006),X7005),hAPP(c_List_Ofoldl(X7006,X7006,c_Groups_Oplus__class_Oplus(X7006),c_Groups_Ozero__class_Ozero(X7006)),X7004))=hAPP(c_List_Ofoldl(X7006,X7006,c_Groups_Oplus__class_Oplus(X7006),X7005),X7004)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_foldl__absorb0])])])). 6.97/7.23 fof(c_0_7507, plain, ![X4857, X4858, X4859, X4860, X4861, X4862]:(~c_Finite__Set_Ofun__left__comm(X4862,X4861,X4860)|hAPP(hAPP(X4860,X4859),hAPP(hAPP(X4860,X4858),X4857))=hAPP(hAPP(X4860,X4858),hAPP(hAPP(X4860,X4859),X4857))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofun__left__comm])])])). 6.97/7.23 cnf(c_0_7508, 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,hAPP(c_Nat_OSuc,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_5225])). 6.97/7.23 fof(c_0_7509, plain, ![X5027, X5028, X5029, X5030]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5030,tc_HOL_Obool)),X5029),X5028))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5030,tc_HOL_Obool)),X5028),X5027))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5030,tc_HOL_Obool)),X5029),X5027)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_psubset__trans])])])). 6.97/7.23 fof(c_0_7510, plain, ![X8206, X8207, X8208, X8209]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8209,tc_HOL_Obool)),X8208),X8207))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X8209,tc_HOL_Obool)),X8207),X8206))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X8209,tc_HOL_Obool)),X8208),X8206)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__psubset__trans])])). 6.97/7.23 fof(c_0_7511, plain, ![X4164, X4165, X4166, X4167]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4167,tc_HOL_Obool)),X4166),X4165))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4167,tc_HOL_Obool)),X4165),X4164))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4167,tc_HOL_Obool)),X4166),X4164)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_psubset__subset__trans])])])). 6.97/7.23 fof(c_0_7512, plain, ![X3146, X3147, X3148, X3149]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3149,tc_HOL_Obool)),X3148),X3147))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3149,tc_HOL_Obool)),X3147),X3146))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3149,tc_HOL_Obool)),X3148),X3146)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_subset__trans])])])). 6.97/7.23 cnf(c_0_7513, 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_5226])). 6.97/7.23 cnf(c_0_7514, 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_5227]), ['final']). 6.97/7.23 fof(c_0_7515, plain, ![X1350, X1351, X1352, X1353]:(~class_Orderings_Olinorder(X1353)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X1353),X1351),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1353),X1352),X1350))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1353),X1352),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1353),X1351),X1350))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__left__commute])])). 6.97/7.23 cnf(c_0_7516, 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_5228])). 6.97/7.23 cnf(c_0_7517, 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_5229]), ['final']). 6.97/7.23 fof(c_0_7518, plain, ![X13462, X13465, X13466, X13467, X13468, X13469, X13470, X13471, X13472]:(((~hBOOL(hAPP(hAPP(X13462,esk449_1(X13462)),esk449_1(X13462)))|hAPP(X13462,esk448_1(X13462))!=hAPP(X13462,esk449_1(X13462))|~hBOOL(hAPP(hAPP(X13462,esk448_1(X13462)),esk448_1(X13462)))|~hBOOL(hAPP(hAPP(X13462,esk448_1(X13462)),esk449_1(X13462)))|~hBOOL(hAPP(hAPP(X13462,X13465),X13465))|c_Equiv__Relations_Opart__equivp(X13466,X13462))&(((hBOOL(hAPP(hAPP(X13462,esk449_1(X13462)),esk449_1(X13462)))|hBOOL(hAPP(hAPP(X13462,esk448_1(X13462)),esk449_1(X13462)))|~hBOOL(hAPP(hAPP(X13462,X13465),X13465))|c_Equiv__Relations_Opart__equivp(X13466,X13462))&(hAPP(X13462,esk448_1(X13462))=hAPP(X13462,esk449_1(X13462))|hBOOL(hAPP(hAPP(X13462,esk448_1(X13462)),esk449_1(X13462)))|~hBOOL(hAPP(hAPP(X13462,X13465),X13465))|c_Equiv__Relations_Opart__equivp(X13466,X13462)))&(hBOOL(hAPP(hAPP(X13462,esk448_1(X13462)),esk448_1(X13462)))|hBOOL(hAPP(hAPP(X13462,esk448_1(X13462)),esk449_1(X13462)))|~hBOOL(hAPP(hAPP(X13462,X13465),X13465))|c_Equiv__Relations_Opart__equivp(X13466,X13462))))&(((~hBOOL(hAPP(hAPP(X13467,X13470),X13470))|hAPP(X13467,X13469)!=hAPP(X13467,X13470)|~hBOOL(hAPP(hAPP(X13467,X13469),X13469))|hBOOL(hAPP(hAPP(X13467,X13469),X13470))|~c_Equiv__Relations_Opart__equivp(X13468,X13467))&(((hBOOL(hAPP(hAPP(X13467,X13472),X13472))|~hBOOL(hAPP(hAPP(X13467,X13471),X13472))|~c_Equiv__Relations_Opart__equivp(X13468,X13467))&(hAPP(X13467,X13471)=hAPP(X13467,X13472)|~hBOOL(hAPP(hAPP(X13467,X13471),X13472))|~c_Equiv__Relations_Opart__equivp(X13468,X13467)))&(hBOOL(hAPP(hAPP(X13467,X13471),X13471))|~hBOOL(hAPP(hAPP(X13467,X13471),X13472))|~c_Equiv__Relations_Opart__equivp(X13468,X13467))))&(hBOOL(hAPP(hAPP(X13467,esk450_1(X13467)),esk450_1(X13467)))|~c_Equiv__Relations_Opart__equivp(X13468,X13467)))), 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_part__equivp__def])])])])])])). 6.97/7.23 cnf(c_0_7519, 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_5230])). 6.97/7.23 cnf(c_0_7520, 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,c_Groups_Oone__class_Oone(tc_Int_Oint),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))), inference(split_conjunct,[status(thm)],[c_0_5231])). 6.97/7.23 fof(c_0_7521, plain, ![X14824, X14825, X14826]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14826),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14825)),X14824)))|hAPP(hAPP(c_List_Otake(X14825),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14826),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X14824)=c_List_Obutlast(X14825,hAPP(hAPP(c_List_Otake(X14825),X14826),X14824))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast__take])])). 6.97/7.23 fof(c_0_7522, plain, ![X438, X439]:(~class_Orderings_Oorder(X439)|hAPP(hAPP(c_Set_Oinsert(X439),X438),c_Orderings_Obot__class_Obot(tc_fun(X439,tc_HOL_Obool)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X439,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X439),X438)),hAPP(c_SetInterval_Oord__class_OatLeast(X439),X438))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__Int__atLeast])])). 6.97/7.23 fof(c_0_7523, plain, ![X6850, X6851, X6852]:((c_Orderings_Otop__class_Otop(tc_fun(X6851,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X6852,X6851,X6850),c_Orderings_Otop__class_Otop(tc_fun(X6852,tc_HOL_Obool)))|hAPP(c_Fun_Ocomp(X6852,X6851,X6851,X6850),c_Hilbert__Choice_Oinv__into(X6852,X6851,c_Orderings_Otop__class_Otop(tc_fun(X6852,tc_HOL_Obool)),X6850))=c_Fun_Oid(X6851))&(hAPP(c_Fun_Ocomp(X6852,X6851,X6851,X6850),c_Hilbert__Choice_Oinv__into(X6852,X6851,c_Orderings_Otop__class_Otop(tc_fun(X6852,tc_HOL_Obool)),X6850))!=c_Fun_Oid(X6851)|c_Orderings_Otop__class_Otop(tc_fun(X6851,tc_HOL_Obool))=hAPP(c_Set_Oimage(X6852,X6851,X6850),c_Orderings_Otop__class_Otop(tc_fun(X6852,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__iff])])). 6.97/7.23 fof(c_0_7524, plain, ![X6442, X6443, X6444, X6445]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6444,X6445)),X6442),X6443))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6444,X6445)),X6443),X6442))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X6444,X6445)),X6443),X6442))|~class_Orderings_Oord(X6445))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6444,X6445)),X6442),X6443))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X6444,X6445)),X6443),X6442))|~class_Orderings_Oord(X6445))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6444,X6445)),X6443),X6442))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X6444,X6445)),X6443),X6442))|~class_Orderings_Oord(X6445)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__fun__def])])])])). 6.97/7.23 fof(c_0_7525, plain, ![X7497, X7498, X7499, X7501, X7502, X7503]:(((hBOOL(hAPP(X7497,esk243_2(X7497,X7498)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7499),X7498))|~hBOOL(hAPP(X7497,X7499))))&(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk243_2(X7497,X7498)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7498)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7499),X7498))|~hBOOL(hAPP(X7497,X7499)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk244_2(X7501,X7502)),X7502))|(~hBOOL(hAPP(X7501,X7503))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X7503),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7502)))))&(hBOOL(hAPP(X7501,esk244_2(X7501,X7502)))|(~hBOOL(hAPP(X7501,X7503))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X7503),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7502))))))), 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])])])])])])). 6.97/7.23 fof(c_0_7526, plain, ![X12987, X12988, X12989, X12990]:(~class_Divides_Oring__div(X12990)|(c_Divides_Odiv__class_Omod(X12990,X12989,X12988)!=c_Divides_Odiv__class_Omod(X12990,X12987,X12988)|c_Divides_Odiv__class_Omod(X12990,hAPP(c_Groups_Ouminus__class_Ouminus(X12990),X12987),X12988)=c_Divides_Odiv__class_Omod(X12990,hAPP(c_Groups_Ouminus__class_Ouminus(X12990),X12989),X12988))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__minus__cong])])])). 6.97/7.23 fof(c_0_7527, plain, ![X14776, X14777, X14778, X14779, X14780, X14781, X14782]:(~c_List_Olist__all2(X14782,X14781,X14780,X14779,X14778)|(~c_List_Olist__all2(X14782,X14781,X14780,X14777,X14776)|c_List_Olist__all2(X14782,X14781,X14780,hAPP(hAPP(c_List_Oappend(X14782),X14779),X14777),hAPP(hAPP(c_List_Oappend(X14781),X14778),X14776)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__all2__appendI])])])). 6.97/7.23 fof(c_0_7528, plain, ![X12906, X12907, X12908, X12909]:(~class_Orderings_Olinorder(X12909)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X12909),X12907),hAPP(hAPP(c_Orderings_Oord__class_Omin(X12909),X12908),X12906))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X12909),X12908),hAPP(hAPP(c_Orderings_Oord__class_Omin(X12909),X12907),X12906))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oleft__commute])])). 6.97/7.23 fof(c_0_7529, plain, ![X7692, X7693, X7694, X7695, X7696, X7697]:(~hBOOL(hAPP(hAPP(X7697,X7696),X7695))|(~hBOOL(hAPP(hAPP(X7694,X7696),X7695))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7693,tc_fun(X7692,tc_HOL_Obool))),X7697),X7694),X7696),X7695)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf2I])])])). 6.97/7.23 cnf(c_0_7530, plain, (c_Relation_Oantisym(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1)))|~c_Relation_Oantisym(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5232])). 6.97/7.23 cnf(c_0_7531, plain, (c_Relation_Otrans(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1)))|~c_Relation_Otrans(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5233])). 6.97/7.23 cnf(c_0_7532, 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_4578])). 6.97/7.23 cnf(c_0_7533, 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_5234]), ['final']). 6.97/7.23 fof(c_0_7534, plain, ![X3614, X3615, X3616]:(((c_Fun_Oinj__on(X3616,X3615,X3614,c_Orderings_Otop__class_Otop(tc_fun(X3616,tc_HOL_Obool)))|~c_Fun_Obij__betw(X3616,X3615,X3614,c_Orderings_Otop__class_Otop(tc_fun(X3616,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3615,tc_HOL_Obool))))&(hAPP(c_Set_Oimage(X3616,X3615,X3614),c_Orderings_Otop__class_Otop(tc_fun(X3616,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X3615,tc_HOL_Obool))|~c_Fun_Obij__betw(X3616,X3615,X3614,c_Orderings_Otop__class_Otop(tc_fun(X3616,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3615,tc_HOL_Obool)))))&(~c_Fun_Oinj__on(X3616,X3615,X3614,c_Orderings_Otop__class_Otop(tc_fun(X3616,tc_HOL_Obool)))|hAPP(c_Set_Oimage(X3616,X3615,X3614),c_Orderings_Otop__class_Otop(tc_fun(X3616,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X3615,tc_HOL_Obool))|c_Fun_Obij__betw(X3616,X3615,X3614,c_Orderings_Otop__class_Otop(tc_fun(X3616,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3615,tc_HOL_Obool))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__def])])])). 6.97/7.23 fof(c_0_7535, plain, ![X3150, X3151, X3152, X3153, X3154]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3154),X3151),X3153))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3154),X3152),X3153))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3154,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X3154,X3153),X3152)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X3154,X3151),X3150)))|~class_Orderings_Olinorder(X3154))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3154),X3152),X3150))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3154),X3152),X3153))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3154,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X3154,X3153),X3152)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X3154,X3151),X3150)))|~class_Orderings_Olinorder(X3154))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__subset__iff])])])])). 6.97/7.23 fof(c_0_7536, plain, ![X2275, X2276]:(~class_Rings_Ocomm__semiring__1(X2276)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2276),X2275),X2275)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2276),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2276),c_Groups_Oone__class_Oone(X2276)),c_Groups_Oone__class_Oone(X2276))),X2275)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J])])). 6.97/7.23 fof(c_0_7537, plain, ![X15774, X15775, X15776, X15777]:(~class_Rings_Ocomm__semiring__1(X15777)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15777),X15776),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15777),X15775),X15774))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15777),X15775),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15777),X15776),X15774))), 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])])])). 6.97/7.23 fof(c_0_7538, plain, ![X12903, X12904, X12905]:(~class_Groups_Omonoid__mult(X12905)|hAPP(hAPP(c_Power_Opower__class_Opower(X12905),X12904),hAPP(c_Nat_OSuc,X12903))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12905),hAPP(hAPP(c_Power_Opower__class_Opower(X12905),X12904),X12903)),X12904)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc2])])). 6.97/7.23 fof(c_0_7539, plain, ![X4344, X4345, X4346]:(~class_Rings_Ocomm__semiring__1(X4346)|hAPP(hAPP(c_Power_Opower__class_Opower(X4346),X4345),hAPP(c_Nat_OSuc,X4344))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4346),hAPP(hAPP(c_Power_Opower__class_Opower(X4346),X4345),X4344)),X4345)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J])])). 6.97/7.23 fof(c_0_7540, plain, ![X3578, X3579, X3580, X3581]:((~hBOOL(hAPP(hAPP(c_member(X3581),X3580),X3579))|~hBOOL(hAPP(hAPP(c_member(X3581),X3580),X3578))|hBOOL(hAPP(hAPP(c_member(X3581),X3580),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3581,tc_HOL_Obool)),X3579),X3578))))&((hBOOL(hAPP(hAPP(c_member(X3581),X3580),X3579))|~hBOOL(hAPP(hAPP(c_member(X3581),X3580),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3581,tc_HOL_Obool)),X3579),X3578))))&(hBOOL(hAPP(hAPP(c_member(X3581),X3580),X3578))|~hBOOL(hAPP(hAPP(c_member(X3581),X3580),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3581,tc_HOL_Obool)),X3579),X3578)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__iff])])])). 6.97/7.23 cnf(c_0_7541, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),X2)=X2|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5235, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.23 fof(c_0_7542, plain, ![X8796, X8797]:((~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),X8797)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X8796)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X8797),X8796))|~c_Nat__Transfer_Onat__set(X8796)|~c_Nat__Transfer_Onat__set(X8797))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X8797),X8796))|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),X8797)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X8796)))|~c_Nat__Transfer_Onat__set(X8796)|~c_Nat__Transfer_Onat__set(X8797))), 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])])])])). 6.97/7.23 fof(c_0_7543, plain, ![X2996, X2997, X2998]:(~class_Orderings_Olinorder(X2998)|(hBOOL(hAPP(hAPP(c_member(X2998),X2997),hAPP(c_List_Oset(X2998),X2996)))|c_List_Olinorder__class_Oinsort__insert__key(X2998,X2998,c_COMBI(X2998),X2997,X2996)=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2998,X2998,c_COMBI(X2998)),X2997),X2996))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insort__insert__insort])])])). 6.97/7.23 fof(c_0_7544, plain, ![X10722, X10723, X10724]:((hBOOL(hAPP(hAPP(c_member(tc_fun(X10724,tc_HOL_Obool)),esk355_3(X10722,X10723,X10724)),X10723))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10724,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10724,tc_HOL_Obool),X10723)),X10722)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10724,tc_HOL_Obool)),esk355_3(X10722,X10723,X10724)),X10722))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10724,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10724,tc_HOL_Obool),X10723)),X10722)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Union__least])])])])])). 6.97/7.23 fof(c_0_7545, plain, ![X666, X667, X668]:(~class_Divides_Osemiring__div(X668)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X668),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X668),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X668),X667),X666)),X666)),c_Divides_Odiv__class_Omod(X668,X667,X666))=X667), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__decomp])])). 6.97/7.23 cnf(c_0_7546, 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))|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))), inference(split_conjunct,[status(thm)],[c_0_5221])). 6.97/7.23 fof(c_0_7547, plain, ![X13997, X13998, X13999, X14000]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14000),X13999))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X13998),hAPP(c_Set_Oimage(X14000,X13998,X13997),X13999))),hAPP(c_Finite__Set_Ocard(X14000),X13999)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__image__le])])])). 6.97/7.23 fof(c_0_7548, plain, ![X12138, X12139, X12140]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12140),X12139))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X12140),X12139)),hAPP(c_Finite__Set_Ocard(X12140),hAPP(hAPP(c_Set_Oinsert(X12140),X12138),X12139))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__insert__le])])). 6.97/7.23 fof(c_0_7549, plain, ![X13823, X13824, X13825]:((hBOOL(hAPP(hAPP(c_member(tc_fun(X13825,tc_HOL_Obool)),esk468_3(X13823,X13824,X13825)),X13824))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13825,tc_HOL_Obool)),X13823),c_Complete__Lattice_OInf__class_OInf(tc_fun(X13825,tc_HOL_Obool),X13824))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13825,tc_HOL_Obool)),X13823),esk468_3(X13823,X13824,X13825)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13825,tc_HOL_Obool)),X13823),c_Complete__Lattice_OInf__class_OInf(tc_fun(X13825,tc_HOL_Obool),X13824))))), 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__greatest])])])])])). 6.97/7.23 fof(c_0_7550, plain, ![X7082, X7083, X7084, X7085, X7086, X7087, X7088, X7089, X7090, X7091, X7092]:((~hBOOL(hAPP(hAPP(X7083,X7087),X7082))|~hBOOL(hAPP(hAPP(c_member(X7086),X7087),X7084))|hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7086,tc_fun(X7085,tc_HOL_Obool)),X7084),X7083),X7082)))&((hBOOL(hAPP(hAPP(X7089,esk227_5(X7088,X7089,X7090,X7091,X7092)),X7088))|~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7092,tc_fun(X7091,tc_HOL_Obool)),X7090),X7089),X7088)))&(hBOOL(hAPP(hAPP(c_member(X7092),esk227_5(X7088,X7089,X7090,X7091,X7092)),X7090))|~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7092,tc_fun(X7091,tc_HOL_Obool)),X7090),X7089),X7088))))), 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])])])])])])). 6.97/7.23 cnf(c_0_7551, plain, (X2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[c_0_5236, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.23 fof(c_0_7552, plain, ![X3446, X3447, X3448, X3449]:(~class_Lattices_Osemilattice__inf(X3449)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3449),X3447),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3449),X3448),X3446))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3449),X3448),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3449),X3447),X3446))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__left__commute])])). 6.97/7.23 fof(c_0_7553, plain, ![X5091, X5092, X5093]:(c_Orderings_Otop__class_Otop(tc_fun(X5092,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X5093,X5092,X5091),c_Orderings_Otop__class_Otop(tc_fun(X5093,tc_HOL_Obool)))|c_Fun_Oinj__on(X5092,X5093,c_Hilbert__Choice_Oinv__into(X5093,X5092,c_Orderings_Otop__class_Otop(tc_fun(X5093,tc_HOL_Obool)),X5091),c_Orderings_Otop__class_Otop(tc_fun(X5092,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__imp__inj__inv])])). 6.97/7.23 fof(c_0_7554, plain, ![X11571, X11572]:((hBOOL(hAPP(hAPP(c_member(tc_fun(X11572,tc_HOL_Obool)),esk386_2(X11571,X11572)),X11571))|hBOOL(hAPP(c_Finite__Set_Ofinite(X11572),c_Complete__Lattice_OSup__class_OSup(tc_fun(X11572,tc_HOL_Obool),X11571)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X11572,tc_HOL_Obool)),X11571)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11572),esk386_2(X11571,X11572)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X11572),c_Complete__Lattice_OSup__class_OSup(tc_fun(X11572,tc_HOL_Obool),X11571)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X11572,tc_HOL_Obool)),X11571)))), 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])])])])])). 6.97/7.23 fof(c_0_7555, plain, ![X16684, X16685, X16686]:(~class_Divides_Osemiring__div(X16686)|X16685=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16686),c_Divides_Odiv__class_Omod(X16686,X16685,X16684)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16686),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X16686),X16685),X16684)),X16684))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__div__class_Omod__div__equality_H])])). 6.97/7.23 fof(c_0_7556, plain, ![X16891, X16892, X16893]:(~class_Divides_Osemiring__div(X16893)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16893),X16892),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X16893),X16891),X16892))),c_Divides_Odiv__class_Omod(X16893,X16891,X16892))=X16891), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__equality2])])). 6.97/7.23 cnf(c_0_7557, plain, (X3=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_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),X3)), inference(split_conjunct,[status(thm)],[c_0_5237])). 6.97/7.23 fof(c_0_7558, plain, ![X1281, X1282]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1282),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)),X1281))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1282),X1281)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__neg__pos__less0])])). 6.97/7.23 fof(c_0_7559, plain, ![X14968, X14969]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14968),X14969)),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)),X14968))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14969),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)),X14968))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14968),X14969)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14969),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__imp__zdiv__neg__iff])])])). 6.97/7.23 fof(c_0_7560, plain, ![X2910, X2911]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2911))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2910),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),X2911),X2910)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__nonneg__neg__le0])])). 6.97/7.23 fof(c_0_7561, plain, ![X4210, X4211]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4211),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)),X4210))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X4211),X4210)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__nonpos__pos__le0])])). 6.97/7.23 cnf(c_0_7562, 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_Oapsnd(X1,X2,X3,X4),X5)!=hAPP(c_Product__Type_Oapsnd(X1,X2,X3,X6),X5)), inference(split_conjunct,[status(thm)],[c_0_5099])). 6.97/7.23 fof(c_0_7563, plain, ![X15998, X15999, X16000, X16001]:(~class_Lattices_Olattice(X16001)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X16001),X16000),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X16001),X15999),X15998))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X16001),X15999),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X16001),X16000),X15998))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__sup__aci_I3_J])])])). 6.97/7.23 fof(c_0_7564, plain, ![X10645, X10646]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10646))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10645))|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),X10646),X10645))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10646))|~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),X10646),X10645))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10645))|~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),X10646),X10645)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff])])])). 6.97/7.23 fof(c_0_7565, plain, ![X2142, X2143]:((~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),X2142),X2143)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2142))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2143)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2142))|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),X2142),X2143)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2143)))), 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])])])])). 6.97/7.23 fof(c_0_7566, plain, ![X993, X994]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X994))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X993))|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),X994),X993))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I1_J])])])). 6.97/7.23 fof(c_0_7567, plain, ![X7356, X7357]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7357))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7356))|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),X7357),X7356))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J])])])). 6.97/7.23 cnf(c_0_7568, 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_Oapfst(X1,X2,X3,X4),X5)!=hAPP(c_Product__Type_Oapfst(X1,X2,X3,X6),X5)), inference(split_conjunct,[status(thm)],[c_0_5100])). 6.97/7.23 fof(c_0_7569, plain, ![X10947, X10948, X10949, X10950]:(~class_Groups_Ocomm__monoid__mult(X10950)|(~c_Fun_Oinj__on(X10949,X10950,X10948,X10947)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10949,X10950),X10948),X10947)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10950,X10950),c_Fun_Oid(X10950)),hAPP(c_Set_Oimage(X10949,X10950,X10948),X10947)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__reindex__id])])). 6.97/7.23 fof(c_0_7570, plain, ![X13934, X13935, X13936, X13937]:(~class_Groups_Ocomm__monoid__add(X13937)|(~c_Fun_Oinj__on(X13936,X13937,X13935,X13934)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13936,X13937),X13935),X13934)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13937,X13937),c_Fun_Oid(X13937)),hAPP(c_Set_Oimage(X13936,X13937,X13935),X13934)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__reindex__id])])])). 6.97/7.23 fof(c_0_7571, plain, ![X16437, X16438, X16439, X16440]:(~class_Rings_Ocomm__semiring__1(X16440)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16440),X16439),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16440),X16438),X16437))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16440),X16438),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16440),X16439),X16437))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J])])). 6.97/7.23 fof(c_0_7572, plain, ![X6983, X6984]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6984))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6983))|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),X6984),X6983))))), 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])])])). 6.97/7.23 fof(c_0_7573, plain, ![X12257, X12258]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12257),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),X12257),X12258)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12258),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),X12257),X12258)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12257),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12258),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])])])])). 6.97/7.23 cnf(c_0_7574, 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_5238])). 6.97/7.23 cnf(c_0_7575, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_4409]), c_0_4410]), c_0_4411])). 6.97/7.23 fof(c_0_7576, plain, ![X7886, X7887, X7888, X7889]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7889),X7888),X7887))|~c_List_Olinorder__class_Osorted(X7889,hAPP(hAPP(c_List_Olist_OCons(X7889),X7888),hAPP(hAPP(c_List_Olist_OCons(X7889),X7887),X7886)))|~class_Orderings_Olinorder(X7889))&(c_List_Olinorder__class_Osorted(X7889,hAPP(hAPP(c_List_Olist_OCons(X7889),X7887),X7886))|~c_List_Olinorder__class_Osorted(X7889,hAPP(hAPP(c_List_Olist_OCons(X7889),X7888),hAPP(hAPP(c_List_Olist_OCons(X7889),X7887),X7886)))|~class_Orderings_Olinorder(X7889)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7889),X7888),X7887))|~c_List_Olinorder__class_Osorted(X7889,hAPP(hAPP(c_List_Olist_OCons(X7889),X7887),X7886))|c_List_Olinorder__class_Osorted(X7889,hAPP(hAPP(c_List_Olist_OCons(X7889),X7888),hAPP(hAPP(c_List_Olist_OCons(X7889),X7887),X7886)))|~class_Orderings_Olinorder(X7889))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__many__eq])])])])). 6.97/7.23 cnf(c_0_7577, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5240, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.23 cnf(c_0_7578, 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_5241])). 6.97/7.23 cnf(c_0_7579, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_5242, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.23 cnf(c_0_7580, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_4409]), c_0_4410]), c_0_4411])). 6.97/7.23 fof(c_0_7581, plain, ![X16777, X16778, X16779]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X16779),X16778))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X16777),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16778),X16777)),X16779)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__add__diff])])])). 6.97/7.23 cnf(c_0_7582, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|~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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5244, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.23 fof(c_0_7583, plain, ![X1773, X1774, X1775, X1776]:(~class_Lattices_Osemilattice__sup(X1776)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1776),X1774),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1776),X1775),X1773))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1776),X1775),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1776),X1774),X1773))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__left__commute])])). 6.97/7.23 cnf(c_0_7584, 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_5245])). 6.97/7.23 cnf(c_0_7585, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Ominus__class_Ominus(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),c_Int_OPls),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5246, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.23 cnf(c_0_7586, 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_5247])). 6.97/7.23 cnf(c_0_7587, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Ominus__class_Ominus(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),c_Int_OPls),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5248, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.23 fof(c_0_7588, plain, ![X5546, X5547, X5548, X5549, X5550]:(~hBOOL(hAPP(hAPP(c_member(X5550),X5549),hAPP(c_Set_Oimage(X5548,X5550,X5547),X5546)))|hBOOL(hAPP(hAPP(c_member(X5548),hAPP(c_Hilbert__Choice_Oinv__into(X5548,X5550,X5546,X5547),X5549)),X5546))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inv__into__into])])])). 6.97/7.23 fof(c_0_7589, plain, ![X17172, X17173, X17174, X17175]:(~class_Lattices_Olattice(X17175)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17175),X17174),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17175),X17173),X17172))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17175),X17173),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17175),X17174),X17172))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I7_J])])). 6.97/7.23 fof(c_0_7590, plain, ![X12280, X12281]:((~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),X12281),X12280)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X12281),X12280)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X12281),X12280))|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),X12281),X12280)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__nat__trancl__eq__le])])). 6.97/7.23 fof(c_0_7591, plain, ![X16209, X16210, X16211]:(((~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X16210),X16209))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16211),X16210)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16211),X16209))))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X16211|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16211),X16210)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16211),X16209)))))&(~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16211),X16210)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16211),X16209)))|(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X16210),X16209))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X16211))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__dvd__cancel__disj])])])). 6.97/7.23 cnf(c_0_7592, 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_5249])). 6.97/7.23 fof(c_0_7593, plain, ![X3784, X3785, X3786, X3787, X3788]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X3788,X3787)),hAPP(hAPP(c_Product__Type_OPair(X3788,X3787),X3786),X3785)),X3784))|hBOOL(hAPP(hAPP(c_member(X3788),X3786),hAPP(c_Relation_ODomain(X3788,X3787),X3784)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_DomainI])])])). 6.97/7.23 cnf(c_0_7594, 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),X2)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_5219])). 6.97/7.23 fof(c_0_7595, plain, ![X6453, X6454, X6455]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6455),X6454))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6455),X6453)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6454),X6453)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zadd__strict__right__mono])])])). 6.97/7.23 fof(c_0_7596, plain, ![X16849, X16850, X16851]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16851),X16850))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16851),X16849)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16850),X16849)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__less__mono1])])])). 6.97/7.23 fof(c_0_7597, plain, ![X1344, X1345, X1346]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1345),X1344))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1346),X1345)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1346),X1344))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1346),X1345)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1346),X1344)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1345),X1344)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])])). 6.97/7.23 cnf(c_0_7598, 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_5250, c_0_4565])). 6.97/7.23 fof(c_0_7599, plain, ![X16147, X16148, X16149, X16150, X16151, X16152, X16153]:(((hBOOL(hAPP(X16149,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16148),X16147))|~hBOOL(hAPP(X16149,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16148),X16147))))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16147),X16150)!=X16148|hBOOL(hAPP(X16149,X16150))|~hBOOL(hAPP(X16149,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16148),X16147)))))&(((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16151),esk545_3(X16151,X16152,X16153))=X16152|~hBOOL(hAPP(X16153,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(X16153,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16152),X16151))))&(~hBOOL(hAPP(X16153,esk545_3(X16151,X16152,X16153)))|~hBOOL(hAPP(X16153,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(X16153,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16152),X16151)))))&((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16151),esk545_3(X16151,X16152,X16153))=X16152|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16152),X16151))|hBOOL(hAPP(X16153,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16152),X16151))))&(~hBOOL(hAPP(X16153,esk545_3(X16151,X16152,X16153)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16152),X16151))|hBOOL(hAPP(X16153,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16152),X16151))))))), 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])])])])])])])). 6.97/7.23 cnf(c_0_7600, 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_5251])). 6.97/7.23 fof(c_0_7601, plain, ![X12849, X12850, X12851]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12851),X12850))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X12849),X12851)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X12849),X12850)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__left__mono])])). 6.97/7.23 fof(c_0_7602, plain, ![X11833, X11834, X11835]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11835),X11834))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X11835),X11833)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X11834),X11833)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__le__mono])])). 6.97/7.23 fof(c_0_7603, plain, ![X8360, X8361, X8362]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8362),X8361))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X8362),X8360)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X8361),X8360)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono])])). 6.97/7.23 fof(c_0_7604, plain, ![X11866, X11867, X11868, X11869, X11870, X11871, X11872]:(((X11867!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11866),X11869)|hBOOL(hAPP(X11868,X11869))|~hBOOL(hAPP(X11868,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11867),X11866))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11867),X11866))|hBOOL(hAPP(X11868,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X11868,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11867),X11866)))))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11871),X11870))|X11871=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11870),esk397_3(X11870,X11871,X11872))|hBOOL(hAPP(X11872,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11871),X11870))))&(~hBOOL(hAPP(X11872,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|X11871=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11870),esk397_3(X11870,X11871,X11872))|hBOOL(hAPP(X11872,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11871),X11870)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11871),X11870))|~hBOOL(hAPP(X11872,esk397_3(X11870,X11871,X11872)))|hBOOL(hAPP(X11872,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11871),X11870))))&(~hBOOL(hAPP(X11872,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X11872,esk397_3(X11870,X11871,X11872)))|hBOOL(hAPP(X11872,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11871),X11870))))))), 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])])])])])])])). 6.97/7.23 fof(c_0_7605, plain, ![X9094, X9095, X9096, X9097, X9098]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9097,tc_HOL_Obool)),hAPP(c_Set_Oimage(X9098,X9097,X9096),X9095)),hAPP(c_Set_Oimage(X9098,X9097,X9096),X9094)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9098,tc_HOL_Obool)),X9095),X9094))|~c_Fun_Oinj__on(X9098,X9097,X9096,c_Orderings_Otop__class_Otop(tc_fun(X9098,tc_HOL_Obool))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9098,tc_HOL_Obool)),X9095),X9094))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9097,tc_HOL_Obool)),hAPP(c_Set_Oimage(X9098,X9097,X9096),X9095)),hAPP(c_Set_Oimage(X9098,X9097,X9096),X9094)))|~c_Fun_Oinj__on(X9098,X9097,X9096,c_Orderings_Otop__class_Otop(tc_fun(X9098,tc_HOL_Obool))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__image__subset__iff])])])). 6.97/7.23 fof(c_0_7606, plain, ![X4168, X4169, X4170]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4170),X4169))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4168),X4169)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4168),X4170)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__le__mono2])])])). 6.97/7.23 fof(c_0_7607, plain, ![X10569, X10570, X10571]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10571),X10570))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10571),X10569)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10570),X10569)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__le__mono1])])])). 6.97/7.23 fof(c_0_7608, plain, ![X10388, X10389, X10390]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10390),X10389)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10390),X10388)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10389),X10388)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10389),X10388))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10390),X10389)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10390),X10388))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])])). 6.97/7.23 fof(c_0_7609, plain, ![X2664, X2665, X2666, X2667]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2667)|hAPP(hAPP(c_List_Odrop(X2666),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2667)),hAPP(hAPP(c_List_Olist_OCons(X2666),X2665),X2664))=hAPP(hAPP(c_List_Odrop(X2666),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2667)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2664))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2667)|hAPP(hAPP(c_List_Olist_OCons(X2666),X2665),X2664)=hAPP(hAPP(c_List_Odrop(X2666),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2667)),hAPP(hAPP(c_List_Olist_OCons(X2666),X2665),X2664)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_drop__Cons__number__of])])])). 6.97/7.23 fof(c_0_7610, plain, ![X14009, X14010, X14011]:(~class_Lattices_Olattice(X14011)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14011),X14010))|c_Big__Operators_Olattice__class_OSup__fin(X14011,hAPP(hAPP(c_Set_Oinsert(X14011),X14009),X14010))=hAPP(hAPP(c_Finite__Set_Ofold(X14011,X14011,c_Lattices_Osemilattice__sup__class_Osup(X14011)),X14009),X14010))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oeq__fold__idem_H])])])). 6.97/7.23 fof(c_0_7611, plain, ![X16499, X16500, X16501]:(~class_Fields_Olinordered__field(X16501)|(X16500=c_Groups_Ozero__class_Ozero(X16501)|hAPP(c_Groups_Oabs__class_Oabs(X16501),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16501),X16499),X16500))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16501),hAPP(c_Groups_Oabs__class_Oabs(X16501),X16499)),hAPP(c_Groups_Oabs__class_Oabs(X16501),X16500)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nonzero__abs__divide])])])). 6.97/7.23 fof(c_0_7612, plain, ![X541, X542, X543]:(~class_Lattices_Olattice(X543)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X543),X542))|c_Big__Operators_Olattice__class_OInf__fin(X543,hAPP(hAPP(c_Set_Oinsert(X543),X541),X542))=hAPP(hAPP(c_Finite__Set_Ofold(X543,X543,c_Lattices_Osemilattice__inf__class_Oinf(X543)),X541),X542))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oeq__fold__idem_H])])])). 6.97/7.23 fof(c_0_7613, plain, ![X15671, X15672, X15673]:(~class_Complete__Lattice_Ocomplete__lattice(X15673)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15673),X15672))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15673),X15671),c_Complete__Lattice_OInf__class_OInf(X15673,X15672))=hAPP(hAPP(c_Finite__Set_Ofold(X15673,X15673,c_Lattices_Osemilattice__inf__class_Oinf(X15673)),X15671),X15672))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__Inf__fold__inf])])])). 6.97/7.23 fof(c_0_7614, plain, ![X4393, X4394]:(~c_Relation_Otrans(X4394,X4393)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4394,X4394),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X4394,X4394,X4394),X4393),X4393)),X4393))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_trans__O__subset])])])). 6.97/7.23 fof(c_0_7615, plain, ![X7659, X7660]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X7660),X7659))|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)),X7660)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X7659))))&(~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)),X7660)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X7659)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X7660),X7659)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I5_J])])). 6.97/7.23 fof(c_0_7616, plain, ![X16903, X16904]:(~hBOOL(hAPP(X16904,X16903))|(hBOOL(hAPP(X16904,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),X16904),c_Nat_OSuc)))=c_Orderings_Oord__class_OLeast(tc_Nat_Onat,X16904))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Least__Suc])])])). 6.97/7.23 cnf(c_0_7617, 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(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_5219])). 6.97/7.23 fof(c_0_7618, plain, ![X14223, X14224, X14225, X14226]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14226,tc_HOL_Obool)),X14224),hAPP(hAPP(c_Set_Oinsert(X14226),X14225),X14223)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14226,tc_HOL_Obool)),X14224),X14223))|hBOOL(hAPP(hAPP(c_member(X14226),X14225),X14224)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14226,tc_HOL_Obool)),X14224),X14223))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14226,tc_HOL_Obool)),X14224),hAPP(hAPP(c_Set_Oinsert(X14226),X14225),X14223)))|hBOOL(hAPP(hAPP(c_member(X14226),X14225),X14224)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_subset__insert])])])])). 6.97/7.23 cnf(c_0_7619, 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))=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_5252])). 6.97/7.23 cnf(c_0_7620, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))=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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5253, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.23 fof(c_0_7621, plain, ![X12329, X12330, X12331, X12332]:(~class_Rings_Olinordered__semidom(X12332)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12332),c_Groups_Ozero__class_Ozero(X12332)),X12331))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12332),X12330),X12329))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12332),X12330),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12332),X12331),X12329)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__add__strict])])). 6.97/7.23 fof(c_0_7622, plain, ![X1559, X1560, X1561, X1562]:(~class_Groups_Oordered__comm__monoid__add(X1562)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1562),c_Groups_Ozero__class_Ozero(X1562)),X1561))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1562),X1560),X1559))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1562),X1560),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1562),X1561),X1559)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__strict__increasing2])])])). 6.97/7.23 fof(c_0_7623, plain, ![X658, X659, X660, X661]:(~class_Groups_Oordered__comm__monoid__add(X661)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X661),c_Groups_Ozero__class_Ozero(X661)),X660))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X661),X659),X658))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X661),X659),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X661),X660),X658)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__strict__increasing])])])). 6.97/7.23 fof(c_0_7624, plain, ![X4908, X4909, X4910, X4911]:(~class_Groups_Oordered__comm__monoid__add(X4911)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4911),c_Groups_Ozero__class_Ozero(X4911)),X4910))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4911),X4909),X4908))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4911),X4909),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4911),X4910),X4908)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__increasing])])])). 6.97/7.23 fof(c_0_7625, plain, ![X15809, X15810, X15811]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X15811,X15811),tc_HOL_Obool)),X15810),X15809))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X15811,X15811),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X15811,X15810)),c_Transitive__Closure_Ortrancl(X15811,X15809)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rtrancl__mono])])])). 6.97/7.23 fof(c_0_7626, plain, ![X14220, X14221, X14222]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X14222,X14222),tc_HOL_Obool)),X14221),X14220))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14222,tc_HOL_Obool)),hAPP(c_Relation_OField(X14222),X14221)),hAPP(c_Relation_OField(X14222),X14220)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mono__Field])])). 6.97/7.23 fof(c_0_7627, plain, ![X6670, X6671, X6672]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6672),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6671)),X6670)))|hBOOL(hAPP(hAPP(c_member(X6671),hAPP(hAPP(c_List_Onth(X6671),X6670),X6672)),hAPP(c_List_Oset(X6671),X6670)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__mem])])])). 6.97/7.23 fof(c_0_7628, plain, ![X15023, X15024]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15024),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X15023)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X15023),X15024)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X15023)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_elem__le__listsum__nat])])). 6.97/7.23 fof(c_0_7629, plain, ![X16690, X16691, X16692, X16693, X16694, X16696, X16697, X16698, X16699, X16700, X16701]:(((hBOOL(hAPP(hAPP(c_member(X16694),esk557_5(X16690,X16691,X16692,X16693,X16694)),X16692))|hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16694,tc_fun(X16693,tc_HOL_Obool)),X16692),X16691),X16690)))&(~hBOOL(hAPP(hAPP(X16691,esk557_5(X16690,X16691,X16692,X16693,X16694)),X16690))|hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16694,tc_fun(X16693,tc_HOL_Obool)),X16692),X16691),X16690))))&(~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16700,tc_fun(X16699,tc_HOL_Obool)),X16698),X16697),X16696))|(~hBOOL(hAPP(hAPP(c_member(X16700),X16701),X16698))|hBOOL(hAPP(hAPP(X16697,X16701),X16696))))), 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_INF1__iff])])])])])])). 6.97/7.23 fof(c_0_7630, plain, ![X12133, X12134, X12135, X12136]:(~class_Groups_Oordered__comm__monoid__add(X12136)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12136),c_Groups_Ozero__class_Ozero(X12136)),X12135))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12136),X12134),X12133))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12136),X12134),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12136),X12133),X12135)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__increasing2])])])). 6.97/7.23 fof(c_0_7631, plain, ![X8386, X8387, X8388, X8389, X8390]:(~hBOOL(hAPP(hAPP(c_member(X8390),X8389),X8388))|hAPP(c_Set_Oimage(X8390,X8387,X8386),X8388)=hAPP(hAPP(c_Set_Oinsert(X8387),hAPP(X8386,X8389)),hAPP(c_Set_Oimage(X8390,X8387,X8386),X8388))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insert__image])])])). 6.97/7.23 fof(c_0_7632, plain, ![X16246, X16247, X16248, X16249, X16250]:(~hBOOL(hAPP(hAPP(c_member(X16250),X16249),X16248))|hAPP(c_Set_Oimage(X16250,X16247,hAPP(c_COMBK(X16247,X16250),X16246)),X16248)=hAPP(hAPP(c_Set_Oinsert(X16247),X16246),c_Orderings_Obot__class_Obot(tc_fun(X16247,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__constant])])). 6.97/7.23 fof(c_0_7633, plain, ![X1667, X1668, X1669, X1670]:(~class_Rings_Osemiring__1(X1670)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1670),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1670),hAPP(c_Finite__Set_Ocard(X1669),X1667))),X1668)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1669,X1670),hAPP(c_COMBK(X1670,X1669),X1668)),X1667)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__constant])])). 6.97/7.23 fof(c_0_7634, plain, ![X7309, X7310, X7311, X7312, X7313]:((hBOOL(hAPP(hAPP(c_member(X7313),esk237_5(X7309,X7310,X7311,X7312,X7313)),X7312))|hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7313,tc_fun(X7309,tc_HOL_Obool)),X7312),X7311),X7310)))&(~hBOOL(hAPP(hAPP(X7311,esk237_5(X7309,X7310,X7311,X7312,X7313)),X7310))|hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7313,tc_fun(X7309,tc_HOL_Obool)),X7312),X7311),X7310)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INF1__I])])])])])). 6.97/7.23 fof(c_0_7635, plain, ![X16171, X16172, X16173]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16173),X16172))|(hBOOL(hAPP(hAPP(c_member(X16173),X16171),X16172))|hAPP(c_Finite__Set_Ocard(X16173),hAPP(hAPP(c_Set_Oinsert(X16173),X16171),X16172))=hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X16173),X16172)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__insert__disjoint])])])). 6.97/7.23 fof(c_0_7636, plain, ![X6723, X6724, X6725]:(c_List_Olist_ONil(X6724)=X6725|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6723),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6724)),X6725)))|hAPP(hAPP(c_List_Onth(X6724),X6725),X6723)=hAPP(c_List_Ohd(X6724),hAPP(hAPP(c_List_Odrop(X6724),X6723),X6725)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_hd__drop__conv__nth])])])). 6.97/7.23 fof(c_0_7637, plain, ![X14987, X14988]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14988,tc_HOL_Obool)),esk506_2(X14987,X14988)),hAPP(c_Relation_OImage(X14988,X14988,X14987),esk506_2(X14987,X14988))))|c_Wellfounded_Owf(X14988,X14987))&(esk506_2(X14987,X14988)!=c_Orderings_Obot__class_Obot(tc_fun(X14988,tc_HOL_Obool))|c_Wellfounded_Owf(X14988,X14987))), 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])])])])])). 6.97/7.23 fof(c_0_7638, plain, ![X435, X436, X437]:(~class_Lattices_Oab__semigroup__idem__mult(X437)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X437),X436))|hAPP(hAPP(c_Finite__Set_Ofold(X437,X437,c_Groups_Otimes__class_Otimes(X437)),X435),X436)=hAPP(c_Finite__Set_Ofold1(X437,c_Groups_Otimes__class_Otimes(X437)),hAPP(hAPP(c_Set_Oinsert(X437),X435),X436)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__eq__fold__idem])])). 6.97/7.23 fof(c_0_7639, plain, ![X11971, X11972, X11973, X11974, X11975, X11976]:((hAPP(hAPP(c_Product__Type_OSigma(X11973,X11976),X11972),hAPP(c_COMBK(tc_fun(X11976,tc_HOL_Obool),X11973),X11974))!=hAPP(hAPP(c_Product__Type_OSigma(X11973,X11976),X11971),hAPP(c_COMBK(tc_fun(X11976,tc_HOL_Obool),X11973),X11974))|X11971=X11972|~hBOOL(hAPP(hAPP(c_member(X11976),X11975),X11974)))&(X11971!=X11972|hAPP(hAPP(c_Product__Type_OSigma(X11973,X11976),X11972),hAPP(c_COMBK(tc_fun(X11976,tc_HOL_Obool),X11973),X11974))=hAPP(hAPP(c_Product__Type_OSigma(X11973,X11976),X11971),hAPP(c_COMBK(tc_fun(X11976,tc_HOL_Obool),X11973),X11974))|~hBOOL(hAPP(hAPP(c_member(X11976),X11975),X11974)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Times__eq__cancel2])])])])). 6.97/7.23 cnf(c_0_7640, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Rings_Oidom(X1)), inference(split_conjunct,[status(thm)],[c_0_5254])). 6.97/7.23 cnf(c_0_7641, 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_5255])). 6.97/7.23 fof(c_0_7642, plain, ![X3513, X3514, X3515, X3516, X3517, X3518, X3519]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3516),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3513)),X3515)))|hAPP(hAPP(c_List_Onth(X3513),X3515),X3516)=hAPP(hAPP(c_List_Onth(X3513),X3514),X3516)|X3514!=X3515)&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3513)),X3514)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3513)),X3515)|X3514!=X3515))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk114_3(X3517,X3518,X3519)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3517)),X3519)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3517)),X3518)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3517)),X3519)|X3518=X3519)&(hAPP(hAPP(c_List_Onth(X3517),X3519),esk114_3(X3517,X3518,X3519))!=hAPP(hAPP(c_List_Onth(X3517),X3518),esk114_3(X3517,X3518,X3519))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3517)),X3518)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3517)),X3519)|X3518=X3519))), 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])])])])])])])). 6.97/7.23 cnf(c_0_7643, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Rings_Oidom(X1)), inference(split_conjunct,[status(thm)],[c_0_5256])). 6.97/7.23 fof(c_0_7644, plain, ![X15475, X15476]:((~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),X15475),X15476)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15476),X15475))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15476)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15476),X15475))|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),X15475),X15476)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15476)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__pos__iff])])])). 6.97/7.23 fof(c_0_7645, plain, ![X7917, X7918, X7919, X7920]:(~class_Groups_Ocomm__monoid__mult(X7920)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7919),X7918))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7919,X7920),X7917),X7918)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X7920,X7919,c_Groups_Otimes__class_Otimes(X7920)),X7917),c_Groups_Oone__class_Oone(X7920)),X7918))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oeq__fold])])). 6.97/7.23 fof(c_0_7646, plain, ![X6526, X6527, X6528, X6529]:(~class_Groups_Ocomm__monoid__add(X6529)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6528),X6527))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6528,X6529),X6526),X6527)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6529,X6528,c_Groups_Oplus__class_Oplus(X6529)),X6526),c_Groups_Ozero__class_Ozero(X6529)),X6527))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum_Oeq__fold])])])). 6.97/7.23 fof(c_0_7647, plain, ![X16796, X16797, X16798, X16799]:(~class_Groups_Oab__semigroup__add(X16799)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16799),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16799),X16798),X16797)),X16796)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16799),X16798),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16799),X16797),X16796))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])])])). 6.97/7.23 fof(c_0_7648, plain, ![X17237, X17238, X17239]:(~class_Orderings_Olinorder(X17239)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17239),X17238))|(c_Orderings_Obot__class_Obot(tc_fun(X17239,tc_HOL_Obool))=X17238|hAPP(hAPP(c_Orderings_Oord__class_Omax(X17239),X17237),c_Big__Operators_Olinorder__class_OMax(X17239,X17238))=c_Big__Operators_Olinorder__class_OMax(X17239,hAPP(hAPP(c_Set_Oinsert(X17239),X17237),X17238))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max__insert])])])). 6.97/7.23 fof(c_0_7649, plain, ![X2491, X2492, X2493, X2494]:(~class_Lattices_Osemilattice__inf(X2494)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2494),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2494),X2493),X2492)),X2491)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2494),X2493),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2494),X2492),X2491))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__assoc])])). 6.97/7.23 fof(c_0_7650, plain, ![X5906, X5907, X5908, X5909]:(~class_Lattices_Olattice(X5909)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5909),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5909),X5908),X5907)),X5906)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5909),X5908),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5909),X5907),X5906))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__sup__aci_I2_J])])])). 6.97/7.23 cnf(c_0_7651, plain, (esk358_4(X3,X1,X4,X5)=X2|hAPP(X1,X2)!=X3|~hBOOL(hAPP(hAPP(c_member(X4),X3),hAPP(c_Set_Oimage(X5,X4,X1),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))|~c_Fun_Oinj__on(X5,X4,X1,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_5257])). 6.97/7.23 cnf(c_0_7652, 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_5258]), ['final']). 6.97/7.23 fof(c_0_7653, plain, ![X17188, X17189, X17190, X17191]:(~class_Groups_Ocomm__monoid__mult(X17191)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17190),X17189))|hAPP(hAPP(c_Power_Opower__class_Opower(X17191),X17188),hAPP(c_Finite__Set_Ocard(X17190),X17189))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X17190,X17191),hAPP(c_COMBK(X17191,X17190),X17188)),X17189))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__constant])])). 6.97/7.23 fof(c_0_7654, plain, ![X13718, X13719, X13720]:(~class_Orderings_Olinorder(X13720)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13720),X13719))|(c_Orderings_Obot__class_Obot(tc_fun(X13720,tc_HOL_Obool))=X13719|hAPP(hAPP(c_Orderings_Oord__class_Omin(X13720),X13718),c_Big__Operators_Olinorder__class_OMin(X13720,X13719))=c_Big__Operators_Olinorder__class_OMin(X13720,hAPP(hAPP(c_Set_Oinsert(X13720),X13718),X13719))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min__insert])])])). 6.97/7.23 fof(c_0_7655, plain, ![X12805, X12806, X12807, X12808]:(~class_Groups_Oab__semigroup__mult(X12808)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12808),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12808),X12807),X12806)),X12805)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12808),X12807),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12808),X12806),X12805))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ab__semigroup__mult__class_Omult__ac_I1_J])])])). 6.97/7.23 fof(c_0_7656, plain, ![X13920, X13921, X13922, X13923]:(~class_Rings_Odivision__ring(X13923)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13923),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13923),X13922),X13921)),X13920)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13923),X13922),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13923),X13921),X13920))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times__divide__eq__right])])). 6.97/7.23 fof(c_0_7657, plain, ![X2320, X2321, X2322, X2323]:(~class_Lattices_Osemilattice__sup(X2323)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2323),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2323),X2322),X2321)),X2320)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2323),X2322),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2323),X2321),X2320))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__assoc])])). 6.97/7.23 fof(c_0_7658, plain, ![X16820, X16821, X16822, X16823]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X16823),tc_List_Olist(X16823))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X16823),tc_List_Olist(X16823)),X16822),X16821)),c_List_Olistrel1(X16823,X16820)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16823)),X16822)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16823)),X16821)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel1__eq__len])])])). 6.97/7.23 fof(c_0_7659, plain, ![X9734, X9735, X9736]:(~class_Lattices_Olattice(X9736)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9736),X9735))|(c_Orderings_Obot__class_Obot(tc_fun(X9736,tc_HOL_Obool))=X9735|c_Big__Operators_Olattice__class_OSup__fin(X9736,hAPP(hAPP(c_Set_Oinsert(X9736),X9734),X9735))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X9736),X9734),c_Big__Operators_Olattice__class_OSup__fin(X9736,X9735))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oinsert__idem])])])). 6.97/7.23 fof(c_0_7660, plain, ![X7113, X7114, X7115, X7116]:(~class_Rings_Ocomm__semiring__1(X7116)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7116),X7115),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7116),X7114),X7113))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7116),X7115),X7114)),X7113)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])])])). 6.97/7.23 fof(c_0_7661, plain, ![X13342, X13343, X13344]:(~class_Groups_Omonoid__mult(X13344)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13344),X13343),hAPP(hAPP(c_Power_Opower__class_Opower(X13344),X13343),X13342))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13344),hAPP(hAPP(c_Power_Opower__class_Opower(X13344),X13343),X13342)),X13343)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__commutes])])])). 6.97/7.23 fof(c_0_7662, plain, ![X508, X509, X510]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X510),X509))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X510,tc_HOL_Obool)),X508),X509))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X510),X508)),hAPP(c_Finite__Set_Ocard(X510),X509)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X510,tc_HOL_Obool)),X508),X509))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__psubset])])])). 6.97/7.23 fof(c_0_7663, plain, ![X5667, X5668, X5669, X5670, X5671, X5672]:(~c_Fun_Oinj__on(X5672,X5671,X5670,X5669)|(hBOOL(hAPP(hAPP(c_member(X5671),X5668),hAPP(c_Set_Oimage(X5672,X5671,X5670),X5669)))|c_Fun_Oinj__on(X5672,X5671,c_Fun_Ofun__upd(X5672,X5671,X5670,X5667,X5668),X5669))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__fun__updI])])])). 6.97/7.23 fof(c_0_7664, plain, ![X16909, X16910, X16911]:(~class_Lattices_Olattice(X16911)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16911),X16910))|(X16910=c_Orderings_Obot__class_Obot(tc_fun(X16911,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X16911),X16909),c_Big__Operators_Olattice__class_OInf__fin(X16911,X16910))=c_Big__Operators_Olattice__class_OInf__fin(X16911,hAPP(hAPP(c_Set_Oinsert(X16911),X16909),X16910))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oinsert__idem])])])). 6.97/7.23 fof(c_0_7665, plain, ![X7672, X7673, X7674, X7675]:(~class_Rings_Ocomm__semiring__1(X7675)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7675),X7674),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7675),X7673),X7672))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7675),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7675),X7674),X7673)),X7672)), 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])])])). 6.97/7.23 fof(c_0_7666, plain, ![X9057, X9058, X9059, X9060]:(~class_Lattices_Olattice(X9060)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X9060),X9059),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X9060),X9058),X9057))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X9060),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X9060),X9059),X9058)),X9057)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__sup__aci_I6_J])])])). 6.97/7.23 fof(c_0_7667, plain, ![X9404, X9405, X9406, X9407]:(~class_Rings_Ocomm__semiring__1(X9407)|hAPP(hAPP(c_Power_Opower__class_Opower(X9407),X9406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9405),X9404))=hAPP(hAPP(c_Power_Opower__class_Opower(X9407),hAPP(hAPP(c_Power_Opower__class_Opower(X9407),X9406),X9405)),X9404)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J])])). 6.97/7.23 fof(c_0_7668, plain, ![X14855, X14856, X14857, X14858]:(~class_Groups_Omonoid__mult(X14858)|hAPP(hAPP(c_Power_Opower__class_Opower(X14858),hAPP(hAPP(c_Power_Opower__class_Opower(X14858),X14857),X14856)),X14855)=hAPP(hAPP(c_Power_Opower__class_Opower(X14858),X14857),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14856),X14855))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__mult])])])). 6.97/7.23 fof(c_0_7669, plain, ![X11754, X11755, X11756, X11757]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11757),X11755),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11757),X11754),X11756)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11757),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11757),X11755),X11756)),X11754))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11757),c_Groups_Ozero__class_Ozero(X11757)),X11756))|~class_Fields_Olinordered__field(X11757))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11757),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11757),X11755),X11756)),X11754))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11757),X11755),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11757),X11754),X11756)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11757),c_Groups_Ozero__class_Ozero(X11757)),X11756))|~class_Fields_Olinordered__field(X11757))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__divide__less__eq])])])). 6.97/7.23 fof(c_0_7670, plain, ![X12507, X12508, X12509, X12510]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12510),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12510),X12508),X12509)),X12507))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12510),X12508),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12510),X12507),X12509)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12510),c_Groups_Ozero__class_Ozero(X12510)),X12509))|~class_Fields_Olinordered__field(X12510))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12510),X12508),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12510),X12507),X12509)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12510),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12510),X12508),X12509)),X12507))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12510),c_Groups_Ozero__class_Ozero(X12510)),X12509))|~class_Fields_Olinordered__field(X12510))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pos__divide__le__eq])])])])). 6.97/7.23 fof(c_0_7671, plain, ![X8878, X8879, X8880, X8881]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8881),X8879),X8880)),X8878))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8881),X8879),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8881),X8878),X8880)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8881),c_Groups_Ozero__class_Ozero(X8881)),X8880))|~class_Fields_Olinordered__field(X8881))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8881),X8879),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8881),X8878),X8880)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8881),X8879),X8880)),X8878))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8881),c_Groups_Ozero__class_Ozero(X8881)),X8880))|~class_Fields_Olinordered__field(X8881))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__less__divide__eq])])])). 6.97/7.23 fof(c_0_7672, plain, ![X1871, X1872, X1873, X1874]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1874),X1872),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1874),X1871),X1873)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1874),X1872),X1873)),X1871))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1874),c_Groups_Ozero__class_Ozero(X1874)),X1873))|~class_Fields_Olinordered__field(X1874))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1874),X1872),X1873)),X1871))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1874),X1872),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1874),X1871),X1873)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1874),c_Groups_Ozero__class_Ozero(X1874)),X1873))|~class_Fields_Olinordered__field(X1874))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pos__le__divide__eq])])])])). 6.97/7.23 cnf(c_0_7673, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk457_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_5259])). 6.97/7.23 cnf(c_0_7674, plain, (X4=hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Ovimage(X1,X2,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(split_conjunct,[status(thm)],[c_0_5260])). 6.97/7.23 cnf(c_0_7675, 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_5261])). 6.97/7.23 fof(c_0_7676, plain, ![X12078, X12079, X12080]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12080,tc_HOL_Obool)),X12079),X12078))|X12078=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12080,tc_HOL_Obool)),X12079),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12080,tc_HOL_Obool)),X12078),X12079))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__partition])])). 6.97/7.23 fof(c_0_7677, plain, ![X2545, X2546]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X2546))|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(X2546),X2545))),X2546))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range])])). 6.97/7.23 fof(c_0_7678, plain, ![X9276, X9277, X9278, X9280, X9281, X9282, X9283]:(((hBOOL(hAPP(hAPP(c_member(X9278),esk306_3(X9276,X9277,X9278)),hAPP(c_List_Oset(X9278),X9277)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X9278)),X9277),c_List_Olists(X9278,X9276))))&(~hBOOL(hAPP(hAPP(c_member(X9278),esk306_3(X9276,X9277,X9278)),X9276))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X9278)),X9277),c_List_Olists(X9278,X9276)))))&(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X9282)),X9281),c_List_Olists(X9282,X9280)))|(~hBOOL(hAPP(hAPP(c_member(X9282),X9283),hAPP(c_List_Oset(X9282),X9281)))|hBOOL(hAPP(hAPP(c_member(X9282),X9283),X9280))))), 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])])])])])])). 6.97/7.23 fof(c_0_7679, plain, ![X3103, X3104, X3105, X3106, X3107, X3108]:(((hBOOL(hAPP(hAPP(X3107,X3106),X3104))|~c_List_Olistrelp(X3108,X3107,hAPP(hAPP(c_List_Olist_OCons(X3108),X3106),X3105),hAPP(hAPP(c_List_Olist_OCons(X3108),X3104),X3103)))&(c_List_Olistrelp(X3108,X3107,X3105,X3103)|~c_List_Olistrelp(X3108,X3107,hAPP(hAPP(c_List_Olist_OCons(X3108),X3106),X3105),hAPP(hAPP(c_List_Olist_OCons(X3108),X3104),X3103))))&(~hBOOL(hAPP(hAPP(X3107,X3106),X3104))|~c_List_Olistrelp(X3108,X3107,X3105,X3103)|c_List_Olistrelp(X3108,X3107,hAPP(hAPP(c_List_Olist_OCons(X3108),X3106),X3105),hAPP(hAPP(c_List_Olist_OCons(X3108),X3104),X3103)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp_Oequations_I2_J])])])). 6.97/7.23 fof(c_0_7680, plain, ![X2537, X2538, X2539]:((~hBOOL(hAPP(hAPP(c_member(X2539),X2538),hAPP(c_List_Oset(X2539),X2537)))|c_List_Oremdups(X2539,X2537)=c_List_Oremdups(X2539,hAPP(hAPP(c_List_Olist_OCons(X2539),X2538),X2537)))&(hBOOL(hAPP(hAPP(c_member(X2539),X2538),hAPP(c_List_Oset(X2539),X2537)))|hAPP(hAPP(c_List_Olist_OCons(X2539),X2538),c_List_Oremdups(X2539,X2537))=c_List_Oremdups(X2539,hAPP(hAPP(c_List_Olist_OCons(X2539),X2538),X2537)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_remdups_Osimps_I2_J])])])). 6.97/7.23 cnf(c_0_7681, 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_Obij__betw(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)))), inference(split_conjunct,[status(thm)],[c_0_5262])). 6.97/7.23 fof(c_0_7682, plain, ![X11801, X11802, X11803, X11804, X11805]:(~class_Complete__Lattice_Ocomplete__lattice(X11805)|(~hBOOL(hAPP(hAPP(c_member(X11804),X11803),X11802))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11805),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11804,X11805),X11802),X11801)),hAPP(X11801,X11803))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INF__leI])])])). 6.97/7.23 fof(c_0_7683, plain, ![X15131, X15132, X15133, X15134, X15135]:(~class_Complete__Lattice_Ocomplete__lattice(X15135)|(~hBOOL(hAPP(hAPP(c_member(X15134),X15133),X15132))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15135),hAPP(X15131,X15133)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15134,X15135),X15132),X15131))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__SUPI])])])). 6.97/7.23 fof(c_0_7684, plain, ![X1984, X1985, X1986]:((~hBOOL(hAPP(hAPP(c_member(X1986),X1985),hAPP(c_List_Oset(X1986),X1984)))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1986)),X1984)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1986)),c_List_Oremove1(X1986,X1985,X1984)))&(hBOOL(hAPP(hAPP(c_member(X1986),X1985),hAPP(c_List_Oset(X1986),X1984)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1986)),X1984)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1986)),c_List_Oremove1(X1986,X1985,X1984)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_length__remove1])])])). 6.97/7.23 fof(c_0_7685, plain, ![X12066, X12067, X12068, X12069]:(~class_Orderings_Oorder(X12069)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12069,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X12069,X12068),X12067)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X12069,X12067),X12066))=c_Orderings_Obot__class_Obot(tc_fun(X12069,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I11_J])])). 6.97/7.23 cnf(c_0_7686, 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_Fun_Obij__betw(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_5262])). 6.97/7.23 cnf(c_0_7687, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_Ovimage(X1,X2,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(split_conjunct,[status(thm)],[c_0_5263])). 6.97/7.23 fof(c_0_7688, plain, ![X6067, X6068, X6069, X6070]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6070),X6068),X6067))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6070),X6069),X6067))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6070),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6070),X6069),X6068)),X6067))|~class_Lattices_Osemilattice__sup(X6070))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6070),X6068),X6067))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6070),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6070),X6069),X6068)),X6067))|~class_Lattices_Osemilattice__sup(X6070))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6070),X6069),X6067))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6070),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6070),X6069),X6068)),X6067))|~class_Lattices_Osemilattice__sup(X6070)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__sup__iff])])])). 6.97/7.23 cnf(c_0_7689, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(c_Set_Ovimage(X4,X1,hAPP(c_COMBK(X1,X4),X2)),X3)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5264])). 6.97/7.23 cnf(c_0_7690, plain, (X4=hAPP(c_Set_Ovimage(X1,X2,X3),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_5265])). 6.97/7.23 cnf(c_0_7691, 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_5266])). 6.97/7.23 cnf(c_0_7692, 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_5267])). 6.97/7.23 cnf(c_0_7693, 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_5268])). 6.97/7.23 fof(c_0_7694, plain, ![X8085, X8086, X8087, X8088]:(~class_Lattices_Osemilattice__inf(X8088)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8088),X8087),X8086))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8088),X8087),X8085))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8088),X8087),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8088),X8086),X8085)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__infI])])])). 6.97/7.23 fof(c_0_7695, plain, ![X12130, X12131, X12132]:(~class_Rings_Olinordered__idom(X12132)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12132),c_Groups_Ozero__class_Ozero(X12132)),X12131))|hAPP(c_Groups_Oabs__class_Oabs(X12132),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12132),X12130),X12131))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12132),hAPP(c_Groups_Oabs__class_Oabs(X12132),X12130)),X12131))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__mult__pos])])])). 6.97/7.23 fof(c_0_7696, plain, ![X356, X357, X358, X359, X360]:(~c_Finite__Set_Ofun__left__comm(X360,X359,X358)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X360),X357))|hBOOL(hAPP(c_Finite__Set_Ofold__graph(X360,X359,X358,X356,X357),hAPP(hAPP(c_Finite__Set_Ofold(X360,X359,X358),X356),X357))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__fold])])). 6.97/7.23 cnf(c_0_7697, plain, (hAPP(c_Set_Ovimage(X4,X1,hAPP(c_COMBK(X1,X4),X2)),X3)=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5264])). 6.97/7.23 fof(c_0_7698, plain, ![X10434, X10435]:(X10435=c_List_Olist_ONil(X10434)|c_Random_Oselect__weight(X10434,hAPP(hAPP(c_List_Omap(X10434,tc_prod(tc_Code__Numeral_Ocode__numeral,X10434)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X10434),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X10435))=c_Random_Oselect(X10434,X10435)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_select__weigth__select])])). 6.97/7.23 fof(c_0_7699, plain, ![X11395, X11396, X11397, X11398]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11398),X11397))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11398),X11395)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11396),X11397)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11396),X11395)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__add__eq__less])])])). 6.97/7.23 cnf(c_0_7700, 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_5269])). 6.97/7.23 fof(c_0_7701, plain, ![X17096, X17097, X17098]:(~class_Rings_Olinordered__semidom(X17098)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17098),c_Groups_Oone__class_Oone(X17098)),X17097))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17098),c_Groups_Oone__class_Oone(X17098)),hAPP(hAPP(c_Power_Opower__class_Opower(X17098),X17097),hAPP(c_Nat_OSuc,X17096)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1])])). 6.97/7.23 fof(c_0_7702, plain, ![X5826, X5827]:(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X5827),hAPP(c_List_Oset(tc_Nat_Onat),X5826)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5827),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)),X5826)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_elem__le__sum])])])). 6.97/7.23 fof(c_0_7703, plain, ![X6173, X6174, X6175, X6178, X6179, X6180, X6181, X6182]:((((X6174=hAPP(hAPP(c_List_Olist_OCons(X6175),esk204_3(X6173,X6174,X6175)),esk205_3(X6173,X6174,X6175))|X6174=c_List_Olist_ONil(X6175)|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6175)),X6174),c_List_Olists(X6175,X6173))))&(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6175)),esk205_3(X6173,X6174,X6175)),c_List_Olists(X6175,X6173)))|X6174=c_List_Olist_ONil(X6175)|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6175)),X6174),c_List_Olists(X6175,X6173)))))&(hBOOL(hAPP(hAPP(c_member(X6175),esk204_3(X6173,X6174,X6175)),X6173))|X6174=c_List_Olist_ONil(X6175)|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6175)),X6174),c_List_Olists(X6175,X6173)))))&((X6179!=hAPP(hAPP(c_List_Olist_OCons(X6180),X6181),X6182)|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6180)),X6182),c_List_Olists(X6180,X6178)))|~hBOOL(hAPP(hAPP(c_member(X6180),X6181),X6178))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6180)),X6179),c_List_Olists(X6180,X6178))))&(X6179!=c_List_Olist_ONil(X6180)|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6180)),X6179),c_List_Olists(X6180,X6178)))))), 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])])])])])])). 6.97/7.23 fof(c_0_7704, plain, ![X3642, X3643, X3644, X3645]:(~c_Relation_Oantisym(X3645,X3644)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X3645,X3645)),hAPP(hAPP(c_Product__Type_OPair(X3645,X3645),X3643),X3642)),X3644))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X3645,X3645)),hAPP(hAPP(c_Product__Type_OPair(X3645,X3645),X3642),X3643)),X3644))|X3643=X3642))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_antisymD])])])). 6.97/7.23 cnf(c_0_7705, 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_5270])). 6.97/7.23 fof(c_0_7706, plain, ![X5098, X5099]:(~class_Groups_Olinordered__ab__group__add(X5099)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5099),X5098))|(c_Orderings_Obot__class_Obot(tc_fun(X5099,tc_HOL_Obool))=X5098|c_Big__Operators_Olinorder__class_OMin(X5099,hAPP(c_Set_Oimage(X5099,X5099,c_Groups_Ouminus__class_Ouminus(X5099)),X5098))=hAPP(c_Groups_Ouminus__class_Ouminus(X5099),c_Big__Operators_Olinorder__class_OMax(X5099,X5098))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__Max__eq__Min])])])). 6.97/7.23 fof(c_0_7707, plain, ![X16002, X16003]:(~class_Groups_Olinordered__ab__group__add(X16003)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16003),X16002))|(X16002=c_Orderings_Obot__class_Obot(tc_fun(X16003,tc_HOL_Obool))|c_Big__Operators_Olinorder__class_OMax(X16003,hAPP(c_Set_Oimage(X16003,X16003,c_Groups_Ouminus__class_Ouminus(X16003)),X16002))=hAPP(c_Groups_Ouminus__class_Ouminus(X16003),c_Big__Operators_Olinorder__class_OMin(X16003,X16002))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__Min__eq__Max])])])). 6.97/7.23 fof(c_0_7708, plain, ![X10930, X10931]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10930))|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),X10931),X10930))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10931))|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),X10931),X10930)))))&(~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),X10931),X10930)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10930))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10931))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])])). 6.97/7.23 fof(c_0_7709, plain, ![X2406, X2407, X2408, X2409, X2410]:(((X2407!=X2408|X2409!=X2406|hAPP(hAPP(c_Set_Oinsert(X2410),X2407),hAPP(hAPP(c_Set_Oinsert(X2410),X2406),c_Orderings_Obot__class_Obot(tc_fun(X2410,tc_HOL_Obool))))=hAPP(hAPP(c_Set_Oinsert(X2410),X2409),hAPP(hAPP(c_Set_Oinsert(X2410),X2408),c_Orderings_Obot__class_Obot(tc_fun(X2410,tc_HOL_Obool)))))&(X2407!=X2409|X2408!=X2406|hAPP(hAPP(c_Set_Oinsert(X2410),X2407),hAPP(hAPP(c_Set_Oinsert(X2410),X2406),c_Orderings_Obot__class_Obot(tc_fun(X2410,tc_HOL_Obool))))=hAPP(hAPP(c_Set_Oinsert(X2410),X2409),hAPP(hAPP(c_Set_Oinsert(X2410),X2408),c_Orderings_Obot__class_Obot(tc_fun(X2410,tc_HOL_Obool))))))&(((X2407=X2409|X2407=X2408|hAPP(hAPP(c_Set_Oinsert(X2410),X2407),hAPP(hAPP(c_Set_Oinsert(X2410),X2406),c_Orderings_Obot__class_Obot(tc_fun(X2410,tc_HOL_Obool))))!=hAPP(hAPP(c_Set_Oinsert(X2410),X2409),hAPP(hAPP(c_Set_Oinsert(X2410),X2408),c_Orderings_Obot__class_Obot(tc_fun(X2410,tc_HOL_Obool)))))&(X2408=X2406|X2407=X2408|hAPP(hAPP(c_Set_Oinsert(X2410),X2407),hAPP(hAPP(c_Set_Oinsert(X2410),X2406),c_Orderings_Obot__class_Obot(tc_fun(X2410,tc_HOL_Obool))))!=hAPP(hAPP(c_Set_Oinsert(X2410),X2409),hAPP(hAPP(c_Set_Oinsert(X2410),X2408),c_Orderings_Obot__class_Obot(tc_fun(X2410,tc_HOL_Obool))))))&((X2407=X2409|X2409=X2406|hAPP(hAPP(c_Set_Oinsert(X2410),X2407),hAPP(hAPP(c_Set_Oinsert(X2410),X2406),c_Orderings_Obot__class_Obot(tc_fun(X2410,tc_HOL_Obool))))!=hAPP(hAPP(c_Set_Oinsert(X2410),X2409),hAPP(hAPP(c_Set_Oinsert(X2410),X2408),c_Orderings_Obot__class_Obot(tc_fun(X2410,tc_HOL_Obool)))))&(X2408=X2406|X2409=X2406|hAPP(hAPP(c_Set_Oinsert(X2410),X2407),hAPP(hAPP(c_Set_Oinsert(X2410),X2406),c_Orderings_Obot__class_Obot(tc_fun(X2410,tc_HOL_Obool))))!=hAPP(hAPP(c_Set_Oinsert(X2410),X2409),hAPP(hAPP(c_Set_Oinsert(X2410),X2408),c_Orderings_Obot__class_Obot(tc_fun(X2410,tc_HOL_Obool)))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_doubleton__eq__iff])])])). 6.97/7.23 fof(c_0_7710, plain, ![X7957, X7958, X7959]:(~class_Groups_Olinordered__ab__group__add(X7959)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X7959),hAPP(c_Groups_Ouminus__class_Ouminus(X7959),X7958)),hAPP(c_Groups_Ouminus__class_Ouminus(X7959),X7957))=hAPP(c_Groups_Ouminus__class_Ouminus(X7959),hAPP(hAPP(c_Orderings_Oord__class_Omin(X7959),X7958),X7957))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__min__eq__max])])). 6.97/7.23 fof(c_0_7711, plain, ![X11519, X11520, X11521]:(~class_Lattices_Oboolean__algebra(X11521)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X11521),hAPP(c_Groups_Ouminus__class_Ouminus(X11521),X11520)),hAPP(c_Groups_Ouminus__class_Ouminus(X11521),X11519))=hAPP(c_Groups_Ouminus__class_Ouminus(X11521),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X11521),X11520),X11519))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_compl__sup])])])). 6.97/7.23 fof(c_0_7712, plain, ![X2441, X2442, X2443]:(~class_Lattices_Oboolean__algebra(X2443)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2443),hAPP(c_Groups_Ouminus__class_Ouminus(X2443),X2442)),hAPP(c_Groups_Ouminus__class_Ouminus(X2443),X2441))=hAPP(c_Groups_Ouminus__class_Ouminus(X2443),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2443),X2442),X2441))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_compl__inf])])])). 6.97/7.23 fof(c_0_7713, plain, ![X17518, X17519]:((X17519!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17519),X17518)=X17518)&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X17519|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17519),X17518)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17519),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X17518)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__eq__if])])])). 6.97/7.23 fof(c_0_7714, plain, ![X5258, X5259, X5260]:(~class_Groups_Olinordered__ab__group__add(X5260)|hAPP(c_Groups_Ouminus__class_Ouminus(X5260),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5260),X5259),X5258))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X5260),hAPP(c_Groups_Ouminus__class_Ouminus(X5260),X5259)),hAPP(c_Groups_Ouminus__class_Ouminus(X5260),X5258))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__max__eq__min])])). 6.97/7.23 fof(c_0_7715, plain, ![X449, X450, X451]:(~class_Groups_Oab__group__add(X451)|hAPP(c_Groups_Ouminus__class_Ouminus(X451),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X451),X450),X449))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X451),hAPP(c_Groups_Ouminus__class_Ouminus(X451),X450)),hAPP(c_Groups_Ouminus__class_Ouminus(X451),X449))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__add__distrib])])])). 6.97/7.23 fof(c_0_7716, plain, ![X3498, X3499, X3500]:(~class_Groups_Ogroup__add(X3500)|hAPP(c_Groups_Ouminus__class_Ouminus(X3500),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3500),X3499),X3498))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3500),hAPP(c_Groups_Ouminus__class_Ouminus(X3500),X3498)),hAPP(c_Groups_Ouminus__class_Ouminus(X3500),X3499))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__add])])])). 6.97/7.23 fof(c_0_7717, plain, ![X8403, X8404]:(X8404=c_List_Olist_ONil(X8403)|hAPP(hAPP(c_List_Onth(X8403),X8404),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8403)),X8404)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_List_Olast(X8403,X8404)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_last__conv__nth])])])). 6.97/7.23 cnf(c_0_7718, 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_5271])). 6.97/7.23 fof(c_0_7719, plain, ![X1162, X1163, X1164]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1164),X1163))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1164,tc_HOL_Obool)),X1162),X1163))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1164),X1162)),hAPP(c_Finite__Set_Ocard(X1164),X1163))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_psubset__card__mono])])])). 6.97/7.23 fof(c_0_7720, plain, ![X6550, X6551, X6552]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6552),X6551))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6552,tc_HOL_Obool)),X6550),X6551))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X6552),X6550)),hAPP(c_Finite__Set_Ocard(X6552),X6551))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__mono])])). 6.97/7.23 cnf(c_0_7721, 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_5272])). 6.97/7.23 fof(c_0_7722, plain, ![X13486, X13487, X13488, X13489, X13490]:(~class_Orderings_Oorder(X13489)|~class_Orderings_Oorder(X13490)|(~c_Orderings_Oorder__class_Ostrict__mono(X13489,X13490,X13488)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13489),X13487),X13486))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13490),hAPP(X13488,X13487)),hAPP(X13488,X13486)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_strict__monoD])])])). 6.97/7.23 fof(c_0_7723, plain, ![X13311, X13312, X13313, X13314, X13315]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13315),hAPP(X13313,X13312)),hAPP(X13313,X13311)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13314),X13312),X13311))|~c_Orderings_Oorder__class_Ostrict__mono(X13314,X13315,X13313)|(~class_Orderings_Olinorder(X13314)|~class_Orderings_Oorder(X13315)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13314),X13312),X13311))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13315),hAPP(X13313,X13312)),hAPP(X13313,X13311)))|~c_Orderings_Oorder__class_Ostrict__mono(X13314,X13315,X13313)|(~class_Orderings_Olinorder(X13314)|~class_Orderings_Oorder(X13315)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_strict__mono__less])])])])). 6.97/7.23 fof(c_0_7724, plain, ![X17087, X17088, X17089, X17090, X17091]:(~class_Orderings_Oorder(X17090)|~class_Orderings_Oorder(X17091)|(~c_Orderings_Oorder__class_Omono(X17090,X17091,X17089)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17090),X17088),X17087))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17091),hAPP(X17089,X17088)),hAPP(X17089,X17087)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_monoD])])])). 6.97/7.23 fof(c_0_7725, plain, ![X842, X843, X844, X845, X846]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X845),X843),X842))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X846),hAPP(X844,X843)),hAPP(X844,X842)))|~c_Orderings_Oorder__class_Ostrict__mono(X845,X846,X844)|(~class_Orderings_Oorder(X846)|~class_Orderings_Olinorder(X845)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X846),hAPP(X844,X843)),hAPP(X844,X842)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X845),X843),X842))|~c_Orderings_Oorder__class_Ostrict__mono(X845,X846,X844)|(~class_Orderings_Oorder(X846)|~class_Orderings_Olinorder(X845)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_strict__mono__less__eq])])])). 6.97/7.23 fof(c_0_7726, plain, ![X6751, X6752, X6753, X6754, X6755]:((hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6755),X6751),X6754)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6755),X6752),X6753)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6755),X6751),X6753)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6755),X6752),X6754)|c_Groups_Ozero__class_Ozero(X6755)=X6753|X6754=c_Groups_Ozero__class_Ozero(X6755)|~class_Fields_Ofield(X6755))&(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6755),X6751),X6753)!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6755),X6752),X6754)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6755),X6751),X6754)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6755),X6752),X6753)|c_Groups_Ozero__class_Ozero(X6755)=X6753|X6754=c_Groups_Ozero__class_Ozero(X6755)|~class_Fields_Ofield(X6755))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_frac__eq__eq])])])])). 6.97/7.23 fof(c_0_7727, plain, ![X8354, X8355, X8357]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X8355)),X8354))|(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X8355)),X8357),X8354))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8355)),X8357)),esk277_2(X8354,X8355))))), 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])])])])])). 6.97/7.23 fof(c_0_7728, plain, ![X9044, X9045, X9046, X9047]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9047),X9045),X9044))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9047),X9046),X9044))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9047),hAPP(hAPP(c_Orderings_Oord__class_Omax(X9047),X9046),X9045)),X9044))|~class_Orderings_Olinorder(X9047))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9047),X9045),X9044))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9047),hAPP(hAPP(c_Orderings_Oord__class_Omax(X9047),X9046),X9045)),X9044))|~class_Orderings_Olinorder(X9047))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9047),X9046),X9044))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9047),hAPP(hAPP(c_Orderings_Oord__class_Omax(X9047),X9046),X9045)),X9044))|~class_Orderings_Olinorder(X9047)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__less__iff__conj])])])). 6.97/7.23 fof(c_0_7729, plain, ![X14348, X14349, X14350, X14351]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14351),X14349),X14348))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14351),X14350),X14348))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14351),hAPP(hAPP(c_Orderings_Oord__class_Omax(X14351),X14350),X14349)),X14348))|~class_Orderings_Olinorder(X14351))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14351),X14349),X14348))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14351),hAPP(hAPP(c_Orderings_Oord__class_Omax(X14351),X14350),X14349)),X14348))|~class_Orderings_Olinorder(X14351))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14351),X14350),X14348))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14351),hAPP(hAPP(c_Orderings_Oord__class_Omax(X14351),X14350),X14349)),X14348))|~class_Orderings_Olinorder(X14351)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__sup__iff])])])). 6.97/7.23 fof(c_0_7730, plain, ![X7188, X7189, X7190, X7191]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7191),X7190),X7188))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7191),X7190),hAPP(hAPP(c_Orderings_Oord__class_Omin(X7191),X7189),X7188)))|~class_Orderings_Olinorder(X7191))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7191),X7190),X7189))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7191),X7190),hAPP(hAPP(c_Orderings_Oord__class_Omin(X7191),X7189),X7188)))|~class_Orderings_Olinorder(X7191)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7191),X7190),X7188))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7191),X7190),X7189))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7191),X7190),hAPP(hAPP(c_Orderings_Oord__class_Omin(X7191),X7189),X7188)))|~class_Orderings_Olinorder(X7191))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__less__iff__conj])])])). 6.97/7.23 fof(c_0_7731, plain, ![X10439, X10440, X10441]:(~class_Fields_Olinordered__field__inverse__zero(X10441)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10441),c_Groups_Ozero__class_Ozero(X10441)),X10440))|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10441),hAPP(c_Groups_Oabs__class_Oabs(X10441),X10439)),X10440)=hAPP(c_Groups_Oabs__class_Oabs(X10441),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10441),X10439),X10440)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__div__pos])])])). 6.97/7.23 fof(c_0_7732, plain, ![X1090, X1091, X1092, X1093]:(~hBOOL(hAPP(hAPP(c_member(X1093),X1092),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1093,tc_HOL_Obool),X1091)))|(~hBOOL(hAPP(hAPP(c_member(tc_fun(X1093,tc_HOL_Obool)),X1090),X1091))|hBOOL(hAPP(hAPP(c_member(X1093),X1092),X1090)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_InterE])])])). 6.97/7.23 fof(c_0_7733, plain, ![X3100, X3101, X3102]:(~class_Rings_Osemiring__1(X3102)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3102),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3102),X3101)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3102),X3100))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3102),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3101),X3100))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__add])])])). 6.97/7.23 fof(c_0_7734, plain, ![X9241, X9242, X9243, X9244]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9244),X9243),X9241))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9244),X9243),hAPP(hAPP(c_Orderings_Oord__class_Omin(X9244),X9242),X9241)))|~class_Orderings_Olinorder(X9244))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9244),X9243),X9242))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9244),X9243),hAPP(hAPP(c_Orderings_Oord__class_Omin(X9244),X9242),X9241)))|~class_Orderings_Olinorder(X9244)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9244),X9243),X9241))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9244),X9243),X9242))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9244),X9243),hAPP(hAPP(c_Orderings_Oord__class_Omin(X9244),X9242),X9241)))|~class_Orderings_Olinorder(X9244))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__inf__iff])])])). 6.97/7.23 fof(c_0_7735, plain, ![X16061, X16062]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X16062),c_Orderings_Otop__class_Otop(tc_fun(X16062,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X16062,X16061)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X16062,X16061),tc_HOL_Obool)))))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X16061),c_Orderings_Otop__class_Otop(tc_fun(X16061,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X16062,X16061)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X16062,X16061),tc_HOL_Obool))))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16062),c_Orderings_Otop__class_Otop(tc_fun(X16062,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16061),c_Orderings_Otop__class_Otop(tc_fun(X16061,tc_HOL_Obool))))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X16062,X16061)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X16062,X16061),tc_HOL_Obool)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus__UNIV__iff])])])). 6.97/7.23 fof(c_0_7736, plain, ![X16231, X16232]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16232),c_Orderings_Otop__class_Otop(tc_fun(X16232,tc_HOL_Obool))))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16231),c_Orderings_Otop__class_Otop(tc_fun(X16231,tc_HOL_Obool))))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X16232,X16231)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X16232,X16231),tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__Prod__UNIV])])])). 6.97/7.23 fof(c_0_7737, plain, ![X1286, X1287]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1287))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1286))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1287),X1286)),X1287)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_int__div__less__self])])])). 6.97/7.23 fof(c_0_7738, plain, ![X15139, X15140, X15141]:(~class_Orderings_Olinorder(X15141)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15141),X15140))|(~hBOOL(hAPP(hAPP(c_member(X15141),X15139),X15140))|c_Big__Operators_Olattice_OSup__fin(X15141,c_Orderings_Oord__class_Omax(X15141),X15140)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X15141),X15139),c_Big__Operators_Olattice_OSup__fin(X15141,c_Orderings_Oord__class_Omax(X15141),X15140))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oin__idem])])). 6.97/7.23 fof(c_0_7739, plain, ![X7246, X7247, X7248]:(~class_Orderings_Olinorder(X7248)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7248),X7247))|(~hBOOL(hAPP(hAPP(c_member(X7248),X7246),X7247))|c_Big__Operators_Olattice_OInf__fin(X7248,c_Orderings_Oord__class_Omin(X7248),X7247)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X7248),X7246),c_Big__Operators_Olattice_OInf__fin(X7248,c_Orderings_Oord__class_Omin(X7248),X7247))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Oin__idem])])])). 6.97/7.23 cnf(c_0_7740, 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,esk232_4(X1,X2,X3,X4))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X3),X4),X2))|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(X1,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))), inference(split_conjunct,[status(thm)],[c_0_5134])). 6.97/7.23 fof(c_0_7741, plain, ![X7325, X7326, X7327, X7328, X7329, X7330, X7331]:(~c_Finite__Set_Ofolding__image__simple(X7331,X7330,X7329,X7328,X7327,X7326)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7330),X7325))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X7331,X7330,X7329),X7327),X7328),X7325)=hAPP(X7326,X7325))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Oeq__fold__g])])])). 6.97/7.23 fof(c_0_7742, plain, ![X12355, X12356]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X12356))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12355))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X12355),X12356)),X12355)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__less__dividend])])])). 6.97/7.23 fof(c_0_7743, plain, ![X11482, X11483]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X11483))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X11482))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11482),X11483)),X11482)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__less])])])). 6.97/7.23 fof(c_0_7744, plain, ![X13108, X13109, X13110, X13112]:(((hBOOL(hAPP(hAPP(c_member(X13110),esk427_3(X13108,X13109,X13110)),X13109))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13110),c_Complete__Lattice_OInf__class_OInf(X13110,X13109)),X13108))|(~class_Orderings_Olinorder(X13110)|~class_Complete__Lattice_Ocomplete__lattice(X13110)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13110),esk427_3(X13108,X13109,X13110)),X13108))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13110),c_Complete__Lattice_OInf__class_OInf(X13110,X13109)),X13108))|(~class_Orderings_Olinorder(X13110)|~class_Complete__Lattice_Ocomplete__lattice(X13110))))&(~hBOOL(hAPP(hAPP(c_member(X13110),X13112),X13109))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13110),X13112),X13108))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13110),c_Complete__Lattice_OInf__class_OInf(X13110,X13109)),X13108))|(~class_Orderings_Olinorder(X13110)|~class_Complete__Lattice_Ocomplete__lattice(X13110)))), 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])])])])])). 6.97/7.23 fof(c_0_7745, plain, ![X3541, X3542, X3543, X3544]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3543),X3542),X3544))|~hBOOL(hAPP(hAPP(c_member(X3543),X3544),X3541))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3543),X3542),c_Complete__Lattice_OSup__class_OSup(X3543,X3541)))|(~class_Orderings_Olinorder(X3543)|~class_Complete__Lattice_Ocomplete__lattice(X3543)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3543),X3542),esk115_3(X3541,X3542,X3543)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3543),X3542),c_Complete__Lattice_OSup__class_OSup(X3543,X3541)))|(~class_Orderings_Olinorder(X3543)|~class_Complete__Lattice_Ocomplete__lattice(X3543)))&(hBOOL(hAPP(hAPP(c_member(X3543),esk115_3(X3541,X3542,X3543)),X3541))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3543),X3542),c_Complete__Lattice_OSup__class_OSup(X3543,X3541)))|(~class_Orderings_Olinorder(X3543)|~class_Complete__Lattice_Ocomplete__lattice(X3543))))), 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])])])])])). 6.97/7.23 cnf(c_0_7746, 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_5273])). 6.97/7.23 cnf(c_0_7747, 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_5274])). 6.97/7.23 cnf(c_0_7748, plain, (hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))=c_Divides_Odiv__class_Omod(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_5275])). 6.97/7.23 cnf(c_0_7749, 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_5276])). 6.97/7.23 fof(c_0_7750, plain, ![X1101, X1102, X1103]:(~class_Orderings_Olinorder(X1103)|(~hBOOL(hAPP(hAPP(c_member(X1103),X1102),hAPP(c_List_Oset(X1103),X1101)))|(~c_List_Olinorder__class_Osorted(X1103,X1101)|X1101=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1103,X1103,c_COMBI(X1103)),X1102),c_List_Oremove1(X1103,X1102,X1101))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insort__remove1])])])). 6.97/7.23 fof(c_0_7751, plain, ![X11417, X11418, X11419]:((hBOOL(hAPP(hAPP(c_member(tc_fun(X11419,tc_HOL_Obool)),esk380_3(X11417,X11418,X11419)),X11418))|hBOOL(hAPP(hAPP(c_member(X11419),X11417),c_Complete__Lattice_OInf__class_OInf(tc_fun(X11419,tc_HOL_Obool),X11418))))&(~hBOOL(hAPP(hAPP(c_member(X11419),X11417),esk380_3(X11417,X11418,X11419)))|hBOOL(hAPP(hAPP(c_member(X11419),X11417),c_Complete__Lattice_OInf__class_OInf(tc_fun(X11419,tc_HOL_Obool),X11418))))), 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])])])])])). 6.97/7.23 fof(c_0_7752, plain, ![X6664, X6665, X6666]:(~class_Rings_Osemiring__1(X6666)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X6666),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6665),X6664))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6666),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X6666),X6665)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X6666),X6664))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__mult])])])). 6.97/7.23 cnf(c_0_7753, 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_5277])). 6.97/7.23 fof(c_0_7754, plain, ![X5532, X5533, X5534]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5534),X5533),X5532))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5534,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5534),X5533)),hAPP(c_SetInterval_Oord__class_OlessThan(X5534),X5532)))|~class_Orderings_Olinorder(X5534))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5534,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5534),X5533)),hAPP(c_SetInterval_Oord__class_OlessThan(X5534),X5532)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5534),X5533),X5532))|~class_Orderings_Olinorder(X5534))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lessThan__strict__subset__iff])])])). 6.97/7.23 cnf(c_0_7755, 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_5278])). 6.97/7.23 cnf(c_0_7756, 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_5279]), ['final']). 6.97/7.23 cnf(c_0_7757, 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_5280])). 6.97/7.23 fof(c_0_7758, plain, ![X13957, X13958, X13959]:(~class_Int_Onumber__ring(X13959)|hAPP(c_Int_Onumber__class_Onumber__of(X13959),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X13958),X13957))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13959),hAPP(c_Int_Onumber__class_Onumber__of(X13959),X13958)),hAPP(c_Int_Onumber__class_Onumber__of(X13959),X13957))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_number__of__diff])])])). 6.97/7.23 fof(c_0_7759, plain, ![X4202, X4203, X4204]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4204),X4202),X4203))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4204,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X4204),X4203)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X4204),X4202)))|~class_Orderings_Olinorder(X4204))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4204,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X4204),X4203)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X4204),X4202)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4204),X4202),X4203))|~class_Orderings_Olinorder(X4204))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__subset__iff])])])). 6.97/7.23 fof(c_0_7760, plain, ![X12042, X12043, X12044]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12044,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X12044),X12043)),hAPP(c_SetInterval_Oord__class_OlessThan(X12044),X12042)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12044),X12043),X12042))|~class_Orderings_Olinorder(X12044))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12044),X12043),X12042))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12044,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X12044),X12043)),hAPP(c_SetInterval_Oord__class_OlessThan(X12044),X12042)))|~class_Orderings_Olinorder(X12044))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lessThan__subset__iff])])])])). 6.97/7.23 fof(c_0_7761, plain, ![X9229, X9230, X9231]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9231),X9229),X9230))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9231,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X9231),X9230)),hAPP(c_SetInterval_Oord__class_OatLeast(X9231),X9229)))|~class_Orderings_Oorder(X9231))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9231,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X9231),X9230)),hAPP(c_SetInterval_Oord__class_OatLeast(X9231),X9229)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9231),X9229),X9230))|~class_Orderings_Oorder(X9231))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeast__subset__iff])])])])). 6.97/7.23 fof(c_0_7762, plain, ![X13492, X13493, X13494]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13494,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X13494),X13493)),hAPP(c_SetInterval_Oord__class_OatMost(X13494),X13492)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13494),X13493),X13492))|~class_Orderings_Oorder(X13494))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13494),X13493),X13492))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13494,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X13494),X13493)),hAPP(c_SetInterval_Oord__class_OatMost(X13494),X13492)))|~class_Orderings_Oorder(X13494))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__subset__iff])])])). 6.97/7.23 fof(c_0_7763, plain, ![X2510, X2511, X2512, X2513]:(~class_Divides_Osemiring__div(X2513)|c_Divides_Odiv__class_Omod(X2513,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2513),c_Divides_Odiv__class_Omod(X2513,X2512,X2510)),X2511),X2510)=c_Divides_Odiv__class_Omod(X2513,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2513),X2512),X2511),X2510)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__add__left__eq])])])). 6.97/7.23 fof(c_0_7764, plain, ![X11278, X11279, X11280, X11281]:(~class_Divides_Oring__div(X11281)|c_Divides_Odiv__class_Omod(X11281,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X11281),X11280),X11279),X11278)=c_Divides_Odiv__class_Omod(X11281,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X11281),c_Divides_Odiv__class_Omod(X11281,X11280,X11278)),X11279),X11278)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__left__eq])])). 6.97/7.23 fof(c_0_7765, plain, ![X3780, X3781, X3782, X3783]:(~class_Divides_Osemiring__div(X3783)|c_Divides_Odiv__class_Omod(X3783,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3783),X3782),X3780),X3781)=c_Divides_Odiv__class_Omod(X3783,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3783),c_Divides_Odiv__class_Omod(X3783,X3782,X3781)),X3780),X3781)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I4_J])])). 6.97/7.23 fof(c_0_7766, plain, ![X9579, X9580, X9581]:(~class_Int_Onumber__ring(X9581)|hAPP(c_Int_Onumber__class_Onumber__of(X9581),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X9580),X9579))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9581),hAPP(c_Int_Onumber__class_Onumber__of(X9581),X9580)),hAPP(c_Int_Onumber__class_Onumber__of(X9581),X9579))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__add])])). 6.97/7.23 fof(c_0_7767, plain, ![X8761, X8762, X8763]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8763,tc_HOL_Obool)),X8762),X8761))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X8763,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(X8763,X8762)),c_Predicate_OPowp(X8763,X8761)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Powp__mono])])])). 6.97/7.23 cnf(c_0_7768, plain, (c_List_Olist_ONil(X3)=c_List_OdropWhile(X3,X1,X2)|~hBOOL(hAPP(X1,esk27_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_5197])). 6.97/7.23 cnf(c_0_7769, 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_5281])). 6.97/7.23 cnf(c_0_7770, 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_5282]), ['final']). 6.97/7.23 fof(c_0_7771, plain, ![X5064, X5065, X5066]:((hBOOL(hAPP(hAPP(c_member(X5066),esk162_3(X5064,X5065,X5066)),X5065))|(~hBOOL(hAPP(hAPP(c_member(X5066),X5064),X5065))|c_Big__Operators_Olinorder__class_OMax(X5066,X5065)=X5064)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5066),X5065))|~class_Orderings_Olinorder(X5066))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5066),esk162_3(X5064,X5065,X5066)),X5064))|(~hBOOL(hAPP(hAPP(c_member(X5066),X5064),X5065))|c_Big__Operators_Olinorder__class_OMax(X5066,X5065)=X5064)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5066),X5065))|~class_Orderings_Olinorder(X5066))), 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])])])])])). 6.97/7.23 fof(c_0_7772, plain, ![X6303, X6304, X6305, X6306]:(~class_Orderings_Olinorder(X6306)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X6306),X6305),hAPP(hAPP(c_Orderings_Oord__class_Omax(X6306),X6304),X6303))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X6306),hAPP(hAPP(c_Orderings_Oord__class_Omax(X6306),X6305),X6304)),X6303)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__assoc])])). 6.97/7.23 fof(c_0_7773, plain, ![X3827, X3828, X3829, X3830]:(~class_Divides_Oring__div(X3830)|c_Divides_Odiv__class_Omod(X3830,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3830),X3829),c_Divides_Odiv__class_Omod(X3830,X3828,X3827)),X3827)=c_Divides_Odiv__class_Omod(X3830,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3830),X3829),X3828),X3827)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__diff__right__eq])])])). 6.97/7.23 fof(c_0_7774, plain, ![X14235, X14236, X14237, X14238]:(~class_Divides_Osemiring__div(X14238)|c_Divides_Odiv__class_Omod(X14238,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14238),X14237),X14236),X14235)=c_Divides_Odiv__class_Omod(X14238,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14238),X14237),c_Divides_Odiv__class_Omod(X14238,X14236,X14235)),X14235)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__right__eq])])). 6.97/7.23 fof(c_0_7775, plain, ![X4810, X4811, X4812, X4813]:(~class_Orderings_Olinorder(X4813)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X4813),X4812),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4813),X4811),X4810))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4813),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4813),X4812),X4811)),X4810)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oassoc])])). 6.97/7.23 fof(c_0_7776, plain, ![X16087, X16088, X16089]:(~class_Int_Onumber__ring(X16089)|hAPP(c_Int_Onumber__class_Onumber__of(X16089),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16088),X16087))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16089),hAPP(c_Int_Onumber__class_Onumber__of(X16089),X16088)),hAPP(c_Int_Onumber__class_Onumber__of(X16089),X16087))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_number__of__mult])])])). 6.97/7.23 fof(c_0_7777, plain, ![X10813, X10814, X10815]:((hBOOL(hAPP(hAPP(c_member(X10815),esk359_3(X10813,X10814,X10815)),X10814))|(~hBOOL(hAPP(hAPP(c_member(X10815),X10813),X10814))|X10813=c_Big__Operators_Olinorder__class_OMin(X10815,X10814))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10815),X10814))|~class_Orderings_Olinorder(X10815))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10815),X10813),esk359_3(X10813,X10814,X10815)))|(~hBOOL(hAPP(hAPP(c_member(X10815),X10813),X10814))|X10813=c_Big__Operators_Olinorder__class_OMin(X10815,X10814))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10815),X10814))|~class_Orderings_Olinorder(X10815))), 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])])])])])). 6.97/7.23 fof(c_0_7778, plain, ![X16824, X16825, X16826]:(((~hBOOL(hAPP(hAPP(c_member(X16826),X16825),hAPP(c_List_Oset(X16826),X16824)))|~hBOOL(hAPP(c_List_Odistinct(X16826),hAPP(hAPP(c_List_Olist_OCons(X16826),X16825),X16824))))&(hBOOL(hAPP(c_List_Odistinct(X16826),X16824))|~hBOOL(hAPP(c_List_Odistinct(X16826),hAPP(hAPP(c_List_Olist_OCons(X16826),X16825),X16824)))))&(hBOOL(hAPP(hAPP(c_member(X16826),X16825),hAPP(c_List_Oset(X16826),X16824)))|~hBOOL(hAPP(c_List_Odistinct(X16826),X16824))|hBOOL(hAPP(c_List_Odistinct(X16826),hAPP(hAPP(c_List_Olist_OCons(X16826),X16825),X16824))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct_Osimps_I2_J])])])])). 6.97/7.23 fof(c_0_7779, plain, ![X8689, X8690]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8690),hAPP(c_Nat_OSuc,X8689)))|c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X8690,hAPP(c_Nat_OSuc,X8689))=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X8689)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X8690,X8689))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMostSuc__conv])])). 6.97/7.23 fof(c_0_7780, plain, ![X14202, X14203, X14204, X14205]:(~class_Divides_Osemiring__div(X14205)|c_Divides_Odiv__class_Omod(X14205,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14205),X14204),X14203),X14202)=c_Divides_Odiv__class_Omod(X14205,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14205),X14204),c_Divides_Odiv__class_Omod(X14205,X14203,X14202)),X14202)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__right__eq])])). 6.97/7.23 fof(c_0_7781, plain, ![X15333, X15334, X15335]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X15335))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X15335),X15334)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X15335),X15333)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15334),X15333)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__less__imp__less])])). 6.97/7.23 cnf(c_0_7782, 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_5283, c_0_4411])). 6.97/7.23 fof(c_0_7783, plain, ![X7174, X7175, X7176]:(~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X7176),X7175)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X7176),X7174)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X7176))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7175),X7174)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__dvd__imp__le])])])). 6.97/7.23 fof(c_0_7784, plain, ![X15405, X15406, X15407, X15408, X15409, X15410]:(~class_Orderings_Olinorder(X15410)|(hBOOL(hAPP(X15409,X15408))|hAPP(c_List_Ofilter(X15407,X15409),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X15407,X15410,X15406),X15408),X15405))=hAPP(c_List_Ofilter(X15407,X15409),X15405))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_filter__insort__triv])])])). 6.97/7.23 fof(c_0_7785, plain, ![X2101, X2102, X2103]:(~c_Fun_Oinj__on(X2103,X2102,X2101,c_Orderings_Otop__class_Otop(tc_fun(X2103,tc_HOL_Obool)))|hAPP(c_Fun_Ocomp(X2102,X2103,X2103,c_Hilbert__Choice_Oinv__into(X2103,X2102,c_Orderings_Otop__class_Otop(tc_fun(X2103,tc_HOL_Obool)),X2101)),X2101)=c_Fun_Oid(X2103)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inv__o__cancel])])])). 6.97/7.23 cnf(c_0_7786, plain, (c_List_Oremove1(X1,X3,X2)=hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(c_fequal,X3))),X2)|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(rw,[status(thm)],[c_0_5284, c_0_4573])). 6.97/7.23 fof(c_0_7787, plain, ![X6798, X6799, X6800, X6801, X6802]:(hBOOL(hAPP(X6802,X6801))|c_List_OtakeWhile(X6800,X6802,X6799)=c_List_OtakeWhile(X6800,X6802,hAPP(hAPP(c_List_Oappend(X6800),X6799),hAPP(hAPP(c_List_Olist_OCons(X6800),X6801),X6798)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_takeWhile__tail])])])). 6.97/7.23 fof(c_0_7788, plain, ![X4121, X4122, X4123, X4124, X4125, X4126]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X4126,X4125),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4124),X4123)))|(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X4126,X4125),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4122),X4121)))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X4125|X4123=X4121))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_unique__remainder])])])). 6.97/7.23 fof(c_0_7789, plain, ![X16511, X16512, X16513, X16514, X16515, X16516]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X16516,X16515),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X16514),X16513)))|(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X16516,X16515),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X16512),X16511)))|(X16515=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X16514=X16512))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient])])). 6.97/7.23 fof(c_0_7790, plain, ![X919, X920]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X920,X919)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X920,X919)),X919)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X920,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X919)))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Divides_Odiv__class_Omod(tc_Int_Oint,X920,X919)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X920,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X919)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zminus2__eq__if])])). 6.97/7.23 fof(c_0_7791, plain, ![X5715, X5716, X5717]:(~class_Rings_Olinordered__idom(X5717)|hAPP(c_Groups_Oabs__class_Oabs(X5717),hAPP(hAPP(c_Power_Opower__class_Opower(X5717),X5716),X5715))=hAPP(c_Groups_Oabs__class_Oabs(X5717),hAPP(hAPP(c_Power_Opower__class_Opower(X5717),hAPP(c_Groups_Ouminus__class_Ouminus(X5717),X5716)),X5715))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__power__minus])])])). 6.97/7.23 cnf(c_0_7792, 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_5285])). 6.97/7.23 cnf(c_0_7793, 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_5286])). 6.97/7.23 fof(c_0_7794, plain, ![X5055, X5056, X5057]:(~class_Groups_Omonoid__add(X5057)|hAPP(c_List_Omonoid__add__class_Olistsum(X5057),hAPP(hAPP(c_List_Oappend(X5057),X5056),X5055))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5057),hAPP(c_List_Omonoid__add__class_Olistsum(X5057),X5056)),hAPP(c_List_Omonoid__add__class_Olistsum(X5057),X5055))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__append])])])). 6.97/7.23 fof(c_0_7795, plain, ![X9271, X9272, X9273]:(~class_Rings_Olinordered__idom(X9273)|hAPP(c_Groups_Oabs__class_Oabs(X9273),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9273),X9272),X9271))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9273),hAPP(c_Groups_Oabs__class_Oabs(X9273),X9272)),hAPP(c_Groups_Oabs__class_Oabs(X9273),X9271))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__mult])])])). 6.97/7.23 cnf(c_0_7796, 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_5143])). 6.97/7.23 fof(c_0_7797, plain, ![X12450, X12451]:((c_Divides_Odiv__class_Omod(tc_Int_Oint,X12451,X12450)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12451),X12450)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(c_Divides_Odiv__class_Omod(tc_Int_Oint,X12451,X12450)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X12450),c_Divides_Odiv__class_Omod(tc_Int_Oint,X12451,X12450))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12451),X12450))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmod__zminus1__eq__if])])])). 6.97/7.23 fof(c_0_7798, plain, ![X3740, X3741, X3742]:(~class_Fields_Olinordered__field__inverse__zero(X3742)|hAPP(c_Groups_Oabs__class_Oabs(X3742),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3742),X3741),X3740))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3742),hAPP(c_Groups_Oabs__class_Oabs(X3742),X3741)),hAPP(c_Groups_Oabs__class_Oabs(X3742),X3740))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__divide])])). 6.97/7.23 fof(c_0_7799, plain, ![X10620, X10621, X10622]:(~class_Rings_Oring__1(X10622)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10622),hAPP(c_Int_Oring__1__class_Oof__int(X10622),X10621)),hAPP(c_Int_Oring__1__class_Oof__int(X10622),X10620))=hAPP(c_Int_Oring__1__class_Oof__int(X10622),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X10621),X10620))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__diff])])). 6.97/7.23 fof(c_0_7800, plain, ![X6530, X6531, X6532]:(~class_Rings_Oring__1(X6532)|hAPP(c_Int_Oring__1__class_Oof__int(X6532),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6531),X6530))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6532),hAPP(c_Int_Oring__1__class_Oof__int(X6532),X6531)),hAPP(c_Int_Oring__1__class_Oof__int(X6532),X6530))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__add])])])). 6.97/7.23 fof(c_0_7801, plain, ![X8201, X8202, X8203]:(~class_Rings_Oring__1(X8203)|hAPP(c_Int_Oring__1__class_Oof__int(X8203),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8202),X8201))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8203),hAPP(c_Int_Oring__1__class_Oof__int(X8203),X8202)),hAPP(c_Int_Oring__1__class_Oof__int(X8203),X8201))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__mult])])). 6.97/7.23 cnf(c_0_7802, 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_5144])). 6.97/7.23 cnf(c_0_7803, 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_5145])). 6.97/7.23 cnf(c_0_7804, 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_5146])). 6.97/7.23 fof(c_0_7805, plain, ![X13557, X13558, X13559, X13560, X13561]:(~class_Rings_Ocomm__semiring__1(X13560)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13559),X13558))|(hAPP(X13557,X13561)!=c_Groups_Ozero__class_Ozero(X13560)|~hBOOL(hAPP(hAPP(c_member(X13559),X13561),X13558))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X13559,X13560),X13557),X13558)=c_Groups_Ozero__class_Ozero(X13560)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__zero])])])])). 6.97/7.23 fof(c_0_7806, plain, ![X9221, X9222, X9223, X9224]:(~class_Rings_Olinordered__semiring(X9224)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9224),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9224),X9223),X9222)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9224),X9221),X9222)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9224),c_Groups_Ozero__class_Ozero(X9224)),X9222))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9224),X9223),X9221))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__right__less__imp__less])])])). 6.97/7.23 fof(c_0_7807, plain, ![X6575, X6576, X6577, X6578]:(~class_Rings_Olinordered__semiring__strict(X6578)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6578),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6578),X6577),X6576)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6578),X6575),X6576)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6578),c_Groups_Ozero__class_Ozero(X6578)),X6576))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6578),X6577),X6575))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__less__imp__less__right])])])). 6.97/7.23 fof(c_0_7808, plain, ![X5523, X5524, X5525, X5526]:((~hBOOL(hAPP(hAPP(c_member(X5524),X5526),hAPP(c_List_Oset(X5524),X5523)))|hBOOL(hAPP(hAPP(c_member(X5524),X5526),hAPP(c_List_Oset(X5524),c_List_Oremove1(X5524,X5525,X5523))))|X5526=X5525)&(~hBOOL(hAPP(hAPP(c_member(X5524),X5526),hAPP(c_List_Oset(X5524),c_List_Oremove1(X5524,X5525,X5523))))|hBOOL(hAPP(hAPP(c_member(X5524),X5526),hAPP(c_List_Oset(X5524),X5523)))|X5526=X5525)), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_in__set__remove1])])])])). 6.97/7.23 cnf(c_0_7809, 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_5287])). 6.97/7.23 fof(c_0_7810, plain, ![X1903, X1904, X1905]:((c_Orderings_Obot__class_Obot(tc_fun(X1905,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1905,tc_HOL_Obool)),X1904),X1903)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1905,tc_HOL_Obool)),X1904),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1905,tc_HOL_Obool)),X1903))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1905,tc_HOL_Obool)),X1904),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1905,tc_HOL_Obool)),X1903)))|c_Orderings_Obot__class_Obot(tc_fun(X1905,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1905,tc_HOL_Obool)),X1904),X1903))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_disjoint__eq__subset__Compl])])). 6.97/7.23 fof(c_0_7811, plain, ![X16936, X16937, X16938, X16939]:(~class_Rings_Olinordered__semiring(X16939)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16939),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16939),X16938),X16937)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16939),X16938),X16936)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16939),c_Groups_Ozero__class_Ozero(X16939)),X16938))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16939),X16937),X16936))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__left__less__imp__less])])])). 6.97/7.23 fof(c_0_7812, plain, ![X349, X350, X351, X352]:(~class_Rings_Olinordered__semiring__strict(X352)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X352),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X352),X351),X350)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X352),X351),X349)))|(~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(X352),X350),X349))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__less__imp__less__left])])])). 6.97/7.23 fof(c_0_7813, plain, ![X16834, X16835, X16836, X16837]:(~class_Rings_Olinordered__semiring__strict(X16837)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16837),X16836),X16835)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16837),X16834),X16835)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16837),c_Groups_Ozero__class_Ozero(X16837)),X16835))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16837),X16836),X16834))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__imp__le])])). 6.97/7.23 fof(c_0_7814, plain, ![X1827, X1828, X1829]:(~hBOOL(hAPP(hAPP(c_member(X1829),X1828),hAPP(c_List_Oset(X1829),X1827)))|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(X1829)),X1827)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__pos__if__in__set])])). 6.97/7.23 fof(c_0_7815, plain, ![X9653, X9654, X9655, X9656]:(~class_Rings_Olinordered__semiring__strict(X9656)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9656),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9656),X9655),X9654)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9656),X9655),X9653)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9656),c_Groups_Ozero__class_Ozero(X9656)),X9655))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9656),X9654),X9653))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__left__le__imp__le])])])). 6.97/7.23 fof(c_0_7816, plain, ![X10746, X10747, X10748, X10749]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10749),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10749),X10748),X10747)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10749),X10748),X10746)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10749),X10746),X10747))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10749),X10748),c_Groups_Ozero__class_Ozero(X10749)))|~class_Rings_Olinordered__ring__strict(X10749))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10749),X10746),X10747))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10749),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10749),X10748),X10747)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10749),X10748),X10746)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10749),X10748),c_Groups_Ozero__class_Ozero(X10749)))|~class_Rings_Olinordered__ring__strict(X10749))), 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])])])])). 6.97/7.23 fof(c_0_7817, plain, ![X6547, X6548, X6549]:((~c_Fun_Oinj__on(X6549,X6548,X6547,c_Orderings_Otop__class_Otop(tc_fun(X6549,tc_HOL_Obool)))|c_Fun_Oinj__on(tc_List_Olist(X6549),tc_List_Olist(X6548),hAPP(c_List_Omap(X6549,X6548),X6547),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X6549),tc_HOL_Obool))))&(~c_Fun_Oinj__on(tc_List_Olist(X6549),tc_List_Olist(X6548),hAPP(c_List_Omap(X6549,X6548),X6547),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X6549),tc_HOL_Obool)))|c_Fun_Oinj__on(X6549,X6548,X6547,c_Orderings_Otop__class_Otop(tc_fun(X6549,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__map])])). 6.97/7.23 fof(c_0_7818, plain, ![X9989, X9990, X9991, X9992]:((X9992!=c_Orderings_Obot__class_Obot(tc_fun(X9991,tc_HOL_Obool))|hAPP(c_Set_Oimage(X9991,X9990,hAPP(c_COMBK(X9990,X9991),X9989)),X9992)=c_Orderings_Obot__class_Obot(tc_fun(X9990,tc_HOL_Obool)))&(c_Orderings_Obot__class_Obot(tc_fun(X9991,tc_HOL_Obool))=X9992|hAPP(c_Set_Oimage(X9991,X9990,hAPP(c_COMBK(X9990,X9991),X9989)),X9992)=hAPP(hAPP(c_Set_Oinsert(X9990),X9989),c_Orderings_Obot__class_Obot(tc_fun(X9990,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__constant__conv])])])). 6.97/7.23 cnf(c_0_7819, 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_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)),esk485_3(X2,X3,X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_5288])). 6.97/7.23 fof(c_0_7820, plain, ![X8423, X8424]:(~class_Rings_Osemiring__1(X8424)|c_Nat_Osemiring__1__class_Oof__nat__aux(X8424,hAPP(hAPP(c_COMBC(X8424,X8424,X8424),c_Groups_Oplus__class_Oplus(X8424)),c_Groups_Oone__class_Oone(X8424)),X8423,c_Groups_Ozero__class_Ozero(X8424))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8424),X8423)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_semiring__1__class_Oof__nat__code])])])). 6.97/7.23 fof(c_0_7821, plain, ![X14783, X14784, X14785]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14785),X14784))|hAPP(hAPP(c_Finite__Set_Ofold(X14785,tc_fun(X14785,tc_HOL_Obool),c_Set_Oinsert(X14785)),X14783),X14784)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14785,tc_HOL_Obool)),X14784),X14783)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_union__fold__insert])])). 6.97/7.23 fof(c_0_7822, plain, ![X13134, X13135, X13136, X13137]:(~class_Orderings_Oorder(X13137)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13137,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X13137,X13136,X13135)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X13137,X13135),X13134))=c_Orderings_Obot__class_Obot(tc_fun(X13137,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I9_J])])). 6.97/7.23 fof(c_0_7823, plain, ![X6099, X6100, X6101, X6102]:(~class_Orderings_Oorder(X6102)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6102,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X6102,X6101),X6100)),c_SetInterval_Oord__class_OatLeastAtMost(X6102,X6100,X6099))=c_Orderings_Obot__class_Obot(tc_fun(X6102,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I15_J])])). 6.97/7.23 fof(c_0_7824, plain, ![X7343, X7344, X7345]:(~class_Orderings_Oorder(X7345)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7345,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7345,X7344),X7343)),hAPP(c_SetInterval_Oord__class_OatLeast(X7345),X7343))=c_Orderings_Obot__class_Obot(tc_fun(X7345,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I8_J])])). 6.97/7.23 fof(c_0_7825, plain, ![X1437, X1438, X1439, X1440, X1442, X1443, X1444, X1445, X1446]:(((hBOOL(hAPP(hAPP(c_member(X1439),esk41_4(X1437,X1438,X1439,X1440)),X1438))|c_Orderings_Otop__class_Otop(tc_fun(X1440,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1439,tc_fun(X1440,tc_HOL_Obool)),X1438),X1437))&(c_Orderings_Otop__class_Otop(tc_fun(X1440,tc_HOL_Obool))!=hAPP(X1437,esk41_4(X1437,X1438,X1439,X1440))|c_Orderings_Otop__class_Otop(tc_fun(X1440,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1439,tc_fun(X1440,tc_HOL_Obool)),X1438),X1437)))&(c_Orderings_Otop__class_Otop(tc_fun(X1445,tc_HOL_Obool))!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1444,tc_fun(X1445,tc_HOL_Obool)),X1443),X1442)|(~hBOOL(hAPP(hAPP(c_member(X1444),X1446),X1443))|c_Orderings_Otop__class_Otop(tc_fun(X1445,tc_HOL_Obool))=hAPP(X1442,X1446)))), 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])])])])])])). 6.97/7.23 fof(c_0_7826, plain, ![X4154, X4155, X4156, X4157, X4159, X4160, X4161, X4162, X4163]:(((hBOOL(hAPP(hAPP(c_member(X4156),esk145_4(X4154,X4155,X4156,X4157)),X4155))|c_Orderings_Obot__class_Obot(tc_fun(X4157,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4156,tc_fun(X4157,tc_HOL_Obool)),X4155),X4154))&(hAPP(X4154,esk145_4(X4154,X4155,X4156,X4157))!=c_Orderings_Obot__class_Obot(tc_fun(X4157,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X4157,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4156,tc_fun(X4157,tc_HOL_Obool)),X4155),X4154)))&(c_Orderings_Obot__class_Obot(tc_fun(X4162,tc_HOL_Obool))!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4161,tc_fun(X4162,tc_HOL_Obool)),X4160),X4159)|(~hBOOL(hAPP(hAPP(c_member(X4161),X4163),X4160))|hAPP(X4159,X4163)=c_Orderings_Obot__class_Obot(tc_fun(X4162,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])])])])])])])). 6.97/7.23 fof(c_0_7827, plain, ![X1796, X1797, X1798]:(~class_Orderings_Olinorder(X1798)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1798),X1797))|c_Big__Operators_Olattice_OSup__fin(X1798,c_Orderings_Oord__class_Omax(X1798),hAPP(hAPP(c_Set_Oinsert(X1798),X1796),X1797))=hAPP(hAPP(c_Finite__Set_Ofold(X1798,X1798,c_Orderings_Oord__class_Omax(X1798)),X1796),X1797))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Oeq__fold__idem_H])])])). 6.97/7.23 fof(c_0_7828, plain, ![X8249, X8250, X8251]:(~class_Orderings_Oorder(X8251)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8251,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X8251),X8250)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X8251,X8250),X8249))=c_Orderings_Obot__class_Obot(tc_fun(X8251,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I2_J])])). 6.97/7.23 fof(c_0_7829, plain, ![X16107, X16108, X16109, X16111, X16112, X16113, X16114]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk544_3(X16107,X16108,X16109)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16109)),X16107)))|~hBOOL(hAPP(hAPP(c_member(X16109),X16108),hAPP(c_List_Oset(X16109),X16107))))&(hAPP(hAPP(c_List_Onth(X16109),X16107),esk544_3(X16107,X16108,X16109))=X16108|~hBOOL(hAPP(hAPP(c_member(X16109),X16108),hAPP(c_List_Oset(X16109),X16107)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16114),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16113)),X16111)))|hAPP(hAPP(c_List_Onth(X16113),X16111),X16114)!=X16112|hBOOL(hAPP(hAPP(c_member(X16113),X16112),hAPP(c_List_Oset(X16113),X16111))))), 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])])])])])])). 6.97/7.23 cnf(c_0_7830, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))|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_5289])). 6.97/7.23 fof(c_0_7831, plain, ![X10305, X10306, X10307, X10308]:((hBOOL(hAPP(hAPP(c_member(X10308),esk341_4(X10305,X10306,X10307,X10308)),X10306))|hAPP(c_Nat_OSuc,X10305)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10308,tc_Nat_Onat),X10307),X10306))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X10307,esk341_4(X10305,X10306,X10307,X10308))))|hAPP(c_Nat_OSuc,X10305)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10308,tc_Nat_Onat),X10307),X10306))), 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])])])])])). 6.97/7.23 fof(c_0_7832, plain, ![X12156, X12157, X12158, X12159, X12161, X12162, X12163, X12164, X12165]:(((hBOOL(hAPP(hAPP(c_member(X12159),esk406_4(X12156,X12157,X12158,X12159)),X12157))|c_Orderings_Otop__class_Otop(tc_fun(X12158,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12159,tc_fun(X12158,tc_HOL_Obool)),X12157),X12156))&(c_Orderings_Otop__class_Otop(tc_fun(X12158,tc_HOL_Obool))!=hAPP(X12156,esk406_4(X12156,X12157,X12158,X12159))|c_Orderings_Otop__class_Otop(tc_fun(X12158,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12159,tc_fun(X12158,tc_HOL_Obool)),X12157),X12156)))&(c_Orderings_Otop__class_Otop(tc_fun(X12163,tc_HOL_Obool))!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12164,tc_fun(X12163,tc_HOL_Obool)),X12162),X12161)|(~hBOOL(hAPP(hAPP(c_member(X12164),X12165),X12162))|c_Orderings_Otop__class_Otop(tc_fun(X12163,tc_HOL_Obool))=hAPP(X12161,X12165)))), 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_INTER__UNIV__conv_I2_J])])])])])])])). 6.97/7.23 fof(c_0_7833, plain, ![X6745, X6746, X6747]:(~class_Orderings_Olinorder(X6747)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6747),X6746))|hAPP(hAPP(c_Finite__Set_Ofold(X6747,X6747,c_Orderings_Oord__class_Omin(X6747)),X6745),X6746)=c_Big__Operators_Olattice_OInf__fin(X6747,c_Orderings_Oord__class_Omin(X6747),hAPP(hAPP(c_Set_Oinsert(X6747),X6745),X6746)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Oeq__fold__idem_H])])])). 6.97/7.23 fof(c_0_7834, plain, ![X17574, X17575, X17576, X17577]:((hAPP(hAPP(c_Set_Oinsert(X17577),X17576),X17575)!=hAPP(hAPP(c_Set_Oinsert(X17577),X17576),X17574)|X17574=X17575|hBOOL(hAPP(hAPP(c_member(X17577),X17576),X17574))|hBOOL(hAPP(hAPP(c_member(X17577),X17576),X17575)))&(X17574!=X17575|hAPP(hAPP(c_Set_Oinsert(X17577),X17576),X17575)=hAPP(hAPP(c_Set_Oinsert(X17577),X17576),X17574)|hBOOL(hAPP(hAPP(c_member(X17577),X17576),X17574))|hBOOL(hAPP(hAPP(c_member(X17577),X17576),X17575)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insert__ident])])])])). 6.97/7.23 fof(c_0_7835, plain, ![X15215, X15216, X15217, X15218, X15219, X15220]:(~c_List_Olist__all2(X15220,X15219,X15218,X15217,X15216)|c_List_Olist__all2(X15220,X15219,X15218,hAPP(hAPP(c_List_Odrop(X15220),X15215),X15217),hAPP(hAPP(c_List_Odrop(X15219),X15215),X15216))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__all2__dropI])])])). 6.97/7.23 fof(c_0_7836, plain, ![X12602, X12603, X12604]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12603),X12602))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12604),hAPP(c_Int_Onumber__class_Onumber__of(X12604),X12603)),hAPP(c_Int_Onumber__class_Onumber__of(X12604),X12602)))|(~class_Rings_Olinordered__idom(X12604)|~class_Int_Onumber__ring(X12604)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12604),hAPP(c_Int_Onumber__class_Onumber__of(X12604),X12603)),hAPP(c_Int_Onumber__class_Onumber__of(X12604),X12602)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12603),X12602))|(~class_Rings_Olinordered__idom(X12604)|~class_Int_Onumber__ring(X12604)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__number__of])])])])). 6.97/7.23 fof(c_0_7837, plain, ![X1314, X1315, X1316]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1316),hAPP(c_Int_Onumber__class_Onumber__of(X1316),X1315)),hAPP(c_Int_Onumber__class_Onumber__of(X1316),X1314)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1315),X1314))|(~class_Rings_Olinordered__idom(X1316)|~class_Int_Onumber__ring(X1316)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1315),X1314))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1316),hAPP(c_Int_Onumber__class_Onumber__of(X1316),X1315)),hAPP(c_Int_Onumber__class_Onumber__of(X1316),X1314)))|(~class_Rings_Olinordered__idom(X1316)|~class_Int_Onumber__ring(X1316)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__number__of])])])])). 6.97/7.23 cnf(c_0_7838, 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_5290])). 6.97/7.23 fof(c_0_7839, plain, ![X3582, X3583, X3584]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3584),X3583))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3583),X3582))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3584)),X3582)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__trans__Suc])])])). 6.97/7.23 fof(c_0_7840, plain, ![X5576, X5577, X5578, X5579, X5580, X5581, X5582, X5583, X5584]:((c_Orderings_Obot__class_Obot(tc_fun(X5578,tc_HOL_Obool))!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5579,tc_fun(X5578,tc_HOL_Obool)),X5577),X5576)|(~hBOOL(hAPP(hAPP(c_member(X5579),X5580),X5577))|c_Orderings_Obot__class_Obot(tc_fun(X5578,tc_HOL_Obool))=hAPP(X5576,X5580)))&((hBOOL(hAPP(hAPP(c_member(X5584),esk184_4(X5581,X5582,X5583,X5584)),X5582))|c_Orderings_Obot__class_Obot(tc_fun(X5583,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5584,tc_fun(X5583,tc_HOL_Obool)),X5582),X5581))&(c_Orderings_Obot__class_Obot(tc_fun(X5583,tc_HOL_Obool))!=hAPP(X5581,esk184_4(X5581,X5582,X5583,X5584))|c_Orderings_Obot__class_Obot(tc_fun(X5583,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5584,tc_fun(X5583,tc_HOL_Obool)),X5582),X5581)))), 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__empty__conv_I2_J])])])])])])). 6.97/7.23 fof(c_0_7841, plain, ![X8614, X8615, X8616, X8617, X8618, X8619]:(~c_List_Olist__all2(X8619,X8618,X8617,X8616,X8615)|c_List_Olist__all2(X8619,X8618,X8617,hAPP(hAPP(c_List_Otake(X8619),X8614),X8616),hAPP(hAPP(c_List_Otake(X8618),X8614),X8615))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__takeI])])). 6.97/7.23 cnf(c_0_7842, 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_5291])). 6.97/7.23 fof(c_0_7843, plain, ![X10178, X10179, X10180, X10181]:(~hBOOL(hAPP(c_List_Olistsp(X10181,X10180),X10179))|(~hBOOL(hAPP(c_List_Olistsp(X10181,X10178),X10179))|hBOOL(hAPP(c_List_Olistsp(X10181,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10181,tc_HOL_Obool)),X10180),X10178)),X10179)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__infI])])). 6.97/7.23 cnf(c_0_7844, 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_5292])). 6.97/7.23 fof(c_0_7845, plain, ![X7532, X7533, X7534]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk247_3(X7532,X7533,X7534)),X7534))|(~hBOOL(hAPP(X7533,X7532))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7532),X7534))|hBOOL(hAPP(X7533,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))&((hBOOL(hAPP(X7533,esk247_3(X7532,X7533,X7534)))|(~hBOOL(hAPP(X7533,X7532))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7532),X7534))|hBOOL(hAPP(X7533,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))&(~hBOOL(hAPP(X7533,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,esk247_3(X7532,X7533,X7534)),X7534)))|(~hBOOL(hAPP(X7533,X7532))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7532),X7534))|hBOOL(hAPP(X7533,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])])])])])). 6.97/7.23 cnf(c_0_7846, plain, (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)))=c_Groups_Ozero__class_Ozero(X3)|~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_5024])). 6.97/7.23 fof(c_0_7847, plain, ![X3465, X3466, X3467, X3468]:((c_Orderings_Obot__class_Obot(tc_fun(X3467,tc_HOL_Obool))!=X3468|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3467,tc_fun(X3466,tc_HOL_Obool)),X3468),hAPP(c_COMBK(tc_fun(X3466,tc_HOL_Obool),X3467),X3465))=c_Orderings_Otop__class_Otop(tc_fun(X3466,tc_HOL_Obool)))&(X3468=c_Orderings_Obot__class_Obot(tc_fun(X3467,tc_HOL_Obool))|X3465=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3467,tc_fun(X3466,tc_HOL_Obool)),X3468),hAPP(c_COMBK(tc_fun(X3466,tc_HOL_Obool),X3467),X3465)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INT__constant])])])). 6.97/7.23 fof(c_0_7848, plain, ![X5197, X5198, X5199, X5200, X5201]:(~class_Orderings_Olinorder(X5201)|c_List_Olinorder__class_Osort__key(X5200,X5201,X5199,hAPP(hAPP(c_List_Olist_OCons(X5200),X5198),X5197))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5200,X5201,X5199),X5198),c_List_Olinorder__class_Osort__key(X5200,X5201,X5199,X5197))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sort__key__simps_I2_J])])). 6.97/7.23 cnf(c_0_7849, 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_5214])). 6.97/7.23 fof(c_0_7850, plain, ![X3168, X3169, X3170]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3170),hAPP(c_Groups_Ouminus__class_Ouminus(X3170),X3169)),X3168))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3170),X3169),X3168))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3170),hAPP(c_Groups_Oabs__class_Oabs(X3170),X3169)),X3168))|~class_Rings_Olinordered__idom(X3170))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3170),hAPP(c_Groups_Ouminus__class_Ouminus(X3170),X3169)),X3168))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3170),hAPP(c_Groups_Oabs__class_Oabs(X3170),X3169)),X3168))|~class_Rings_Olinordered__idom(X3170))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3170),X3169),X3168))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3170),hAPP(c_Groups_Oabs__class_Oabs(X3170),X3169)),X3168))|~class_Rings_Olinordered__idom(X3170)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__less__iff])])])])). 6.97/7.23 fof(c_0_7851, plain, ![X4819, X4820, X4821]:(~class_Groups_Oordered__ab__group__add__abs(X4821)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4821),X4820),X4819))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4821),hAPP(c_Groups_Ouminus__class_Ouminus(X4821),X4820)),X4819))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4821),hAPP(c_Groups_Oabs__class_Oabs(X4821),X4820)),X4819))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__leI])])])). 6.97/7.23 fof(c_0_7852, plain, ![X14050, X14051]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14051),X14050))|c_Fun_Obij__betw(tc_Nat_Onat,X14051,esk477_2(X14050,X14051),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X14051),X14050)),X14050)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ex__bij__betw__nat__finite])])])])). 6.97/7.23 fof(c_0_7853, plain, ![X6857, X6858]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6858),X6857))|c_Fun_Obij__betw(X6858,tc_Nat_Onat,esk223_2(X6857,X6858),X6857,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X6858),X6857)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ex__bij__betw__finite__nat])])])). 6.97/7.23 cnf(c_0_7854, 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_5293])). 6.97/7.23 fof(c_0_7855, plain, ![X11826, X11827]:(~class_Int_Onumber__ring(X11827)|~class_Fields_Ofield__inverse__zero(X11827)|hAPP(c_Groups_Ouminus__class_Ouminus(X11827),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11827),c_Groups_Oone__class_Oone(X11827)),X11826))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11827),hAPP(c_Int_Onumber__class_Onumber__of(X11827),c_Int_OMin)),X11826)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus1__divide])])). 6.97/7.23 fof(c_0_7856, plain, ![X16487, X16488, X16489]:((~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X16489))|c_List_Osublist(X16488,hAPP(hAPP(c_List_Olist_OCons(X16488),X16487),c_List_Olist_ONil(X16488)),X16489)=hAPP(hAPP(c_List_Olist_OCons(X16488),X16487),c_List_Olist_ONil(X16488)))&(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X16489))|c_List_Olist_ONil(X16488)=c_List_Osublist(X16488,hAPP(hAPP(c_List_Olist_OCons(X16488),X16487),c_List_Olist_ONil(X16488)),X16489))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sublist__singleton])])])). 6.97/7.23 fof(c_0_7857, plain, ![X7771, X7772]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7772))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7771))|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,X7772,X7771))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I2_J])])])). 6.97/7.23 fof(c_0_7858, plain, ![X16067, X16068]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16068),X16067))|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),X16068),X16067)),c_Wellfounded_Oless__than)))&(~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),X16068),X16067)),c_Wellfounded_Oless__than))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16068),X16067)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__than__iff])])). 6.97/7.23 fof(c_0_7859, plain, ![X8057, X8058, X8059]:(~class_Orderings_Olinorder(X8059)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8059),X8058))|(~hBOOL(hAPP(hAPP(c_member(X8059),X8057),X8058))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8059),hAPP(c_Finite__Set_Ofold1(X8059,c_Orderings_Oord__class_Omin(X8059)),X8058)),X8057))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ofold1__belowI])])])). 6.97/7.23 fof(c_0_7860, plain, ![X14371, X14372, X14373]:(~class_Lattices_Osemilattice__inf(X14373)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14373),X14372))|(~hBOOL(hAPP(hAPP(c_member(X14373),X14371),X14372))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14373),hAPP(c_Finite__Set_Ofold1(X14373,c_Lattices_Osemilattice__inf__class_Oinf(X14373)),X14372)),X14371))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__belowI])])])). 6.97/7.23 fof(c_0_7861, plain, ![X5607, X5608, X5609, X5610]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5610,X5609)),hAPP(hAPP(c_Product__Type_OSigma(X5610,X5609),X5608),hAPP(c_COMBK(tc_fun(X5609,tc_HOL_Obool),X5610),X5607))))|(c_Orderings_Obot__class_Obot(tc_fun(X5610,tc_HOL_Obool))=X5608|hBOOL(hAPP(c_Finite__Set_Ofinite(X5609),X5607)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__cartesian__productD2])])])). 6.97/7.23 fof(c_0_7862, plain, ![X8237, X8238, X8239, X8240]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X8240,X8239)),hAPP(hAPP(c_Product__Type_OSigma(X8240,X8239),X8238),hAPP(c_COMBK(tc_fun(X8239,tc_HOL_Obool),X8240),X8237))))|(c_Orderings_Obot__class_Obot(tc_fun(X8239,tc_HOL_Obool))=X8237|hBOOL(hAPP(c_Finite__Set_Ofinite(X8240),X8238)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__cartesian__productD1])])])). 6.97/7.23 fof(c_0_7863, plain, ![X14839, X14840]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14840))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14839))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14840),X14839)=hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X14840,X14839)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__pos])])). 6.97/7.23 fof(c_0_7864, plain, ![X6017, X6018]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6018),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)),X6017))|hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X6018,X6017))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6018),X6017))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__neg__pos])])])). 6.97/7.23 fof(c_0_7865, plain, ![X8161, X8162, X8163, X8164]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8164),X8163))|hAPP(hAPP(c_List_Onth(X8162),X8161),X8164)=hAPP(hAPP(c_List_Onth(X8162),hAPP(hAPP(c_List_Otake(X8162),X8163),X8161)),X8164)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__take])])). 6.97/7.23 fof(c_0_7866, plain, ![X2903, X2904, X2905]:((hBOOL(hAPP(hAPP(c_member(X2905),esk94_3(X2903,X2904,X2905)),X2903))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2905,X2905)),X2904),c_Relation_OId__on(X2905,X2903))))&(hAPP(hAPP(c_Product__Type_OPair(X2905,X2905),esk94_3(X2903,X2904,X2905)),esk94_3(X2903,X2904,X2905))=X2904|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2905,X2905)),X2904),c_Relation_OId__on(X2905,X2903))))), 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])])])])])). 6.97/7.23 fof(c_0_7867, plain, ![X3456, X3457, X3458, X3459]:(~class_Rings_Olinordered__semidom(X3459)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3459),hAPP(hAPP(c_Power_Opower__class_Opower(X3459),X3458),X3457)),hAPP(hAPP(c_Power_Opower__class_Opower(X3459),X3456),X3457)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3459),c_Groups_Ozero__class_Ozero(X3459)),X3456))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3459),X3458),X3456))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__less__imp__less__base])])])). 6.97/7.23 cnf(c_0_7868, 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_5294])). 6.97/7.23 fof(c_0_7869, plain, ![X15742, X15743, X15744]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15744,tc_HOL_Obool)),X15743),X15742))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X15744),tc_HOL_Obool)),c_List_Olistsp(X15744,X15743)),c_List_Olistsp(X15744,X15742)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__mono])])). 6.97/7.23 fof(c_0_7870, plain, ![X13528, X13529, X13530]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13530,tc_HOL_Obool)),X13529),X13528))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X13530),tc_HOL_Obool)),c_List_Olists(X13530,X13529)),c_List_Olists(X13530,X13528)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lists__mono])])])). 6.97/7.23 fof(c_0_7871, plain, ![X2065, X2066, X2067, X2068]:(~hBOOL(hAPP(hAPP(c_member(X2068),X2067),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2068,tc_HOL_Obool)),X2066),X2065)))|(hBOOL(hAPP(hAPP(c_member(X2068),X2067),X2066))|hBOOL(hAPP(hAPP(c_member(X2068),X2067),X2065)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UnE])])])). 6.97/7.23 fof(c_0_7872, plain, ![X6966, X6967, X6968]:(~hBOOL(hAPP(hAPP(c_member(tc_fun(X6967,tc_HOL_Obool)),X6968),X6966))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6967),X6968))|hBOOL(hAPP(c_Finite__Set_Ofinite(X6967),c_Complete__Lattice_OInf__class_OInf(tc_fun(X6967,tc_HOL_Obool),X6966)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__Inter])])])])). 6.97/7.23 cnf(c_0_7873, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|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_5295])). 6.97/7.23 fof(c_0_7874, plain, ![X1358, X1359, X1360, X1361]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1361,tc_HOL_Obool)),X1360),X1359))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1361,tc_HOL_Obool)),X1360),hAPP(hAPP(c_Set_Oinsert(X1361),X1358),X1359)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__insertI2])])). 6.97/7.23 cnf(c_0_7875, 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_5208])). 6.97/7.23 fof(c_0_7876, plain, ![X11373, X11374, X11375, X11376, X11377, X11378]:(~c_Finite__Set_Ofolding(X11378,X11377,X11376,X11375)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11378),X11374))|hAPP(hAPP(X11375,X11374),X11373)=hAPP(hAPP(c_Finite__Set_Ofold(X11378,X11377,X11376),X11373),X11374))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Oeq__fold])])). 6.97/7.23 cnf(c_0_7877, plain, (c_Divides_OnegDivAlg(X1,X2)=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))|~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_4509])). 6.97/7.23 fof(c_0_7878, plain, ![X8039, X8040, X8041, X8042, X8043, X8044, X8045, X8046, X8047]:(hAPP(c_Fun_Ocomp(X8042,X8046,X8045,X8041),X8040)!=hAPP(c_Fun_Ocomp(X8047,X8046,X8045,X8044),X8043)|hAPP(X8041,hAPP(X8040,X8039))=hAPP(X8044,hAPP(X8043,X8039))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_o__eq__dest])])])). 6.97/7.23 fof(c_0_7879, plain, ![X2962, X2963, X2964, X2965]:(~class_Divides_Osemiring__div(X2965)|c_Divides_Odiv__class_Omod(X2965,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2965),X2964),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2965),X2963),X2962)),X2962)=c_Divides_Odiv__class_Omod(X2965,X2964,X2962)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self1])])). 6.97/7.23 fof(c_0_7880, plain, ![X15297, X15298, X15299, X15300]:(~class_Divides_Osemiring__div(X15300)|c_Divides_Odiv__class_Omod(X15300,X15299,X15298)=c_Divides_Odiv__class_Omod(X15300,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15300),X15299),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15300),X15298),X15297)),X15298)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__mult__self2])])])). 6.97/7.23 cnf(c_0_7881, 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,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_5163])). 6.97/7.23 fof(c_0_7882, plain, ![X17414, X17415, X17416, X17417, X17418]:(~c_Fun_Oinj__on(X17418,X17417,X17416,X17415)|(~hBOOL(hAPP(hAPP(c_member(X17417),X17414),hAPP(c_Set_Oimage(X17418,X17417,X17416),X17415)))|hAPP(X17416,hAPP(c_Fun_Othe__inv__into(X17418,X17417,X17415,X17416),X17414))=X17414)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_f__the__inv__into__f])])])). 6.97/7.23 cnf(c_0_7883, plain, (X2=hAPP(c_List_Orotate(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)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_5296])). 6.97/7.23 fof(c_0_7884, plain, ![X13240, X13241]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13241),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13241),X13240),X13240)),c_Groups_Ozero__class_Ozero(X13241)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13241),X13240),c_Groups_Ozero__class_Ozero(X13241)))|~class_Groups_Olinordered__ab__group__add(X13241))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13241),X13240),c_Groups_Ozero__class_Ozero(X13241)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13241),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13241),X13240),X13240)),c_Groups_Ozero__class_Ozero(X13241)))|~class_Groups_Olinordered__ab__group__add(X13241))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__add__less__zero__iff__single__add__less__zero])])])). 6.97/7.23 fof(c_0_7885, plain, ![X15389, X15390]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15390),X15389),c_Groups_Ozero__class_Ozero(X15390)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15390),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15390),X15389),X15389)),c_Groups_Ozero__class_Ozero(X15390)))|~class_Rings_Olinordered__idom(X15390))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15390),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15390),X15389),X15389)),c_Groups_Ozero__class_Ozero(X15390)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15390),X15389),c_Groups_Ozero__class_Ozero(X15390)))|~class_Rings_Olinordered__idom(X15390))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_even__less__0__iff])])])])). 6.97/7.23 fof(c_0_7886, plain, ![X12756, X12757]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12757),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12757),X12756),X12756)),c_Groups_Ozero__class_Ozero(X12757)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12757),X12756),c_Groups_Ozero__class_Ozero(X12757)))|~class_Groups_Olinordered__ab__group__add(X12757))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12757),X12756),c_Groups_Ozero__class_Ozero(X12757)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12757),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12757),X12756),X12756)),c_Groups_Ozero__class_Ozero(X12757)))|~class_Groups_Olinordered__ab__group__add(X12757))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__add__le__zero__iff__single__add__le__zero])])])). 6.97/7.23 fof(c_0_7887, plain, ![X10341, X10342, X10343]:((~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,X10343)),X10342)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X10343)),X10341)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10342),X10341)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10342),X10341))|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,X10343)),X10342)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X10343)),X10341))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__le__cancel1])])). 6.97/7.23 fof(c_0_7888, plain, ![X9334, X9335, X9336]:(~class_Rings_Olinordered__semidom(X9336)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9336),c_Groups_Ozero__class_Ozero(X9336)),X9335))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9336),c_Groups_Ozero__class_Ozero(X9336)),hAPP(hAPP(c_Power_Opower__class_Opower(X9336),X9335),X9334))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__less__power])])])). 6.97/7.23 fof(c_0_7889, plain, ![X8192, X8193]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8193),c_Groups_Ozero__class_Ozero(X8193)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8193),X8192),X8192)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8193),c_Groups_Ozero__class_Ozero(X8193)),X8192))|~class_Groups_Olinordered__ab__group__add(X8193))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8193),c_Groups_Ozero__class_Ozero(X8193)),X8192))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8193),c_Groups_Ozero__class_Ozero(X8193)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8193),X8192),X8192)))|~class_Groups_Olinordered__ab__group__add(X8193))), 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])])])])). 6.97/7.23 fof(c_0_7890, plain, ![X5012, X5013, X5014]:(~class_Rings_Olinordered__semidom(X5014)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5014),c_Groups_Oone__class_Oone(X5014)),X5013))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5014),c_Groups_Oone__class_Oone(X5014)),hAPP(hAPP(c_Power_Opower__class_Opower(X5014),X5013),X5012))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_one__le__power])])])). 6.97/7.23 fof(c_0_7891, plain, ![X14290, X14291, X14292]:(~class_Rings_Olinordered__semidom(X14292)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14292),c_Groups_Ozero__class_Ozero(X14292)),X14291))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14292),c_Groups_Ozero__class_Ozero(X14292)),hAPP(hAPP(c_Power_Opower__class_Opower(X14292),X14291),X14290))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power])])). 6.97/7.23 cnf(c_0_7892, 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_5297, c_0_4922])). 6.97/7.23 cnf(c_0_7893, 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_5298, c_0_4922])). 6.97/7.23 fof(c_0_7894, plain, ![X14658, X14659, X14660, X14661, X14662]:(~class_Orderings_Olinorder(X14662)|(~c_List_Olinorder__class_Osorted(X14662,hAPP(hAPP(c_List_Omap(X14661,X14662),X14660),X14659))|c_List_Olinorder__class_Osorted(X14662,hAPP(hAPP(c_List_Omap(X14661,X14662),X14660),c_List_Olinorder__class_Oinsort__insert__key(X14661,X14662,X14660,X14658,X14659))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__insort__insert__key])])])). 6.97/7.23 fof(c_0_7895, plain, ![X16573, X16574, X16575, X16576, X16577, X16578, X16579, X16580, X16581, X16582, X16583]:((~hBOOL(hAPP(hAPP(c_member(X16575),X16577),X16573))|X16576!=hAPP(X16574,X16577)|hBOOL(hAPP(hAPP(c_member(X16578),X16576),hAPP(c_Set_Oimage(X16575,X16578,X16574),X16573))))&((hBOOL(hAPP(hAPP(c_member(X16581),esk552_4(X16579,X16580,X16581,X16582)),X16579))|~hBOOL(hAPP(hAPP(c_member(X16583),X16582),hAPP(c_Set_Oimage(X16581,X16583,X16580),X16579))))&(X16582=hAPP(X16580,esk552_4(X16579,X16580,X16581,X16582))|~hBOOL(hAPP(hAPP(c_member(X16583),X16582),hAPP(c_Set_Oimage(X16581,X16583,X16580),X16579)))))), 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])])])])])])). 6.97/7.23 fof(c_0_7896, plain, ![X7177, X7178]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7178),c_Groups_Ozero__class_Ozero(X7178)),X7177))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7178),c_Groups_Ozero__class_Ozero(X7178)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7178),X7177),X7177)))|~class_Groups_Olinordered__ab__group__add(X7178))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7178),c_Groups_Ozero__class_Ozero(X7178)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7178),X7177),X7177)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7178),c_Groups_Ozero__class_Ozero(X7178)),X7177))|~class_Groups_Olinordered__ab__group__add(X7178))), 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])])])])). 6.97/7.23 fof(c_0_7897, plain, ![X8844, X8845, X8846]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X8846,X8846),tc_HOL_Obool)),X8845),X8844))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8846,tc_HOL_Obool)),c_Wellfounded_Oacc(X8846,X8844)),c_Wellfounded_Oacc(X8846,X8845)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_acc__subset])])])). 6.97/7.23 fof(c_0_7898, plain, ![X5349, X5350, X5351]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5351,tc_fun(X5351,tc_HOL_Obool))),X5350),X5349))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5351,tc_HOL_Obool)),c_Wellfounded_Oaccp(X5351,X5349)),c_Wellfounded_Oaccp(X5351,X5350)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_accp__subset])])])). 6.97/7.23 fof(c_0_7899, plain, ![X12780, X12781, X12782, X12783, X12784]:((X12783=hAPP(X12781,esk417_4(X12780,X12781,X12782,X12783))|~hBOOL(hAPP(hAPP(c_member(X12784),X12783),hAPP(c_Set_Oimage(X12782,X12784,X12781),X12780))))&(hBOOL(hAPP(hAPP(c_member(X12782),esk417_4(X12780,X12781,X12782,X12783)),X12780))|~hBOOL(hAPP(hAPP(c_member(X12784),X12783),hAPP(c_Set_Oimage(X12782,X12784,X12781),X12780))))), 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_imageE])])])])])])])). 6.97/7.23 cnf(c_0_7900, 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_5193])). 6.97/7.23 fof(c_0_7901, plain, ![X7773, X7774, X7775]:(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X7775)),X7774),c_Wellfounded_Oacc(tc_List_Olist(X7775),c_List_Olistrel1(X7775,X7773))))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X7775)),X7774),c_List_Olists(X7775,c_Wellfounded_Oacc(X7775,X7773))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__accI])])). 6.97/7.23 fof(c_0_7902, plain, ![X14480, X14481, X14482, X14484]:(((hBOOL(hAPP(hAPP(c_member(X14482),esk487_3(X14480,X14481,X14482)),X14481))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X14482,tc_Nat_Onat),X14480),X14481)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14482),X14481)))&(hAPP(X14480,esk487_3(X14480,X14481,X14482))!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X14482,tc_Nat_Onat),X14480),X14481)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14482),X14481))))&(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X14482,tc_Nat_Onat),X14480),X14481)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|(~hBOOL(hAPP(hAPP(c_member(X14482),X14484),X14481))|hAPP(X14480,X14484)=c_Groups_Oone__class_Oone(tc_Nat_Onat))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14482),X14481)))), 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])])])])])])). 6.97/7.23 fof(c_0_7903, plain, ![X13619, X13620, X13621, X13622, X13624]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13622),hAPP(X13620,esk456_4(X13619,X13620,X13621,X13622))),hAPP(X13619,esk456_4(X13619,X13620,X13621,X13622))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13621,X13622)),X13620),X13619))|~class_Orderings_Oord(X13622))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13621,X13622)),X13620),X13619))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13622),hAPP(X13620,X13624)),hAPP(X13619,X13624)))|~class_Orderings_Oord(X13622))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__fun__def])])])])])). 6.97/7.23 fof(c_0_7904, plain, ![X8128, X8129, X8130, X8131, X8132]:(~c_Finite__Set_Ofolding__one__idem(X8132,X8131,X8130)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8132),X8129))|(~hBOOL(hAPP(hAPP(c_member(X8132),X8128),X8129))|hAPP(X8130,X8129)=hAPP(hAPP(X8131,X8128),hAPP(X8130,X8129))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one__idem_Oin__idem])])])). 6.97/7.23 fof(c_0_7905, plain, ![X11412, X11413, X11414, X11416]:(((hBOOL(hAPP(hAPP(c_member(X11414),esk379_3(X11412,X11413,X11414)),X11413))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11414,tc_Nat_Onat),X11412),X11413)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11414),X11413)))&(hAPP(X11412,esk379_3(X11412,X11413,X11414))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11414,tc_Nat_Onat),X11412),X11413)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11414),X11413))))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11414,tc_Nat_Onat),X11412),X11413)|(~hBOOL(hAPP(hAPP(c_member(X11414),X11416),X11413))|hAPP(X11412,X11416)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11414),X11413)))), 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])])])])])])). 6.97/7.23 fof(c_0_7906, plain, ![X2393, X2394, X2395, X2396]:(c_Orderings_Otop__class_Otop(tc_fun(X2395,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X2396,X2395,X2394),c_Orderings_Otop__class_Otop(tc_fun(X2396,tc_HOL_Obool)))|X2393=hAPP(X2394,hAPP(c_Hilbert__Choice_Oinv__into(X2396,X2395,c_Orderings_Otop__class_Otop(tc_fun(X2396,tc_HOL_Obool)),X2394),X2393))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_surj__f__inv__f])])])). 6.97/7.23 cnf(c_0_7907, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2))=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(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_5299])). 6.97/7.23 fof(c_0_7908, plain, ![X622, X623, X624]:((~hBOOL(hAPP(hAPP(c_member(X624),X623),hAPP(c_List_Oset(X624),X622)))|c_List_Oinsert(X624,X623,X622)=X622)&(hBOOL(hAPP(hAPP(c_member(X624),X623),hAPP(c_List_Oset(X624),X622)))|c_List_Oinsert(X624,X623,X622)=hAPP(hAPP(c_List_Olist_OCons(X624),X623),X622))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_List_Oinsert__def])])])). 6.97/7.23 fof(c_0_7909, plain, ![X3535, X3536, X3537, X3538, X3539, X3540]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X3540,X3539)),hAPP(hAPP(c_Product__Type_OPair(X3540,X3539),X3538),X3537)),hAPP(hAPP(c_Product__Type_OSigma(X3540,X3539),X3536),X3535)))|hBOOL(hAPP(hAPP(c_member(X3539),X3537),hAPP(X3535,X3538)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaD2])])). 6.97/7.23 cnf(c_0_7910, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)=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))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_4835])). 6.97/7.23 cnf(c_0_7911, 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),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_5177])). 6.97/7.23 cnf(c_0_7912, 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_5300])). 6.97/7.23 cnf(c_0_7913, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=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)),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_5301])). 6.97/7.23 fof(c_0_7914, plain, ![X15794, X15795, X15796, X15797]:(((hBOOL(hAPP(c_List_Odistinct(X15796),X15794))|~hBOOL(hAPP(c_List_Odistinct(X15797),hAPP(hAPP(c_List_Omap(X15796,X15797),X15795),X15794))))&(c_Fun_Oinj__on(X15796,X15797,X15795,hAPP(c_List_Oset(X15796),X15794))|~hBOOL(hAPP(c_List_Odistinct(X15797),hAPP(hAPP(c_List_Omap(X15796,X15797),X15795),X15794)))))&(~hBOOL(hAPP(c_List_Odistinct(X15796),X15794))|~c_Fun_Oinj__on(X15796,X15797,X15795,hAPP(c_List_Oset(X15796),X15794))|hBOOL(hAPP(c_List_Odistinct(X15797),hAPP(hAPP(c_List_Omap(X15796,X15797),X15795),X15794))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__map])])])). 6.97/7.23 fof(c_0_7915, plain, ![X3914, X3915, X3916, X3917, X3918]:((~hBOOL(hAPP(hAPP(c_member(X3916),X3918),X3915))|c_Groups_Ozero__class_Ozero(X3917)!=hAPP(X3914,X3918)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3916,X3917),X3914),X3915)=c_Groups_Ozero__class_Ozero(X3917)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3916),X3915))|(~class_Rings_Ocomm__semiring__1(X3917)|~class_Rings_Ono__zero__divisors(X3917)))&((hBOOL(hAPP(hAPP(c_member(X3916),esk132_4(X3914,X3915,X3916,X3917)),X3915))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3916,X3917),X3914),X3915)!=c_Groups_Ozero__class_Ozero(X3917)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3916),X3915))|(~class_Rings_Ocomm__semiring__1(X3917)|~class_Rings_Ono__zero__divisors(X3917)))&(c_Groups_Ozero__class_Ozero(X3917)=hAPP(X3914,esk132_4(X3914,X3915,X3916,X3917))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3916,X3917),X3914),X3915)!=c_Groups_Ozero__class_Ozero(X3917)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3916),X3915))|(~class_Rings_Ocomm__semiring__1(X3917)|~class_Rings_Ono__zero__divisors(X3917))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__zero__iff])])])])])). 6.97/7.23 cnf(c_0_7916, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X2)),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))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_5302])). 6.97/7.23 fof(c_0_7917, plain, ![X11358, X11359]:((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk377_2(X11358,X11359)),X11359))|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)),X11358),X11359))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11358),esk377_2(X11358,X11359)))|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)),X11358),X11359))), 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__diff__nat])])])])])). 6.97/7.23 fof(c_0_7918, plain, ![X12662, X12663, X12664, X12665, X12666]:(~class_Orderings_Olinorder(X12666)|hAPP(hAPP(c_Set_Oinsert(X12665),X12663),hAPP(c_List_Oset(X12665),X12662))=hAPP(c_List_Oset(X12665),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X12665,X12666,X12664),X12663),X12662))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__insort])])). 6.97/7.23 fof(c_0_7919, plain, ![X8101, X8102, X8103, X8104]:(~c_Wellfounded_Owf(X8104,X8103)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X8104,X8104)),hAPP(hAPP(c_Product__Type_OPair(X8104,X8104),X8102),X8101)),X8103))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X8104,X8104)),hAPP(hAPP(c_Product__Type_OPair(X8104,X8104),X8101),X8102)),X8103)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__not__sym])])])). 6.97/7.23 fof(c_0_7920, plain, ![X594, X595, X596, X598, X599, X600, X601]:((hAPP(X594,hAPP(c_Hilbert__Choice_Oinv__into(X596,X595,c_Orderings_Otop__class_Otop(tc_fun(X596,tc_HOL_Obool)),X594),esk10_3(X594,X595,X596)))!=esk10_3(X594,X595,X596)|hAPP(c_Set_Oimage(X596,X595,X594),c_Orderings_Otop__class_Otop(tc_fun(X596,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X595,tc_HOL_Obool)))&(hAPP(c_Set_Oimage(X600,X599,X598),c_Orderings_Otop__class_Otop(tc_fun(X600,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X599,tc_HOL_Obool))|hAPP(X598,hAPP(c_Hilbert__Choice_Oinv__into(X600,X599,c_Orderings_Otop__class_Otop(tc_fun(X600,tc_HOL_Obool)),X598),X601))=X601)), 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_surj__iff__all])])])])])). 6.97/7.23 cnf(c_0_7921, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_member(X2),X3),X4))|hAPP(c_Finite__Set_Ocard(X2),X5)=hAPP(c_Nat_OSuc,X1)|hAPP(hAPP(c_Set_Oinsert(X2),X3),X4)!=X5|hAPP(c_Finite__Set_Ocard(X2),X4)!=X1), inference(split_conjunct,[status(thm)],[c_0_5303])). 6.97/7.23 fof(c_0_7922, plain, ![X9843, X9844, X9845, X9846, X9847, X9848]:((~hBOOL(hAPP(hAPP(X9848,X9847),X9846))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9844,tc_fun(X9843,tc_HOL_Obool))),X9845),X9848),X9847),X9846)))&(~hBOOL(hAPP(hAPP(X9845,X9847),X9846))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9844,tc_fun(X9843,tc_HOL_Obool))),X9845),X9848),X9847),X9846)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup2CI])])])])). 6.97/7.23 fof(c_0_7923, plain, ![X3296, X3297, X3298, X3299, X3300]:(~c_Relation_Orefl__on(X3300,X3299,X3298)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X3300,X3300)),hAPP(hAPP(c_Product__Type_OPair(X3300,X3300),X3297),X3296)),X3298))|hBOOL(hAPP(hAPP(c_member(X3300),X3297),X3299)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_refl__onD1])])])). 6.97/7.23 fof(c_0_7924, plain, ![X7094, X7095, X7096, X7097, X7098]:(~c_Relation_Orefl__on(X7098,X7097,X7096)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X7098,X7098)),hAPP(hAPP(c_Product__Type_OPair(X7098,X7098),X7095),X7094)),X7096))|hBOOL(hAPP(hAPP(c_member(X7098),X7094),X7097)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_refl__onD2])])])). 6.97/7.23 fof(c_0_7925, plain, ![X10726, X10727, X10728]:(~class_Divides_Osemiring__div(X10728)|(~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10728),X10727),X10726))|X10726=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10728),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X10728),X10726),X10727)),X10727))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dvd__div__mult__self])])])). 6.97/7.23 fof(c_0_7926, plain, ![X8228, X8229, X8230]:(~class_Divides_Osemiring__div(X8230)|(~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X8230),X8229),X8228))|X8228=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8230),X8229),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8230),X8228),X8229)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dvd__mult__div__cancel])])])). 6.97/7.23 cnf(c_0_7927, 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_5197])). 6.97/7.23 fof(c_0_7928, plain, ![X15041, X15042, X15043]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15043),hAPP(c_Groups_Ouminus__class_Ouminus(X15043),X15042)),X15041))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15043),hAPP(c_Groups_Ouminus__class_Ouminus(X15043),X15041)),X15042))|~class_Groups_Oordered__ab__group__add(X15043))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15043),hAPP(c_Groups_Ouminus__class_Ouminus(X15043),X15041)),X15042))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15043),hAPP(c_Groups_Ouminus__class_Ouminus(X15043),X15042)),X15041))|~class_Groups_Oordered__ab__group__add(X15043))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__less__iff])])])). 6.97/7.23 fof(c_0_7929, plain, ![X6316, X6317]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X6317),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6317,tc_HOL_Obool)),X6316)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X6317),c_Orderings_Otop__class_Otop(tc_fun(X6317,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6317),X6316)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6317),c_Orderings_Otop__class_Otop(tc_fun(X6317,tc_HOL_Obool))))|hBOOL(hAPP(c_Finite__Set_Ofinite(X6317),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6317,tc_HOL_Obool)),X6316)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6317),X6316)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__compl])])])])). 6.97/7.23 fof(c_0_7930, plain, ![X16403, X16404]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X16403),X16404)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16403),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)),X16404)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16403),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),X16403),X16404)),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)),X16404)))), 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])])])])). 6.97/7.23 fof(c_0_7931, plain, ![X1141, X1142, X1143]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1143),hAPP(c_Groups_Ouminus__class_Ouminus(X1143),X1142)),X1141))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1143),hAPP(c_Groups_Ouminus__class_Ouminus(X1143),X1141)),X1142))|~class_Groups_Oordered__ab__group__add(X1143))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1143),hAPP(c_Groups_Ouminus__class_Ouminus(X1143),X1141)),X1142))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1143),hAPP(c_Groups_Ouminus__class_Ouminus(X1143),X1142)),X1141))|~class_Groups_Oordered__ab__group__add(X1143))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__le__iff])])])])). 6.97/7.23 fof(c_0_7932, plain, ![X9821, X9822, X9823]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9823),X9821),hAPP(c_Groups_Ouminus__class_Ouminus(X9823),X9822)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9823),X9822),hAPP(c_Groups_Ouminus__class_Ouminus(X9823),X9821)))|~class_Groups_Oordered__ab__group__add(X9823))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9823),X9822),hAPP(c_Groups_Ouminus__class_Ouminus(X9823),X9821)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9823),X9821),hAPP(c_Groups_Ouminus__class_Ouminus(X9823),X9822)))|~class_Groups_Oordered__ab__group__add(X9823))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__minus__iff])])])])). 6.97/7.23 fof(c_0_7933, plain, ![X17610, X17611]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17610))|~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),X17611),X17610)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17611)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X17610),X17611))|~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),X17611),X17610)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17611))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17610))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X17610),X17611))|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),X17611),X17610)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17611)))), 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])])])])). 6.97/7.23 fof(c_0_7934, plain, ![X15959, X15960]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X15960))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X15960),hAPP(c_Nat_OSuc,X15959))),X15960))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__Suc__less])])])). 6.97/7.23 fof(c_0_7935, plain, ![X10080, X10081, X10082]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10082),X10080),hAPP(c_Groups_Ouminus__class_Ouminus(X10082),X10081)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10082),X10081),hAPP(c_Groups_Ouminus__class_Ouminus(X10082),X10080)))|~class_Groups_Oordered__ab__group__add(X10082))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10082),X10081),hAPP(c_Groups_Ouminus__class_Ouminus(X10082),X10080)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10082),X10080),hAPP(c_Groups_Ouminus__class_Ouminus(X10082),X10081)))|~class_Groups_Oordered__ab__group__add(X10082))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__iff])])])). 6.97/7.23 fof(c_0_7936, plain, ![X308]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X308),c_Orderings_Otop__class_Otop(tc_fun(X308,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(X308),c_Orderings_Otop__class_Otop(tc_fun(X308,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__card__ge__0])])). 6.97/7.23 fof(c_0_7937, plain, ![X6039]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6039))|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)),X6039)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__0__less])])). 6.97/7.23 fof(c_0_7938, plain, ![X7170, X7171, X7172, X7173]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7173),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7172)),X7171)))|hAPP(hAPP(c_List_Onth(X7172),hAPP(hAPP(c_List_Olist__update(X7172,X7171),X7173),X7170)),X7173)=X7170), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__list__update__eq])])])). 6.97/7.23 fof(c_0_7939, plain, ![X17455, X17456, X17457]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17457),X17456),X17455))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17457),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17457),X17456),X17455)),c_Groups_Ozero__class_Ozero(X17457)))|~class_Groups_Oordered__ab__group__add(X17457))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17457),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17457),X17456),X17455)),c_Groups_Ozero__class_Ozero(X17457)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17457),X17456),X17455))|~class_Groups_Oordered__ab__group__add(X17457))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__iff__diff__less__0])])])])). 6.97/7.23 fof(c_0_7940, plain, ![X4544, X4545, X4546]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4546),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4546),X4545),X4544)),c_Groups_Ozero__class_Ozero(X4546)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4546),X4545),X4544))|~class_Groups_Oordered__ab__group__add(X4546))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4546),X4545),X4544))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4546),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4546),X4545),X4544)),c_Groups_Ozero__class_Ozero(X4546)))|~class_Groups_Oordered__ab__group__add(X4546))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__diff__le__0])])])). 6.97/7.23 fof(c_0_7941, plain, ![X455, X456, X457, X458, X459]:(~class_Orderings_Olinorder(X459)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X458)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X458,X459,X457),X456),X455))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X458)),X455))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_length__insort])])])). 6.97/7.23 fof(c_0_7942, plain, ![X8289, X8290, X8291]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8291),X8289),X8290))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8291),hAPP(c_Groups_Ouminus__class_Ouminus(X8291),X8290)),hAPP(c_Groups_Ouminus__class_Ouminus(X8291),X8289)))|~class_Groups_Oordered__ab__group__add(X8291))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8291),hAPP(c_Groups_Ouminus__class_Ouminus(X8291),X8290)),hAPP(c_Groups_Ouminus__class_Ouminus(X8291),X8289)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8291),X8289),X8290))|~class_Groups_Oordered__ab__group__add(X8291))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__less__iff__less])])])])). 6.97/7.23 fof(c_0_7943, plain, ![X1257, X1258, X1259, X1260]:(~c_Fun_Oinj__on(X1260,X1259,X1258,X1257)|hAPP(c_Set_Oimage(X1259,X1260,c_Fun_Othe__inv__into(X1260,X1259,X1257,X1258)),hAPP(c_Set_Oimage(X1260,X1259,X1258),X1257))=X1257), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_the__inv__into__onto])])])). 6.97/7.23 fof(c_0_7944, plain, ![X6084, X6085, X6086, X6087]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6087),X6085),X6084))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6087),hAPP(hAPP(c_Orderings_Oord__class_Omin(X6087),X6086),X6085)),X6084))|~class_Orderings_Olinorder(X6087))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6087),X6086),X6084))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6087),hAPP(hAPP(c_Orderings_Oord__class_Omin(X6087),X6086),X6085)),X6084))|~class_Orderings_Olinorder(X6087)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6087),hAPP(hAPP(c_Orderings_Oord__class_Omin(X6087),X6086),X6085)),X6084))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6087),X6085),X6084))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6087),X6086),X6084)))|~class_Orderings_Olinorder(X6087))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__less__iff__disj])])])])). 6.97/7.23 fof(c_0_7945, plain, ![X9993, X9994, X9995, X9996]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9996),X9994),X9993))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9996),hAPP(hAPP(c_Orderings_Oord__class_Omin(X9996),X9995),X9994)),X9993))|~class_Orderings_Olinorder(X9996))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9996),X9995),X9993))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9996),hAPP(hAPP(c_Orderings_Oord__class_Omin(X9996),X9995),X9994)),X9993))|~class_Orderings_Olinorder(X9996)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9996),hAPP(hAPP(c_Orderings_Oord__class_Omin(X9996),X9995),X9994)),X9993))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9996),X9994),X9993))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9996),X9995),X9993)))|~class_Orderings_Olinorder(X9996))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__le__iff__disj])])])])). 6.97/7.23 fof(c_0_7946, plain, ![X12698, X12699, X12700, X12701]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12701),X12700),X12698))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12701),X12700),hAPP(hAPP(c_Orderings_Oord__class_Omax(X12701),X12699),X12698)))|~class_Orderings_Olinorder(X12701))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12701),X12700),X12699))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12701),X12700),hAPP(hAPP(c_Orderings_Oord__class_Omax(X12701),X12699),X12698)))|~class_Orderings_Olinorder(X12701)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12701),X12700),hAPP(hAPP(c_Orderings_Oord__class_Omax(X12701),X12699),X12698)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12701),X12700),X12698))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12701),X12700),X12699)))|~class_Orderings_Olinorder(X12701))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__max__iff__disj])])])). 6.97/7.23 fof(c_0_7947, plain, ![X5366, X5367, X5368]:(~class_Lattices_Oboolean__algebra(X5368)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5368),X5367),X5366))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5368),hAPP(c_Groups_Ouminus__class_Ouminus(X5368),X5366)),hAPP(c_Groups_Ouminus__class_Ouminus(X5368),X5367))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__mono])])). 6.97/7.23 fof(c_0_7948, plain, ![X2647, X2648, X2649]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2649),hAPP(c_Groups_Ouminus__class_Ouminus(X2649),X2648)),hAPP(c_Groups_Ouminus__class_Ouminus(X2649),X2647)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2649),X2647),X2648))|~class_Groups_Oordered__ab__group__add(X2649))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2649),X2647),X2648))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2649),hAPP(c_Groups_Ouminus__class_Ouminus(X2649),X2648)),hAPP(c_Groups_Ouminus__class_Ouminus(X2649),X2647)))|~class_Groups_Oordered__ab__group__add(X2649))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__iff__le])])])). 6.97/7.23 fof(c_0_7949, plain, ![X7634, X7635, X7636, X7637]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7637),X7636),hAPP(hAPP(c_Orderings_Oord__class_Omax(X7637),X7635),X7634)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7637),X7636),X7634))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7637),X7636),X7635)))|~class_Orderings_Olinorder(X7637))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7637),X7636),X7634))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7637),X7636),hAPP(hAPP(c_Orderings_Oord__class_Omax(X7637),X7635),X7634)))|~class_Orderings_Olinorder(X7637))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7637),X7636),X7635))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7637),X7636),hAPP(hAPP(c_Orderings_Oord__class_Omax(X7637),X7635),X7634)))|~class_Orderings_Olinorder(X7637)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__max__iff__disj])])])])). 6.97/7.23 fof(c_0_7950, plain, ![X17520, X17521, X17522]:(~class_Groups_Oordered__ab__group__add(X17522)|hAPP(c_Set_Oimage(X17522,X17522,c_Groups_Ouminus__class_Ouminus(X17522)),c_SetInterval_Oord__class_OgreaterThanAtMost(X17522,X17521,X17520))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X17522,hAPP(c_Groups_Ouminus__class_Ouminus(X17522),X17520)),hAPP(c_Groups_Ouminus__class_Ouminus(X17522),X17521))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThanAtMost])])). 6.97/7.23 fof(c_0_7951, plain, ![X4289, X4290, X4291, X4292]:((hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4292)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_List_Otake(X4291),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4292)),hAPP(hAPP(c_List_Olist_OCons(X4291),X4290),X4289))=hAPP(hAPP(c_List_Olist_OCons(X4291),X4290),hAPP(hAPP(c_List_Otake(X4291),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4292)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X4289)))&(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4292)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_List_Otake(X4291),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4292)),hAPP(hAPP(c_List_Olist_OCons(X4291),X4290),X4289))=c_List_Olist_ONil(X4291))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__Cons__number__of])])). 6.97/7.23 fof(c_0_7952, plain, ![X4669, X4670, X4671, X4672]:(~class_Orderings_Oorder(X4672)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4672,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4672,X4671,X4670)),c_SetInterval_Oord__class_OatLeastAtMost(X4672,X4670,X4669))=c_Orderings_Obot__class_Obot(tc_fun(X4672,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__int_I13_J])])])). 6.97/7.23 fof(c_0_7953, plain, ![X16608, X16609, X16610, X16611]:(~class_Orderings_Oorder(X16611)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16611,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X16611,X16610,X16609)),c_SetInterval_Oord__class_OgreaterThanLessThan(X16611,X16609,X16608))=c_Orderings_Obot__class_Obot(tc_fun(X16611,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__int_I12_J])])])). 6.97/7.23 fof(c_0_7954, plain, ![X2170, X2171, X2172, X2173]:(~class_Orderings_Oorder(X2173)|c_Orderings_Obot__class_Obot(tc_fun(X2173,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2173,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X2173,X2172,X2171)),c_SetInterval_Oord__class_OgreaterThanLessThan(X2173,X2171,X2170))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I10_J])])). 6.97/7.23 fof(c_0_7955, plain, ![X7373, X7374, X7375, X7376]:(~class_Orderings_Oorder(X7376)|c_Orderings_Obot__class_Obot(tc_fun(X7376,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7376,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X7376,X7375,X7374)),c_SetInterval_Oord__class_OgreaterThanAtMost(X7376,X7374,X7373))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__int_I14_J])])])). 6.97/7.23 fof(c_0_7956, plain, ![X1566, X1567, X1568, X1569, X1570, X1571, X1572, X1573, X1574, X1575, X1576, X1577, X1578, X1579, X1580]:((~hBOOL(hAPP(hAPP(X1569,X1567),X1570))|~hBOOL(hAPP(hAPP(X1568,X1570),X1566))|hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X1573,X1572,X1571,X1569,X1568),X1567),X1566)))&((hBOOL(hAPP(hAPP(X1577,X1575),esk44_4(X1574,X1575,X1576,X1577)))|~hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X1580,X1579,X1578,X1577,X1576),X1575),X1574)))&(hBOOL(hAPP(hAPP(X1576,esk44_4(X1574,X1575,X1576,X1577)),X1574))|~hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X1580,X1579,X1578,X1577,X1576),X1575),X1574))))), 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])])])])])])). 6.97/7.23 fof(c_0_7957, plain, ![X3163, X3164, X3165, X3166, X3167]:((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3167)),X3165)=X3163|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3167),tc_List_Olist(X3167))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3167),tc_List_Olist(X3167)),X3166),X3165)),hAPP(c_List_Olexn(X3167,X3164),X3163))))&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3167)),X3166)=X3163|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3167),tc_List_Olist(X3167))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3167),tc_List_Olist(X3167)),X3166),X3165)),hAPP(c_List_Olexn(X3167,X3164),X3163))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lexn__length])])])])). 6.97/7.23 fof(c_0_7958, plain, ![X15301, X15302, X15303]:(~class_Groups_Oordered__ab__group__add__abs(X15303)|hAPP(c_Groups_Oabs__class_Oabs(X15303),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15303),X15301),X15302))=hAPP(c_Groups_Oabs__class_Oabs(X15303),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15303),X15302),X15301))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__commute])])). 6.97/7.23 fof(c_0_7959, plain, ![X7813, X7814, X7815, X7816]:(~class_Orderings_Oorder(X7816)|c_Orderings_Obot__class_Obot(tc_fun(X7816,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7816,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X7816,X7815,X7814)),c_SetInterval_Oord__class_OgreaterThanAtMost(X7816,X7814,X7813))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__int_I16_J])])])). 6.97/7.23 fof(c_0_7960, plain, ![X13772, X13773, X13774]:(~class_Orderings_Oorder(X13774)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13774,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X13774,X13773,X13772)),hAPP(c_SetInterval_Oord__class_OatLeast(X13774),X13772))=c_Orderings_Obot__class_Obot(tc_fun(X13774,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I6_J])])). 6.97/7.23 fof(c_0_7961, plain, ![X5750, X5751, X5752]:(~class_Orderings_Oorder(X5752)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5752,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5752,X5751,X5750)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5752),X5750))=c_Orderings_Obot__class_Obot(tc_fun(X5752,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I5_J])])). 6.97/7.23 fof(c_0_7962, plain, ![X11333, X11334, X11335]:(~class_Orderings_Oorder(X11335)|c_Orderings_Obot__class_Obot(tc_fun(X11335,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11335,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X11335,X11334,X11333)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X11335),X11333))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__int_I7_J])])])). 6.97/7.23 fof(c_0_7963, plain, ![X11664, X11665, X11666, X11667]:(~c_Fun_Obij__betw(X11667,X11666,X11665,X11664,c_Orderings_Otop__class_Otop(tc_fun(X11666,tc_HOL_Obool)))|c_Orderings_Otop__class_Otop(tc_fun(X11666,tc_HOL_Obool))=hAPP(c_Set_Oimage(X11667,X11666,X11665),c_Orderings_Otop__class_Otop(tc_fun(X11667,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bij__betw__imp__surj])])])). 6.97/7.23 fof(c_0_7964, plain, ![X12196, X12197, X12198, X12199, X12200]:(~class_Orderings_Olinorder(X12200)|(~c_List_Olinorder__class_Osorted(X12200,hAPP(hAPP(c_List_Omap(X12199,X12200),X12198),X12197))|c_List_Olinorder__class_Osorted(X12200,hAPP(hAPP(c_List_Omap(X12199,X12200),X12198),hAPP(c_List_Ofilter(X12199,X12196),X12197))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__filter])])])). 6.97/7.23 fof(c_0_7965, plain, ![X16157, X16158, X16159]:(~class_Orderings_Oorder(X16159)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16159,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X16159),X16158)),c_SetInterval_Oord__class_OatLeastAtMost(X16159,X16158,X16157))=c_Orderings_Obot__class_Obot(tc_fun(X16159,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__int_I4_J])])])). 6.97/7.23 fof(c_0_7966, plain, ![X10492, X10493, X10494]:(~class_Orderings_Oorder(X10494)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10494,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X10494),X10493)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10494,X10493,X10492))=c_Orderings_Obot__class_Obot(tc_fun(X10494,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I1_J])])). 6.97/7.23 fof(c_0_7967, plain, ![X11296, X11297, X11298]:(~class_Orderings_Oorder(X11298)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11298,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X11298),X11297)),c_SetInterval_Oord__class_OgreaterThanAtMost(X11298,X11297,X11296))=c_Orderings_Obot__class_Obot(tc_fun(X11298,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__int_I3_J])])])). 6.97/7.23 cnf(c_0_7968, 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)|esk232_4(X1,X2,X3,X4)!=X4|~hBOOL(hAPP(hAPP(c_member(X3),X4),X2))|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(X1,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))), inference(split_conjunct,[status(thm)],[c_0_5134])). 6.97/7.23 fof(c_0_7969, plain, ![X9594, X9595, X9596]:(~class_Rings_Oring__1(X9596)|(~hBOOL(hAPP(hAPP(c_member(X9596),X9595),c_Int_Oring__1__class_OInts(X9596)))|hBOOL(hAPP(hAPP(c_member(X9596),hAPP(hAPP(c_Power_Opower__class_Opower(X9596),X9595),X9594)),c_Int_Oring__1__class_OInts(X9596))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__power])])). 6.97/7.23 fof(c_0_7970, plain, ![X3115, X3116]:(~class_Lattices_Olattice(X3116)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3116),X3115))|(c_Orderings_Obot__class_Obot(tc_fun(X3116,tc_HOL_Obool))=X3115|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3116),c_Big__Operators_Olattice__class_OInf__fin(X3116,X3115)),c_Big__Operators_Olattice__class_OSup__fin(X3116,X3115)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__le__Sup])])])). 6.97/7.23 fof(c_0_7971, plain, ![X423, X424, X425]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X425),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X424),X423)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X425),X423)),X424)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X425),X423)),X424))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X425),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X424),X423))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__conv])])). 6.97/7.23 fof(c_0_7972, plain, ![X14530, X14531, X14532]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14532),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14530),X14531)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14532),X14531)),X14530)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14532),X14531)),X14530))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14532),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14530),X14531))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv])])). 6.97/7.23 cnf(c_0_7973, 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_5304])). 6.97/7.23 fof(c_0_7974, plain, ![X12828, X12829, X12830]:(~class_Complete__Lattice_Ocomplete__lattice(X12830)|(~c_Orderings_Oorder__class_Omono(X12830,X12830,X12829)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12830),hAPP(X12829,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X12830),c_Inductive_Ocomplete__lattice__class_Olfp(X12830,X12829)),X12828))),X12828))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12830),c_Inductive_Ocomplete__lattice__class_Olfp(X12830,X12829)),X12828))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lfp__induct])])])). 6.97/7.23 fof(c_0_7975, plain, ![X8645, X8646, X8647]:(~class_Complete__Lattice_Ocomplete__lattice(X8647)|(~c_Orderings_Oorder__class_Omono(X8647,X8647,X8646)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8647),X8645),hAPP(X8646,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8647),X8645),c_Inductive_Ocomplete__lattice__class_Ogfp(X8647,X8646)))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8647),X8645),c_Inductive_Ocomplete__lattice__class_Ogfp(X8647,X8646)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_coinduct])])])). 6.97/7.23 cnf(c_0_7976, 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))))|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_5305])). 6.97/7.23 cnf(c_0_7977, 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_5306, c_0_4413]), c_0_4413]), ['final']). 6.97/7.23 cnf(c_0_7978, 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_5307, c_0_4413]), ['final']). 6.97/7.23 fof(c_0_7979, plain, ![X9250, X9251]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9251),X9250))|c_Fun_Obij__betw(tc_Nat_Onat,X9251,esk305_2(X9250,X9251),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X9251),X9250)),X9250)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ex__bij__betw__nat__finite__1])])])). 6.97/7.23 cnf(c_0_7980, 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_5308])). 6.97/7.23 cnf(c_0_7981, plain, (c_Big__Operators_Olattice__class_OInf__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__inf__class_Oinf(X1),X2),X3)|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_5309])). 6.97/7.23 fof(c_0_7982, plain, ![X3599, X3600, X3601]:(~class_Rings_Olinordered__semiring__strict(X3601)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3601),c_Groups_Ozero__class_Ozero(X3601)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3601),X3600),X3599)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3601),c_Groups_Ozero__class_Ozero(X3601)),X3599))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3601),c_Groups_Ozero__class_Ozero(X3601)),X3600))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__less__mult__pos2])])])). 6.97/7.23 fof(c_0_7983, plain, ![X12627, X12628, X12629]:(~class_Rings_Olinordered__semiring__strict(X12629)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12629),c_Groups_Ozero__class_Ozero(X12629)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12629),X12628),X12627)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12629),c_Groups_Ozero__class_Ozero(X12629)),X12628))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12629),c_Groups_Ozero__class_Ozero(X12629)),X12627))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__less__mult__pos])])])). 6.97/7.23 fof(c_0_7984, plain, ![X7899, X7900, X7901]:(~class_Rings_Osemiring__1(X7901)|hAPP(hAPP(c_Power_Opower__class_Opower(X7901),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7901),X7900)),X7899)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7901),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X7900),X7899))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__power])])). 6.97/7.23 cnf(c_0_7985, 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_5310])). 6.97/7.23 cnf(c_0_7986, plain, (hAPP(c_List_Ofoldl(X1,X1,c_Orderings_Oord__class_Omin(X1),X2),X3)=c_Big__Operators_Olinorder__class_OMin(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_5311])). 6.97/7.23 fof(c_0_7987, plain, ![X6103, X6104, X6105]:(~class_Groups_Omonoid__add(X6105)|c_Groups_Ozero__class_Ozero(X6105)=hAPP(c_List_Omonoid__add__class_Olistsum(X6105),hAPP(hAPP(c_List_Omap(X6104,X6105),hAPP(c_COMBK(X6105,X6104),c_Groups_Ozero__class_Ozero(X6105))),X6103))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__0])])). 6.97/7.23 cnf(c_0_7988, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk238_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_5312])). 6.97/7.23 fof(c_0_7989, plain, ![X331, X332, X333]:(~class_Rings_Oring__1(X333)|hAPP(hAPP(c_Power_Opower__class_Opower(X333),hAPP(c_Int_Oring__1__class_Oof__int(X333),X332)),X331)=hAPP(c_Int_Oring__1__class_Oof__int(X333),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X332),X331))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__power])])])). 6.97/7.23 fof(c_0_7990, plain, ![X8634, X8635]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8635))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8634))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X8635,X8634))))), 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])])])). 6.97/7.23 fof(c_0_7991, plain, ![X14543, X14544, X14545]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14545),X14544))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14545),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14544),X14543)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_start__le__sum])])). 6.97/7.23 fof(c_0_7992, plain, ![X5644, X5645, X5646, X5647, X5648]:(~hBOOL(hAPP(hAPP(c_member(X5648),X5647),X5646))|hBOOL(hAPP(hAPP(c_member(X5645),hAPP(X5644,X5647)),hAPP(c_Set_Oimage(X5648,X5645,X5644),X5646)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_imageI])])])). 6.97/7.23 fof(c_0_7993, plain, ![X12058, X12059, X12061, X12062, X12063]:(((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X12059)),esk402_2(X12058,X12059)),hAPP(c_List_Oset(tc_List_Olist(X12059)),X12058)))|c_List_Olist_ONil(tc_List_Olist(X12059))=c_List_Otranspose(X12059,X12058))&(c_List_Olist_ONil(X12059)!=esk402_2(X12058,X12059)|c_List_Olist_ONil(tc_List_Olist(X12059))=c_List_Otranspose(X12059,X12058)))&(c_List_Olist_ONil(tc_List_Olist(X12062))!=c_List_Otranspose(X12062,X12061)|(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X12062)),X12063),hAPP(c_List_Oset(tc_List_Olist(X12062)),X12061)))|c_List_Olist_ONil(X12062)=X12063))), 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_transpose__empty])])])])])])). 6.97/7.23 fof(c_0_7994, plain, ![X5372, X5373, X5374, X5375, X5376, X5377]:(~c_Fun_Obij__betw(X5377,X5376,X5375,X5374,X5373)|(~hBOOL(hAPP(hAPP(c_member(X5377),X5372),X5374))|hAPP(c_Hilbert__Choice_Oinv__into(X5376,X5377,X5373,c_Hilbert__Choice_Oinv__into(X5377,X5376,X5374,X5375)),X5372)=hAPP(X5375,X5372))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__inv__into__eq])])). 6.97/7.23 fof(c_0_7995, plain, ![X9709, X9710, X9711, X9712, X9713, X9714]:((~c_Fun_Oinj__on(X9713,X9710,X9709,hAPP(c_Set_Oimage(X9714,X9713,X9712),X9711))|c_Fun_Oinj__on(X9714,X9710,hAPP(c_Fun_Ocomp(X9713,X9710,X9714,X9709),X9712),X9711)|~c_Fun_Oinj__on(X9714,X9713,X9712,X9711))&(~c_Fun_Oinj__on(X9714,X9710,hAPP(c_Fun_Ocomp(X9713,X9710,X9714,X9709),X9712),X9711)|c_Fun_Oinj__on(X9713,X9710,X9709,hAPP(c_Set_Oimage(X9714,X9713,X9712),X9711))|~c_Fun_Oinj__on(X9714,X9713,X9712,X9711))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__inj__on__iff])])])). 6.97/7.23 cnf(c_0_7996, 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),X2)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_5219])). 6.97/7.23 fof(c_0_7997, plain, ![X1220, X1221, X1222, X1223]:((~hBOOL(hAPP(hAPP(c_member(X1223),X1222),X1221))|hBOOL(hAPP(hAPP(c_member(X1223),X1222),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1223,tc_HOL_Obool)),X1220),X1221))))&(~hBOOL(hAPP(hAPP(c_member(X1223),X1222),X1220))|hBOOL(hAPP(hAPP(c_member(X1223),X1222),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1223,tc_HOL_Obool)),X1220),X1221))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UnCI])])])])). 6.97/7.23 fof(c_0_7998, plain, ![X1396, X1397, X1398, X1399, X1400, X1401, X1402]:((hAPP(c_List_Ofilter(X1398,X1397),X1396)!=c_List_Olist_ONil(X1398)|(~hBOOL(hAPP(hAPP(c_member(X1398),X1399),hAPP(c_List_Oset(X1398),X1396)))|~hBOOL(hAPP(X1397,X1399))))&((hBOOL(hAPP(hAPP(c_member(X1402),esk40_3(X1400,X1401,X1402)),hAPP(c_List_Oset(X1402),X1400)))|hAPP(c_List_Ofilter(X1402,X1401),X1400)=c_List_Olist_ONil(X1402))&(hBOOL(hAPP(X1401,esk40_3(X1400,X1401,X1402)))|hAPP(c_List_Ofilter(X1402,X1401),X1400)=c_List_Olist_ONil(X1402)))), 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])])])])])])])). 6.97/7.23 fof(c_0_7999, plain, ![X5551, X5552, X5553, X5554]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5553),c_Complete__Lattice_OSup__class_OSup(X5553,X5552)),X5551))|(~hBOOL(hAPP(hAPP(c_member(X5553),X5554),X5552))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5553),X5554),X5551)))|~class_Complete__Lattice_Ocomplete__lattice(X5553))&((hBOOL(hAPP(hAPP(c_member(X5553),esk182_3(X5551,X5552,X5553)),X5552))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5553),c_Complete__Lattice_OSup__class_OSup(X5553,X5552)),X5551))|~class_Complete__Lattice_Ocomplete__lattice(X5553))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5553),esk182_3(X5551,X5552,X5553)),X5551))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5553),c_Complete__Lattice_OSup__class_OSup(X5553,X5552)),X5551))|~class_Complete__Lattice_Ocomplete__lattice(X5553)))), 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])])])])])])). 6.97/7.23 fof(c_0_8000, plain, ![X2263, X2264, X2265, X2267]:(((hBOOL(hAPP(hAPP(c_member(X2265),esk72_3(X2263,X2264,X2265)),X2263))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2265),X2264),c_Complete__Lattice_OInf__class_OInf(X2265,X2263)))|~class_Complete__Lattice_Ocomplete__lattice(X2265))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2265),X2264),esk72_3(X2263,X2264,X2265)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2265),X2264),c_Complete__Lattice_OInf__class_OInf(X2265,X2263)))|~class_Complete__Lattice_Ocomplete__lattice(X2265)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2265),X2264),c_Complete__Lattice_OInf__class_OInf(X2265,X2263)))|(~hBOOL(hAPP(hAPP(c_member(X2265),X2267),X2263))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2265),X2264),X2267)))|~class_Complete__Lattice_Ocomplete__lattice(X2265))), 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])])])])])])). 6.97/7.23 fof(c_0_8001, plain, ![X1586, X1587, X1588]:(~class_Power_Opower(X1588)|hAPP(hAPP(c_Power_Opower__class_Opower(X1588),X1587),hAPP(c_Nat_OSuc,X1586))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1588),X1587),hAPP(hAPP(c_Power_Opower__class_Opower(X1588),X1587),X1586))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc])])). 6.97/7.23 cnf(c_0_8002, 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_5313])). 6.97/7.23 fof(c_0_8003, plain, ![X17653, X17654, X17655, X17656]:(~class_Orderings_Oord(X17656)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17656),hAPP(X17655,esk600_4(X17653,X17654,X17655,X17656))),hAPP(X17654,esk600_4(X17653,X17654,X17655,X17656))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17653,X17656)),X17655),X17654)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__funI])])])])). 6.97/7.23 fof(c_0_8004, plain, ![X13850, X13851, X13852]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13851),X13850))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13852),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X13852),X13851)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X13852),X13850)))|~class_Rings_Olinordered__semidom(X13852))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13852),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X13852),X13851)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X13852),X13850)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13851),X13850))|~class_Rings_Olinordered__semidom(X13852))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__less__iff])])])])). 6.97/7.23 fof(c_0_8005, plain, ![X7284, X7285, X7286]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7286),hAPP(c_Int_Oring__1__class_Oof__int(X7286),X7285)),hAPP(c_Int_Oring__1__class_Oof__int(X7286),X7284)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7285),X7284))|~class_Rings_Olinordered__idom(X7286))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7285),X7284))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7286),hAPP(c_Int_Oring__1__class_Oof__int(X7286),X7285)),hAPP(c_Int_Oring__1__class_Oof__int(X7286),X7284)))|~class_Rings_Olinordered__idom(X7286))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__less__iff])])])])). 6.97/7.23 fof(c_0_8006, plain, ![X5308, X5309, X5310]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5310),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5310),X5309)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5310),X5308)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5309),X5308))|~class_Rings_Olinordered__semidom(X5310))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5309),X5308))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5310),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5310),X5309)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5310),X5308)))|~class_Rings_Olinordered__semidom(X5310))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__le__iff])])])). 6.97/7.23 fof(c_0_8007, plain, ![X334, X335, X336]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X336),hAPP(c_Int_Oring__1__class_Oof__int(X336),X335)),hAPP(c_Int_Oring__1__class_Oof__int(X336),X334)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X335),X334))|~class_Rings_Olinordered__idom(X336))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X335),X334))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X336),hAPP(c_Int_Oring__1__class_Oof__int(X336),X335)),hAPP(c_Int_Oring__1__class_Oof__int(X336),X334)))|~class_Rings_Olinordered__idom(X336))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__le__iff])])])). 6.97/7.23 fof(c_0_8008, plain, ![X2656, X2657, X2658, X2659, X2660, X2661, X2662, X2663]:((~c_Fun_Obij__betw(X2662,X2658,X2657,X2659,X2656)|c_Fun_Obij__betw(X2663,X2658,hAPP(c_Fun_Ocomp(X2662,X2658,X2663,X2657),X2661),X2660,X2656)|~c_Fun_Obij__betw(X2663,X2662,X2661,X2660,X2659))&(~c_Fun_Obij__betw(X2663,X2658,hAPP(c_Fun_Ocomp(X2662,X2658,X2663,X2657),X2661),X2660,X2656)|c_Fun_Obij__betw(X2662,X2658,X2657,X2659,X2656)|~c_Fun_Obij__betw(X2663,X2662,X2661,X2660,X2659))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bij__betw__comp__iff])])])])). 6.97/7.23 fof(c_0_8009, plain, ![X826, X827, X828, X829, X830, X831]:(~c_Equiv__Relations_Ocongruent(X831,X830,X829,X828)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X831,X831)),hAPP(hAPP(c_Product__Type_OPair(X831,X831),X827),X826)),X829))|hAPP(X828,X827)=hAPP(X828,X826))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruentD])])). 6.97/7.23 fof(c_0_8010, plain, ![X10942, X10943, X10944]:(~class_Rings_Ocomm__semiring__1(X10944)|hAPP(hAPP(c_Power_Opower__class_Opower(X10944),X10943),hAPP(c_Nat_OSuc,X10942))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10944),X10943),hAPP(hAPP(c_Power_Opower__class_Opower(X10944),X10943),X10942))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J])])). 6.97/7.23 fof(c_0_8011, plain, ![X5382, X5383, X5385, X5386, X5387]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X5383,X5383)),hAPP(hAPP(c_Product__Type_OPair(X5383,X5383),esk172_2(X5382,X5383)),esk172_2(X5382,X5383))),X5382))|c_Nitpick_Orefl_H(X5383,X5382))&(~c_Nitpick_Orefl_H(X5386,X5385)|hBOOL(hAPP(hAPP(c_member(tc_prod(X5386,X5386)),hAPP(hAPP(c_Product__Type_OPair(X5386,X5386),X5387),X5387)),X5385)))), 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])])])])])). 6.97/7.23 fof(c_0_8012, plain, ![X7974, X7975, X7976, X7978, X7979, X7980, X7981]:(((hBOOL(hAPP(hAPP(c_member(X7976),esk259_3(X7974,X7975,X7976)),hAPP(c_List_Oset(X7976),X7974)))|hBOOL(hAPP(c_List_Olistsp(X7976,X7975),X7974)))&(~hBOOL(hAPP(X7975,esk259_3(X7974,X7975,X7976)))|hBOOL(hAPP(c_List_Olistsp(X7976,X7975),X7974))))&(~hBOOL(hAPP(c_List_Olistsp(X7980,X7979),X7978))|(~hBOOL(hAPP(hAPP(c_member(X7980),X7981),hAPP(c_List_Oset(X7980),X7978)))|hBOOL(hAPP(X7979,X7981))))), 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])])])])])])). 6.97/7.23 fof(c_0_8013, plain, ![X7079, X7080, X7081]:(~hBOOL(hAPP(hAPP(c_member(tc_fun(X7081,tc_HOL_Obool)),X7080),X7079))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7081,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X7081,tc_HOL_Obool),X7079)),X7080))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inter__lower])])). 6.97/7.23 fof(c_0_8014, plain, ![X8006, X8007, X8008]:(~hBOOL(hAPP(hAPP(c_member(tc_fun(X8008,tc_HOL_Obool)),X8007),X8006))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8008,tc_HOL_Obool)),X8007),c_Complete__Lattice_OSup__class_OSup(tc_fun(X8008,tc_HOL_Obool),X8006)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Union__upper])])). 6.97/7.23 fof(c_0_8015, plain, ![X3066, X3067, X3068, X3069]:((hBOOL(hAPP(X3069,esk101_4(X3066,X3067,X3068,X3069)))|c_Wellfounded_Owf(tc_prod(X3066,X3068),c_Recdef_Osame__fst(X3066,X3068,X3069,X3067)))&(~c_Wellfounded_Owf(X3068,hAPP(X3067,esk101_4(X3066,X3067,X3068,X3069)))|c_Wellfounded_Owf(tc_prod(X3066,X3068),c_Recdef_Osame__fst(X3066,X3068,X3069,X3067)))), 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])])])])])). 6.97/7.23 cnf(c_0_8016, 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_5314])). 6.97/7.23 fof(c_0_8017, plain, ![X15725, X15726, X15727, X15728]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15728)|hAPP(hAPP(c_List_Onth(X15727),hAPP(hAPP(c_List_Olist_OCons(X15727),X15726),X15725)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15728))=X15726)&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15728)|hAPP(hAPP(c_List_Onth(X15727),X15725),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15728)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_List_Onth(X15727),hAPP(hAPP(c_List_Olist_OCons(X15727),X15726),X15725)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15728)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__Cons__number__of])])). 6.97/7.23 fof(c_0_8018, plain, ![X13388, X13389, X13390]:((hBOOL(hAPP(hAPP(c_member(X13390),esk443_3(X13388,X13389,X13390)),X13389))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13390),c_Complete__Lattice_OSup__class_OSup(X13390,X13389)),X13388))|~class_Complete__Lattice_Ocomplete__lattice(X13390))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13390),esk443_3(X13388,X13389,X13390)),X13388))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13390),c_Complete__Lattice_OSup__class_OSup(X13390,X13389)),X13388))|~class_Complete__Lattice_Ocomplete__lattice(X13390))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__least])])])])])). 6.97/7.23 fof(c_0_8019, plain, ![X14681, X14682, X14683]:((~hBOOL(hAPP(hAPP(c_member(X14683),X14681),X14682))|hAPP(c_Finite__Set_Ocard(X14683),hAPP(hAPP(c_Set_Oinsert(X14683),X14681),X14682))=hAPP(c_Finite__Set_Ocard(X14683),X14682)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14683),X14682)))&(hBOOL(hAPP(hAPP(c_member(X14683),X14681),X14682))|hAPP(c_Finite__Set_Ocard(X14683),hAPP(hAPP(c_Set_Oinsert(X14683),X14681),X14682))=hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X14683),X14682))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14683),X14682)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__insert__if])])])])). 6.97/7.23 fof(c_0_8020, plain, ![X7232, X7233, X7234, X7235, X7236, X7237, X7238]:((~hBOOL(hAPP(hAPP(c_member(X7236),X7237),hAPP(c_List_Oset(X7236),X7232)))|~hBOOL(hAPP(X7235,X7237))|hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7236),tc_List_Olist(X7236)),X7233),X7232)!=c_List_Opartition(X7236,X7235,X7234))&(~hBOOL(hAPP(hAPP(c_member(X7236),X7238),hAPP(c_List_Oset(X7236),X7233)))|hBOOL(hAPP(X7235,X7238))|hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7236),tc_List_Olist(X7236)),X7233),X7232)!=c_List_Opartition(X7236,X7235,X7234))), 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])])])])])). 6.97/7.23 fof(c_0_8021, plain, ![X6300, X6301, X6302]:(~class_Rings_Odivision__ring(X6302)|(c_Groups_Ozero__class_Ozero(X6302)=X6301|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6302),hAPP(c_Groups_Ouminus__class_Ouminus(X6302),X6300)),hAPP(c_Groups_Ouminus__class_Ouminus(X6302),X6301))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6302),X6300),X6301))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nonzero__minus__divide__divide])])])). 6.97/7.23 fof(c_0_8022, plain, ![X1535, X1536, X1537]:((hBOOL(hAPP(hAPP(c_member(X1537),esk42_3(X1535,X1536,X1537)),X1536))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1537),X1535),c_Complete__Lattice_OInf__class_OInf(X1537,X1536)))|~class_Complete__Lattice_Ocomplete__lattice(X1537))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1537),X1535),esk42_3(X1535,X1536,X1537)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1537),X1535),c_Complete__Lattice_OInf__class_OInf(X1537,X1536)))|~class_Complete__Lattice_Ocomplete__lattice(X1537))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__greatest])])])])). 6.97/7.23 fof(c_0_8023, plain, ![X17297, X17298, X17299]:(~class_Groups_Oordered__ab__group__add(X17299)|c_SetInterval_Oord__class_OgreaterThanLessThan(X17299,hAPP(c_Groups_Ouminus__class_Ouminus(X17299),X17297),hAPP(c_Groups_Ouminus__class_Ouminus(X17299),X17298))=hAPP(c_Set_Oimage(X17299,X17299,c_Groups_Ouminus__class_Ouminus(X17299)),c_SetInterval_Oord__class_OgreaterThanLessThan(X17299,X17298,X17297))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThanLessThan])])). 6.97/7.23 fof(c_0_8024, plain, ![X12220, X12221, X12222]:(~class_Groups_Oordered__ab__group__add(X12222)|c_SetInterval_Oord__class_OatLeastAtMost(X12222,hAPP(c_Groups_Ouminus__class_Ouminus(X12222),X12220),hAPP(c_Groups_Ouminus__class_Ouminus(X12222),X12221))=hAPP(c_Set_Oimage(X12222,X12222,c_Groups_Ouminus__class_Ouminus(X12222)),c_SetInterval_Oord__class_OatLeastAtMost(X12222,X12221,X12220))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeastAtMost])])). 6.97/7.23 fof(c_0_8025, plain, ![X5015, X5016, X5017, X5018, X5019, X5020]:(~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5020,tc_fun(X5019,tc_HOL_Obool))),X5018),X5017),X5016),X5015))|(hBOOL(hAPP(hAPP(X5018,X5016),X5015))|hBOOL(hAPP(hAPP(X5017,X5016),X5015)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup2E])])])). 6.97/7.23 cnf(c_0_8026, plain, (X4=c_List_Olast(X1,hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4))|c_List_Olist_ONil(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), inference(split_conjunct,[status(thm)],[c_0_5315])). 6.97/7.23 cnf(c_0_8027, 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_4953])). 6.97/7.23 cnf(c_0_8028, 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_5316])). 6.97/7.23 fof(c_0_8029, plain, ![X12476, X12477, X12478]:((hBOOL(hAPP(hAPP(c_member(X12478),X12477),esk410_3(X12476,X12477,X12478)))|~hBOOL(hAPP(hAPP(c_member(X12478),X12477),c_Complete__Lattice_OSup__class_OSup(tc_fun(X12478,tc_HOL_Obool),X12476))))&(hBOOL(hAPP(hAPP(c_member(tc_fun(X12478,tc_HOL_Obool)),esk410_3(X12476,X12477,X12478)),X12476))|~hBOOL(hAPP(hAPP(c_member(X12478),X12477),c_Complete__Lattice_OSup__class_OSup(tc_fun(X12478,tc_HOL_Obool),X12476))))), 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])])])])])). 6.97/7.23 fof(c_0_8030, plain, ![X13510, X13511, X13512]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13512,tc_HOL_Obool)),hAPP(c_Relation_OImage(X13512,X13512,X13511),X13510)),X13510))|X13510=hAPP(c_Relation_OImage(X13512,X13512,c_Transitive__Closure_Ortrancl(X13512,X13511)),X13510)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__closed__trancl])])). 6.97/7.23 fof(c_0_8031, plain, ![X9408, X9409, X9410, X9411, X9412]:((~hBOOL(hAPP(hAPP(c_member(X9412),X9409),X9408))|hBOOL(hAPP(hAPP(c_member(X9411),hAPP(X9410,X9409)),hAPP(c_Set_Oimage(X9412,X9411,X9410),X9408)))|~c_Fun_Oinj__on(X9412,X9411,X9410,c_Orderings_Otop__class_Otop(tc_fun(X9412,tc_HOL_Obool))))&(~hBOOL(hAPP(hAPP(c_member(X9411),hAPP(X9410,X9409)),hAPP(c_Set_Oimage(X9412,X9411,X9410),X9408)))|hBOOL(hAPP(hAPP(c_member(X9412),X9409),X9408))|~c_Fun_Oinj__on(X9412,X9411,X9410,c_Orderings_Otop__class_Otop(tc_fun(X9412,tc_HOL_Obool))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__image__mem__iff])])])). 6.97/7.23 fof(c_0_8032, plain, ![X14999, X15000, X15001]:(~class_Rings_Olinordered__idom(X15001)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15001),c_Groups_Ozero__class_Ozero(X15001)),hAPP(hAPP(c_Power_Opower__class_Opower(X15001),hAPP(c_Groups_Oabs__class_Oabs(X15001),X15000)),X14999)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__le__power__abs])])])). 6.97/7.23 fof(c_0_8033, plain, ![X16058, X16059]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16058),X16059))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16059))|X16058=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X16059),X16058)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X16059),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)),X16059))|X16058=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X16059),X16058)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16058),X16059))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16059),X16058))|X16058=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X16059),X16058)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X16059),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16059),X16058))|X16058=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X16059),X16058)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))))&(((X16058!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X16059),X16058)=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)),X16059))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16059),X16058))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X16059),X16058)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16058),X16059))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X16059),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X16059),X16058)=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])])])). 6.97/7.23 fof(c_0_8034, plain, ![X4552, X4553, X4554, X4555, X4556, X4557]:(~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4557,tc_fun(X4556,tc_HOL_Obool)),X4555),X4554),X4553))|(hBOOL(hAPP(hAPP(X4554,X4552),X4553))|~hBOOL(hAPP(hAPP(c_member(X4557),X4552),X4555)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INF1__E])])])). 6.97/7.23 fof(c_0_8035, plain, ![X17182, X17183, X17184]:(~class_Orderings_Olinorder(X17184)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17184),X17183))|hAPP(hAPP(c_Finite__Set_Ofold(X17184,X17184,c_Orderings_Oord__class_Omax(X17184)),X17182),X17183)=c_Big__Operators_Olinorder__class_OMax(X17184,hAPP(hAPP(c_Set_Oinsert(X17184),X17182),X17183)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max_Oeq__fold__idem_H])])])). 6.97/7.23 cnf(c_0_8036, plain, (hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2))=hAPP(hAPP(c_Power_Opower__class_Opower(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_5317])). 6.97/7.23 fof(c_0_8037, plain, ![X4628, X4629]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4629))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4628))|c_Divides_Odiv__class_Omod(tc_Int_Oint,X4629,X4628)=hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X4629,X4628)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__pos])])). 6.97/7.23 fof(c_0_8038, plain, ![X8548, X8549, X8550]:(~class_Orderings_Olinorder(X8550)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8550),X8549))|c_Big__Operators_Olinorder__class_OMin(X8550,hAPP(hAPP(c_Set_Oinsert(X8550),X8548),X8549))=hAPP(hAPP(c_Finite__Set_Ofold(X8550,X8550,c_Orderings_Oord__class_Omin(X8550)),X8548),X8549))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min_Oeq__fold__idem_H])])])). 6.97/7.23 fof(c_0_8039, plain, ![X11454, X11455, X11456]:(~class_Complete__Lattice_Ocomplete__lattice(X11456)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11456),X11455))|hAPP(hAPP(c_Finite__Set_Ofold(X11456,X11456,c_Lattices_Osemilattice__sup__class_Osup(X11456)),X11454),X11455)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X11456),X11454),c_Complete__Lattice_OSup__class_OSup(X11456,X11455)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Sup__fold__sup])])). 6.97/7.23 fof(c_0_8040, plain, ![X12996, X12997, X12998]:(~class_Orderings_Olinorder(X12998)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12998),X12997))|(~hBOOL(hAPP(hAPP(c_member(X12998),X12996),X12997))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X12998),X12996),c_Big__Operators_Olattice_OSup__fin(X12998,c_Orderings_Oord__class_Omax(X12998),X12997))=X12996))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oinf__Sup__absorb])])])). 6.97/7.23 fof(c_0_8041, plain, ![X11259, X11260, X11261]:(~class_Orderings_Olinorder(X11261)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11261),X11260))|(~hBOOL(hAPP(hAPP(c_member(X11261),X11259),X11260))|X11259=hAPP(hAPP(c_Orderings_Oord__class_Omax(X11261),X11259),c_Big__Operators_Olattice_OInf__fin(X11261,c_Orderings_Oord__class_Omin(X11261),X11260))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup__Inf__absorb])])])). 6.97/7.23 fof(c_0_8042, plain, ![X11178, X11179]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11179),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)),X11178))|hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X11179,X11178))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X11179,X11178))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__neg__pos])])])). 6.97/7.23 fof(c_0_8043, plain, ![X12444, X12445]:(~class_Groups_Ocomm__monoid__add(X12445)|(~hBOOL(hAPP(c_List_Odistinct(X12445),X12444))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12445,X12445),c_COMBI(X12445)),hAPP(c_List_Oset(X12445),X12444))=hAPP(c_List_Omonoid__add__class_Olistsum(X12445),X12444))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__listsum__conv__Setsum])])). 6.97/7.23 cnf(c_0_8044, plain, (hAPP(c_List_Orotate(X2,X1),X3)=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_5318])). 6.97/7.23 fof(c_0_8045, plain, ![X8557, X8558, X8559, X8560, X8561]:(X8561=X8560|hAPP(hAPP(c_List_Onth(X8559),hAPP(hAPP(c_List_Olist__update(X8559,X8558),X8561),X8557)),X8560)=hAPP(hAPP(c_List_Onth(X8559),X8558),X8560)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__list__update__neq])])). 6.97/7.23 fof(c_0_8046, plain, ![X11688, X11689, X11690, X11691, X11692]:((hBOOL(hAPP(hAPP(c_member(X11692),esk393_5(X11688,X11689,X11690,X11691,X11692)),X11690))|~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11692,tc_fun(X11691,tc_HOL_Obool)),X11690),X11689),X11688)))&(hBOOL(hAPP(hAPP(X11689,esk393_5(X11688,X11689,X11690,X11691,X11692)),X11688))|~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11692,tc_fun(X11691,tc_HOL_Obool)),X11690),X11689),X11688)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SUP1__E])])])])])). 6.97/7.23 fof(c_0_8047, plain, ![X16677]:(X16677=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X16677),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)],[inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__0])])])). 6.97/7.23 cnf(c_0_8048, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,esk53_5(X1,X2,X3,X4,X5)))|~hBOOL(hAPP(hAPP(c_member(X4),X2),X5))|~c_Orderings_Oorder__class_Omono(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X3)|c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X4,tc_HOL_Obool),X3)!=X5), inference(split_conjunct,[status(thm)],[c_0_4979])). 6.97/7.23 cnf(c_0_8049, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_List_Olast(tc_Nat_Onat,c_List_Oupt(X1,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5319])). 6.97/7.23 cnf(c_0_8050, 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_5166])). 6.97/7.23 fof(c_0_8051, plain, ![X1246, X1247, X1248, X1249]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1249),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1248)),c_List_OtakeWhile(X1248,X1247,X1246))))|hAPP(hAPP(c_List_Onth(X1248),c_List_OtakeWhile(X1248,X1247,X1246)),X1249)=hAPP(hAPP(c_List_Onth(X1248),X1246),X1249)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_takeWhile__nth])])). 6.97/7.23 fof(c_0_8052, plain, ![X10975, X10976]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10976))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X10976),X10975)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X10976),X10975)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X10976,X10975))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__pos__neg__trivial])])])). 6.97/7.23 fof(c_0_8053, plain, ![X8734, X8735]:(~class_Rings_Olinordered__idom(X8735)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8735),hAPP(c_Groups_Oabs__class_Oabs(X8735),X8734)),hAPP(c_Groups_Oabs__class_Oabs(X8735),X8734))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8735),X8734),X8734)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__mult__self])])])). 6.97/7.23 cnf(c_0_8054, 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_5166])). 6.97/7.23 fof(c_0_8055, plain, ![X12715, X12716, X12717]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12717),c_Groups_Ozero__class_Ozero(X12717)),esk416_3(X12715,X12716,X12717)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12717),X12716),X12715))|~class_Fields_Olinordered__field__inverse__zero(X12717))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12717),esk416_3(X12715,X12716,X12717)),c_Groups_Oone__class_Oone(X12717)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12717),X12716),X12715))|~class_Fields_Olinordered__field__inverse__zero(X12717))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12717),esk416_3(X12715,X12716,X12717)),X12716)),X12715))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12717),X12716),X12715))|~class_Fields_Olinordered__field__inverse__zero(X12717)))), 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])])])])])). 6.97/7.23 fof(c_0_8056, plain, ![X14959, X14960, X14961]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14961),c_Groups_Ozero__class_Ozero(X14961)),esk505_3(X14959,X14960,X14961)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14961),X14960),X14959))|~class_Fields_Olinordered__field(X14961))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14961),X14960),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14961),X14959),esk505_3(X14959,X14960,X14961))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14961),X14960),X14959))|~class_Fields_Olinordered__field(X14961))), 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])])])])])). 6.97/7.23 fof(c_0_8057, plain, ![X13336, X13337, X13338, X13339, X13340, X13341]:(((hBOOL(hAPP(hAPP(X13338,X13337),X13340))|~hBOOL(hAPP(hAPP(c_member(X13341),X13340),c_SetInterval_Oord_OgreaterThanAtMost(X13341,X13339,X13338,X13337,X13336))))&(hBOOL(hAPP(hAPP(X13339,X13340),X13336))|~hBOOL(hAPP(hAPP(c_member(X13341),X13340),c_SetInterval_Oord_OgreaterThanAtMost(X13341,X13339,X13338,X13337,X13336)))))&(~hBOOL(hAPP(hAPP(X13338,X13337),X13340))|~hBOOL(hAPP(hAPP(X13339,X13340),X13336))|hBOOL(hAPP(hAPP(c_member(X13341),X13340),c_SetInterval_Oord_OgreaterThanAtMost(X13341,X13339,X13338,X13337,X13336))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanAtMost__iff])])])). 6.97/7.23 fof(c_0_8058, plain, ![X15157, X15158, X15159, X15160, X15161, X15162]:((~hBOOL(hAPP(hAPP(X15160,X15158),X15161))|~hBOOL(hAPP(hAPP(X15159,X15161),X15157))|hBOOL(hAPP(hAPP(c_member(X15162),X15161),c_SetInterval_Oord_OatLeastLessThan(X15162,X15160,X15159,X15158,X15157))))&((hBOOL(hAPP(hAPP(X15160,X15158),X15161))|~hBOOL(hAPP(hAPP(c_member(X15162),X15161),c_SetInterval_Oord_OatLeastLessThan(X15162,X15160,X15159,X15158,X15157))))&(hBOOL(hAPP(hAPP(X15159,X15161),X15157))|~hBOOL(hAPP(hAPP(c_member(X15162),X15161),c_SetInterval_Oord_OatLeastLessThan(X15162,X15160,X15159,X15158,X15157)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeastLessThan__iff])])])). 6.97/7.23 fof(c_0_8059, plain, ![X13978, X13979, X13980]:(~class_Rings_Oring(X13980)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13980),hAPP(c_Groups_Ouminus__class_Ouminus(X13980),X13979)),hAPP(c_Groups_Ouminus__class_Ouminus(X13980),X13978))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13980),X13979),X13978)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__mult__minus])])])). 6.97/7.23 fof(c_0_8060, plain, ![X718, X719, X720]:((~c_Orderings_Oorder__class_Omono(tc_Nat_Onat,X719,X718)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X719),hAPP(X718,X720)),hAPP(X718,hAPP(c_Nat_OSuc,X720))))|~class_Orderings_Oorder(X719))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X719),hAPP(X718,esk16_2(X718,X719))),hAPP(X718,hAPP(c_Nat_OSuc,esk16_2(X718,X719)))))|c_Orderings_Oorder__class_Omono(tc_Nat_Onat,X719,X718)|~class_Orderings_Oorder(X719))), 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_mono__iff__le__Suc])])])])])])). 6.97/7.23 fof(c_0_8061, plain, ![X9618, X9619]:((~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),X9619),X9618)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X9619))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X9618))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X9619))|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),X9619),X9618))))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X9618|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),X9619),X9618)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff])])])). 6.97/7.23 fof(c_0_8062, plain, ![X15539, X15540, X15541, X15542]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X15542,tc_HOL_Obool)),X15541),X15540))|(~hBOOL(hAPP(hAPP(c_member(X15542),X15539),X15541))|hBOOL(hAPP(hAPP(c_member(X15542),X15539),X15540)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_psubsetD])])])). 6.97/7.23 cnf(c_0_8063, plain, (c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),X1),X2,X3)|c_List_Olist__ex(tc_Nat_Onat,X1,c_List_Oupt(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_5320])). 6.97/7.23 fof(c_0_8064, plain, ![X10617, X10618, X10619]:(~class_Fields_Ofield__inverse__zero(X10619)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10619),X10618),X10617)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10619),hAPP(c_Groups_Ouminus__class_Ouminus(X10619),X10618)),hAPP(c_Groups_Ouminus__class_Ouminus(X10619),X10617))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__divide])])). 6.97/7.23 fof(c_0_8065, plain, ![X14909, X14910]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14910))|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),X14910),X14909)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J])])). 6.97/7.23 fof(c_0_8066, plain, ![X11347, X11348]:(((X11347!=c_Orderings_Obot__class_Obot(tc_fun(X11348,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(X11348),X11347))))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X11348),X11347))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X11348),X11347)))))&(X11347=c_Orderings_Obot__class_Obot(tc_fun(X11348,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11348),X11347))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X11348),X11347))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__gt__0__iff])])])). 6.97/7.23 fof(c_0_8067, plain, ![X11699, X11700, X11701]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11701),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11700)),X11699)))|hAPP(hAPP(c_List_Otake(X11700),X11701),c_List_Obutlast(X11700,X11699))=hAPP(hAPP(c_List_Otake(X11700),X11701),X11699)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__butlast])])). 6.97/7.23 fof(c_0_8068, plain, ![X7438, X7439, X7440, X7442, X7443, X7444, X7445]:(((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk239_3(X7438,X7439,X7440)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X7439),X7438)))|c_List_Oall__interval__nat(X7440,X7439,X7438))&(~hBOOL(hAPP(X7440,esk239_3(X7438,X7439,X7440)))|c_List_Oall__interval__nat(X7440,X7439,X7438)))&(~c_List_Oall__interval__nat(X7444,X7443,X7442)|(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X7445),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X7443),X7442)))|hBOOL(hAPP(X7444,X7445))))), 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__interval__nat__def])])])])])])). 6.97/7.23 fof(c_0_8069, plain, ![X5709, X5710, X5711, X5712]:(~class_Lattices_Osemilattice__inf(X5712)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5712),X5711),X5710))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5712),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5712),X5711),X5709)),X5710)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__infI1])])). 6.97/7.23 fof(c_0_8070, plain, ![X16950, X16951, X16952, X16954, X16955, X16956, X16957]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk569_3(X16950,X16951,X16952)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16952)),X16950)))|c_List_Olist__all(X16952,X16951,X16950))&(~hBOOL(hAPP(X16951,hAPP(hAPP(c_List_Onth(X16952),X16950),esk569_3(X16950,X16951,X16952))))|c_List_Olist__all(X16952,X16951,X16950)))&(~c_List_Olist__all(X16956,X16955,X16954)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16957),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16956)),X16954)))|hBOOL(hAPP(X16955,hAPP(hAPP(c_List_Onth(X16956),X16954),X16957)))))), 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])])])])])])). 6.97/7.23 fof(c_0_8071, plain, ![X16407, X16408, X16409]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16408),X16407))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16409),X16408)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16409),X16407))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X16409))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16409),X16408)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16409),X16407)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16408),X16407))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X16409))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16409),X16408)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16409),X16407))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1])])])). 6.97/7.23 fof(c_0_8072, plain, ![X16533, X16534, X16535, X16536]:(~class_Lattices_Osemilattice__inf(X16536)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16536),X16535),X16534))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16536),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X16536),X16533),X16535)),X16534)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__infI2])])])). 6.97/7.23 fof(c_0_8073, plain, ![X12956, X12957, X12958, X12959]:(~class_Lattices_Osemilattice__inf(X12959)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12959),X12958),X12957))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12959),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X12959),X12958),X12956)),X12957)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI1])])). 6.97/7.23 fof(c_0_8074, plain, ![X14978, X14979, X14980, X14981]:(~class_Lattices_Osemilattice__inf(X14981)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14981),X14980),X14979))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14981),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X14981),X14978),X14980)),X14979)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__infI2])])])). 6.97/7.23 fof(c_0_8075, plain, ![X6010, X6011, X6012, X6013]:(~class_Rings_Ocomm__semiring__1(X6013)|(~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X6013),X6012),X6011))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X6013),X6012),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6013),X6011),X6010))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult2])])). 6.97/7.23 fof(c_0_8076, plain, ![X15315, X15316, X15317]:(hBOOL(hAPP(hAPP(c_member(X15317),X15316),X15315))|hBOOL(hAPP(hAPP(c_member(X15317),X15316),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X15317,tc_HOL_Obool)),X15315)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ComplI])])])). 6.97/7.23 fof(c_0_8077, plain, ![X17079, X17080, X17081, X17082, X17083, X17084, X17085]:((hAPP(c_List_Ofilter(X17081,X17080),X17079)!=X17079|(~hBOOL(hAPP(hAPP(c_member(X17081),X17082),hAPP(c_List_Oset(X17081),X17079)))|hBOOL(hAPP(X17080,X17082))))&((hBOOL(hAPP(hAPP(c_member(X17085),esk578_3(X17083,X17084,X17085)),hAPP(c_List_Oset(X17085),X17083)))|hAPP(c_List_Ofilter(X17085,X17084),X17083)=X17083)&(~hBOOL(hAPP(X17084,esk578_3(X17083,X17084,X17085)))|hAPP(c_List_Ofilter(X17085,X17084),X17083)=X17083))), 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_filter__id__conv])])])])])])). 6.97/7.23 fof(c_0_8078, plain, ![X1625, X1626, X1627]:(~class_Rings_Odivision__ring(X1627)|(c_Groups_Ozero__class_Ozero(X1627)=X1626|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1627),X1625),hAPP(c_Groups_Ouminus__class_Ouminus(X1627),X1626))=hAPP(c_Groups_Ouminus__class_Ouminus(X1627),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1627),X1625),X1626)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__right])])). 6.97/7.23 fof(c_0_8079, plain, ![X2704, X2705, X2706, X2707]:(~class_Rings_Ocomm__semiring__1(X2707)|(~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2707),X2706),X2705))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2707),X2706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2707),X2704),X2705))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult])])). 6.97/7.23 fof(c_0_8080, plain, ![X16126, X16127, X16128, X16129]:(~class_Lattices_Osemilattice__sup(X16129)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16129),X16128),X16127))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16129),X16128),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X16129),X16127),X16126))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__supI1])])])). 6.97/7.23 fof(c_0_8081, plain, ![X3723, X3724, X3725, X3726]:(~class_Lattices_Osemilattice__sup(X3726)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3726),X3725),X3724))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3726),X3725),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3726),X3723),X3724))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__supI2])])])). 6.97/7.23 fof(c_0_8082, plain, ![X6571, X6572, X6573, X6574]:(~class_Lattices_Osemilattice__sup(X6574)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6574),X6573),X6572))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6574),X6573),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6574),X6572),X6571))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__supI1])])])). 6.97/7.23 fof(c_0_8083, plain, ![X12762, X12763, X12764, X12765, X12766]:(~class_Orderings_Olinorder(X12766)|(~hBOOL(hAPP(hAPP(c_member(X12766),hAPP(X12765,X12764)),hAPP(c_Set_Oimage(X12763,X12766,X12765),hAPP(c_List_Oset(X12763),X12762))))|X12762=c_List_Olinorder__class_Oinsort__insert__key(X12763,X12766,X12765,X12764,X12762))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insort__insert__key__triv])])])). 6.97/7.23 fof(c_0_8084, plain, ![X14111, X14112, X14113, X14114]:(~class_Lattices_Osemilattice__sup(X14114)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14114),X14113),X14112))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14114),X14113),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X14114),X14111),X14112))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__supI2])])])). 6.97/7.23 fof(c_0_8085, plain, ![X10124, X10125, X10126]:(~class_Orderings_Olinorder(X10126)|hAPP(hAPP(c_Set_Oinsert(X10126),X10125),hAPP(c_List_Oset(X10126),X10124))=hAPP(c_List_Oset(X10126),c_List_Olinorder__class_Oinsort__insert__key(X10126,X10126,c_COMBI(X10126),X10125,X10124))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__insort__insert])])). 6.97/7.23 fof(c_0_8086, plain, ![X6991, X6992, X6993]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X6993),X6991))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6993),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6993,tc_HOL_Obool)),X6992),X6991))))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X6993),X6992))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6993),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6993,tc_HOL_Obool)),X6992),X6991)))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6993),X6991))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6993),X6992))|hBOOL(hAPP(c_Finite__Set_Ofinite(X6993),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6993,tc_HOL_Obool)),X6992),X6991))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Un])])])). 6.97/7.23 cnf(c_0_8087, 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_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(X2)), inference(split_conjunct,[status(thm)],[c_0_5321])). 6.97/7.23 cnf(c_0_8088, 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_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)), inference(split_conjunct,[status(thm)],[c_0_5322])). 6.97/7.23 cnf(c_0_8089, 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_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(X2)), inference(split_conjunct,[status(thm)],[c_0_5323])). 6.97/7.23 cnf(c_0_8090, 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_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)), inference(split_conjunct,[status(thm)],[c_0_5324])). 6.97/7.23 fof(c_0_8091, plain, ![X5252, X5253]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5253),X5252))|hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5252),X5253))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X5252)),X5253)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Suc__diff__le])])])). 6.97/7.23 fof(c_0_8092, plain, ![X8601, X8602, X8603, X8604, X8605, X8606]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X8606,X8605)),hAPP(hAPP(c_Product__Type_OPair(X8606,X8605),X8604),X8603)),hAPP(hAPP(c_Product__Type_OSigma(X8606,X8605),X8602),X8601)))|hBOOL(hAPP(hAPP(c_member(X8606),X8604),X8602))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaD1])])). 6.97/7.23 fof(c_0_8093, plain, ![X14488, X14489, X14490, X14491, X14492]:(~hBOOL(hAPP(hAPP(c_member(X14492),X14491),hAPP(c_Set_Oimage(X14490,X14492,X14489),X14488)))|hAPP(X14489,hAPP(c_Hilbert__Choice_Oinv__into(X14490,X14492,X14488,X14489),X14491))=X14491), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_f__inv__into__f])])])). 6.97/7.23 cnf(c_0_8094, 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_5218])). 6.97/7.23 fof(c_0_8095, plain, ![X10625]:(~class_Rings_Olinordered__semidom(X10625)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10625),c_Groups_Ozero__class_Ozero(X10625)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10625),c_Groups_Oone__class_Oone(X10625)),c_Groups_Oone__class_Oone(X10625))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])])). 6.97/7.23 fof(c_0_8096, plain, ![X14723, X14724, X14725, X14726]:(~class_Orderings_Opreorder(X14726)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14726),X14725),X14724))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14726),X14724),X14723))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14726),X14725),X14723))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__trans])])])). 6.97/7.23 cnf(c_0_8097, 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_5313])). 6.97/7.23 fof(c_0_8098, plain, ![X12965, X12966, X12967, X12968]:(~class_Orderings_Opreorder(X12968)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12968),X12967),X12966))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12968),X12966),X12965))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12968),X12967),X12965))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__le__less__trans])])])). 6.97/7.23 fof(c_0_8099, plain, ![X14621, X14622, X14623, X14624]:(~class_Orderings_Opreorder(X14624)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14624),X14623),X14622))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14624),X14622),X14621))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14624),X14623),X14621))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__le__trans])])])). 6.97/7.23 fof(c_0_8100, plain, ![X15884, X15885, X15886, X15887]:(~class_Orderings_Oorder(X15887)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15887),X15886),X15885))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15887),X15884),X15886))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15887),X15884),X15885))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_xt1_I10_J])])])). 6.97/7.23 fof(c_0_8101, plain, ![X13053, X13054, X13055, X13056]:(~class_Orderings_Oorder(X13056)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13056),X13055),X13054))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13056),X13053),X13055))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13056),X13053),X13054))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_xt1_I8_J])])])). 6.97/7.23 fof(c_0_8102, plain, ![X15102, X15103, X15104, X15105]:(~c_Fun_Oinj__on(X15105,X15104,X15103,c_Orderings_Otop__class_Otop(tc_fun(X15105,tc_HOL_Obool)))|hAPP(c_Fun_Othe__inv__into(X15105,X15104,c_Orderings_Otop__class_Otop(tc_fun(X15105,tc_HOL_Obool)),X15103),hAPP(X15103,X15102))=X15102), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_the__inv__f__f])])])). 6.97/7.23 fof(c_0_8103, plain, ![X752, X753, X754, X755]:(~c_Fun_Oinj__on(X755,X754,X753,c_Orderings_Otop__class_Otop(tc_fun(X755,tc_HOL_Obool)))|hAPP(c_Hilbert__Choice_Oinv__into(X755,X754,c_Orderings_Otop__class_Otop(tc_fun(X755,tc_HOL_Obool)),X753),hAPP(X753,X752))=X752), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inv__f__f])])])). 6.97/7.23 fof(c_0_8104, plain, ![X17132, X17133, X17134]:(c_List_Olist_ONil(X17133)=X17134|hAPP(c_List_Otl(X17133),hAPP(hAPP(c_List_Oappend(X17133),X17134),X17132))=hAPP(hAPP(c_List_Oappend(X17133),hAPP(c_List_Otl(X17133),X17134)),X17132)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_tl__append2])])])). 6.97/7.23 fof(c_0_8105, plain, ![X2048, X2049, X2050, X2051]:(~class_Orderings_Oorder(X2051)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2051),X2050),X2049))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2051),X2048),X2050))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2051),X2048),X2049))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_xt1_I7_J])])])). 6.97/7.23 fof(c_0_8106, plain, ![X15006, X15007, X15008, X15009]:(~class_Orderings_Opreorder(X15009)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15009),X15008),X15007))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15009),X15007),X15006))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15009),X15008),X15006))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__trans])])])). 6.97/7.23 fof(c_0_8107, plain, ![X10822, X10823, X10824, X10825]:(~class_Orderings_Oorder(X10825)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10825),X10824),X10823))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10825),X10822),X10824))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10825),X10822),X10823))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_xt1_I6_J])])])). 6.97/7.23 fof(c_0_8108, plain, ![X8029, X8030, X8031]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8031),X8029),X8030))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8031),X8030),X8029))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8031),X8030),X8029))|~class_Orderings_Opreorder(X8031))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8031),X8029),X8030))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8031),X8030),X8029))|~class_Orderings_Opreorder(X8031))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8031),X8030),X8029))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8031),X8030),X8029))|~class_Orderings_Opreorder(X8031)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__le__not__le])])])])). 6.97/7.23 cnf(c_0_8109, plain, (c_Fun_Oinj__on(X1,X2,esk502_4(X3,X2,X1,X4),X4)|X4=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(c_Set_Oimage(X2,X1,X5),X3)!=X4), inference(split_conjunct,[status(thm)],[c_0_5128])). 6.97/7.23 cnf(c_0_8110, 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_5325])). 6.97/7.23 fof(c_0_8111, plain, ![X8411, X8412]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8412),X8411))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X8412),X8411)),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),X8412),X8411)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8412),X8411)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__bin__lemma])])). 6.97/7.23 fof(c_0_8112, plain, ![X6643, X6644, X6645]:(~class_Rings_Odivision__ring(X6645)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6645),hAPP(c_Groups_Ouminus__class_Ouminus(X6645),X6644)),X6643)=hAPP(c_Groups_Ouminus__class_Ouminus(X6645),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6645),X6644),X6643))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__divide__left])])])). 6.97/7.23 fof(c_0_8113, plain, ![X15635, X15636, X15637]:(~class_Rings_Oring(X15637)|hAPP(c_Groups_Ouminus__class_Ouminus(X15637),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15637),X15636),X15635))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15637),hAPP(c_Groups_Ouminus__class_Ouminus(X15637),X15636)),X15635)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__left])])). 6.97/7.23 fof(c_0_8114, plain, ![X9029, X9030, X9031]:(~class_Rings_Oring(X9031)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9031),hAPP(c_Groups_Ouminus__class_Ouminus(X9031),X9030)),X9029)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9031),X9030),hAPP(c_Groups_Ouminus__class_Ouminus(X9031),X9029))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__mult__commute])])])). 6.97/7.23 fof(c_0_8115, plain, ![X1547, X1548, X1549]:(~class_Orderings_Olinorder(X1549)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1549),X1548),X1547))|(X1547=X1548|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1549),X1547),X1548))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__cases])])])). 6.97/7.23 fof(c_0_8116, plain, ![X4926, X4927]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4927),X4926))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4927)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4926))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4927)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4926)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4927),X4926)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I2_J])])). 6.97/7.23 fof(c_0_8117, plain, ![X6693, X6694]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6694)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6693)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6694),X6693)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6694),X6693))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6694)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6693))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I3_J])])). 6.97/7.23 cnf(c_0_8118, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[c_0_5326, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.23 cnf(c_0_8119, 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_5230])). 6.97/7.23 fof(c_0_8120, plain, ![X14546, X14547, X14548, X14549, X14550, X14551]:((~hBOOL(hAPP(c_List_Odistinct(X14547),X14546))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14548),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14547)),X14546)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14549),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14547)),X14546)))|(X14549=X14548|hAPP(hAPP(c_List_Onth(X14547),X14546),X14548)!=hAPP(hAPP(c_List_Onth(X14547),X14546),X14549)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk491_2(X14550,X14551)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14551)),X14550)))|hBOOL(hAPP(c_List_Odistinct(X14551),X14550)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk492_2(X14550,X14551)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14551)),X14550)))|hBOOL(hAPP(c_List_Odistinct(X14551),X14550)))&((esk492_2(X14550,X14551)!=esk491_2(X14550,X14551)|hBOOL(hAPP(c_List_Odistinct(X14551),X14550)))&(hAPP(hAPP(c_List_Onth(X14551),X14550),esk491_2(X14550,X14551))=hAPP(hAPP(c_List_Onth(X14551),X14550),esk492_2(X14550,X14551))|hBOOL(hAPP(c_List_Odistinct(X14551),X14550))))))), 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])])])])])])])). 6.97/7.23 cnf(c_0_8121, 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))))|c_Groups_Ozero__class_Ozero(X1)!=X3|X2!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_5327])). 6.97/7.23 fof(c_0_8122, plain, ![X14414, X14415]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14414),X14415))|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),X14415),X14414))))&(~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),X14415),X14414)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14414),X14415)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__diff])])). 6.97/7.23 cnf(c_0_8123, 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_5328])). 6.97/7.23 fof(c_0_8124, plain, ![X5649, X5650, X5651]:(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5651)),X5650),c_List_Olists(X5651,c_Wellfounded_Oacc(X5651,X5649))))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5651)),X5650),c_Wellfounded_Oacc(tc_List_Olist(X5651),c_List_Olistrel1(X5651,X5649))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__accD])])). 6.97/7.23 fof(c_0_8125, plain, ![X7805, X7806, X7807]:(~class_Rings_Olinordered__idom(X7807)|(X7806=X7805|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7807),X7806),X7805))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7807),X7805),X7806))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom])])])). 6.97/7.23 cnf(c_0_8126, 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_5329])). 6.97/7.23 cnf(c_0_8127, 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_5330])). 6.97/7.23 cnf(c_0_8128, 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_5294])). 6.97/7.23 fof(c_0_8129, plain, ![X5984, X5985, X5987, X5988]:((~hBOOL(hAPP(X5984,X5985))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5985))|hBOOL(hAPP(X5984,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk200_1(X5984)))))&((hBOOL(hAPP(X5987,esk201_1(X5987)))|~hBOOL(hAPP(X5987,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5988))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk201_1(X5987)))|~hBOOL(hAPP(X5987,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5988)))))), 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])])])])])])). 6.97/7.23 fof(c_0_8130, plain, ![X9919, X9920, X9921]:(~class_Rings_Olinordered__idom(X9921)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9921),c_Groups_Osgn__class_Osgn(X9921,X9920)),c_Groups_Osgn__class_Osgn(X9921,X9919))=c_Groups_Osgn__class_Osgn(X9921,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9921),X9920),X9919))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sgn__times])])])). 6.97/7.23 fof(c_0_8131, plain, ![X13788, X13789, X13790, X13791, X13792]:(~class_Orderings_Olinorder(X13792)|(~c_List_Olinorder__class_Osorted(X13792,hAPP(hAPP(c_List_Omap(X13791,X13792),X13790),X13789))|c_List_Olinorder__class_Osorted(X13792,hAPP(hAPP(c_List_Omap(X13791,X13792),X13790),c_List_Oremove1(X13791,X13788,X13789))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__map__remove1])])])). 6.97/7.23 cnf(c_0_8132, plain, (X1=c_List_Olist_ONil(X2)|hAPP(hAPP(c_List_Oappend(X2),X4),hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2)))=X1|c_List_Olast(X2,X1)!=X3|c_List_Obutlast(X2,X1)!=X4), inference(split_conjunct,[status(thm)],[c_0_5331])). 6.97/7.23 fof(c_0_8133, plain, ![X2107, X2108, X2109, X2110]:((~hBOOL(hAPP(c_List_Olistsp(X2110,X2109),X2107))|~hBOOL(hAPP(c_List_Olistsp(X2110,X2109),X2108))|hBOOL(hAPP(c_List_Olistsp(X2110,X2109),hAPP(hAPP(c_List_Oappend(X2110),X2108),X2107))))&((hBOOL(hAPP(c_List_Olistsp(X2110,X2109),X2107))|~hBOOL(hAPP(c_List_Olistsp(X2110,X2109),hAPP(hAPP(c_List_Oappend(X2110),X2108),X2107))))&(hBOOL(hAPP(c_List_Olistsp(X2110,X2109),X2108))|~hBOOL(hAPP(c_List_Olistsp(X2110,X2109),hAPP(hAPP(c_List_Oappend(X2110),X2108),X2107)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__in__listsp__conv])])])). 6.97/7.23 fof(c_0_8134, plain, ![X2084, X2085, X2086]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2086),X2085))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2085),X2084))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2086),X2084)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__trans])])). 6.97/7.23 fof(c_0_8135, plain, ![X1906, X1907, X1908]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1908),X1907))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1907),X1906))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1908),X1906)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])])). 6.97/7.23 fof(c_0_8136, plain, ![X9310, X9311, X9312, X9313]:(~class_Orderings_Olinorder(X9313)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9313),X9312),X9311))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9313),hAPP(hAPP(c_Orderings_Oord__class_Omin(X9313),X9310),X9312)),X9311)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ole__infI2])])])). 6.97/7.23 fof(c_0_8137, plain, ![X14811, X14812, X14813]:(~class_Rings_Oring(X14813)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14813),X14812),hAPP(c_Groups_Ouminus__class_Ouminus(X14813),X14811))=hAPP(c_Groups_Ouminus__class_Ouminus(X14813),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14813),X14812),X14811))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__mult__right])])])). 6.97/7.23 fof(c_0_8138, plain, ![X2233, X2234, X2235, X2236]:(~class_Orderings_Olinorder(X2236)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2236),X2235),X2234))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2236),X2235),hAPP(hAPP(c_Orderings_Oord__class_Omax(X2236),X2234),X2233))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oless__supI1])])])). 6.97/7.23 fof(c_0_8139, plain, ![X1950, X1951, X1952, X1953]:(~class_Orderings_Olinorder(X1953)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1953),X1952),X1951))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1953),X1952),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1953),X1950),X1951))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oless__supI2])])])). 6.97/7.23 fof(c_0_8140, plain, ![X5785, X5786, X5787, X5788, X5789]:((~c_Fun_Obij__betw(X5788,X5786,X5789,X5787,X5785)|hAPP(c_Finite__Set_Ocard(X5786),X5785)=hAPP(c_Finite__Set_Ocard(X5788),X5787)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5786),X5785))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5788),X5787)))&(hAPP(c_Finite__Set_Ocard(X5786),X5785)!=hAPP(c_Finite__Set_Ocard(X5788),X5787)|c_Fun_Obij__betw(X5788,X5786,esk189_4(X5785,X5786,X5787,X5788),X5787,X5785)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5786),X5785))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5788),X5787)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_BIJ])])])])])). 6.97/7.23 cnf(c_0_8141, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk231_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_5134])). 6.97/7.23 fof(c_0_8142, plain, ![X364, X365, X366, X367]:((~hBOOL(hAPP(X367,X366))|hAPP(hAPP(c_List_Olist_OCons(X365),X366),c_List_OtakeWhile(X365,X367,X364))=c_List_OtakeWhile(X365,X367,hAPP(hAPP(c_List_Olist_OCons(X365),X366),X364)))&(hBOOL(hAPP(X367,X366))|c_List_OtakeWhile(X365,X367,hAPP(hAPP(c_List_Olist_OCons(X365),X366),X364))=c_List_Olist_ONil(X365))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_takeWhile_Osimps_I2_J])])])). 6.97/7.23 fof(c_0_8143, plain, ![X7337, X7338, X7339]:(~class_Fields_Ofield__inverse__zero(X7339)|hAPP(c_Groups_Ouminus__class_Ouminus(X7339),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7339),X7338),X7337))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7339),X7338),hAPP(c_Groups_Ouminus__class_Ouminus(X7339),X7337))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__right])])). 6.97/7.23 fof(c_0_8144, plain, ![X1699, X1700, X1701, X1702]:(~class_Orderings_Olinorder(X1702)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1702),X1701),X1700))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1702),X1701),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1702),X1699),X1700))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supI2])])). 6.97/7.23 cnf(c_0_8145, 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_5129])). 6.97/7.23 cnf(c_0_8146, 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_5332])). 6.97/7.23 fof(c_0_8147, plain, ![X1497, X1498, X1499]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1499,tc_HOL_Obool)),X1498),X1497))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1499,tc_HOL_Obool)),X1498),hAPP(c_Set_OPow(X1499),X1497)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_PowI])])])). 6.97/7.23 cnf(c_0_8148, 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_5238])). 6.97/7.23 fof(c_0_8149, plain, ![X10729, X10730, X10731]:((hBOOL(hAPP(hAPP(c_member(X10731),esk356_3(X10729,X10730,X10731)),X10730))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10731,tc_HOL_Obool)),X10730),X10729)))&(~hBOOL(hAPP(hAPP(c_member(X10731),esk356_3(X10729,X10730,X10731)),X10729))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10731,tc_HOL_Obool)),X10730),X10729)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_subsetI])])])])])). 6.97/7.23 cnf(c_0_8150, plain, (c_Divides_OnegDivAlg(X2,X1)=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))|~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_4509])). 6.97/7.23 fof(c_0_8151, plain, ![X9700, X9701]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9701))|c_SMT_Oz3div(X9700,X9701)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X9700),X9701))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9701))|c_SMT_Oz3div(X9700,X9701)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X9700),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X9701))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_z3div__def])])])). 6.97/7.23 cnf(c_0_8152, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_5333, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.23 cnf(c_0_8153, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_5334, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.23 cnf(c_0_8154, 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_5241])). 6.97/7.23 cnf(c_0_8155, 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_Ominus__class_Ominus(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_5335, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.23 fof(c_0_8156, plain, ![X8374, X8375]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8375),X8374))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X8375),X8374),X8374)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X8375,X8374)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__geq])])])). 6.97/7.23 cnf(c_0_8157, plain, (c_Fun_Obij__betw(X1,X2,X3,X6,X7)|~c_Fun_Obij__betw(X1,X2,X3,X4,X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X6),X4))|hAPP(c_Set_Oimage(X1,X2,X3),X6)!=X7), inference(split_conjunct,[status(thm)],[c_0_5336])). 6.97/7.23 cnf(c_0_8158, 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_5245])). 6.97/7.23 cnf(c_0_8159, 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_5247])). 6.97/7.23 cnf(c_0_8160, 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_Ominus__class_Ominus(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_5337, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.23 fof(c_0_8161, plain, ![X9415, X9416]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9416),X9415))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9415),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X9416),X9415))=X9416), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__diff__inverse])])])). 6.97/7.23 fof(c_0_8162, plain, ![X12300, X12301, X12302, X12303, X12304, X12305, X12306]:((~c_List_Olist__all2(X12306,X12304,X12302,X12305,X12303)|~c_List_Olist__all2(X12306,X12304,X12302,X12301,X12300)|c_List_Olist__all2(X12306,X12304,X12302,hAPP(hAPP(c_List_Oappend(X12306),X12305),X12301),hAPP(hAPP(c_List_Oappend(X12304),X12303),X12300))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12304)),X12303)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12306)),X12305))&((c_List_Olist__all2(X12306,X12304,X12302,X12305,X12303)|~c_List_Olist__all2(X12306,X12304,X12302,hAPP(hAPP(c_List_Oappend(X12306),X12305),X12301),hAPP(hAPP(c_List_Oappend(X12304),X12303),X12300))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12304)),X12303)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12306)),X12305))&(c_List_Olist__all2(X12306,X12304,X12302,X12301,X12300)|~c_List_Olist__all2(X12306,X12304,X12302,hAPP(hAPP(c_List_Oappend(X12306),X12305),X12301),hAPP(hAPP(c_List_Oappend(X12304),X12303),X12300))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12304)),X12303)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12306)),X12305)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__append])])])). 6.97/7.23 fof(c_0_8163, plain, ![X12106, X12107, X12108, X12110, X12111, X12112, X12113]:(((hBOOL(hAPP(hAPP(c_member(X12108),esk405_3(X12106,X12107,X12108)),hAPP(c_List_Oset(X12108),X12106)))|c_List_OtakeWhile(X12108,X12107,X12106)=X12106)&(~hBOOL(hAPP(X12107,esk405_3(X12106,X12107,X12108)))|c_List_OtakeWhile(X12108,X12107,X12106)=X12106))&(c_List_OtakeWhile(X12112,X12111,X12110)!=X12110|(~hBOOL(hAPP(hAPP(c_member(X12112),X12113),hAPP(c_List_Oset(X12112),X12110)))|hBOOL(hAPP(X12111,X12113))))), 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_takeWhile__eq__all__conv])])])])])])])). 6.97/7.23 fof(c_0_8164, plain, ![X2451, X2452, X2453]:(~class_Lattices_Oab__semigroup__idem__mult(X2453)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2453),X2452),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2453),X2452),X2451))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2453),X2452),X2451)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__idem])])). 6.97/7.23 cnf(c_0_8165, 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_Ominus__class_Ominus(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_5338, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.23 cnf(c_0_8166, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X1=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk116_2(X1,X2))|hBOOL(hAPP(X2,hAPP(c_Int_Onat,X1)))), inference(split_conjunct,[status(thm)],[c_0_5339])). 6.97/7.23 fof(c_0_8167, plain, ![X4222, X4223, X4224, X4225, X4226]:(~c_Fun_Oinj__on(X4226,X4225,X4224,X4223)|(~c_Fun_Oinj__on(X4226,X4225,X4224,X4222)|c_Fun_Oinj__on(X4226,X4225,X4224,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4226,tc_HOL_Obool)),X4223),X4222)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__Int])])])). 6.97/7.23 fof(c_0_8168, plain, ![X1734, X1735]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1735),c_Orderings_Otop__class_Otop(tc_fun(X1735,tc_HOL_Obool))))|(~c_Fun_Oinj__on(X1735,X1735,X1734,c_Orderings_Otop__class_Otop(tc_fun(X1735,tc_HOL_Obool)))|hAPP(c_Set_Oimage(X1735,X1735,X1734),c_Orderings_Otop__class_Otop(tc_fun(X1735,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X1735,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__UNIV__inj__surj])])])). 6.97/7.23 fof(c_0_8169, plain, ![X17105, X17106]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17106),c_Orderings_Otop__class_Otop(tc_fun(X17106,tc_HOL_Obool))))|(hAPP(c_Set_Oimage(X17106,X17106,X17105),c_Orderings_Otop__class_Otop(tc_fun(X17106,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X17106,tc_HOL_Obool))|c_Fun_Oinj__on(X17106,X17106,X17105,c_Orderings_Otop__class_Otop(tc_fun(X17106,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__UNIV__surj__inj])])])). 6.97/7.23 fof(c_0_8170, plain, ![X2315, X2316, X2317]:(~class_Groups_Ogroup__add(X2317)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2317),X2316),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2317),hAPP(c_Groups_Ouminus__class_Ouminus(X2317),X2316)),X2315))=X2315), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__minus__cancel])])])). 6.97/7.23 cnf(c_0_8171, 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_5157])). 6.97/7.23 fof(c_0_8172, plain, ![X6027, X6028, X6029]:(~class_Groups_Ogroup__add(X6029)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6029),hAPP(c_Groups_Ouminus__class_Ouminus(X6029),X6028)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6029),X6028),X6027))=X6027), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__cancel])])). 6.97/7.23 fof(c_0_8173, plain, ![X9015, X9016, X9017, X9018, X9020]:(((hBOOL(hAPP(X9015,esk297_3(X9015,X9016,X9017)))|~hBOOL(hAPP(X9015,X9018))|~c_Equiv__Relations_Oequivp(X9017,X9016))&(hBOOL(hAPP(hAPP(c_member(X9017),esk297_3(X9015,X9016,X9017)),c_Quotient_ORespects(X9017,X9016)))|~hBOOL(hAPP(X9015,X9018))|~c_Equiv__Relations_Oequivp(X9017,X9016)))&(~hBOOL(hAPP(X9015,X9020))|~hBOOL(hAPP(hAPP(c_member(X9017),X9020),c_Quotient_ORespects(X9017,X9016)))|hBOOL(hAPP(X9015,esk298_3(X9015,X9016,X9017)))|~c_Equiv__Relations_Oequivp(X9017,X9016))), 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_bex__reg__eqv])])])])])])). 6.97/7.23 fof(c_0_8174, plain, ![X10224, X10225, X10226]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X10226),esk334_3(X10224,X10225,X10226)))|hBOOL(hAPP(X10224,X10225))|~hBOOL(hAPP(X10224,c_Orderings_Obot__class_Obot(tc_fun(X10226,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10226),X10225)))&((~hBOOL(hAPP(hAPP(c_member(X10226),esk333_3(X10224,X10225,X10226)),esk334_3(X10224,X10225,X10226)))|hBOOL(hAPP(X10224,X10225))|~hBOOL(hAPP(X10224,c_Orderings_Obot__class_Obot(tc_fun(X10226,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10226),X10225)))&((hBOOL(hAPP(X10224,esk334_3(X10224,X10225,X10226)))|hBOOL(hAPP(X10224,X10225))|~hBOOL(hAPP(X10224,c_Orderings_Obot__class_Obot(tc_fun(X10226,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10226),X10225)))&(~hBOOL(hAPP(X10224,hAPP(hAPP(c_Set_Oinsert(X10226),esk333_3(X10224,X10225,X10226)),esk334_3(X10224,X10225,X10226))))|hBOOL(hAPP(X10224,X10225))|~hBOOL(hAPP(X10224,c_Orderings_Obot__class_Obot(tc_fun(X10226,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10226),X10225)))))), 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])])])])])). 6.97/7.23 fof(c_0_8175, plain, ![X4921, X4922, X4923]:(~class_Lattices_Osemilattice__sup(X4923)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4923),X4922),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4923),X4922),X4921))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4923),X4922),X4921)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup_Oleft__idem])])])). 6.97/7.23 fof(c_0_8176, plain, ![X14663, X14664]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14664),hAPP(c_Groups_Ouminus__class_Ouminus(X14664),X14663)),c_Groups_Ozero__class_Ozero(X14664)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14664),c_Groups_Ozero__class_Ozero(X14664)),X14663))|~class_Groups_Oordered__ab__group__add(X14664))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14664),c_Groups_Ozero__class_Ozero(X14664)),X14663))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14664),hAPP(c_Groups_Ouminus__class_Ouminus(X14664),X14663)),c_Groups_Ozero__class_Ozero(X14664)))|~class_Groups_Oordered__ab__group__add(X14664))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__0__iff__less])])])). 6.97/7.23 fof(c_0_8177, plain, ![X15674, X15675]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15675),hAPP(c_Groups_Ouminus__class_Ouminus(X15675),X15674)),c_Groups_Ozero__class_Ozero(X15675)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15675),c_Groups_Ozero__class_Ozero(X15675)),X15674))|~class_Groups_Oordered__ab__group__add(X15675))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15675),c_Groups_Ozero__class_Ozero(X15675)),X15674))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15675),hAPP(c_Groups_Ouminus__class_Ouminus(X15675),X15674)),c_Groups_Ozero__class_Ozero(X15675)))|~class_Groups_Oordered__ab__group__add(X15675))), 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])])])])). 6.97/7.23 fof(c_0_8178, plain, ![X17065, X17066]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17066),c_Groups_Ozero__class_Ozero(X17066)),hAPP(c_Groups_Ouminus__class_Ouminus(X17066),X17065)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17066),X17065),c_Groups_Ozero__class_Ozero(X17066)))|~class_Groups_Oordered__ab__group__add(X17066))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17066),X17065),c_Groups_Ozero__class_Ozero(X17066)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17066),c_Groups_Ozero__class_Ozero(X17066)),hAPP(c_Groups_Ouminus__class_Ouminus(X17066),X17065)))|~class_Groups_Oordered__ab__group__add(X17066))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__0__less__iff__less])])])])). 6.97/7.23 fof(c_0_8179, plain, ![X12442, X12443]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12443),X12442),c_Groups_Ozero__class_Ozero(X12443)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12443),c_Groups_Ozero__class_Ozero(X12443)),hAPP(c_Groups_Ouminus__class_Ouminus(X12443),X12442)))|~class_Groups_Oordered__ab__group__add(X12443))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12443),c_Groups_Ozero__class_Ozero(X12443)),hAPP(c_Groups_Ouminus__class_Ouminus(X12443),X12442)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12443),X12442),c_Groups_Ozero__class_Ozero(X12443)))|~class_Groups_Oordered__ab__group__add(X12443))), 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])])])])). 6.97/7.23 fof(c_0_8180, plain, ![X7570, X7571, X7572, X7573, X7574, X7575, X7576, X7577]:(~c_Equiv__Relations_Oequiv(X7577,X7576,X7575)|(~c_Equiv__Relations_Ocongruent2(X7577,X7574,X7573,X7575,X7572,X7571)|(~hBOOL(hAPP(hAPP(c_member(X7577),X7570),X7576))|c_Equiv__Relations_Ocongruent(X7574,X7573,X7572,hAPP(X7571,X7570))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_congruent2__implies__congruent])])])). 6.97/7.23 fof(c_0_8181, plain, ![X6929, X6930, X6931]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6931),X6930))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6931,tc_HOL_Obool)),hAPP(c_Set_Oimage(X6931,X6931,X6929),X6930)),X6930))|(~c_Fun_Oinj__on(X6931,X6931,X6929,X6930)|X6930=hAPP(c_Set_Oimage(X6931,X6931,X6929),X6930)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_endo__inj__surj])])])). 6.97/7.23 fof(c_0_8182, plain, ![X17229, X17230, X17231]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X17231,X17231),tc_HOL_Obool)),X17230),X17229))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X17231,X17231),tc_HOL_Obool)),X17229),c_Transitive__Closure_Ortrancl(X17231,X17230)))|c_Transitive__Closure_Ortrancl(X17231,X17230)=c_Transitive__Closure_Ortrancl(X17231,X17229))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__subset])])). 6.97/7.23 fof(c_0_8183, plain, ![X17368, X17369, X17370]:(~class_Lattices_Olattice(X17370)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17370),X17369),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17370),X17369),X17368))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17370),X17369),X17368)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I8_J])])). 6.97/7.23 fof(c_0_8184, plain, ![X1050, X1051]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1050))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1051),c_Groups_Ozero__class_Ozero(X1051)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1051),X1050)))|~class_Rings_Olinordered__semidom(X1051))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1051),c_Groups_Ozero__class_Ozero(X1051)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1051),X1050)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1050))|~class_Rings_Olinordered__semidom(X1051))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__0__less__iff])])])])). 6.97/7.23 fof(c_0_8185, plain, ![X402, X403]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk4_2(X402,X403)),esk5_2(X402,X403)))|c_List_Olinorder__class_Osorted(X403,X402)|~class_Orderings_Olinorder(X403))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk5_2(X402,X403)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X403)),X402)))|c_List_Olinorder__class_Osorted(X403,X402)|~class_Orderings_Olinorder(X403))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X403),hAPP(hAPP(c_List_Onth(X403),X402),esk4_2(X402,X403))),hAPP(hAPP(c_List_Onth(X403),X402),esk5_2(X402,X403))))|c_List_Olinorder__class_Osorted(X403,X402)|~class_Orderings_Olinorder(X403)))), 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])])])])])). 6.97/7.23 cnf(c_0_8186, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=hAPP(c_Int_Onumber__class_Onumber__of(X2),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_5314])). 6.97/7.23 fof(c_0_8187, plain, ![X15993, X15994, X15995, X15996, X15997]:((~hBOOL(hAPP(hAPP(X15995,X15996),X15993))|~hBOOL(hAPP(hAPP(X15995,X15994),X15996))|hBOOL(hAPP(hAPP(c_member(X15997),X15996),c_SetInterval_Oord_OatLeastAtMost(X15997,X15995,X15994,X15993))))&((hBOOL(hAPP(hAPP(X15995,X15996),X15993))|~hBOOL(hAPP(hAPP(c_member(X15997),X15996),c_SetInterval_Oord_OatLeastAtMost(X15997,X15995,X15994,X15993))))&(hBOOL(hAPP(hAPP(X15995,X15994),X15996))|~hBOOL(hAPP(hAPP(c_member(X15997),X15996),c_SetInterval_Oord_OatLeastAtMost(X15997,X15995,X15994,X15993)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeastAtMost__iff])])])). 6.97/7.23 fof(c_0_8188, plain, ![X6140, X6141, X6142, X6143, X6144]:(((hBOOL(hAPP(hAPP(X6142,X6143),X6140))|~hBOOL(hAPP(hAPP(c_member(X6144),X6143),c_SetInterval_Oord_OgreaterThanLessThan(X6144,X6142,X6141,X6140))))&(hBOOL(hAPP(hAPP(X6142,X6141),X6143))|~hBOOL(hAPP(hAPP(c_member(X6144),X6143),c_SetInterval_Oord_OgreaterThanLessThan(X6144,X6142,X6141,X6140)))))&(~hBOOL(hAPP(hAPP(X6142,X6143),X6140))|~hBOOL(hAPP(hAPP(X6142,X6141),X6143))|hBOOL(hAPP(hAPP(c_member(X6144),X6143),c_SetInterval_Oord_OgreaterThanLessThan(X6144,X6142,X6141,X6140))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanLessThan__iff])])])). 6.97/7.23 fof(c_0_8189, plain, ![X9859, X9860, X9861, X9862, X9863, X9864]:(~hBOOL(hAPP(hAPP(X9864,X9863),X9862))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9861,tc_fun(X9860,tc_HOL_Obool))),X9864),X9859))|hBOOL(hAPP(hAPP(X9859,X9863),X9862)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rev__predicate2D])])])). 6.97/7.23 fof(c_0_8190, plain, ![X14636, X14637, X14638]:(~class_Lattices_Osemilattice__inf(X14638)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X14638),X14637),X14636)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X14638),X14637),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X14638),X14637),X14636))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__left__idem])])). 6.97/7.23 cnf(c_0_8191, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(c_List_Oset(X4),c_List_Oreplicate(X4,X1,X3))))|X2!=X3), inference(split_conjunct,[status(thm)],[c_0_5340])). 6.97/7.23 fof(c_0_8192, plain, ![X6370, X6371, X6372]:(~class_Orderings_Olinorder(X6372)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6372),X6371))|(~hBOOL(hAPP(hAPP(c_member(X6372),X6370),X6371))|c_Big__Operators_Olinorder__class_OMax(X6372,X6371)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X6372),X6370),c_Big__Operators_Olinorder__class_OMax(X6372,X6371))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max_Oin__idem])])])). 6.97/7.23 fof(c_0_8193, plain, ![X1518, X1519, X1520]:(~class_Lattices_Olattice(X1520)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1520),X1519))|(~hBOOL(hAPP(hAPP(c_member(X1520),X1518),X1519))|c_Big__Operators_Olattice__class_OSup__fin(X1520,X1519)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1520),X1518),c_Big__Operators_Olattice__class_OSup__fin(X1520,X1519))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oin__idem])])])). 6.97/7.23 fof(c_0_8194, plain, ![X5981, X5982, X5983]:(~class_Orderings_Olinorder(X5983)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5983),X5982))|(~hBOOL(hAPP(hAPP(c_member(X5983),X5981),X5982))|c_Big__Operators_Olinorder__class_OMin(X5983,X5982)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X5983),X5981),c_Big__Operators_Olinorder__class_OMin(X5983,X5982))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min_Oin__idem])])])). 6.97/7.23 fof(c_0_8195, plain, ![X10810, X10811, X10812]:(~class_Lattices_Olattice(X10812)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10812),X10811),X10810)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10812),X10811),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10812),X10811),X10810))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I4_J])])). 6.97/7.23 fof(c_0_8196, plain, ![X11864, X11865]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X11865))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11865),X11864)),X11865)=c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__times__mod__eq])])). 6.97/7.23 cnf(c_0_8197, 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_5341])). 6.97/7.23 fof(c_0_8198, plain, ![X10032, X10033, X10034]:(~class_Rings_Olinordered__idom(X10034)|hAPP(c_Groups_Oabs__class_Oabs(X10034),hAPP(hAPP(c_Power_Opower__class_Opower(X10034),X10033),X10032))=hAPP(hAPP(c_Power_Opower__class_Opower(X10034),hAPP(c_Groups_Oabs__class_Oabs(X10034),X10033)),X10032)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__abs])])). 6.97/7.23 fof(c_0_8199, plain, ![X12583, X12584, X12585]:(~class_Lattices_Olattice(X12585)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12585),X12584))|(~hBOOL(hAPP(hAPP(c_member(X12585),X12583),X12584))|c_Big__Operators_Olattice__class_OInf__fin(X12585,X12584)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X12585),X12583),c_Big__Operators_Olattice__class_OInf__fin(X12585,X12584))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oin__idem])])])). 6.97/7.23 fof(c_0_8200, plain, ![X10331, X10332, X10333]:(~class_Groups_Omonoid__add(X10333)|hAPP(c_List_Omonoid__add__class_Olistsum(X10333),hAPP(hAPP(c_List_Olist_OCons(X10333),X10332),X10331))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10333),X10332),hAPP(c_List_Omonoid__add__class_Olistsum(X10333),X10331))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__simps_I2_J])])). 6.97/7.23 fof(c_0_8201, plain, ![X14818, X14819, X14820]:(~class_Orderings_Olinorder(X14820)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X14820),X14819),hAPP(hAPP(c_Orderings_Oord__class_Omax(X14820),X14819),X14818))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X14820),X14819),X14818)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup_Oleft__idem])])])). 6.97/7.23 fof(c_0_8202, plain, ![X714, X715, X716, X717]:(~hBOOL(hAPP(hAPP(c_member(X717),X716),hAPP(c_List_Oset(X717),hAPP(hAPP(c_List_Odrop(X717),X715),X714))))|hBOOL(hAPP(hAPP(c_member(X717),X716),hAPP(c_List_Oset(X717),X714)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__dropD])])). 6.97/7.23 fof(c_0_8203, plain, ![X17503, X17504, X17505, X17506]:(~hBOOL(hAPP(hAPP(c_member(X17506),X17505),hAPP(c_List_Oset(X17506),hAPP(hAPP(c_List_Otake(X17506),X17504),X17503))))|hBOOL(hAPP(hAPP(c_member(X17506),X17505),hAPP(c_List_Oset(X17506),X17503)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__takeD])])). 6.97/7.23 fof(c_0_8204, plain, ![X5495, X5497, X5498, X5500]:((~hBOOL(hAPP(X5495,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk177_1(X5495))))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5497))|hBOOL(hAPP(X5495,X5497))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk178_1(X5498)))|hBOOL(hAPP(X5498,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5500))))&(~hBOOL(hAPP(X5498,esk178_1(X5498)))|hBOOL(hAPP(X5498,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5500)))))), 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])])])])])])). 6.97/7.23 fof(c_0_8205, plain, ![X9648, X9649, X9650]:(~class_Orderings_Olinorder(X9650)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X9650),X9649),hAPP(hAPP(c_Orderings_Oord__class_Omin(X9650),X9649),X9648))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X9650),X9649),X9648)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oleft__idem])])). 6.97/7.23 fof(c_0_8206, plain, ![X2606, X2607, X2608, X2610, X2611, X2612, X2613]:(((hBOOL(hAPP(X2607,hAPP(hAPP(c_List_Onth(X2608),X2606),esk84_3(X2606,X2607,X2608))))|~c_List_Olist__ex(X2608,X2607,X2606))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk84_3(X2606,X2607,X2608)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2608)),X2606)))|~c_List_Olist__ex(X2608,X2607,X2606)))&(~hBOOL(hAPP(X2611,hAPP(hAPP(c_List_Onth(X2612),X2610),X2613)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2613),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2612)),X2610)))|c_List_Olist__ex(X2612,X2611,X2610))), 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])])])])])])). 6.97/7.23 fof(c_0_8207, plain, ![X9041, X9042, X9043]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9043)),c_List_OtakeWhile(X9043,X9042,X9041))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9043)),X9041)))|~hBOOL(hAPP(X9042,hAPP(hAPP(c_List_Onth(X9043),X9041),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9043)),c_List_OtakeWhile(X9043,X9042,X9041)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__length__takeWhile])])])). 6.97/7.23 cnf(c_0_8208, plain, (hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=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))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_5231])). 6.97/7.23 fof(c_0_8209, plain, ![X13185, X13186]:(~class_Complete__Lattice_Ocomplete__lattice(X13186)|(~c_Orderings_Oorder__class_Omono(X13186,X13186,X13185)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13186),hAPP(X13185,c_Inductive_Ocomplete__lattice__class_Olfp(X13186,X13185))),c_Inductive_Ocomplete__lattice__class_Olfp(X13186,X13185))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lfp__lemma2])])])). 6.97/7.23 fof(c_0_8210, plain, ![X6042, X6043]:(~class_Complete__Lattice_Ocomplete__lattice(X6043)|(~c_Orderings_Oorder__class_Omono(X6043,X6043,X6042)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6043),hAPP(X6042,c_Inductive_Ocomplete__lattice__class_Ogfp(X6043,X6042))),c_Inductive_Ocomplete__lattice__class_Ogfp(X6043,X6042))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_gfp__lemma3])])])). 6.97/7.23 fof(c_0_8211, plain, ![X14389, X14390]:(~class_Complete__Lattice_Ocomplete__lattice(X14390)|(~c_Orderings_Oorder__class_Omono(X14390,X14390,X14389)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14390),c_Inductive_Ocomplete__lattice__class_Olfp(X14390,X14389)),hAPP(X14389,c_Inductive_Ocomplete__lattice__class_Olfp(X14390,X14389)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lfp__lemma3])])])). 6.97/7.23 fof(c_0_8212, plain, ![X908, X909]:(~class_Complete__Lattice_Ocomplete__lattice(X909)|(~c_Orderings_Oorder__class_Omono(X909,X909,X908)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X909),c_Inductive_Ocomplete__lattice__class_Ogfp(X909,X908)),hAPP(X908,c_Inductive_Ocomplete__lattice__class_Ogfp(X909,X908)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gfp__lemma2])])). 6.97/7.23 fof(c_0_8213, plain, ![X10658, X10659, X10660, X10662, X10663, X10664, X10665]:(((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk352_3(X10658,X10659,X10660)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X10659,X10658)))|c_List_Oall__interval__int(X10660,X10659,X10658))&(~hBOOL(hAPP(X10660,esk352_3(X10658,X10659,X10660)))|c_List_Oall__interval__int(X10660,X10659,X10658)))&(~c_List_Oall__interval__int(X10664,X10663,X10662)|(~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X10665),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X10663,X10662)))|hBOOL(hAPP(X10664,X10665))))), 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__interval__int__def])])])])])])])). 6.97/7.23 fof(c_0_8214, plain, ![X17346, X17347]:((hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk591_2(X17346,X17347)),c_Int_OInteg))|hBOOL(hAPP(X17347,X17346)))&(~hBOOL(hAPP(X17347,hAPP(c_Int_OAbs__Integ,esk591_2(X17346,X17347))))|hBOOL(hAPP(X17347,X17346)))), 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])])])])])). 6.97/7.23 fof(c_0_8215, plain, ![X15221, X15222, X15223, X15224, X15225, X15226, X15227]:((~c_List_Olist__all(X15223,X15221,X15222)|(~hBOOL(hAPP(hAPP(c_member(X15223),X15224),hAPP(c_List_Oset(X15223),X15222)))|hBOOL(hAPP(X15221,X15224))))&((hBOOL(hAPP(hAPP(c_member(X15227),esk513_3(X15225,X15226,X15227)),hAPP(c_List_Oset(X15227),X15226)))|c_List_Olist__all(X15227,X15225,X15226))&(~hBOOL(hAPP(X15225,esk513_3(X15225,X15226,X15227)))|c_List_Olist__all(X15227,X15225,X15226)))), 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__set__list__all])])])])])])])). 6.97/7.23 fof(c_0_8216, plain, ![X11815, X11816, X11817, X11818]:(~class_Groups_Oordered__ab__semigroup__add__imp__le(X11818)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11818),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11818),X11817),X11816)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11818),X11817),X11815)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11818),X11816),X11815)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__le__imp__le__left])])])). 6.97/7.23 fof(c_0_8217, plain, ![X17254, X17255, X17256, X17257, X17258]:(~c_Finite__Set_Ofolding__idem(X17258,X17257,X17256,X17255)|hAPP(X17256,X17254)=hAPP(c_Fun_Ocomp(X17257,X17257,X17257,hAPP(X17256,X17254)),hAPP(X17256,X17254))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oidem__comp])])). 6.97/7.23 fof(c_0_8218, plain, ![X13760, X13761, X13762, X13763, X13764, X13765, X13766]:((~c_List_Olist__all(X13762,X13761,X13760)|(~hBOOL(hAPP(hAPP(c_member(X13762),X13763),hAPP(c_List_Oset(X13762),X13760)))|hBOOL(hAPP(X13761,X13763))))&((hBOOL(hAPP(hAPP(c_member(X13766),esk461_3(X13764,X13765,X13766)),hAPP(c_List_Oset(X13766),X13764)))|c_List_Olist__all(X13766,X13765,X13764))&(~hBOOL(hAPP(X13765,esk461_3(X13764,X13765,X13766)))|c_List_Olist__all(X13766,X13765,X13764)))), 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__raw])])])])])])])). 6.97/7.23 fof(c_0_8219, plain, ![X12927, X12928, X12929, X12930, X12931, X12932, X12933]:((~c_List_Olist__all(X12929,X12928,X12927)|(~hBOOL(hAPP(hAPP(c_member(X12929),X12930),hAPP(c_List_Oset(X12929),X12927)))|hBOOL(hAPP(X12928,X12930))))&((hBOOL(hAPP(hAPP(c_member(X12933),esk423_3(X12931,X12932,X12933)),hAPP(c_List_Oset(X12933),X12931)))|c_List_Olist__all(X12933,X12932,X12931))&(~hBOOL(hAPP(X12932,esk423_3(X12931,X12932,X12933)))|c_List_Olist__all(X12933,X12932,X12931)))), 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])])])])])])). 6.97/7.23 fof(c_0_8220, plain, ![X7652, X7653, X7654]:(~class_Divides_Oring__div(X7654)|c_Divides_Odiv__class_Omod(X7654,hAPP(c_Groups_Ouminus__class_Ouminus(X7654),X7653),X7652)=c_Divides_Odiv__class_Omod(X7654,hAPP(c_Groups_Ouminus__class_Ouminus(X7654),c_Divides_Odiv__class_Omod(X7654,X7653,X7652)),X7652)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__minus__eq])])). 6.97/7.23 cnf(c_0_8221, plain, (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))=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)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X1), inference(split_conjunct,[status(thm)],[c_0_5342])). 6.97/7.23 fof(c_0_8222, plain, ![X15876, X15877, X15878]:(~c_Wellfounded_Owf(X15878,X15877)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X15878,X15878)),hAPP(hAPP(c_Product__Type_OPair(X15878,X15878),hAPP(X15876,hAPP(c_Nat_OSuc,esk537_3(X15876,X15877,X15878)))),hAPP(X15876,esk537_3(X15876,X15877,X15878)))),X15877))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__no__infinite__down__chainE])])])])). 6.97/7.23 fof(c_0_8223, plain, ![X6925, X6926, X6927, X6928]:(~class_Complete__Lattice_Ocomplete__lattice(X6928)|(c_Orderings_Obot__class_Obot(tc_fun(X6926,tc_HOL_Obool))=X6927|X6925=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6926,X6928),X6927),hAPP(c_COMBK(X6928,X6926),X6925)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SUP__const])])])). 6.97/7.23 fof(c_0_8224, plain, ![X9530, X9531, X9532]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9532),X9531))|(c_Orderings_Obot__class_Obot(tc_fun(X9532,tc_HOL_Obool))=X9531|hBOOL(hAPP(c_Finite__Set_Ofold1Set(X9532,X9530,X9531),esk310_3(X9530,X9531,X9532))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__nonempty__imp__fold1Set])])])). 6.97/7.23 cnf(c_0_8225, 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_5343])). 6.97/7.23 cnf(c_0_8226, 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_Oring__char__0(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_5344])). 6.97/7.23 cnf(c_0_8227, plain, (c_List_Oembed__list(c_List_Oreturn__list(X1))=X1|~c_List_Onat__list(X1)), inference(split_conjunct,[status(thm)],[c_0_5345])). 6.97/7.23 fof(c_0_8228, plain, ![X2008, X2009, X2010, X2011, X2012]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2012),X2009),X2008))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2012),X2011),X2010))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2012),X2011),X2010)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2012),X2009),X2008)|~class_Groups_Oordered__ab__group__add(X2012))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2012),X2011),X2010))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2012),X2009),X2008))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2012),X2011),X2010)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2012),X2009),X2008)|~class_Groups_Oordered__ab__group__add(X2012))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__eq__diff__less])])])])). 6.97/7.23 fof(c_0_8229, plain, ![X9836, X9837, X9838, X9839, X9840]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9840),X9837),X9836))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9840),X9839),X9838))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9840),X9837),X9836)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9840),X9839),X9838)|~class_Groups_Oordered__ab__group__add(X9840))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9840),X9839),X9838))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9840),X9837),X9836))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9840),X9837),X9836)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9840),X9839),X9838)|~class_Groups_Oordered__ab__group__add(X9840))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less__eq])])])). 6.97/7.23 fof(c_0_8230, plain, ![X12814, X12815, X12816, X12817]:(~class_Complete__Lattice_Ocomplete__lattice(X12817)|(X12816=c_Orderings_Obot__class_Obot(tc_fun(X12815,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12815,X12817),X12816),hAPP(c_COMBK(X12817,X12815),X12814))=X12814)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INF__const])])])). 6.97/7.23 fof(c_0_8231, plain, ![X4137, X4138]:(~class_Groups_Oordered__ab__group__add(X4138)|hAPP(c_Set_Oimage(X4138,X4138,c_Groups_Ouminus__class_Ouminus(X4138)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X4138),X4137))=hAPP(c_SetInterval_Oord__class_OlessThan(X4138),hAPP(c_Groups_Ouminus__class_Ouminus(X4138),X4137))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__uminus__greaterThan])])])). 6.97/7.23 fof(c_0_8232, plain, ![X13535, X13536]:(~class_Groups_Oordered__ab__group__add(X13536)|hAPP(c_Set_Oimage(X13536,X13536,c_Groups_Ouminus__class_Ouminus(X13536)),hAPP(c_SetInterval_Oord__class_OlessThan(X13536),X13535))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X13536),hAPP(c_Groups_Ouminus__class_Ouminus(X13536),X13535))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__uminus__lessThan])])])). 6.97/7.23 fof(c_0_8233, plain, ![X6921, X6922]:(~class_Groups_Oordered__ab__group__add(X6922)|hAPP(c_Set_Oimage(X6922,X6922,c_Groups_Ouminus__class_Ouminus(X6922)),hAPP(c_SetInterval_Oord__class_OatLeast(X6922),X6921))=hAPP(c_SetInterval_Oord__class_OatMost(X6922),hAPP(c_Groups_Ouminus__class_Ouminus(X6922),X6921))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeast])])). 6.97/7.23 fof(c_0_8234, plain, ![X4781, X4782]:(~class_Groups_Oordered__ab__group__add(X4782)|hAPP(c_SetInterval_Oord__class_OatLeast(X4782),hAPP(c_Groups_Ouminus__class_Ouminus(X4782),X4781))=hAPP(c_Set_Oimage(X4782,X4782,c_Groups_Ouminus__class_Ouminus(X4782)),hAPP(c_SetInterval_Oord__class_OatMost(X4782),X4781))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__atMost])])). 6.97/7.23 fof(c_0_8235, plain, ![X2378, X2379, X2380]:(~class_Lattices_Oboolean__algebra(X2380)|(c_Orderings_Obot__class_Obot(X2380)!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2380),X2379),X2378)|(c_Orderings_Otop__class_Otop(X2380)!=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2380),X2379),X2378)|X2378=hAPP(c_Groups_Ouminus__class_Ouminus(X2380),X2379)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_compl__unique])])])). 6.97/7.23 cnf(c_0_8236, 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_5249])). 6.97/7.23 fof(c_0_8237, plain, ![X16544, X16545, X16546, X16547]:(X16547=c_List_Olist_ONil(X16546)|hAPP(c_List_Ohd(X16545),hAPP(hAPP(c_List_Omap(X16546,X16545),X16544),X16547))=hAPP(X16544,hAPP(c_List_Ohd(X16546),X16547))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_hd__map])])])). 6.97/7.23 fof(c_0_8238, plain, ![X7877, X7878]:(~class_Rings_Oring__1(X7878)|(~hBOOL(hAPP(hAPP(c_member(X7878),X7877),c_Int_Oring__1__class_OInts(X7878)))|hBOOL(hAPP(hAPP(c_member(X7878),hAPP(c_Groups_Ouminus__class_Ouminus(X7878),X7877)),c_Int_Oring__1__class_OInts(X7878))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Ints__minus])])])). 6.97/7.23 fof(c_0_8239, plain, ![X2594, X2595, X2596, X2597]:((~hBOOL(hAPP(c_List_Olistsp(X2597,X2596),X2594))|~hBOOL(hAPP(X2596,X2595))|hBOOL(hAPP(c_List_Olistsp(X2597,X2596),hAPP(hAPP(c_List_Olist_OCons(X2597),X2595),X2594))))&((hBOOL(hAPP(c_List_Olistsp(X2597,X2596),X2594))|~hBOOL(hAPP(c_List_Olistsp(X2597,X2596),hAPP(hAPP(c_List_Olist_OCons(X2597),X2595),X2594))))&(hBOOL(hAPP(X2596,X2595))|~hBOOL(hAPP(c_List_Olistsp(X2597,X2596),hAPP(hAPP(c_List_Olist_OCons(X2597),X2595),X2594)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp_Oequations_I2_J])])])). 6.97/7.23 fof(c_0_8240, plain, ![X14862, X14863]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14863),hAPP(c_Int_Oring__1__class_Oof__int(X14863),X14862)),c_Groups_Ozero__class_Ozero(X14863)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14862),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Rings_Olinordered__idom(X14863))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14862),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14863),hAPP(c_Int_Oring__1__class_Oof__int(X14863),X14862)),c_Groups_Ozero__class_Ozero(X14863)))|~class_Rings_Olinordered__idom(X14863))), 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])])])])). 6.97/7.23 fof(c_0_8241, plain, ![X5519, X5520]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5520),hAPP(c_Int_Oring__1__class_Oof__int(X5520),X5519)),c_Groups_Ozero__class_Ozero(X5520)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5519),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Rings_Olinordered__idom(X5520))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5519),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5520),hAPP(c_Int_Oring__1__class_Oof__int(X5520),X5519)),c_Groups_Ozero__class_Ozero(X5520)))|~class_Rings_Olinordered__idom(X5520))), 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])])])])). 6.97/7.23 cnf(c_0_8242, plain, (hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),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)],[c_0_5346, c_0_4411])). 6.97/7.23 cnf(c_0_8243, 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_5251])). 6.97/7.23 fof(c_0_8244, plain, ![X2547, X2548]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2547))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2548),c_Groups_Ozero__class_Ozero(X2548)),hAPP(c_Int_Oring__1__class_Oof__int(X2548),X2547)))|~class_Rings_Olinordered__idom(X2548))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2548),c_Groups_Ozero__class_Ozero(X2548)),hAPP(c_Int_Oring__1__class_Oof__int(X2548),X2547)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2547))|~class_Rings_Olinordered__idom(X2548))), 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])])])])). 6.97/7.23 fof(c_0_8245, plain, ![X14445, X14446]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14446),c_Groups_Ozero__class_Ozero(X14446)),hAPP(c_Int_Oring__1__class_Oof__int(X14446),X14445)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14445))|~class_Rings_Olinordered__idom(X14446))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14445))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14446),c_Groups_Ozero__class_Ozero(X14446)),hAPP(c_Int_Oring__1__class_Oof__int(X14446),X14445)))|~class_Rings_Olinordered__idom(X14446))), 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])])])])). 6.97/7.23 fof(c_0_8246, plain, ![X15950, X15951]:(~class_Orderings_Olinorder(X15951)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15951),X15950))|(c_Orderings_Obot__class_Obot(tc_fun(X15951,tc_HOL_Obool))=X15950|hBOOL(hAPP(hAPP(c_member(X15951),c_Big__Operators_Olinorder__class_OMax(X15951,X15950)),X15950))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max__in])])])). 6.97/7.23 fof(c_0_8247, plain, ![X6886, X6887]:(~class_Orderings_Olinorder(X6887)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6887),X6886))|(X6886=c_Orderings_Obot__class_Obot(tc_fun(X6887,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X6887),c_Big__Operators_Olinorder__class_OMin(X6887,X6886)),X6886))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__in])])). 6.97/7.23 fof(c_0_8248, plain, ![X8315, X8316, X8317]:(~class_Complete__Lattice_Ocomplete__lattice(X8317)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8317),hAPP(X8316,X8315)),X8315))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8317),c_Inductive_Ocomplete__lattice__class_Olfp(X8317,X8316)),X8315)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lfp__lowerbound])])])). 6.97/7.23 fof(c_0_8249, plain, ![X11164, X11165, X11166]:(~class_Complete__Lattice_Ocomplete__lattice(X11166)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11166),X11165),hAPP(X11164,X11165)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11166),X11165),c_Inductive_Ocomplete__lattice__class_Ogfp(X11166,X11164))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_gfp__upperbound])])])). 6.97/7.23 fof(c_0_8250, plain, ![X1595, X1596, X1597, X1598, X1599, X1600, X1601]:(hAPP(hAPP(c_List_Omap(X1597,X1600),X1596),X1595)!=hAPP(hAPP(c_List_Omap(X1601,X1600),X1599),X1598)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1601)),X1598)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1597)),X1595)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__eq__imp__length__eq])])])). 6.97/7.23 fof(c_0_8251, plain, ![X5735, X5736, X5737]:(~class_Orderings_Olinorder(X5737)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5737),X5736),X5735))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5737),X5735),X5736)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__le__cases])])])). 6.97/7.23 fof(c_0_8252, plain, ![X13024, X13025, X13026, X13027]:(~hBOOL(hAPP(hAPP(c_member(X13027),X13026),hAPP(c_Set_Oimage(X13025,X13027,X13024),c_Orderings_Otop__class_Otop(tc_fun(X13025,tc_HOL_Obool)))))|hAPP(X13024,esk426_3(X13024,X13025,X13026))=X13026), 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_rangeE])])])])])). 6.97/7.23 cnf(c_0_8253, 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_5281])). 6.97/7.23 cnf(c_0_8254, 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_4906])). 6.97/7.23 fof(c_0_8255, plain, ![X8698, X8699]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8698),X8699))|X8699=X8698|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8699),X8698))), inference(variable_rename,[status(thm)],[fact_zless__linear])). 6.97/7.23 fof(c_0_8256, plain, ![X6088, X6089]:(~class_Groups_Oordered__ab__group__add__abs(X6089)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6089),hAPP(c_Groups_Ouminus__class_Ouminus(X6089),hAPP(c_Groups_Oabs__class_Oabs(X6089),X6088))),c_Groups_Ozero__class_Ozero(X6089)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__minus__le__zero])])])). 6.97/7.23 fof(c_0_8257, plain, ![X7567, X7568, X7569]:(~c_Equiv__Relations_Oequiv(X7569,X7568,X7567)|X7567=hAPP(hAPP(c_Relation_Orel__comp(X7569,X7569,X7569),hAPP(c_Relation_Oconverse(X7569,X7569),X7567)),X7567)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__comp__eq])])). 6.97/7.23 fof(c_0_8258, plain, ![X1363, X1364, X1365, X1366, X1367, X1368, X1369]:((X1363!=X1364|hAPP(X1366,X1364)=hAPP(X1366,X1363)|~hBOOL(hAPP(hAPP(c_member(X1368),X1363),X1365))|~hBOOL(hAPP(hAPP(c_member(X1368),X1364),X1365))|~c_Typedef_Otype__definition(X1369,X1368,X1367,X1366,X1365))&(hAPP(X1366,X1364)!=hAPP(X1366,X1363)|X1363=X1364|~hBOOL(hAPP(hAPP(c_member(X1368),X1363),X1365))|~hBOOL(hAPP(hAPP(c_member(X1368),X1364),X1365))|~c_Typedef_Otype__definition(X1369,X1368,X1367,X1366,X1365))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_type__definition_OAbs__inject])])])])). 6.97/7.23 fof(c_0_8259, plain, ![X2641, X2642, X2643, X2644]:(~hBOOL(hAPP(c_List_Odistinct(X2644),X2643))|hBOOL(hAPP(c_List_Odistinct(tc_prod(X2644,X2642)),hAPP(hAPP(c_List_Ozip(X2644,X2642),X2643),X2641)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__zipI1])])). 6.97/7.23 fof(c_0_8260, plain, ![X6876, X6877, X6878, X6879]:(~hBOOL(hAPP(c_List_Odistinct(X6879),X6878))|hBOOL(hAPP(c_List_Odistinct(tc_prod(X6877,X6879)),hAPP(hAPP(c_List_Ozip(X6877,X6879),X6876),X6878)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__zipI2])])). 6.97/7.23 fof(c_0_8261, plain, ![X17147, X17148]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17148))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17148),X17147)),X17148)=X17147), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__m])])). 6.97/7.23 fof(c_0_8262, plain, ![X12625, X12626]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12626))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12625),X12626)),X12626)=X12625), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self__is__m])])). 6.97/7.23 cnf(c_0_8263, 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_5347])). 6.97/7.23 fof(c_0_8264, plain, ![X9306, X9307]:(X9306=X9307|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9307),X9306))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9306),X9307)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat])])])). 6.97/7.23 cnf(c_0_8265, 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_5348])). 6.97/7.23 cnf(c_0_8266, 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_5349])). 6.97/7.23 cnf(c_0_8267, 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_5347])). 6.97/7.23 fof(c_0_8268, plain, ![X16310, X16311, X16312]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16312),X16311))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16312),X16310)),X16311))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__imp__diff__less])])])). 6.97/7.23 cnf(c_0_8269, 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_5350])). 6.97/7.23 cnf(c_0_8270, 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_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))), inference(rw,[status(thm)],[c_0_5351, c_0_4410])). 6.97/7.23 cnf(c_0_8271, 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_5352])). 6.97/7.23 fof(c_0_8272, plain, ![X8512, X8513, X8514, X8515]:(~c_Fun_Oinj__on(X8515,X8514,X8513,X8512)|c_Fun_Oinj__on(X8514,X8515,c_Fun_Othe__inv__into(X8515,X8514,X8512,X8513),hAPP(c_Set_Oimage(X8515,X8514,X8513),X8512))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__the__inv__into])])])). 6.97/7.23 fof(c_0_8273, plain, ![X4456, X4457, X4458, X4459]:(~hBOOL(hAPP(c_List_Odistinct(X4459),X4458))|(~hBOOL(hAPP(c_List_Odistinct(X4457),X4456))|hBOOL(hAPP(c_List_Odistinct(tc_prod(X4459,X4457)),c_Enum_Oproduct(X4459,X4457,X4458,X4456))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__product])])])). 6.97/7.23 fof(c_0_8274, plain, ![X5810, X5811]:((X5810!=c_Groups_Ozero__class_Ozero(X5811)|c_Groups_Ozero__class_Ozero(X5811)=c_Groups_Osgn__class_Osgn(X5811,X5810)|~class_Groups_Osgn__if(X5811))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5811),c_Groups_Ozero__class_Ozero(X5811)),X5810))|c_Groups_Osgn__class_Osgn(X5811,X5810)=hAPP(c_Groups_Ouminus__class_Ouminus(X5811),c_Groups_Oone__class_Oone(X5811))|X5810=c_Groups_Ozero__class_Ozero(X5811)|~class_Groups_Osgn__if(X5811))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5811),c_Groups_Ozero__class_Ozero(X5811)),X5810))|c_Groups_Osgn__class_Osgn(X5811,X5810)=c_Groups_Oone__class_Oone(X5811)|X5810=c_Groups_Ozero__class_Ozero(X5811)|~class_Groups_Osgn__if(X5811)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sgn__if])])])])). 6.97/7.23 cnf(c_0_8275, 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_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))), inference(rw,[status(thm)],[c_0_5353, c_0_4410])). 6.97/7.23 cnf(c_0_8276, 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),X1))))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(rw,[status(thm)],[c_0_5354, c_0_4410])). 6.97/7.23 cnf(c_0_8277, 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_5355])). 6.97/7.23 fof(c_0_8278, plain, ![X2982, X2983, X2984, X2985]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X2985),X2983))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X2985,X2984)),c_Sum__Type_OPlus(X2985,X2984,X2983,X2982))))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X2984),X2982))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X2985,X2984)),c_Sum__Type_OPlus(X2985,X2984,X2983,X2982)))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2985),X2983))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2984),X2982))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X2985,X2984)),c_Sum__Type_OPlus(X2985,X2984,X2983,X2982))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus__iff])])])). 6.97/7.23 fof(c_0_8279, plain, ![X6062, X6063]:((~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6063)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X6062)))|hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X6063),X6062)))&(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X6063),X6062))|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6063)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X6062))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I2_J])])). 6.97/7.23 fof(c_0_8280, plain, ![X10672, X10673, X10674, X10675]:((~hBOOL(hAPP(hAPP(c_member(X10675),X10674),hAPP(hAPP(c_Set_Oinsert(X10675),X10673),X10672)))|(hBOOL(hAPP(hAPP(c_member(X10675),X10674),X10672))|X10673=X10674))&((~hBOOL(hAPP(hAPP(c_member(X10675),X10674),X10672))|hBOOL(hAPP(hAPP(c_member(X10675),X10674),hAPP(hAPP(c_Set_Oinsert(X10675),X10673),X10672))))&(X10673!=X10674|hBOOL(hAPP(hAPP(c_member(X10675),X10674),hAPP(hAPP(c_Set_Oinsert(X10675),X10673),X10672)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__iff])])])). 6.97/7.23 fof(c_0_8281, plain, ![X1716, X1717, X1718]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1718),X1717))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1718),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1717),X1716)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J])])). 6.97/7.23 fof(c_0_8282, plain, ![X9054, X9055, X9056]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X9056|hAPP(c_List_Otl(X9055),c_List_Oreplicate(X9055,X9056,X9054))=c_List_Oreplicate(X9055,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X9056),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X9054)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_tl__replicate])])])). 6.97/7.23 fof(c_0_8283, plain, ![X6880, X6881, X6882, X6883, X6884, X6885]:(~c_Fun_Oinj__on(X6885,X6884,hAPP(c_Fun_Ocomp(X6883,X6884,X6885,X6882),X6881),X6880)|c_Fun_Oinj__on(X6883,X6884,X6882,hAPP(c_Set_Oimage(X6885,X6883,X6881),X6880))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__imageI])])). 6.97/7.23 fof(c_0_8284, plain, ![X16946, X16947, X16948, X16949]:(~c_Finite__Set_Ofun__left__comm__idem(X16949,X16948,X16947)|hAPP(X16947,X16946)=hAPP(c_Fun_Ocomp(X16948,X16948,X16948,hAPP(X16947,X16946)),hAPP(X16947,X16946))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__comp__idem])])). 6.97/7.23 fof(c_0_8285, plain, ![X9754, X9755, X9756]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9756),X9755))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9756),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9754),X9755)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add2])])). 6.97/7.23 fof(c_0_8286, plain, ![X15304, X15305, X15306]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15306),X15305))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15306),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15305),X15304)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_trans__le__add1])])])). 6.97/7.23 cnf(c_0_8287, plain, (X1=X2|c_Int_OBit1(X1)!=c_Int_OBit1(X2)), inference(split_conjunct,[status(thm)],[c_0_5356])). 6.97/7.23 fof(c_0_8288, plain, ![X938, X939, X940, X941, X942]:(((X940=X938|hAPP(hAPP(c_List_Oappend(X942),X939),hAPP(hAPP(c_List_Olist_OCons(X942),X938),c_List_Olist_ONil(X942)))!=hAPP(hAPP(c_List_Oappend(X942),X941),hAPP(hAPP(c_List_Olist_OCons(X942),X940),c_List_Olist_ONil(X942))))&(X939=X941|hAPP(hAPP(c_List_Oappend(X942),X939),hAPP(hAPP(c_List_Olist_OCons(X942),X938),c_List_Olist_ONil(X942)))!=hAPP(hAPP(c_List_Oappend(X942),X941),hAPP(hAPP(c_List_Olist_OCons(X942),X940),c_List_Olist_ONil(X942)))))&(X940!=X938|X939!=X941|hAPP(hAPP(c_List_Oappend(X942),X939),hAPP(hAPP(c_List_Olist_OCons(X942),X938),c_List_Olist_ONil(X942)))=hAPP(hAPP(c_List_Oappend(X942),X941),hAPP(hAPP(c_List_Olist_OCons(X942),X940),c_List_Olist_ONil(X942))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append1__eq__conv])])])). 6.97/7.23 fof(c_0_8289, plain, ![X13201, X13204, X13205, X13206, X13207, X13208, X13209, X13210]:(((hAPP(X13201,esk432_1(X13201))!=hAPP(X13201,esk431_1(X13201))|~hBOOL(hAPP(hAPP(X13201,esk431_1(X13201)),esk432_1(X13201)))|c_Equiv__Relations_Oequivp(X13204,X13201))&(hAPP(X13201,esk432_1(X13201))=hAPP(X13201,esk431_1(X13201))|hBOOL(hAPP(hAPP(X13201,esk431_1(X13201)),esk432_1(X13201)))|c_Equiv__Relations_Oequivp(X13204,X13201)))&((hAPP(X13205,X13208)!=hAPP(X13205,X13207)|hBOOL(hAPP(hAPP(X13205,X13207),X13208))|~c_Equiv__Relations_Oequivp(X13206,X13205))&(~hBOOL(hAPP(hAPP(X13205,X13209),X13210))|hAPP(X13205,X13210)=hAPP(X13205,X13209)|~c_Equiv__Relations_Oequivp(X13206,X13205)))), 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])])])])])])). 6.97/7.23 fof(c_0_8290, plain, ![X7910, X7911, X7912]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7912),X7911))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7912),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7910),X7911)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_termination__basic__simps_I4_J])])])). 6.97/7.23 cnf(c_0_8291, 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_5357])). 6.97/7.23 cnf(c_0_8292, 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),X1),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1))), inference(rw,[status(thm)],[c_0_5358, c_0_4410])). 6.97/7.23 cnf(c_0_8293, 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_5359])). 6.97/7.23 cnf(c_0_8294, 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),X1),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))), inference(rw,[status(thm)],[c_0_5360, c_0_4410])). 6.97/7.23 fof(c_0_8295, plain, ![X9939, X9940]:(~class_Complete__Lattice_Ocomplete__lattice(X9940)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9940),X9939))|hAPP(hAPP(c_Finite__Set_Ofold(X9940,X9940,c_Lattices_Osemilattice__inf__class_Oinf(X9940)),c_Orderings_Otop__class_Otop(X9940)),X9939)=c_Complete__Lattice_OInf__class_OInf(X9940,X9939))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fold__inf])])])). 6.97/7.23 fof(c_0_8296, plain, ![X1145, X1146]:(~class_Complete__Lattice_Ocomplete__lattice(X1146)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1146),X1145))|c_Complete__Lattice_OSup__class_OSup(X1146,X1145)=hAPP(hAPP(c_Finite__Set_Ofold(X1146,X1146,c_Lattices_Osemilattice__sup__class_Osup(X1146)),c_Orderings_Obot__class_Obot(X1146)),X1145))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fold__sup])])). 6.97/7.23 fof(c_0_8297, plain, ![X4041, X4042]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4042))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4041))|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X4042,X4041),c_Divides_OposDivAlg(X4042,X4041))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_posDivAlg__correct])])])). 6.97/7.23 fof(c_0_8298, plain, ![X6025, X6026]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6026),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)),X6025))|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X6026,X6025),c_Divides_OnegDivAlg(X6026,X6025))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_negDivAlg__correct])])])). 6.97/7.23 fof(c_0_8299, plain, ![X7431, X7432, X7433, X7434]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X7434,X7434)),hAPP(hAPP(c_Product__Type_OPair(X7434,X7434),X7433),X7432)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7434,X7434),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7431)))|X7433=X7432), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rel__pow__0__E])])])). 6.97/7.23 fof(c_0_8300, plain, ![X10967, X10968]:(~class_Rings_Olinordered__idom(X10968)|~class_Int_Onumber__ring(X10968)|hAPP(c_Groups_Oabs__class_Oabs(X10968),hAPP(hAPP(c_Power_Opower__class_Opower(X10968),hAPP(c_Int_Onumber__class_Onumber__of(X10968),c_Int_OMin)),X10967))=c_Groups_Oone__class_Oone(X10968)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__power__minus__one])])])). 6.97/7.23 cnf(c_0_8301, 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_5361])). 6.97/7.23 fof(c_0_8302, plain, ![X9706, X9707, X9708]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X9708,X9708)),X9707),X9706))|hBOOL(hAPP(hAPP(c_member(tc_prod(X9708,X9708)),X9707),c_Transitive__Closure_Ortrancl(X9708,X9706)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__into__rtrancl])])). 6.97/7.23 fof(c_0_8303, plain, ![X13598, X13599, X13600, X13601, X13602]:(((X13599!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13599),hAPP(c_Nat_OSuc,X13598))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13600),X13598))|hAPP(c_Nat_OSuc,X13600)!=X13599|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13599),hAPP(c_Nat_OSuc,X13598)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk455_2(X13601,X13602)),X13601))|X13602=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13602),hAPP(c_Nat_OSuc,X13601))))&(hAPP(c_Nat_OSuc,esk455_2(X13601,X13602))=X13602|X13602=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13602),hAPP(c_Nat_OSuc,X13601)))))), 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])])])])])])). 6.97/7.23 fof(c_0_8304, plain, ![X10280, X10281]:(c_List_Olist_ONil(X10280)=X10281|hBOOL(hAPP(hAPP(c_member(X10280),hAPP(c_List_Ohd(X10280),X10281)),hAPP(c_List_Oset(X10280),X10281)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_hd__in__set])])])). 6.97/7.23 fof(c_0_8305, plain, ![X511, X512, X513, X514, X515, X516, X517]:(~c_Big__Operators_Ocomm__monoid__big(X517,X516,X515,X514,X513)|(hBOOL(hAPP(c_Finite__Set_Ofinite(X516),X512))|hAPP(hAPP(X513,X511),X512)=X514)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__monoid__big_Oinfinite])])])). 6.97/7.23 cnf(c_0_8306, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)=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),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3))))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_5289])). 6.97/7.23 fof(c_0_8307, plain, ![X12772, X12773, X12774]:(~class_Orderings_Olinorder(X12774)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12774),X12773))|(~hBOOL(hAPP(hAPP(c_member(X12774),X12772),X12773))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12774),c_Big__Operators_Olinorder__class_OMin(X12774,X12773)),X12772))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min__le])])])). 6.97/7.23 fof(c_0_8308, plain, ![X11992, X11993, X11994]:(~class_Orderings_Olinorder(X11994)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11994),X11993))|(~hBOOL(hAPP(hAPP(c_member(X11994),X11992),X11993))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11994),X11992),c_Big__Operators_Olinorder__class_OMax(X11994,X11993)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max__ge])])])). 6.97/7.23 fof(c_0_8309, plain, ![X7259, X7260, X7261]:(~class_Divides_Osemiring__div(X7261)|(X7260=c_Groups_Ozero__class_Ozero(X7261)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X7261),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7261),X7260),X7259)),X7260)=X7259)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__mult__self1__is__id])])])). 6.97/7.23 fof(c_0_8310, plain, ![X546, X547, X548]:(~class_Divides_Osemiring__div(X548)|(X547=c_Groups_Ozero__class_Ozero(X548)|X546=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X548),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X548),X546),X547)),X547))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self2__is__id])])). 6.97/7.23 fof(c_0_8311, plain, ![X11944, X11945]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11945),c_Groups_Ozero__class_Ozero(X11945)),X11944))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11945),hAPP(c_Groups_Ouminus__class_Ouminus(X11945),X11944)),X11944))|~class_Groups_Olinordered__ab__group__add(X11945))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11945),hAPP(c_Groups_Ouminus__class_Ouminus(X11945),X11944)),X11944))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11945),c_Groups_Ozero__class_Ozero(X11945)),X11944))|~class_Groups_Olinordered__ab__group__add(X11945))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__less__nonneg])])])])). 6.97/7.23 fof(c_0_8312, plain, ![X4106, X4107, X4108, X4109, X4112, X4113, X4114, X4115, X4116, X4117]:(((hBOOL(hAPP(hAPP(c_member(X4109),esk143_4(X4106,X4107,X4108,X4109)),X4106))|c_Fun_Oinj__on(X4109,X4108,X4107,X4106))&((hBOOL(hAPP(hAPP(c_member(X4109),esk144_4(X4106,X4107,X4108,X4109)),X4106))|c_Fun_Oinj__on(X4109,X4108,X4107,X4106))&((hAPP(X4107,esk144_4(X4106,X4107,X4108,X4109))=hAPP(X4107,esk143_4(X4106,X4107,X4108,X4109))|c_Fun_Oinj__on(X4109,X4108,X4107,X4106))&(esk143_4(X4106,X4107,X4108,X4109)!=esk144_4(X4106,X4107,X4108,X4109)|c_Fun_Oinj__on(X4109,X4108,X4107,X4106)))))&(~c_Fun_Oinj__on(X4115,X4114,X4113,X4112)|(~hBOOL(hAPP(hAPP(c_member(X4115),X4116),X4112))|(~hBOOL(hAPP(hAPP(c_member(X4115),X4117),X4112))|(hAPP(X4113,X4117)!=hAPP(X4113,X4116)|X4116=X4117))))), 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])])])])])])])). 6.97/7.23 fof(c_0_8313, plain, ![X15546, X15547]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15547),c_Groups_Ozero__class_Ozero(X15547)),X15546))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15547),hAPP(c_Groups_Ouminus__class_Ouminus(X15547),X15546)),X15546))|~class_Groups_Olinordered__ab__group__add(X15547))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15547),hAPP(c_Groups_Ouminus__class_Ouminus(X15547),X15546)),X15546))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15547),c_Groups_Ozero__class_Ozero(X15547)),X15546))|~class_Groups_Olinordered__ab__group__add(X15547))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__le__self__iff])])])])). 6.97/7.23 fof(c_0_8314, plain, ![X5828, X5829]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5829),X5828),c_Groups_Ozero__class_Ozero(X5829)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5829),X5828),hAPP(c_Groups_Ouminus__class_Ouminus(X5829),X5828)))|~class_Rings_Olinordered__idom(X5829))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5829),X5828),hAPP(c_Groups_Ouminus__class_Ouminus(X5829),X5828)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5829),X5828),c_Groups_Ozero__class_Ozero(X5829)))|~class_Rings_Olinordered__idom(X5829))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__minus__self__iff])])])])). 6.97/7.23 fof(c_0_8315, plain, ![X10256, X10257]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10257),X10256),c_Groups_Ozero__class_Ozero(X10257)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10257),X10256),hAPP(c_Groups_Ouminus__class_Ouminus(X10257),X10256)))|~class_Groups_Olinordered__ab__group__add(X10257))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10257),X10256),hAPP(c_Groups_Ouminus__class_Ouminus(X10257),X10256)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10257),X10256),c_Groups_Ozero__class_Ozero(X10257)))|~class_Groups_Olinordered__ab__group__add(X10257))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__self__iff])])])). 6.97/7.23 cnf(c_0_8316, 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_5362])). 6.97/7.23 fof(c_0_8317, plain, ![X14667, X14668, X14669, X14670]:(~class_Rings_Osemiring__1(X14670)|c_Nat_Osemiring__1__class_Oof__nat__aux(X14670,X14669,X14668,hAPP(X14669,X14667))=c_Nat_Osemiring__1__class_Oof__nat__aux(X14670,X14669,hAPP(c_Nat_OSuc,X14668),X14667)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__aux_Osimps_I2_J])])])). 6.97/7.23 fof(c_0_8318, plain, ![X6908, X6909, X6910]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6910),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6909)),X6908)))|c_List_Olast(X6909,hAPP(hAPP(c_List_Odrop(X6909),X6910),X6908))=c_List_Olast(X6909,X6908)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_last__drop])])])). 6.97/7.23 fof(c_0_8319, plain, ![X12166, X12167, X12168]:((c_List_Olist_ONil(X12167)=X12168|c_List_Obutlast(X12167,hAPP(hAPP(c_List_Oappend(X12167),X12166),X12168))=hAPP(hAPP(c_List_Oappend(X12167),X12166),c_List_Obutlast(X12167,X12168)))&(c_List_Olist_ONil(X12167)!=X12168|c_List_Obutlast(X12167,X12166)=c_List_Obutlast(X12167,hAPP(hAPP(c_List_Oappend(X12167),X12166),X12168)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast__append])])). 6.97/7.23 cnf(c_0_8320, 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_member(X1),X4),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X3))|X4!=X5), inference(split_conjunct,[status(thm)],[c_0_5363])). 6.97/7.23 fof(c_0_8321, plain, ![X4279, X4280, X4281]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4281),tc_List_Olist(X4281))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4281),tc_List_Olist(X4281)),c_List_Olist_ONil(X4281)),X4280)),c_List_Olistrel(X4281,X4279)))|X4280=c_List_Olist_ONil(X4281)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel__Nil1])])])). 6.97/7.23 cnf(c_0_8322, 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),hAPP(c_Nat_OSuc,X2)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[c_0_5364, c_0_4471])). 6.97/7.23 fof(c_0_8323, plain, ![X10236, X10237, X10238, X10239, X10240, X10241, X10242]:((~hBOOL(hAPP(X10236,X10239))|~hBOOL(hAPP(hAPP(c_member(X10238),X10239),hAPP(c_List_Oset(X10238),X10237)))|c_List_Olist__ex(X10238,X10236,X10237))&((hBOOL(hAPP(X10240,esk335_3(X10240,X10241,X10242)))|~c_List_Olist__ex(X10242,X10240,X10241))&(hBOOL(hAPP(hAPP(c_member(X10242),esk335_3(X10240,X10241,X10242)),hAPP(c_List_Oset(X10242),X10241)))|~c_List_Olist__ex(X10242,X10240,X10241)))), 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__list__ex])])])])])])). 6.97/7.23 fof(c_0_8324, plain, ![X5538, X5539, X5540, X5542, X5543, X5544, X5545]:(((hBOOL(hAPP(hAPP(c_member(X5540),esk181_3(X5538,X5539,X5540)),hAPP(c_List_Oset(X5540),X5538)))|~c_List_Olist__ex(X5540,X5539,X5538))&(hBOOL(hAPP(X5539,esk181_3(X5538,X5539,X5540)))|~c_List_Olist__ex(X5540,X5539,X5538)))&(~hBOOL(hAPP(hAPP(c_member(X5544),X5545),hAPP(c_List_Oset(X5544),X5542)))|~hBOOL(hAPP(X5543,X5545))|c_List_Olist__ex(X5544,X5543,X5542))), 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])])])])])])). 6.97/7.23 fof(c_0_8325, plain, ![X2180, X2181, X2182, X2183, X2184, X2185, X2186]:((~hBOOL(hAPP(hAPP(c_member(X2182),X2183),hAPP(c_List_Oset(X2182),X2180)))|~hBOOL(hAPP(X2181,X2183))|c_List_Olist__ex(X2182,X2181,X2180))&((hBOOL(hAPP(hAPP(c_member(X2186),esk66_3(X2184,X2185,X2186)),hAPP(c_List_Oset(X2186),X2184)))|~c_List_Olist__ex(X2186,X2185,X2184))&(hBOOL(hAPP(X2185,esk66_3(X2184,X2185,X2186)))|~c_List_Olist__ex(X2186,X2185,X2184)))), 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__raw])])])])])])). 6.97/7.23 fof(c_0_8326, plain, ![X11405, X11406, X11407]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X11407),tc_List_Olist(X11407))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X11407),tc_List_Olist(X11407)),X11406),c_List_Olist_ONil(X11407))),c_List_Olistrel(X11407,X11405)))|c_List_Olist_ONil(X11407)=X11406), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel__Nil2])])])). 6.97/7.23 fof(c_0_8327, plain, ![X13398, X13399, X13400, X13401, X13402]:(~class_Orderings_Olinorder(X13402)|hAPP(c_List_Ofilter(X13401,X13400),c_List_Olinorder__class_Osort__key(X13401,X13402,X13399,X13398))=c_List_Olinorder__class_Osort__key(X13401,X13402,X13399,hAPP(c_List_Ofilter(X13401,X13400),X13398))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_filter__sort])])). 6.97/7.23 cnf(c_0_8328, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,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))=hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)|~class_Int_Onumber__ring(X2)), inference(split_conjunct,[status(thm)],[c_0_5365])). 6.97/7.23 fof(c_0_8329, plain, ![X6377, X6378]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6378),X6377))|(hAPP(c_Nat_OSuc,X6378)=X6377|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X6378)),X6377)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Suc__lessI])])])). 6.97/7.23 cnf(c_0_8330, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk504_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_5366])). 6.97/7.23 cnf(c_0_8331, 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_5367]), ['final']). 6.97/7.23 fof(c_0_8332, plain, ![X15944, X15945]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15945),X15944))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X15944),X15945),X15945)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X15944,X15945)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__mod__geq])])). 6.97/7.23 fof(c_0_8333, plain, ![X9675, X9676]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X9676),X9675))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X9675),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X9675),X9676))=X9676), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__diff__cancel])])])). 6.97/7.23 fof(c_0_8334, plain, ![X15852, X15853, X15854]:(~class_Lattices_Olattice(X15854)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15854),X15853))|(~hBOOL(hAPP(hAPP(c_member(X15854),X15852),X15853))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15854),X15852),c_Big__Operators_Olattice__class_OInf__fin(X15854,X15853))=X15852))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__Inf__absorb])])])). 6.97/7.23 fof(c_0_8335, plain, ![X4173, X4174, X4175]:(~class_Lattices_Olattice(X4175)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4175),X4174))|(~hBOOL(hAPP(hAPP(c_member(X4175),X4173),X4174))|X4173=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4175),X4173),c_Big__Operators_Olattice__class_OSup__fin(X4175,X4174))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__Sup__absorb])])])). 6.97/7.23 cnf(c_0_8336, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)=X1|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),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_5368])). 6.97/7.23 fof(c_0_8337, plain, ![X3733, X3734, X3735]:(~c_Relation_Otrans(X3735,X3734)|(~c_Relation_Otrans(X3735,X3733)|c_Relation_Otrans(X3735,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3735,X3735),tc_HOL_Obool)),X3734),X3733)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__Int])])). 6.97/7.23 fof(c_0_8338, plain, ![X1347, X1348, X1349]:(~c_Relation_Osym(X1349,X1348)|(~c_Relation_Osym(X1349,X1347)|c_Relation_Osym(X1349,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1349,X1349),tc_HOL_Obool)),X1348),X1347)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sym__Int])])])). 6.97/7.23 cnf(c_0_8339, plain, (hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(X1,esk231_3(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(X3,tc_Nat_Onat),X1),X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))), inference(split_conjunct,[status(thm)],[c_0_5134])). 6.97/7.23 fof(c_0_8340, plain, ![X17041, X17042, X17043]:(~c_Relation_Osym(X17043,X17042)|(~c_Relation_Osym(X17043,X17041)|c_Relation_Osym(X17043,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X17043,X17043),tc_HOL_Obool)),X17042),X17041)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sym__Un])])])). 6.97/7.23 fof(c_0_8341, plain, ![X12809, X12810, X12811, X12812, X12813]:(~c_Finite__Set_Ofun__left__comm__idem(X12813,X12812,X12811)|c_Finite__Set_Ofun__left__comm__idem(X12810,X12812,hAPP(hAPP(c_COMBB(X12813,tc_fun(X12812,X12812),X12810),X12811),X12809))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__comm__idem__apply])])])). 6.97/7.23 fof(c_0_8342, plain, ![X5565, X5566, X5567, X5568, X5569]:(~c_Finite__Set_Ofun__left__comm(X5569,X5568,X5567)|c_Finite__Set_Ofun__left__comm(X5566,X5568,hAPP(hAPP(c_COMBB(X5569,tc_fun(X5568,X5568),X5566),X5567),X5565))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofun__left__comm__apply])])])). 6.97/7.23 fof(c_0_8343, plain, ![X2054, X2055, X2056]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2056|hAPP(c_List_Oset(X2055),c_List_Oreplicate(X2055,X2056,X2054))=hAPP(hAPP(c_Set_Oinsert(X2055),X2054),c_Orderings_Obot__class_Obot(tc_fun(X2055,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__replicate])])). 6.97/7.23 fof(c_0_8344, plain, ![X16755, X16756]:(~class_Rings_Osemiring__1(X16756)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16756),c_Groups_Oone__class_Oone(X16756)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X16756),X16755))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X16756),hAPP(c_Nat_OSuc,X16755))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__Suc])])])). 6.97/7.23 cnf(c_0_8345, plain, (X2=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),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_5328])). 6.97/7.23 cnf(c_0_8346, 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_5276])). 6.97/7.23 fof(c_0_8347, plain, ![X13507, X13508, X13509]:(hBOOL(hAPP(hAPP(c_member(X13509),X13508),hAPP(c_List_Oset(X13509),X13507)))|X13507=c_List_Oremove1(X13509,X13508,X13507)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_remove1__idem])])])). 6.97/7.23 cnf(c_0_8348, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)!=X2|~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_5369])). 6.97/7.23 fof(c_0_8349, plain, ![X12397, X12398, X12399, X12400, X12401]:(~c_Finite__Set_Ofun__left__comm__idem(X12401,X12400,X12399)|hAPP(hAPP(X12399,X12398),X12397)=hAPP(hAPP(X12399,X12398),hAPP(hAPP(X12399,X12398),X12397))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__idem])])])). 6.97/7.23 fof(c_0_8350, plain, ![X8992, X8993, X8994, X8995]:(~hBOOL(hAPP(hAPP(c_member(X8995),X8994),hAPP(c_List_Oset(X8995),c_List_Osublist(X8995,X8993,X8992))))|hBOOL(hAPP(hAPP(c_member(X8995),X8994),hAPP(c_List_Oset(X8995),X8993)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_in__set__sublistD])])])). 6.97/7.23 fof(c_0_8351, plain, ![X8808, X8809, X8810, X8811]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X8811,X8810),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X8809),X8808)))|(X8810=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X8809=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8811),X8810))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__div])])])). 6.97/7.23 fof(c_0_8352, plain, ![X3792, X3793, X3794, X3795]:(~hBOOL(hAPP(X3795,X3794))|(~hBOOL(hAPP(X3793,X3794))|hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3792,tc_HOL_Obool)),X3795),X3793),X3794)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf1I])])])). 6.97/7.23 fof(c_0_8353, plain, ![X14974, X14975, X14976, X14977]:(hBOOL(hAPP(hAPP(c_member(X14977),X14976),hAPP(c_List_Oset(X14977),X14975)))|~hBOOL(hAPP(hAPP(c_member(X14977),X14976),hAPP(c_List_Oset(X14977),c_List_Oremove1(X14977,X14974,X14975))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_notin__set__remove1])])])). 6.97/7.23 fof(c_0_8354, plain, ![X16744, X16745, X16746, X16747]:((hBOOL(hAPP(X16745,X16746))|~hBOOL(hAPP(hAPP(c_member(X16747),X16746),hAPP(c_List_Oset(X16747),c_List_OtakeWhile(X16747,X16745,X16744)))))&(hBOOL(hAPP(hAPP(c_member(X16747),X16746),hAPP(c_List_Oset(X16747),X16744)))|~hBOOL(hAPP(hAPP(c_member(X16747),X16746),hAPP(c_List_Oset(X16747),c_List_OtakeWhile(X16747,X16745,X16744)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_set__takeWhileD])])])])). 6.97/7.23 fof(c_0_8355, plain, ![X16370, X16371]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16371),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,X16370,X16371)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__mod__sign])])])). 6.97/7.23 fof(c_0_8356, plain, ![X6416, X6417]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6417))|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,X6416,X6417)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__sign])])). 6.97/7.23 fof(c_0_8357, plain, ![X3301]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3301))|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),X3301))))&(~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),X3301)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3301)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__int__conv])])). 6.97/7.23 fof(c_0_8358, plain, ![X15383, X15384, X15385, X15386]:(~class_Orderings_Olinorder(X15386)|hAPP(hAPP(c_List_Olist_OCons(X15385),X15383),c_List_Olist_ONil(X15385))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X15385,X15386,X15384),X15383),c_List_Olist_ONil(X15385))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__key_Osimps_I1_J])])). 6.97/7.23 fof(c_0_8359, plain, ![X1688, X1689]:(~class_Orderings_Olinorder(X1689)|X1688=c_Big__Operators_Olattice_OSup__fin(X1689,c_Orderings_Oord__class_Omax(X1689),hAPP(hAPP(c_Set_Oinsert(X1689),X1688),c_Orderings_Obot__class_Obot(tc_fun(X1689,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Osingleton])])). 6.97/7.23 fof(c_0_8360, plain, ![X12048, X12049]:(~class_Orderings_Olinorder(X12049)|X12048=c_Big__Operators_Olattice_OInf__fin(X12049,c_Orderings_Oord__class_Omin(X12049),hAPP(hAPP(c_Set_Oinsert(X12049),X12048),c_Orderings_Obot__class_Obot(tc_fun(X12049,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Osingleton])])])). 6.97/7.23 fof(c_0_8361, plain, ![X3219, X3220]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3220),X3219),c_Groups_Ozero__class_Ozero(X3220)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3220),c_Groups_Osgn__class_Osgn(X3220,X3219)),c_Groups_Ozero__class_Ozero(X3220)))|~class_Rings_Olinordered__idom(X3220))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3220),c_Groups_Osgn__class_Osgn(X3220,X3219)),c_Groups_Ozero__class_Ozero(X3220)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3220),X3219),c_Groups_Ozero__class_Ozero(X3220)))|~class_Rings_Olinordered__idom(X3220))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sgn__less])])])])). 6.97/7.23 fof(c_0_8362, plain, ![X15511, X15512, X15513, X15514]:((~hBOOL(hAPP(hAPP(c_member(X15514),X15513),X15511))|X15512!=X15513|hBOOL(hAPP(hAPP(c_member(tc_prod(X15514,X15514)),hAPP(hAPP(c_Product__Type_OPair(X15514,X15514),X15513),X15512)),c_Relation_OId__on(X15514,X15511))))&((hBOOL(hAPP(hAPP(c_member(X15514),X15513),X15511))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X15514,X15514)),hAPP(hAPP(c_Product__Type_OPair(X15514,X15514),X15513),X15512)),c_Relation_OId__on(X15514,X15511))))&(X15512=X15513|~hBOOL(hAPP(hAPP(c_member(tc_prod(X15514,X15514)),hAPP(hAPP(c_Product__Type_OPair(X15514,X15514),X15513),X15512)),c_Relation_OId__on(X15514,X15511)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__on__iff])])])). 6.97/7.23 fof(c_0_8363, plain, ![X6115, X6116]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6116),c_Groups_Ozero__class_Ozero(X6116)),X6115))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6116),c_Groups_Ozero__class_Ozero(X6116)),c_Groups_Osgn__class_Osgn(X6116,X6115)))|~class_Rings_Olinordered__idom(X6116))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6116),c_Groups_Ozero__class_Ozero(X6116)),c_Groups_Osgn__class_Osgn(X6116,X6115)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6116),c_Groups_Ozero__class_Ozero(X6116)),X6115))|~class_Rings_Olinordered__idom(X6116))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sgn__greater])])])])). 6.97/7.23 fof(c_0_8364, plain, ![X14160, X14161, X14162]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14162),X14161))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14162,tc_HOL_Obool)),X14160),X14161))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X14162),X14161)),hAPP(c_Finite__Set_Ocard(X14162),X14160)))|X14160=X14161))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__seteq])])])). 6.97/7.23 cnf(c_0_8365, 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_4607])). 6.97/7.23 cnf(c_0_8366, 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_4608])). 6.97/7.23 fof(c_0_8367, plain, ![X16703, X16704]:(~class_Groups_Oordered__ab__group__add__abs(X16704)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16704),hAPP(c_Groups_Ouminus__class_Ouminus(X16704),X16703)),hAPP(c_Groups_Oabs__class_Oabs(X16704),X16703)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__ge__minus__self])])])). 6.97/7.23 fof(c_0_8368, plain, ![X14304, X14305]:(~class_Rings_Olinordered__ring(X14305)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14305),c_Groups_Ozero__class_Ozero(X14305)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14305),X14304),X14304)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__le__square])])])). 6.97/7.23 fof(c_0_8369, plain, ![X2431, X2432, X2433, X2434, X2435, X2436]:(hBOOL(hAPP(hAPP(c_member(X2436),X2435),X2434))|hAPP(X2432,X2435)=hAPP(c_Fun_Ooverride__on(X2436,X2433,X2432,X2431,X2434),X2435)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_override__on__apply__notin])])])). 6.97/7.23 fof(c_0_8370, plain, ![X17160, X17161, X17162, X17164, X17165, X17166, X17167, X17168, X17171]:((~hBOOL(hAPP(X17162,esk583_3(X17160,X17161,X17162)))|hBOOL(hAPP(X17162,hAPP(hAPP(c_Product__Type_OPair(X17161,X17160),X17164),X17165))))&(~hBOOL(hAPP(X17168,hAPP(hAPP(c_Product__Type_OPair(X17167,X17166),esk584_3(X17166,X17167,X17168)),esk585_3(X17166,X17167,X17168))))|hBOOL(hAPP(X17168,X17171)))), 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])])])])])). 6.97/7.23 fof(c_0_8371, plain, ![X13354, X13355]:(~class_Rings_Olinordered__semidom(X13355)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13355),X13354),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13355),X13354),c_Groups_Oone__class_Oone(X13355))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])])). 6.97/7.23 cnf(c_0_8372, 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))))|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_5370, c_0_4565])). 6.97/7.23 fof(c_0_8373, plain, ![X16096, X16097, X16098, X16099, X16100]:(~c_Equiv__Relations_Opart__equivp(X16100,X16099)|(~hBOOL(hAPP(hAPP(X16099,X16098),X16097))|(~hBOOL(hAPP(hAPP(X16099,X16097),X16096))|hBOOL(hAPP(hAPP(X16099,X16098),X16096))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_part__equivp__transp])])])). 6.97/7.23 fof(c_0_8374, plain, ![X9563, X9564, X9565, X9566, X9567]:(~c_Predicate_Otransp(X9567,X9566)|(~hBOOL(hAPP(hAPP(X9566,X9565),X9564))|(~hBOOL(hAPP(hAPP(X9566,X9564),X9563))|hBOOL(hAPP(hAPP(X9566,X9565),X9563))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transpE])])])). 6.97/7.23 cnf(c_0_8375, 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_5371])). 6.97/7.23 cnf(c_0_8376, plain, (c_Relation_Otrans(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))|~c_Predicate_Otransp(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5372])). 6.97/7.23 cnf(c_0_8377, plain, (c_Relation_Osym(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))|~c_Predicate_Osymp(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5373])). 6.97/7.23 fof(c_0_8378, plain, ![X1320, X1321, X1322, X1323, X1324]:(~c_Equiv__Relations_Oequivp(X1324,X1323)|(~hBOOL(hAPP(hAPP(X1323,X1322),X1321))|(~hBOOL(hAPP(hAPP(X1323,X1321),X1320))|hBOOL(hAPP(hAPP(X1323,X1322),X1320))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equivp__transp])])])). 6.97/7.23 fof(c_0_8379, plain, ![X9450, X9451, X9452, X9453, X9454]:((~c_List_Olist__all2(X9454,X9453,X9452,hAPP(c_List_Orev(X9454),X9451),hAPP(c_List_Orev(X9453),X9450))|c_List_Olist__all2(X9454,X9453,X9452,X9451,X9450))&(~c_List_Olist__all2(X9454,X9453,X9452,X9451,X9450)|c_List_Olist__all2(X9454,X9453,X9452,hAPP(c_List_Orev(X9454),X9451),hAPP(c_List_Orev(X9453),X9450)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__rev])])). 6.97/7.23 fof(c_0_8380, plain, ![X13013, X13015, X13016]:(((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk425_1(X13013)),hAPP(c_List_Oset(tc_Nat_Onat),X13013)))|hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X13013)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(esk425_1(X13013)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X13013)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X13015)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X13016),hAPP(c_List_Oset(tc_Nat_Onat),X13015)))|X13016=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_listsum__eq__0__nat__iff__nat])])])])])])). 6.97/7.23 cnf(c_0_8381, 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_5374])). 6.97/7.23 cnf(c_0_8382, 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_5365])). 6.97/7.23 fof(c_0_8383, plain, ![X15351, X15352, X15353, X15354]:(~c_Finite__Set_Ofolding__one(X15354,X15353,X15352)|X15351=hAPP(X15352,hAPP(hAPP(c_Set_Oinsert(X15354),X15351),c_Orderings_Obot__class_Obot(tc_fun(X15354,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Osingleton])])). 6.97/7.23 fof(c_0_8384, plain, ![X612, X613, X614, X615, X616]:(~c_Fun_Oinj__on(X616,X615,X614,X613)|(~hBOOL(hAPP(hAPP(c_member(X616),X612),X613))|hAPP(c_Hilbert__Choice_Oinv__into(X616,X615,X613,X614),hAPP(X614,X612))=X612)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__f__f])])). 6.97/7.23 cnf(c_0_8385, plain, (X3=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X4)|X1!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X4)|c_Groups_Ozero__class_Ozero(X2)!=X3|~class_Fields_Ofield__inverse__zero(X2)), inference(split_conjunct,[status(thm)],[c_0_5375])). 6.97/7.23 fof(c_0_8386, plain, ![X3268, X3269, X3270]:(~class_Groups_Oab__group__add(X3270)|hAPP(c_Groups_Ouminus__class_Ouminus(X3270),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3270),X3269),X3268))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3270),X3268),X3269)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__diff__eq])])])). 6.97/7.23 fof(c_0_8387, plain, ![X15168, X15169]:(~class_Orderings_Oorder(X15169)|c_SetInterval_Oord__class_OatLeastAtMost(X15169,X15168,X15168)=hAPP(hAPP(c_Set_Oinsert(X15169),X15168),c_Orderings_Obot__class_Obot(tc_fun(X15169,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton])])). 6.97/7.23 fof(c_0_8388, plain, ![X10861, X10862, X10863, X10864, X10865]:(~c_Fun_Oinj__on(X10865,X10864,X10863,X10862)|c_Fun_Oinj__on(X10865,X10864,X10863,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10865,tc_HOL_Obool)),X10862),X10861))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__diff])])])). 6.97/7.23 fof(c_0_8389, plain, ![X1013, X1014, X1015, X1016, X1017]:(~c_Fun_Oinj__on(X1017,X1016,X1015,X1014)|(~hBOOL(hAPP(hAPP(c_member(X1017),X1013),X1014))|X1013=hAPP(c_Fun_Othe__inv__into(X1017,X1016,X1014,X1015),hAPP(X1015,X1013)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_the__inv__into__f__f])])])). 6.97/7.23 fof(c_0_8390, plain, ![X17619, X17620, X17621]:((X17619!=X17620|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17619),X17621)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17620),X17621)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17621),X17619))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17621),X17620)))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17619),X17621)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17620),X17621)|X17619=X17620|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17621),X17619))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17621),X17620)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__diff__iff])])])])). 6.97/7.23 fof(c_0_8391, plain, ![X6333, X6334, X6335]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6335),X6334))|hBOOL(hAPP(c_Finite__Set_Ofinite(X6335),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6335,tc_HOL_Obool)),X6334),X6333)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Diff])])). 6.97/7.23 fof(c_0_8392, plain, ![X5417, X5418, X5419]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X5419),X5417))|hBOOL(hAPP(c_Finite__Set_Ofinite(X5419),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5419,tc_HOL_Obool)),X5418),X5417))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5419),X5418))|hBOOL(hAPP(c_Finite__Set_Ofinite(X5419),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5419,tc_HOL_Obool)),X5418),X5417))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__Int])])])])). 6.97/7.23 fof(c_0_8393, plain, ![X7382, X7383]:((hAPP(c_Groups_Ouminus__class_Ouminus(X7383),c_Groups_Oone__class_Oone(X7383))!=c_Groups_Osgn__class_Osgn(X7383,X7382)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7383),X7382),c_Groups_Ozero__class_Ozero(X7383)))|~class_Rings_Olinordered__idom(X7383))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7383),X7382),c_Groups_Ozero__class_Ozero(X7383)))|hAPP(c_Groups_Ouminus__class_Ouminus(X7383),c_Groups_Oone__class_Oone(X7383))=c_Groups_Osgn__class_Osgn(X7383,X7382)|~class_Rings_Olinordered__idom(X7383))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sgn__1__neg])])])])). 6.97/7.23 fof(c_0_8394, plain, ![X7400, X7401]:(~class_Rings_Olinordered__idom(X7401)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7401),X7400),c_Groups_Ozero__class_Ozero(X7401)))|c_Groups_Osgn__class_Osgn(X7401,X7400)=hAPP(c_Groups_Ouminus__class_Ouminus(X7401),c_Groups_Oone__class_Oone(X7401)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__neg])])). 6.97/7.23 cnf(c_0_8395, plain, (c_List_Oconcat(X2,X1)=c_List_Olist_ONil(X2)|esk590_2(X1,X2)!=c_List_Olist_ONil(X2)), inference(split_conjunct,[status(thm)],[c_0_5129])). 6.97/7.23 cnf(c_0_8396, plain, (X3=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4)|c_Groups_Ozero__class_Ozero(X2)=X4|X1!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X3),X4)|~class_Rings_Odivision__ring(X2)), inference(split_conjunct,[status(thm)],[c_0_5376])). 6.97/7.23 cnf(c_0_8397, plain, (c_List_Oconcat(X1,X2)=c_List_Olist_ONil(X1)|c_List_Olist_ONil(X1)!=esk462_2(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_5130])). 6.97/7.23 fof(c_0_8398, plain, ![X6055, X6056, X6057]:(~class_Groups_Ocomm__monoid__mult(X6057)|c_Groups_Oone__class_Oone(X6057)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X6056,X6057),hAPP(c_COMBK(X6057,X6056),c_Groups_Oone__class_Oone(X6057))),X6055)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__1])])). 6.97/7.23 fof(c_0_8399, plain, ![X8785, X8786, X8787]:(~class_Groups_Ocomm__monoid__add(X8787)|c_Groups_Ozero__class_Ozero(X8787)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8786,X8787),hAPP(c_COMBK(X8787,X8786),c_Groups_Ozero__class_Ozero(X8787))),X8785)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__0])])])). 6.97/7.23 fof(c_0_8400, plain, ![X9291, X9292, X9293]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9293),X9292),X9291))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9293),hAPP(c_Groups_Ouminus__class_Ouminus(X9293),X9292)),X9291))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9293),hAPP(c_Groups_Oabs__class_Oabs(X9293),X9292)),X9291))|~class_Groups_Oordered__ab__group__add__abs(X9293))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9293),X9292),X9291))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9293),hAPP(c_Groups_Oabs__class_Oabs(X9293),X9292)),X9291))|~class_Groups_Oordered__ab__group__add__abs(X9293))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9293),hAPP(c_Groups_Ouminus__class_Ouminus(X9293),X9292)),X9291))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9293),hAPP(c_Groups_Oabs__class_Oabs(X9293),X9292)),X9291))|~class_Groups_Oordered__ab__group__add__abs(X9293)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__iff])])])). 6.97/7.23 fof(c_0_8401, plain, ![X13291]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13291),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,esk435_1(X13291))))=X13291), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_negD])])])])). 6.97/7.23 fof(c_0_8402, plain, ![X6705, X6706, X6707]:(~class_Complete__Lattice_Ocomplete__lattice(X6707)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6707),X6706),c_Complete__Lattice_OInf__class_OInf(X6707,X6705))=c_Complete__Lattice_OInf__class_OInf(X6707,hAPP(hAPP(c_Set_Oinsert(X6707),X6706),X6705))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__insert])])). 6.97/7.23 fof(c_0_8403, plain, ![X1317, X1318, X1319]:(~class_Complete__Lattice_Ocomplete__lattice(X1319)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1319),X1318),c_Complete__Lattice_OSup__class_OSup(X1319,X1317))=c_Complete__Lattice_OSup__class_OSup(X1319,hAPP(hAPP(c_Set_Oinsert(X1319),X1318),X1317))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__insert])])])). 6.97/7.23 fof(c_0_8404, plain, ![X4595, X4596, X4597]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4597,X4596)),hAPP(c_Relation_Oconverse(X4596,X4597),X4595)))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4596,X4597)),X4595)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4596,X4597)),X4595))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4597,X4596)),hAPP(c_Relation_Oconverse(X4596,X4597),X4595))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__converse])])). 6.97/7.23 fof(c_0_8405, plain, ![X5037, X5038, X5039]:(~hBOOL(hAPP(hAPP(c_member(X5039),X5038),hAPP(c_List_Oset(X5039),c_List_Obutlast(X5039,X5037))))|hBOOL(hAPP(hAPP(c_member(X5039),X5038),hAPP(c_List_Oset(X5039),X5037)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__butlastD])])). 6.97/7.23 cnf(c_0_8406, 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|hAPP(c_Relation_ODomain(X1,X1),X2)!=X3), inference(split_conjunct,[status(thm)],[c_0_5377])). 6.97/7.23 cnf(c_0_8407, 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_5378])). 6.97/7.23 fof(c_0_8408, plain, ![X9508, X9509]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X9509),X9508))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X9509)),hAPP(c_Code__Numeral_Onat__of,X9508))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X9509)),hAPP(c_Code__Numeral_Onat__of,X9508)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X9509),X9508)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__code__numeral__def])])). 6.97/7.23 fof(c_0_8409, plain, ![X1356, X1357]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1357),X1356))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1357)),hAPP(c_Nat_OSuc,X1356)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mono])])). 6.97/7.23 fof(c_0_8410, plain, ![X11108, X11109, X11110, X11111, X11112, X11113]:((~c_Predicate_Oinv__imagep(X11113,X11112,X11111,X11110,X11109,X11108)|hBOOL(hAPP(hAPP(X11111,hAPP(X11110,X11109)),hAPP(X11110,X11108))))&(~hBOOL(hAPP(hAPP(X11111,hAPP(X11110,X11109)),hAPP(X11110,X11108)))|c_Predicate_Oinv__imagep(X11113,X11112,X11111,X11110,X11109,X11108))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__inv__imagep])])). 6.97/7.23 fof(c_0_8411, plain, ![X12692, X12693, X12694]:(~class_Rings_Olinordered__ring(X12694)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12694),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12694),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12694),X12693),X12693)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12694),X12692),X12692))),c_Groups_Ozero__class_Ozero(X12694)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__sum__squares__lt__zero])])])). 6.97/7.23 cnf(c_0_8412, 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_5379])). 6.97/7.23 fof(c_0_8413, plain, ![X16415, X16416]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X16416),X16415))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X16416)),hAPP(c_Code__Numeral_Onat__of,X16415))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X16416)),hAPP(c_Code__Numeral_Onat__of,X16415)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X16416),X16415)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__code__numeral__def])])). 6.97/7.23 fof(c_0_8414, plain, ![X406, X407, X408]:((~c_Nat__Transfer_Onat__set(X406)|(~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X407),X406))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X407))))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk6_1(X408)),X408))|c_Nat__Transfer_Onat__set(X408))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk6_1(X408)))|c_Nat__Transfer_Onat__set(X408)))), 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])])])])])])])). 6.97/7.23 fof(c_0_8415, plain, ![X9695, X9696, X9697]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9697),X9696),X9695))|hBOOL(hAPP(hAPP(c_member(X9697),X9696),hAPP(c_SetInterval_Oord__class_OlessThan(X9697),X9695)))|~class_Orderings_Oord(X9697))&(~hBOOL(hAPP(hAPP(c_member(X9697),X9696),hAPP(c_SetInterval_Oord__class_OlessThan(X9697),X9695)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9697),X9696),X9695))|~class_Orderings_Oord(X9697))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lessThan__iff])])])). 6.97/7.23 fof(c_0_8416, plain, ![X9975, X9976]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9975),X9976))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9976),X9975))), inference(variable_rename,[status(thm)],[fact_zle__linear])). 6.97/7.23 fof(c_0_8417, plain, ![X8472, X8473, X8474, X8475]:((X8473!=X8472|hAPP(hAPP(c_Power_Opower__class_Opower(X8475),X8474),X8473)=hAPP(hAPP(c_Power_Opower__class_Opower(X8475),X8474),X8472)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8475),c_Groups_Oone__class_Oone(X8475)),X8474))|~class_Rings_Olinordered__semidom(X8475))&(hAPP(hAPP(c_Power_Opower__class_Opower(X8475),X8474),X8473)!=hAPP(hAPP(c_Power_Opower__class_Opower(X8475),X8474),X8472)|X8473=X8472|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8475),c_Groups_Oone__class_Oone(X8475)),X8474))|~class_Rings_Olinordered__semidom(X8475))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__inject__exp])])])])). 6.97/7.23 cnf(c_0_8418, 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_5045])). 6.97/7.23 fof(c_0_8419, plain, ![X5560, X5561, X5562]:((~c_Fun_Oinj__on(X5562,X5561,X5560,c_Orderings_Otop__class_Otop(tc_fun(X5562,tc_HOL_Obool)))|hAPP(c_Fun_Ocomp(X5561,X5562,X5562,c_Hilbert__Choice_Oinv__into(X5562,X5561,c_Orderings_Otop__class_Otop(tc_fun(X5562,tc_HOL_Obool)),X5560)),X5560)=c_Fun_Oid(X5562))&(hAPP(c_Fun_Ocomp(X5561,X5562,X5562,c_Hilbert__Choice_Oinv__into(X5562,X5561,c_Orderings_Otop__class_Otop(tc_fun(X5562,tc_HOL_Obool)),X5560)),X5560)!=c_Fun_Oid(X5562)|c_Fun_Oinj__on(X5562,X5561,X5560,c_Orderings_Otop__class_Otop(tc_fun(X5562,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__iff])])). 6.97/7.23 fof(c_0_8420, plain, ![X11241, X11242]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11241),X11242))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11242),X11241))), inference(variable_rename,[status(thm)],[fact_nat__le__linear])). 6.97/7.23 cnf(c_0_8421, 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_5380])). 6.97/7.23 fof(c_0_8422, plain, ![X16434, X16435, X16436]:((~hBOOL(hAPP(hAPP(c_member(X16436),X16435),hAPP(c_SetInterval_Oord__class_OatMost(X16436),X16434)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16436),X16435),X16434))|~class_Orderings_Oord(X16436))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16436),X16435),X16434))|hBOOL(hAPP(hAPP(c_member(X16436),X16435),hAPP(c_SetInterval_Oord__class_OatMost(X16436),X16434)))|~class_Orderings_Oord(X16436))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__iff])])])). 6.97/7.23 fof(c_0_8423, plain, ![X7130, X7131, X7132]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7132),X7130),X7131))|hBOOL(hAPP(hAPP(c_member(X7132),X7131),hAPP(c_SetInterval_Oord__class_OgreaterThan(X7132),X7130)))|~class_Orderings_Oord(X7132))&(~hBOOL(hAPP(hAPP(c_member(X7132),X7131),hAPP(c_SetInterval_Oord__class_OgreaterThan(X7132),X7130)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7132),X7130),X7131))|~class_Orderings_Oord(X7132))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__iff])])])). 6.97/7.23 fof(c_0_8424, plain, ![X8919, X8920, X8921]:((~hBOOL(hAPP(hAPP(c_member(X8921),X8920),hAPP(c_SetInterval_Oord__class_OatLeast(X8921),X8919)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8921),X8919),X8920))|~class_Orderings_Oord(X8921))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8921),X8919),X8920))|hBOOL(hAPP(hAPP(c_member(X8921),X8920),hAPP(c_SetInterval_Oord__class_OatLeast(X8921),X8919)))|~class_Orderings_Oord(X8921))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeast__iff])])])])). 6.97/7.23 fof(c_0_8425, plain, ![X452, X453, X454]:((~c_List_Olist__ex(tc_Int_Oint,X454,c_List_Oupto(X453,X452))|~c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),X454),X453,X452))&(c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),X454),X453,X452)|c_List_Olist__ex(tc_Int_Oint,X454,c_List_Oupto(X453,X452)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__ex__iff__not__all__inverval__int])])])). 6.97/7.23 fof(c_0_8426, plain, ![X6959, X6960]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6960),c_Orderings_Otop__class_Otop(tc_fun(X6960,tc_HOL_Obool))))|(hAPP(c_Finite__Set_Ocard(X6960),c_Orderings_Otop__class_Otop(tc_fun(X6960,tc_HOL_Obool)))!=hAPP(c_Finite__Set_Ocard(X6960),X6959)|X6959=c_Orderings_Otop__class_Otop(tc_fun(X6960,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])])])). 6.97/7.23 cnf(c_0_8427, 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_5381])). 6.97/7.23 fof(c_0_8428, plain, ![X5640, X5641, X5642, X5643]:((X5640!=hAPP(hAPP(c_List_Onth(X5642),X5641),X5643)|X5641=hAPP(hAPP(c_List_Olist__update(X5642,X5641),X5643),X5640)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5643),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5642)),X5641))))&(X5641!=hAPP(hAPP(c_List_Olist__update(X5642,X5641),X5643),X5640)|X5640=hAPP(hAPP(c_List_Onth(X5642),X5641),X5643)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5643),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5642)),X5641))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__update__same__conv])])])])). 6.97/7.23 fof(c_0_8429, plain, ![X3982, X3983, X3984, X3986, X3987, X3988, X3989]:(((hBOOL(hAPP(hAPP(c_member(X3984),esk134_3(X3982,X3983,X3984)),X3982))|hBOOL(hAPP(c_Predicate_OPowp(X3984,X3983),X3982)))&(~hBOOL(hAPP(X3983,esk134_3(X3982,X3983,X3984)))|hBOOL(hAPP(c_Predicate_OPowp(X3984,X3983),X3982))))&(~hBOOL(hAPP(c_Predicate_OPowp(X3988,X3987),X3986))|(~hBOOL(hAPP(hAPP(c_member(X3988),X3989),X3986))|hBOOL(hAPP(X3987,X3989))))), 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_Powp__def])])])])])])). 6.97/7.23 fof(c_0_8430, plain, ![X5211, X5212]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5212))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5212),X5211))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X5212),X5211))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__pos__trivial])])). 6.97/7.23 cnf(c_0_8431, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2))=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5299])). 6.97/7.23 cnf(c_0_8432, 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_5194])). 6.97/7.23 fof(c_0_8433, plain, ![X7881, X7882]:((hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X7882,X7881))!=X7881|c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X7882),X7881)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X7882,X7881))=X7881|hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X7882,X7881))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X7882),X7881))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__Suc])])])). 6.97/7.23 fof(c_0_8434, plain, ![X1056, X1057, X1058, X1059, X1060]:(~c_Typedef_Otype__definition(X1060,X1059,X1058,X1057,X1056)|X1056=hAPP(c_Set_Oimage(X1060,X1059,X1058),c_Orderings_Otop__class_Otop(tc_fun(X1060,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__range])])). 6.97/7.23 cnf(c_0_8435, 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_5273])). 6.97/7.23 fof(c_0_8436, plain, ![X4573, X4574, X4575, X4576, X4577]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4577,tc_HOL_Obool)),X4576),hAPP(c_Set_Oimage(X4575,X4577,X4574),X4573)))|c_Fun_Oinj__on(X4577,X4575,c_Hilbert__Choice_Oinv__into(X4575,X4577,X4573,X4574),X4576)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__inv__into])])). 6.97/7.23 fof(c_0_8437, plain, ![X3695, X3696, X3697]:(~hBOOL(hAPP(hAPP(c_member(tc_fun(X3697,tc_HOL_Obool)),X3696),hAPP(c_Set_OPow(X3697),X3695)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3697,tc_HOL_Obool)),X3696),X3695))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_PowD])])])). 6.97/7.23 cnf(c_0_8438, 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_5382])). 6.97/7.23 fof(c_0_8439, plain, ![X9236, X9237, X9238, X9239, X9240]:(~c_Relation_Osingle__valued(X9240,X9239,X9238)|(~c_Relation_Osingle__valued(X9239,X9237,X9236)|c_Relation_Osingle__valued(X9240,X9237,hAPP(hAPP(c_Relation_Orel__comp(X9240,X9239,X9237),X9238),X9236)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_single__valued__rel__comp])])])). 6.97/7.23 cnf(c_0_8440, 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_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_5321])). 6.97/7.23 cnf(c_0_8441, 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_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_5322])). 6.97/7.23 cnf(c_0_8442, 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_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_5323])). 6.97/7.23 fof(c_0_8443, plain, ![X12460, X12461]:(~class_Rings_Ocomm__ring__1(X12461)|hAPP(c_Groups_Ouminus__class_Ouminus(X12461),X12460)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12461),hAPP(c_Groups_Ouminus__class_Ouminus(X12461),c_Groups_Oone__class_Oone(X12461))),X12460)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J])])])). 6.97/7.23 fof(c_0_8444, plain, ![X7239, X7240, X7241, X7242]:(~class_Orderings_Olinorder(X7242)|c_List_Olinorder__class_Osorted(X7242,hAPP(hAPP(c_List_Omap(X7241,X7242),X7240),c_List_Olinorder__class_Osort__key(X7241,X7242,X7240,X7239)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__sort__key])])). 6.97/7.23 cnf(c_0_8445, 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_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_5324])). 6.97/7.23 fof(c_0_8446, plain, ![X7838, X7839, X7840]:((X7838!=X7839|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7840),X7838)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7840),X7839)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7840)))&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7840),X7838)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7840),X7839)|X7838=X7839|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7840)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel1])])])). 6.97/7.23 fof(c_0_8447, plain, ![X11677, X11678, X11679, X11680]:(~c_Fun_Oinj__on(X11680,X11679,X11678,X11677)|hAPP(c_Finite__Set_Ocard(X11680),X11677)=hAPP(c_Finite__Set_Ocard(X11679),hAPP(c_Set_Oimage(X11680,X11679,X11678),X11677))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image])])). 6.97/7.23 fof(c_0_8448, plain, ![X15622, X15623, X15624]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X15624),X15623))|c_Random_Ominus__shift(X15622,X15624,X15623)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X15624),X15623))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X15624),X15623))|c_Random_Ominus__shift(X15622,X15624,X15623)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X15622),X15624)),X15623))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__shift__def])])])). 6.97/7.23 fof(c_0_8449, plain, ![X11885, X11886, X11887]:(~class_Lazy__Sequence_Osmall__lazy(X11886)|~class_Lazy__Sequence_Osmall__lazy(X11887)|c_Lazy__Sequence_Oproduct(X11887,X11886,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X11887,X11885),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X11886,X11885))=c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(X11887,X11886),X11885)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_small__lazy__prod__def])])])). 6.97/7.23 cnf(c_0_8450, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|X3=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)|~class_Rings_Odivision__ring(X1)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)!=X4), inference(split_conjunct,[status(thm)],[c_0_5383])). 6.97/7.23 fof(c_0_8451, plain, ![X17672, X17673]:(~class_Complete__Lattice_Ocomplete__lattice(X17673)|c_Complete__Lattice_OSup__class_OSup(X17673,hAPP(c_List_Oset(X17673),X17672))=hAPP(c_List_Ofoldl(X17673,X17673,c_Lattices_Osemilattice__sup__class_Osup(X17673),c_Orderings_Obot__class_Obot(X17673)),X17672)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__set__fold])])])). 6.97/7.23 fof(c_0_8452, plain, ![X8829, X8830]:(~class_Complete__Lattice_Ocomplete__lattice(X8830)|c_Complete__Lattice_OInf__class_OInf(X8830,hAPP(c_List_Oset(X8830),X8829))=hAPP(c_List_Ofoldl(X8830,X8830,c_Lattices_Osemilattice__inf__class_Oinf(X8830),c_Orderings_Otop__class_Otop(X8830)),X8829)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__set__fold])])])). 6.97/7.23 fof(c_0_8453, plain, ![X3885, X3886, X3887]:(~c_Relation_Osingle__valued(X3887,X3887,X3886)|c_Relation_Osingle__valued(X3887,X3887,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X3887,X3887),tc_HOL_Obool),X3885),X3886))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__rel__pow])])). 6.97/7.23 fof(c_0_8454, plain, ![X3302, X3303, X3304]:(~class_Orderings_Olinorder(X3304)|(~c_List_Olinorder__class_Osorted(X3304,X3303)|(~hBOOL(hAPP(c_List_Odistinct(X3304),X3303))|(~c_List_Olinorder__class_Osorted(X3304,X3302)|(~hBOOL(hAPP(c_List_Odistinct(X3304),X3302))|(hAPP(c_List_Oset(X3304),X3303)!=hAPP(c_List_Oset(X3304),X3302)|X3303=X3302)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__distinct__set__unique])])])). 6.97/7.23 fof(c_0_8455, plain, ![X10914, X10915, X10916, X10918, X10919, X10920, X10921, X10922]:(((~hBOOL(hAPP(X10916,X10918))|X10918=esk364_3(X10914,X10915,X10916)|c_FunDef_OTHE__default(X10915,X10914,X10916)=X10914)&(hBOOL(hAPP(X10916,esk364_3(X10914,X10915,X10916)))|c_FunDef_OTHE__default(X10915,X10914,X10916)=X10914))&((hBOOL(hAPP(X10921,esk365_4(X10919,X10920,X10921,X10922)))|~hBOOL(hAPP(X10921,X10922))|c_HOL_OThe(X10920,X10921)=c_FunDef_OTHE__default(X10920,X10919,X10921))&(esk365_4(X10919,X10920,X10921,X10922)!=X10922|~hBOOL(hAPP(X10921,X10922))|c_HOL_OThe(X10920,X10921)=c_FunDef_OTHE__default(X10920,X10919,X10921)))), 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])])])])])])])). 6.97/7.23 fof(c_0_8456, plain, ![X3947, X3948]:(X3948=c_List_Olist_ONil(X3947)|hBOOL(hAPP(hAPP(c_member(X3947),c_List_Olast(X3947,X3948)),hAPP(c_List_Oset(X3947),X3948)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__in__set])])). 6.97/7.23 cnf(c_0_8457, 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_5384])). 6.97/7.23 cnf(c_0_8458, plain, (hAPP(c_Int_Onat,X2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X2)),hAPP(c_Int_Onat,X1))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(split_conjunct,[status(thm)],[c_0_4878])). 6.97/7.23 cnf(c_0_8459, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Groups_Oabs__class_Oabs(X2),X1)),c_Groups_Ozero__class_Ozero(X2)))|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Oordered__ab__group__add__abs(X2)), inference(split_conjunct,[status(thm)],[c_0_5385])). 6.97/7.23 fof(c_0_8460, plain, ![X5768, X5769, X5770, X5771, X5772]:((~c_List_Olist__all2(X5772,X5771,X5770,hAPP(c_List_Orev(X5772),X5769),X5768)|c_List_Olist__all2(X5772,X5771,X5770,X5769,hAPP(c_List_Orev(X5771),X5768)))&(~c_List_Olist__all2(X5772,X5771,X5770,X5769,hAPP(c_List_Orev(X5771),X5768))|c_List_Olist__all2(X5772,X5771,X5770,hAPP(c_List_Orev(X5772),X5769),X5768))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__rev1])])). 6.97/7.23 fof(c_0_8461, plain, ![X990, X991, X992]:((c_Orderings_Obot__class_Obot(tc_fun(X992,tc_HOL_Obool))!=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X992,X991),X990)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X992),X991),X990))|~class_Orderings_Oorder(X992))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X992),X991),X990))|c_Orderings_Obot__class_Obot(tc_fun(X992,tc_HOL_Obool))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X992,X991),X990)|~class_Orderings_Oorder(X992))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__empty__iff])])])])). 6.97/7.23 fof(c_0_8462, plain, ![X17578, X17579, X17580, X17581]:(X17581=c_List_Olist_ONil(X17580)|hAPP(X17578,c_List_Olast(X17580,X17581))=c_List_Olast(X17579,hAPP(hAPP(c_List_Omap(X17580,X17579),X17578),X17581))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_last__map])])])). 6.97/7.23 fof(c_0_8463, plain, ![X8970, X8971]:((~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(X8971)),X8970)))|c_List_Olist_ONil(X8971)!=X8970)&(c_List_Olist_ONil(X8971)=X8970|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(X8971)),X8970))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__greater__0__conv])])). 6.97/7.23 cnf(c_0_8464, 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_5375])). 6.97/7.23 fof(c_0_8465, plain, ![X12390, X12391]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12391))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X12390,X12391)),X12391))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__bound])])). 6.97/7.23 fof(c_0_8466, plain, ![X13101, X13102]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13102))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X13101,X13102)),X13102))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__less__divisor])])])). 6.97/7.23 fof(c_0_8467, plain, ![X14966, X14967]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14967))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X14967,X14966)),X14967))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__le__nonneg__dividend])])). 6.97/7.23 fof(c_0_8468, plain, ![X11266, X11267]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X11267))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X11266,X11267)),X11267))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__le__divisor])])])). 6.97/7.23 fof(c_0_8469, plain, ![X3230, X3231]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3231),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3231),c_Divides_Odiv__class_Omod(tc_Int_Oint,X3230,X3231)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__mod__bound])])). 6.97/7.23 fof(c_0_8470, plain, ![X10347, X10348, X10349]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10349),X10347),X10348))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10349),hAPP(c_Groups_Ouminus__class_Ouminus(X10349),X10348)),hAPP(c_Groups_Ouminus__class_Ouminus(X10349),X10347)))|~class_Lattices_Oboolean__algebra(X10349))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10349),hAPP(c_Groups_Ouminus__class_Ouminus(X10349),X10348)),hAPP(c_Groups_Ouminus__class_Ouminus(X10349),X10347)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10349),X10347),X10348))|~class_Lattices_Oboolean__algebra(X10349))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_compl__le__compl__iff])])])])). 6.97/7.23 fof(c_0_8471, plain, ![X16243, X16244, X16245]:(~class_Groups_Ogroup__add(X16245)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X16245),X16244),hAPP(c_Groups_Ouminus__class_Ouminus(X16245),X16243))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16245),X16244),X16243)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__minus__eq__add])])])). 6.97/7.23 fof(c_0_8472, plain, ![X3631]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X3631)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X3631),tc_HOL_Obool))))|hBOOL(hAPP(c_Finite__Set_Ofinite(X3631),c_Orderings_Otop__class_Otop(tc_fun(X3631,tc_HOL_Obool)))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3631),c_Orderings_Otop__class_Otop(tc_fun(X3631,tc_HOL_Obool))))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X3631)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X3631),tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__option__UNIV])])). 6.97/7.23 cnf(c_0_8473, 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_5386])). 6.97/7.23 cnf(c_0_8474, 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_5387])). 6.97/7.23 fof(c_0_8475, plain, ![X15085, X15086, X15087]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15087),X15086))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15087,tc_HOL_Obool)),X15085),X15086))|hBOOL(hAPP(c_Finite__Set_Ofinite(X15087),X15085)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rev__finite__subset])])])). 6.97/7.23 fof(c_0_8476, plain, ![X5821, X5822, X5823]:(~class_Orderings_Olinorder(X5823)|c_List_Oremove1(X5823,X5822,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5823,X5823,c_COMBI(X5823)),X5822),X5821))=X5821), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_remove1__insort])])])). 6.97/7.23 fof(c_0_8477, plain, ![X8536, X8537, X8538]:(~class_Rings_Ocomm__ring__1(X8538)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8538),X8537),hAPP(c_Groups_Ouminus__class_Ouminus(X8538),X8536))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8538),X8537),X8536)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J])])). 6.97/7.23 cnf(c_0_8478, 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,esk116_2(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_5339])). 6.97/7.23 fof(c_0_8479, plain, ![X320, X321, X323, X325]:(((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk2_2(X320,X321)),X320))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X320)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk2_2(X320,X321)),X321))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X320))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X323))|(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X325),X323))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X325),esk3_1(X323)))))), 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])])])])])])])). 6.97/7.23 fof(c_0_8480, plain, ![X11657, X11658, X11660, X11662]:(((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk391_2(X11657,X11658)),X11657))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X11657)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk391_2(X11657,X11658)),X11658))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X11657))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X11660))|(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X11662),X11660))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11662),esk392_1(X11660)))))), 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_finite__nat__set__iff__bounded__le])])])])])])). 6.97/7.23 fof(c_0_8481, plain, ![X6200, X6201, X6202]:(~class_Lattices_Osemilattice__inf(X6202)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6202),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6202),X6201),X6200)),X6201))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__le1])])). 6.97/7.23 cnf(c_0_8482, 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_5388])). 6.97/7.23 fof(c_0_8483, plain, ![X7763, X7764, X7765]:(~class_Groups_Ogroup__add(X7765)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7765),X7764),hAPP(c_Groups_Ouminus__class_Ouminus(X7765),X7763))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7765),X7764),X7763)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__def])])). 6.97/7.23 fof(c_0_8484, plain, ![X2087, X2088, X2089]:(~class_Lattices_Olattice(X2089)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2089),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2089),X2088),X2087)),X2088))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__sup__ord_I1_J])])])). 6.97/7.23 fof(c_0_8485, plain, ![X8889, X8890, X8891]:(~class_Lattices_Osemilattice__inf(X8891)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8891),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8891),X8890),X8889)),X8889))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__le2])])])). 6.97/7.23 fof(c_0_8486, plain, ![X316, X317, X318]:(~class_Lattices_Olattice(X318)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X318),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X318),X317),X316)),X316))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I2_J])])). 6.97/7.23 fof(c_0_8487, plain, ![X13395, X13396, X13397]:(~class_Rings_Ocomm__semiring__1(X13397)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X13397),X13396),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13397),X13396),X13395)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__triv__left])])). 6.97/7.23 fof(c_0_8488, plain, ![X3625, X3626]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3626),X3625))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3625),hAPP(c_Nat_OSuc,X3626))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3625),hAPP(c_Nat_OSuc,X3626)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3626),X3625)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__less__eq])])])). 6.97/7.23 cnf(c_0_8489, plain, (hBOOL(hAPP(X3,esk586_1(X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_5389])). 6.97/7.23 cnf(c_0_8490, 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_5390]), ['final']). 6.97/7.23 fof(c_0_8491, plain, ![X9379, X9380, X9381, X9382, X9383]:(hAPP(hAPP(c_List_Omap(X9383,X9382),X9381),X9379)!=hAPP(hAPP(c_List_Omap(X9383,X9382),X9381),X9380)|(~c_Fun_Oinj__on(X9383,X9382,X9381,c_Orderings_Otop__class_Otop(tc_fun(X9383,tc_HOL_Obool)))|X9379=X9380)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__injective])])])). 6.97/7.23 cnf(c_0_8492, plain, (hBOOL(hAPP(X1,X2))|c_List_Oremove1(X3,X2,hAPP(c_List_Ofilter(X3,X1),X4))=hAPP(c_List_Ofilter(X3,X1),X4)), inference(split_conjunct,[status(thm)],[c_0_5391])). 6.97/7.23 cnf(c_0_8493, 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_5392]), ['final']). 6.97/7.23 fof(c_0_8494, plain, ![X2326, X2327, X2328]:(~class_Groups_Oab__group__add(X2328)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2328),X2327),hAPP(c_Groups_Ouminus__class_Ouminus(X2328),X2326))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2328),X2327),X2326)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__diff__minus])])). 6.97/7.23 fof(c_0_8495, plain, ![X470, X471, X472]:(~class_Rings_Ocomm__semiring__1(X472)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X472),X471),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X472),X470),X471)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dvd__triv__right])])])). 6.97/7.23 fof(c_0_8496, plain, ![X7410, X7411, X7412]:(~class_Lattices_Osemilattice__sup(X7412)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7412),X7411),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7412),X7411),X7410)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__ge1])])). 6.97/7.23 fof(c_0_8497, plain, ![X10563, X10564, X10565]:(~class_Lattices_Olattice(X10565)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10565),X10564),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10565),X10564),X10563)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I3_J])])). 6.97/7.23 fof(c_0_8498, plain, ![X8916, X8917, X8918]:(~class_Lattices_Osemilattice__sup(X8918)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8918),X8917),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8918),X8916),X8917)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__ge2])])])). 6.97/7.23 fof(c_0_8499, plain, ![X13938, X13939, X13940]:(~class_Lattices_Oboolean__algebra(X13940)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13940),X13939),X13938)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X13940),X13939),hAPP(c_Groups_Ouminus__class_Ouminus(X13940),X13938))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__eq])])])). 6.97/7.23 fof(c_0_8500, plain, ![X288, X289, X290]:(~class_Lattices_Olattice(X290)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X290),X289),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X290),X288),X289)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I4_J])])). 6.97/7.23 fof(c_0_8501, plain, ![X679, X680, X681]:(~c_Wellfounded_Owf(X681,X680)|c_Wellfounded_Owf(X681,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X681,X681),tc_HOL_Obool)),X680),X679))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__Int1])])). 6.97/7.23 fof(c_0_8502, plain, ![X389, X390, X391]:(~c_Wellfounded_Owf(X391,X390)|c_Wellfounded_Owf(X391,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X391,X391),tc_HOL_Obool)),X389),X390))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__Int2])])])). 6.97/7.23 fof(c_0_8503, plain, ![X10696, X10697, X10698]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X10698),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X10697)),X10696))|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X10698,X10697),hAPP(c_Divides_OnegateSnd,X10696)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__neg])])). 6.97/7.23 fof(c_0_8504, plain, ![X4867, X4868, X4869]:(~class_Rings_Olinordered__semidom(X4869)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4869),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4869),X4868)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4869),X4867)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4868),X4867)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__less__imp__less])])). 6.97/7.23 fof(c_0_8505, plain, ![X15954, X15955]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15955),X15954),c_Groups_Ozero__class_Ozero(X15955)))|hAPP(c_Groups_Ouminus__class_Ouminus(X15955),X15954)=hAPP(c_Groups_Oabs__class_Oabs(X15955),X15954)|~class_Groups_Oabs__if(X15955))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15955),X15954),c_Groups_Ozero__class_Ozero(X15955)))|hAPP(c_Groups_Oabs__class_Oabs(X15955),X15954)=X15954|~class_Groups_Oabs__if(X15955))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__if])])])])). 6.97/7.23 cnf(c_0_8506, plain, (c_Relation_Osym(X1,c_Transitive__Closure_Otrancl(X1,X2))|~c_Relation_Osym(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5393])). 6.97/7.23 cnf(c_0_8507, plain, (X1=X2|c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3,X1)!=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_5394])). 6.97/7.23 cnf(c_0_8508, plain, (X1=X2|c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2,X1)!=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_5394])). 6.97/7.23 cnf(c_0_8509, plain, (c_Wellfounded_Owf(X1,c_Transitive__Closure_Otrancl(X1,X2))|~c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5395])). 6.97/7.23 cnf(c_0_8510, 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_5325])). 6.97/7.23 cnf(c_0_8511, plain, (esk469_2(X1,X2)=X3|X1!=hAPP(c_List_Oset(X2),X3)|~hBOOL(hAPP(c_List_Odistinct(X2),X3))|~c_List_Olinorder__class_Osorted(X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))|~class_Orderings_Olinorder(X2)), inference(split_conjunct,[status(thm)],[c_0_5396])). 6.97/7.23 cnf(c_0_8512, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_5397]), ['final']). 6.97/7.23 fof(c_0_8513, plain, ![X1852, X1853, X1854, X1855, X1856, X1857, X1858]:(~c_Finite__Set_Ofun__left__comm(X1858,X1857,X1856)|(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1858,X1857,X1856,X1855,X1854),X1853))|(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1858,X1857,X1856,X1855,X1854),X1852))|X1852=X1853))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__graph__determ])])])). 6.97/7.23 cnf(c_0_8514, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)|X1!=hAPP(c_Groups_Ouminus__class_Ouminus(X2),X3)|~class_Rings_Oidom(X2)), inference(split_conjunct,[status(thm)],[c_0_5398])). 6.97/7.23 fof(c_0_8515, plain, ![X16986, X16987, X16988, X16989, X16990]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16990),X16989))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16988,tc_HOL_Obool)),X16987),hAPP(c_Set_Oimage(X16990,X16988,X16986),X16989)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X16988),X16987)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__surj])])])). 6.97/7.23 cnf(c_0_8516, 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_5330])). 6.97/7.23 cnf(c_0_8517, 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_5329])). 6.97/7.23 fof(c_0_8518, plain, ![X10246, X10247]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X10247,X10246)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X10247,X10246),tc_HOL_Obool))))|hBOOL(hAPP(c_Finite__Set_Ofinite(X10246),c_Orderings_Otop__class_Otop(tc_fun(X10246,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__fun__UNIVD2])])])). 6.97/7.23 cnf(c_0_8519, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1), inference(split_conjunct,[status(thm)],[c_0_5399])). 6.97/7.23 cnf(c_0_8520, 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_5343])). 6.97/7.23 fof(c_0_8521, plain, ![X6998, X6999]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6999),hAPP(c_Nat_OSuc,X6998)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6999),X6998))|hAPP(c_Nat_OSuc,X6998)=X6999)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__SucE])])])). 6.97/7.23 fof(c_0_8522, plain, ![X16336, X16337, X16338, X16339]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X16339,X16338),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X16337),X16336)))|(X16338=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X16336=c_Divides_Odiv__class_Omod(tc_Int_Oint,X16339,X16338))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__mod])])])). 6.97/7.23 cnf(c_0_8523, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X3),X4)!=c_List_Oupt(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_4593])). 6.97/7.23 fof(c_0_8524, plain, ![X6652, X6653, X6654, X6655]:(~class_Groups_Ouminus(X6655)|hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6654,X6655)),X6653),X6652)=hAPP(c_Groups_Ouminus__class_Ouminus(X6655),hAPP(X6653,X6652))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__apply])])). 6.97/7.23 fof(c_0_8525, plain, ![X13361, X13362, X13363]:((~c_List_Olinorder__class_Osorted(X13363,X13361)|c_List_Olinorder__class_Osorted(X13363,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13363,X13363,c_COMBI(X13363)),X13362),X13361))|~class_Orderings_Olinorder(X13363))&(~c_List_Olinorder__class_Osorted(X13363,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13363,X13363,c_COMBI(X13363)),X13362),X13361))|c_List_Olinorder__class_Osorted(X13363,X13361)|~class_Orderings_Olinorder(X13363))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__insort])])])])). 6.97/7.23 fof(c_0_8526, plain, ![X773, X774, X775, X776]:(~hBOOL(hAPP(hAPP(c_member(X776),X775),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X776,tc_HOL_Obool)),X774),X773)))|hBOOL(hAPP(hAPP(c_member(X776),X775),X774))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_DiffD1])])])). 6.97/7.23 cnf(c_0_8527, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X1)=hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)|X1!=c_Groups_Ozero__class_Ozero(X2)|c_Groups_Ozero__class_Ozero(X2)!=hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)|~class_Fields_Ofield__inverse__zero(X2)|~class_Int_Onumber(X2)), inference(split_conjunct,[status(thm)],[c_0_5223])). 6.97/7.23 fof(c_0_8528, plain, ![X5431, X5432, X5433, X5434]:(~class_Orderings_Olinorder(X5434)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5433)),c_List_Olinorder__class_Osort__key(X5433,X5434,X5432,X5431))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5433)),X5431)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_length__sort])])])). 6.97/7.23 fof(c_0_8529, plain, ![X8302]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X8302))|X8302=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X8302),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__pred_H])])). 6.97/7.23 fof(c_0_8530, plain, ![X1108, X1109, X1110, X1111]:(~hBOOL(hAPP(hAPP(c_member(X1111),X1110),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1111,tc_HOL_Obool)),X1109),X1108)))|hBOOL(hAPP(hAPP(c_member(X1111),X1110),X1108))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_IntD2])])])). 6.97/7.23 fof(c_0_8531, plain, ![X4452, X4453, X4454, X4455]:(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4455)),X4454),hAPP(c_List_Oset(tc_List_Olist(X4455)),c_Enum_On__lists(X4455,X4453,X4452))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4455)),X4454)=X4453), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__n__lists__elem])])). 6.97/7.23 cnf(c_0_8532, 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_5304])). 6.97/7.23 cnf(c_0_8533, 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),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_5305])). 6.97/7.23 cnf(c_0_8534, plain, (hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1|X2=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_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_5400])). 6.97/7.23 fof(c_0_8535, plain, ![X3819, X3820, X3821]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3821),X3819),X3820))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3821),X3820),X3819))|~class_Orderings_Olinorder(X3821))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3821),X3820),X3819))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3821),X3819),X3820))|~class_Orderings_Olinorder(X3821))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__not__less])])])])). 6.97/7.23 fof(c_0_8536, plain, ![X4118, X4119, X4120]:(~class_Complete__Lattice_Ocomplete__lattice(X4120)|(~hBOOL(hAPP(hAPP(c_member(X4120),X4119),X4118))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4120),c_Complete__Lattice_OInf__class_OInf(X4120,X4118)),X4119)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__lower])])])). 6.97/7.23 fof(c_0_8537, plain, ![X749, X750, X751]:(~class_Complete__Lattice_Ocomplete__lattice(X751)|(~hBOOL(hAPP(hAPP(c_member(X751),X750),X749))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X751),X750),c_Complete__Lattice_OSup__class_OSup(X751,X749))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__upper])])])). 6.97/7.23 fof(c_0_8538, plain, ![X12529, X12530, X12531]:((~hBOOL(hAPP(hAPP(c_member(X12531),X12530),c_Quotient_ORespects(X12531,X12529)))|hBOOL(hAPP(hAPP(X12529,X12530),X12530)))&(~hBOOL(hAPP(hAPP(X12529,X12530),X12530))|hBOOL(hAPP(hAPP(c_member(X12531),X12530),c_Quotient_ORespects(X12531,X12529))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__respects])])). 6.97/7.23 cnf(c_0_8539, 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_5401])). 6.97/7.23 fof(c_0_8540, plain, ![X16183, X16184, X16185, X16186, X16187]:(~class_Orderings_Olinorder(X16187)|(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X16187,X16184),X16183)!=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X16187,X16186),X16185)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16187),X16186),X16185))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16187),X16184),X16183))|X16184=X16186)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__inj_I1_J])])])). 6.97/7.23 fof(c_0_8541, plain, ![X1620, X1621, X1622, X1623, X1624]:(~class_Orderings_Olinorder(X1624)|(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1624,X1623),X1622)!=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1624,X1621),X1620)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1624),X1623),X1622))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1624),X1621),X1620))|X1620=X1622)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__inj_I2_J])])])). 6.97/7.23 fof(c_0_8542, plain, ![X12314, X12315, X12316]:(~class_Groups_Ogroup__add(X12316)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X12316),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12316),X12315),X12314)),X12314)=X12315), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__cancel])])). 6.97/7.23 cnf(c_0_8543, plain, (~class_Int_Onumber__ring(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_Ozero__class_Ozero(tc_Int_Oint)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5402, c_0_4413]), c_0_4413]), c_0_4456])). 6.97/7.23 fof(c_0_8544, plain, ![X6646, X6647, X6648, X6649, X6650, X6651]:(~c_Finite__Set_Ofun__left__comm(X6651,X6650,X6649)|(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X6651,X6650,X6649,X6648,X6647),X6646))|X6646=hAPP(hAPP(c_Finite__Set_Ofold(X6651,X6650,X6649),X6648),X6647))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__equality])])])). 6.97/7.23 fof(c_0_8545, plain, ![X15642, X15643, X15644, X15645, X15646]:(~class_Orderings_Olinorder(X15646)|(~hBOOL(hAPP(c_List_Odistinct(X15645),X15644))|hBOOL(hAPP(c_List_Odistinct(X15645),c_List_Olinorder__class_Oinsort__insert__key(X15645,X15646,X15643,X15642,X15644))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__insort__insert])])])). 6.97/7.23 fof(c_0_8546, plain, ![X10376, X10377, X10378, X10379, X10380, X10381]:(~c_Typedef_Otype__definition(X10381,X10380,X10379,X10378,X10377)|(~hBOOL(hAPP(hAPP(c_member(X10380),X10376),X10377))|X10376=hAPP(X10379,hAPP(X10378,X10376)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_type__definition_OAbs__inverse])])])). 6.97/7.23 fof(c_0_8547, plain, ![X10957, X10958, X10959]:(~class_Groups_Ogroup__add(X10959)|X10958=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10959),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10959),X10958),X10957)),X10957)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__cancel])])). 6.97/7.23 fof(c_0_8548, plain, ![X13269, X13270, X13271]:(~class_Divides_Osemiring__div(X13271)|c_Divides_Odiv__class_Omod(X13271,X13270,X13269)=c_Divides_Odiv__class_Omod(X13271,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13271),X13270),X13269),X13269)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__add__self2])])])). 6.97/7.23 fof(c_0_8549, plain, ![X14924, X14925, X14926]:(~class_Divides_Osemiring__div(X14926)|c_Divides_Odiv__class_Omod(X14926,X14924,X14925)=c_Divides_Odiv__class_Omod(X14926,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14926),X14925),X14924),X14925)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__self1])])). 6.97/7.23 fof(c_0_8550, plain, ![X17553, X17554, X17555]:(~class_Lattices_Olattice(X17555)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17555),X17554),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17555),X17554),X17553))=X17554), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__absorb])])). 6.97/7.23 fof(c_0_8551, plain, ![X14758, X14759, X14760]:(~c_Wellfounded_Owf(X14760,X14759)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14760,tc_HOL_Obool)),X14758),hAPP(c_Relation_OImage(X14760,X14760,X14759),X14758)))|c_Orderings_Obot__class_Obot(tc_fun(X14760,tc_HOL_Obool))=X14758)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wfE__pf])])])). 6.97/7.23 fof(c_0_8552, plain, ![X15734, X15735, X15736, X15737]:(~class_Rings_Ocomm__semiring__1(X15737)|(~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X15737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15737),X15736),X15735)),X15734))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X15737),X15736),X15734)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dvd__mult__left])])])). 6.97/7.23 fof(c_0_8553, plain, ![X10158, X10159, X10160, X10161]:(~class_Rings_Ocomm__semiring__1(X10161)|(~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10161),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10161),X10160),X10159)),X10158))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10161),X10159),X10158)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dvd__mult__right])])])). 6.97/7.23 fof(c_0_8554, plain, ![X14528, X14529]:(~class_Fields_Ofield__inverse__zero(X14529)|~class_Int_Onumber__ring(X14529)|hAPP(c_Groups_Ouminus__class_Ouminus(X14529),X14528)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14529),X14528),hAPP(c_Int_Onumber__class_Onumber__of(X14529),c_Int_OMin))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__minus1])])])). 6.97/7.23 fof(c_0_8555, plain, ![X8125, X8126, X8127]:(~class_Lattices_Olattice(X8127)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8127),X8126),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8127),X8126),X8125))=X8126), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__inf__absorb])])). 6.97/7.23 fof(c_0_8556, plain, ![X3271, X3272]:(~class_Int_Onumber__ring(X3272)|hAPP(c_Groups_Ouminus__class_Ouminus(X3272),X3271)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3272),hAPP(c_Int_Onumber__class_Onumber__of(X3272),c_Int_OMin)),X3271)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__minus1])])])). 6.97/7.23 cnf(c_0_8557, plain, (hBOOL(hAPP(X1,hAPP(c_Int_Onat,X2)))|~hBOOL(hAPP(X1,esk19_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_5403])). 6.97/7.23 fof(c_0_8558, plain, ![X9803, X9804, X9805]:(~class_Orderings_Olinorder(X9805)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9805),hAPP(hAPP(c_Orderings_Oord__class_Omin(X9805),X9804),X9803)),X9804))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oinf__le1])])])). 6.97/7.23 fof(c_0_8559, plain, ![X6249, X6250, X6251]:(~class_Orderings_Olinorder(X6251)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6251),hAPP(hAPP(c_Orderings_Oord__class_Omin(X6251),X6250),X6249)),X6249))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oinf__le2])])])). 6.97/7.23 fof(c_0_8560, plain, ![X13480, X13481, X13482]:(~class_Orderings_Olinorder(X13482)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13482),X13481),hAPP(hAPP(c_Orderings_Oord__class_Omax(X13482),X13481),X13480)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__maxI1])])). 6.97/7.23 fof(c_0_8561, plain, ![X16419, X16420, X16421]:((X16421=c_List_Olist_ONil(X16420)|hAPP(c_List_Ohd(X16420),X16421)=hAPP(c_List_Ohd(X16420),hAPP(hAPP(c_List_Oappend(X16420),X16421),X16419)))&(c_List_Olist_ONil(X16420)!=X16421|hAPP(c_List_Ohd(X16420),hAPP(hAPP(c_List_Oappend(X16420),X16421),X16419))=hAPP(c_List_Ohd(X16420),X16419))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_hd__append])])])). 6.97/7.23 fof(c_0_8562, plain, ![X6286, X6287, X6288, X6289]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6289),X6288),X6287))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6289),X6288),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6289),X6287),X6286)))|~class_Lattices_Osemilattice__inf(X6289))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6289),X6288),X6286))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6289),X6288),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6289),X6287),X6286)))|~class_Lattices_Osemilattice__inf(X6289))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__infE])])])])). 6.97/7.23 fof(c_0_8563, plain, ![X15828, X15829, X15830, X15831, X15832, X15833, X15834]:((~hBOOL(hAPP(c_Wellfounded_Oaccp(X15830,X15829),X15828))|(~hBOOL(hAPP(hAPP(X15829,X15831),X15828))|hBOOL(hAPP(c_Wellfounded_Oaccp(X15830,X15829),X15831))))&((hBOOL(hAPP(hAPP(X15833,esk532_3(X15832,X15833,X15834)),X15832))|hBOOL(hAPP(c_Wellfounded_Oaccp(X15834,X15833),X15832)))&(~hBOOL(hAPP(c_Wellfounded_Oaccp(X15834,X15833),esk532_3(X15832,X15833,X15834)))|hBOOL(hAPP(c_Wellfounded_Oaccp(X15834,X15833),X15832))))), 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_Oequations])])])])])])])). 6.97/7.23 fof(c_0_8564, plain, ![X9132, X9133]:(~class_Rings_Oring__1(X9133)|hAPP(c_Groups_Ouminus__class_Ouminus(X9133),hAPP(c_Int_Oring__1__class_Oof__int(X9133),X9132))=hAPP(c_Int_Oring__1__class_Oof__int(X9133),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X9132))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__minus])])])). 6.97/7.23 fof(c_0_8565, plain, ![X11671, X11672, X11673]:(~class_Orderings_Olinorder(X11673)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11673),X11672),hAPP(hAPP(c_Orderings_Oord__class_Omax(X11673),X11671),X11672)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__maxI2])])])). 6.97/7.23 cnf(c_0_8566, plain, (X2=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk116_2(X2,X1))|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_5339])). 6.97/7.23 fof(c_0_8567, plain, ![X11850, X11851, X11852, X11853, X11854, X11855, X11856]:((~hBOOL(hAPP(c_Wellfounded_Oaccp(X11852,X11851),X11850))|(~hBOOL(hAPP(hAPP(X11851,X11853),X11850))|hBOOL(hAPP(c_Wellfounded_Oaccp(X11852,X11851),X11853))))&((hBOOL(hAPP(hAPP(X11855,esk396_3(X11854,X11855,X11856)),X11854))|hBOOL(hAPP(c_Wellfounded_Oaccp(X11856,X11855),X11854)))&(~hBOOL(hAPP(c_Wellfounded_Oaccp(X11856,X11855),esk396_3(X11854,X11855,X11856)))|hBOOL(hAPP(c_Wellfounded_Oaccp(X11856,X11855),X11854))))), 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])])])])])])])). 6.97/7.23 fof(c_0_8568, plain, ![X7015, X7016, X7017, X7018]:(~hBOOL(hAPP(c_Wellfounded_Oaccp(X7018,X7017),X7016))|(~hBOOL(hAPP(hAPP(X7017,X7015),X7016))|hBOOL(hAPP(c_Wellfounded_Oaccp(X7018,X7017),X7015)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_accp__downward])])])). 6.97/7.23 fof(c_0_8569, plain, ![X5730, X5731]:(~class_Int_Onumber__ring(X5731)|hAPP(c_Groups_Ouminus__class_Ouminus(X5731),hAPP(c_Int_Onumber__class_Onumber__of(X5731),X5730))=hAPP(c_Int_Onumber__class_Onumber__of(X5731),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X5730))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I30_J])])). 6.97/7.23 cnf(c_0_8570, 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_5028])). 6.97/7.23 cnf(c_0_8571, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X2))|~class_Rings_Odvd(X1)|X2!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)), inference(split_conjunct,[status(thm)],[c_0_5404])). 6.97/7.23 cnf(c_0_8572, plain, (c_Relation_Oantisym(X1,X2)|~c_Relation_Oantisym(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_5232])). 6.97/7.23 cnf(c_0_8573, 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_5293])). 6.97/7.23 fof(c_0_8574, plain, ![X12660, X12661]:(~class_Int_Onumber__ring(X12661)|hAPP(c_Groups_Ouminus__class_Ouminus(X12661),X12660)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12661),X12660),hAPP(c_Int_Onumber__class_Onumber__of(X12661),c_Int_OMin))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__minus1__right])])])). 6.97/7.23 fof(c_0_8575, plain, ![X3911, X3912, X3913]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3913),X3912),X3911))|X3911=X3912|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3913),X3912),X3911))|~class_Orderings_Olinorder(X3913))&(X3911!=X3912|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3913),X3912),X3911))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3913),X3912),X3911))|~class_Orderings_Olinorder(X3913))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv1])])])])). 6.97/7.23 fof(c_0_8576, plain, ![X14032, X14033, X14034]:(~class_Orderings_Oorder(X14034)|(X14032=X14033|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14034),X14033),X14032))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14034),X14033),X14032))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__neq__le__trans])])])). 6.97/7.23 fof(c_0_8577, plain, ![X1010, X1011, X1012]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1012),X1011))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1012,tc_HOL_Obool)),X1011),hAPP(c_Set_Oimage(X1012,X1012,X1010),X1011)))|c_Fun_Oinj__on(X1012,X1012,X1010,X1011))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__surj__inj])])])). 6.97/7.23 fof(c_0_8578, plain, ![X12352, X12353]:(~class_Int_Oring__char__0(X12353)|(~hBOOL(hAPP(hAPP(c_member(X12353),X12352),c_Int_Oring__1__class_OInts(X12353)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12353),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12353),c_Groups_Oone__class_Oone(X12353)),X12352)),X12352)!=c_Groups_Ozero__class_Ozero(X12353))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__nonzero])])). 6.97/7.23 fof(c_0_8579, plain, ![X7728, X7729]:(~class_Orderings_Olinorder(X7729)|c_List_Olinorder__class_Osort__key(X7729,X7729,c_COMBI(X7729),c_List_Oremdups(X7729,X7728))=c_List_Olinorder__class_Osorted__list__of__set(X7729,hAPP(c_List_Oset(X7729),X7728))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__sort__remdups])])). 6.97/7.23 fof(c_0_8580, plain, ![X1389, X1390, X1391]:(~class_Orderings_Olinorder(X1391)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X1391),X1390),X1389)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1391),X1389),X1390)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Ocommute])])). 6.97/7.23 fof(c_0_8581, plain, ![X8572, X8573, X8574]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8574,tc_HOL_Obool)),X8573),X8572)!=c_Orderings_Obot__class_Obot(tc_fun(X8574,tc_HOL_Obool))|X8573=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8574,tc_HOL_Obool)),X8573),X8572)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__triv])])). 6.97/7.23 cnf(c_0_8582, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_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(split_conjunct,[status(thm)],[c_0_5405])). 6.97/7.23 fof(c_0_8583, plain, ![X1917, X1918, X1919]:(~class_Orderings_Olinorder(X1919)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X1919),X1917),X1918)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1919),X1918),X1917)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__commute])])). 6.97/7.23 fof(c_0_8584, plain, ![X3531, X3532, X3533, X3534]:((~hBOOL(hAPP(X3534,X3533))|hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3531,tc_HOL_Obool)),X3532),X3534),X3533)))&(~hBOOL(hAPP(X3532,X3533))|hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3531,tc_HOL_Obool)),X3532),X3534),X3533)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup1CI])])])])). 6.97/7.23 cnf(c_0_8585, plain, (c_Groups_Ozero__class_Ozero(X2)=hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)|X1!=c_Groups_Ozero__class_Ozero(X2)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X1)!=hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)|~class_Fields_Ofield__inverse__zero(X2)|~class_Int_Onumber(X2)), inference(split_conjunct,[status(thm)],[c_0_5223])). 6.97/7.23 fof(c_0_8586, plain, ![X650, X651, X652]:(~class_Rings_Ocomm__semiring__1(X652)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X652),X651),X650)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X652),X650),X651)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])])). 6.97/7.23 fof(c_0_8587, plain, ![X6426, X6427, X6428, X6429]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6429),X6428))|hAPP(hAPP(c_List_Onth(X6427),c_List_Oreplicate(X6427,X6428,X6426)),X6429)=X6426), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__replicate])])). 6.97/7.23 fof(c_0_8588, plain, ![X14786, X14787, X14788, X14789]:((~hBOOL(hAPP(hAPP(c_member(X14789),X14788),c_SetInterval_Oord_OatMost(X14789,X14787,X14786)))|hBOOL(hAPP(hAPP(X14787,X14788),X14786)))&(~hBOOL(hAPP(hAPP(X14787,X14788),X14786))|hBOOL(hAPP(hAPP(c_member(X14789),X14788),c_SetInterval_Oord_OatMost(X14789,X14787,X14786))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatMost__iff])])). 6.97/7.23 fof(c_0_8589, plain, ![X6318, X6319, X6320, X6321]:((~hBOOL(hAPP(hAPP(c_member(X6321),X6320),c_SetInterval_Oord_OlessThan(X6321,X6319,X6318)))|hBOOL(hAPP(hAPP(X6319,X6320),X6318)))&(~hBOOL(hAPP(hAPP(X6319,X6320),X6318))|hBOOL(hAPP(hAPP(c_member(X6321),X6320),c_SetInterval_Oord_OlessThan(X6321,X6319,X6318))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OlessThan__iff])])). 6.97/7.23 fof(c_0_8590, plain, ![X3002, X3003, X3004, X3005, X3006, X3007]:(~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3007,tc_fun(X3006,tc_HOL_Obool))),X3005),X3004),X3003),X3002))|hBOOL(hAPP(hAPP(X3005,X3003),X3002))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf2D1])])])). 6.97/7.23 fof(c_0_8591, plain, ![X10575, X10576, X10577, X10578, X10579, X10580]:(~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10580,tc_fun(X10579,tc_HOL_Obool))),X10578),X10577),X10576),X10575))|hBOOL(hAPP(hAPP(X10577,X10576),X10575))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2D2])])). 6.97/7.23 fof(c_0_8592, plain, ![X13009, X13010, X13011, X13012]:((~hBOOL(hAPP(hAPP(c_member(X13012),X13011),c_SetInterval_Oord_OgreaterThan(X13012,X13010,X13009)))|hBOOL(hAPP(hAPP(X13010,X13009),X13011)))&(~hBOOL(hAPP(hAPP(X13010,X13009),X13011))|hBOOL(hAPP(hAPP(c_member(X13012),X13011),c_SetInterval_Oord_OgreaterThan(X13012,X13010,X13009))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThan__iff])])). 6.97/7.23 fof(c_0_8593, plain, ![X9889, X9890, X9891, X9892]:((~hBOOL(hAPP(hAPP(X9890,X9889),X9891))|hBOOL(hAPP(hAPP(c_member(X9892),X9891),c_SetInterval_Oord_OatLeast(X9892,X9890,X9889))))&(~hBOOL(hAPP(hAPP(c_member(X9892),X9891),c_SetInterval_Oord_OatLeast(X9892,X9890,X9889)))|hBOOL(hAPP(hAPP(X9890,X9889),X9891)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeast__iff])])). 6.97/7.23 cnf(c_0_8594, 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),X1),X1)),c_Int_OPls))), inference(rw,[status(thm)],[c_0_5406, c_0_4410])). 6.97/7.23 cnf(c_0_8595, 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_5350])). 6.97/7.23 fof(c_0_8596, plain, ![X8662, X8663, X8664, X8665, X8666, X8667]:(~c_Typedef_Otype__definition(X8667,X8666,X8665,X8664,X8663)|hBOOL(hAPP(hAPP(c_member(X8666),hAPP(X8665,X8662)),X8663))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep])])). 6.97/7.23 fof(c_0_8597, plain, ![X3942, X3943, X3944]:(~class_Lattices_Osemilattice__inf(X3944)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3944),X3942),X3943)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3944),X3943),X3942)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__commute])])). 6.97/7.23 cnf(c_0_8598, 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_5352])). 6.97/7.23 cnf(c_0_8599, 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),X1),X1)),c_Int_OPls))), inference(rw,[status(thm)],[c_0_5407, c_0_4410])). 6.97/7.23 cnf(c_0_8600, 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),X1),X1))))), inference(rw,[status(thm)],[c_0_5408, c_0_4410])). 6.97/7.23 cnf(c_0_8601, 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_5355])). 6.97/7.23 fof(c_0_8602, plain, ![X14199, X14200, X14201]:(~class_Lattices_Olattice(X14201)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X14201),X14199),X14200)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X14201),X14200),X14199)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__sup__aci_I1_J])])])). 6.97/7.23 cnf(c_0_8603, 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_5357])). 6.97/7.23 cnf(c_0_8604, 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_5359])). 6.97/7.23 cnf(c_0_8605, 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),X1),X1)))), inference(rw,[status(thm)],[c_0_5409, c_0_4410])). 6.97/7.23 fof(c_0_8606, plain, ![X14835, X14836, X14837]:(~class_Rings_Ocomm__semiring__1(X14837)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14837),X14835),X14836)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14837),X14836),X14835)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])])])). 6.97/7.23 cnf(c_0_8607, 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),X1),X1)))), inference(rw,[status(thm)],[c_0_5410, c_0_4410])). 6.97/7.23 cnf(c_0_8608, 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_5302])). 6.97/7.23 cnf(c_0_8609, 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_5387])). 6.97/7.23 fof(c_0_8610, plain, ![X6720, X6721, X6722]:((c_SetInterval_Oord__class_OatLeastAtMost(X6722,X6721,X6720)!=c_Orderings_Obot__class_Obot(tc_fun(X6722,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6722),X6721),X6720))|~class_Orderings_Oorder(X6722))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6722),X6721),X6720))|c_SetInterval_Oord__class_OatLeastAtMost(X6722,X6721,X6720)=c_Orderings_Obot__class_Obot(tc_fun(X6722,tc_HOL_Obool))|~class_Orderings_Oorder(X6722))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastatMost__empty__iff2])])])])). 6.97/7.23 fof(c_0_8611, plain, ![X5824, X5825]:((c_Groups_Oone__class_Oone(tc_Int_Oint)!=X5824|c_Groups_Oone__class_Oone(tc_Int_Oint)!=X5825|c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5825),X5824)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5825)))&((c_Groups_Oone__class_Oone(tc_Int_Oint)=X5824|c_Groups_Oone__class_Oone(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5825),X5824)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5825)))&(c_Groups_Oone__class_Oone(tc_Int_Oint)=X5825|c_Groups_Oone__class_Oone(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5825),X5824)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5825))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pos__zmult__eq__1__iff])])])])). 6.97/7.23 cnf(c_0_8612, plain, (hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1|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_5411])). 6.97/7.23 fof(c_0_8613, plain, ![X4600, X4601]:(~class_Groups_Oordered__ab__group__add__abs(X4601)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4601),X4600),c_Groups_Ozero__class_Ozero(X4601)))|hAPP(c_Groups_Oabs__class_Oabs(X4601),X4600)=hAPP(c_Groups_Ouminus__class_Ouminus(X4601),X4600))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__neg])])). 6.97/7.23 fof(c_0_8614, plain, ![X16537, X16538]:(~class_Groups_Oordered__ab__group__add__abs(X16538)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16538),X16537),c_Groups_Ozero__class_Ozero(X16538)))|hAPP(c_Groups_Ouminus__class_Ouminus(X16538),X16537)=hAPP(c_Groups_Oabs__class_Oabs(X16538),X16537))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__of__nonpos])])])). 6.97/7.23 fof(c_0_8615, plain, ![X3311, X3312, X3313]:(~class_Lattices_Osemilattice__sup(X3313)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3313),X3312),X3311)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3313),X3311),X3312)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__commute])])). 6.97/7.23 fof(c_0_8616, plain, ![X9606, X9607, X9608]:(~class_Groups_Ocomm__monoid__add(X9608)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9607,X9608),X9606),c_Orderings_Obot__class_Obot(tc_fun(X9607,tc_HOL_Obool)))=c_Groups_Ozero__class_Ozero(X9608)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oempty])])). 6.97/7.23 fof(c_0_8617, plain, ![X6096, X6097, X6098]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6098,tc_HOL_Obool)),X6097),X6096))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6098,tc_HOL_Obool)),X6096),X6097)=X6097), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__absorb1])])])). 6.97/7.23 fof(c_0_8618, plain, ![X13562, X13563]:((X13563!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X13562|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X13563)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X13562)))))&((X13563=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),X13563)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X13562)))))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X13562|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X13563)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X13562))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__zle__neg])])])). 6.97/7.23 fof(c_0_8619, plain, ![X15477, X15478, X15479, X15480]:(~c_Finite__Set_Ofolding__one(X15480,X15479,X15478)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15480),X15477))|hAPP(X15478,X15477)=hAPP(c_Finite__Set_Ofold1(X15480,X15479),X15477))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one_Oeq__fold])])])). 6.97/7.23 fof(c_0_8620, plain, ![X13483, X13484]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13484))|c_SMT_Oz3mod(X13483,X13484)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X13483,X13484))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13484))|c_Divides_Odiv__class_Omod(tc_Int_Oint,X13483,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X13484))=c_SMT_Oz3mod(X13483,X13484))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_z3mod__def])])])). 6.97/7.23 fof(c_0_8621, plain, ![X1935, X1936, X1937]:(~class_Lattices_Olattice(X1937)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1937),X1935),X1936)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1937),X1936),X1935)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I5_J])])). 6.97/7.23 fof(c_0_8622, plain, ![X10786, X10787, X10788]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10788,tc_HOL_Obool)),X10787),X10786))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10788,tc_HOL_Obool)),X10786),X10787)=X10786), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__absorb2])])). 6.97/7.23 fof(c_0_8623, plain, ![X7834, X7835, X7836]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7836,tc_HOL_Obool)),X7835),X7834))|X7835=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7836,tc_HOL_Obool)),X7835),X7834)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__absorb2])])])). 6.97/7.23 fof(c_0_8624, plain, ![X9367, X9368, X9369]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9369,tc_HOL_Obool)),X9368),X9367))|X9367=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9369,tc_HOL_Obool)),X9368),X9367)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Un__absorb1])])])). 6.97/7.23 fof(c_0_8625, plain, ![X16517]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk549_1(X16517)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16517)))&(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk549_1(X16517))=X16517|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16517)))), 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])])])])])). 6.97/7.23 fof(c_0_8626, plain, ![X573, X574, X575, X576]:(~c_Big__Operators_Osemilattice__big(X576,X575,X574)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X576),X573))|hAPP(X574,X573)=hAPP(c_Finite__Set_Ofold1(X576,X575),X573))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_semilattice__big_OF__eq])])])). 6.97/7.23 cnf(c_0_8627, 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_5191])). 6.97/7.23 cnf(c_0_8628, 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_5196])). 6.97/7.23 cnf(c_0_8629, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)=c_Groups_Oone__class_Oone(X2)|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_5412])). 6.97/7.23 cnf(c_0_8630, plain, (hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1)))|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_5135])). 6.97/7.23 fof(c_0_8631, plain, ![X13893, X13894, X13895, X13896]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13896)),X13895)),X13894))|X13895=hAPP(hAPP(c_List_Olist__update(X13896,X13895),X13894),X13893)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__update__beyond])])])). 6.97/7.23 fof(c_0_8632, plain, ![X9257]:(~c_Nat__Transfer_Onat__set(X9257)|hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X9257))=hAPP(c_Finite__Set_Ocard(tc_Int_Oint),X9257)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J])])). 6.97/7.23 fof(c_0_8633, plain, ![X4924, X4925]:(~class_Orderings_Olinorder(X4925)|c_Big__Operators_Olinorder__class_OMax(X4925,hAPP(hAPP(c_Set_Oinsert(X4925),X4924),c_Orderings_Obot__class_Obot(tc_fun(X4925,tc_HOL_Obool))))=X4924), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Osingleton])])). 6.97/7.23 fof(c_0_8634, plain, ![X12187, X12188]:(~class_Lattices_Olattice(X12188)|c_Big__Operators_Olattice__class_OSup__fin(X12188,hAPP(hAPP(c_Set_Oinsert(X12188),X12187),c_Orderings_Obot__class_Obot(tc_fun(X12188,tc_HOL_Obool))))=X12187), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Osingleton])])])). 6.97/7.23 fof(c_0_8635, plain, ![X15462, X15463, X15464]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15464),X15463)),X15462))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15464),X15462))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])])). 6.97/7.23 cnf(c_0_8636, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls))=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Onumber__ring(X1)|~class_Fields_Ofield__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_5413])). 6.97/7.23 fof(c_0_8637, plain, ![X8425, X8426]:(~class_Complete__Lattice_Ocomplete__lattice(X8426)|c_Complete__Lattice_OSup__class_OSup(X8426,hAPP(hAPP(c_Set_Oinsert(X8426),X8425),c_Orderings_Obot__class_Obot(tc_fun(X8426,tc_HOL_Obool))))=X8425), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__singleton])])). 6.97/7.23 fof(c_0_8638, plain, ![X13181, X13182]:(~class_Lattices_Olattice(X13182)|c_Big__Operators_Olattice__class_OInf__fin(X13182,hAPP(hAPP(c_Set_Oinsert(X13182),X13181),c_Orderings_Obot__class_Obot(tc_fun(X13182,tc_HOL_Obool))))=X13181), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Osingleton])])])). 6.97/7.23 fof(c_0_8639, plain, ![X2277, X2278]:(~class_Orderings_Olinorder(X2278)|X2277=c_Big__Operators_Olinorder__class_OMin(X2278,hAPP(hAPP(c_Set_Oinsert(X2278),X2277),c_Orderings_Obot__class_Obot(tc_fun(X2278,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min_Osingleton])])])). 6.97/7.23 fof(c_0_8640, plain, ![X15684, X15685]:(~class_Complete__Lattice_Ocomplete__lattice(X15685)|X15684=c_Complete__Lattice_OInf__class_OInf(X15685,hAPP(hAPP(c_Set_Oinsert(X15685),X15684),c_Orderings_Obot__class_Obot(tc_fun(X15685,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__singleton])])])). 6.97/7.23 fof(c_0_8641, plain, ![X5241, X5242, X5243]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5243),X5242)),X5241))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5243),X5241))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__leD1])])])). 6.97/7.23 fof(c_0_8642, plain, ![X9308, X9309]:(~class_Power_Opower(X9309)|~class_Rings_Osemiring__0(X9309)|c_Groups_Ozero__class_Ozero(X9309)=hAPP(hAPP(c_Power_Opower__class_Opower(X9309),c_Groups_Ozero__class_Ozero(X9309)),hAPP(c_Nat_OSuc,X9308))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__Suc])])). 6.97/7.23 fof(c_0_8643, plain, ![X6166, X6167, X6168]:(~class_Orderings_Olinorder(X6168)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X6168),X6167),hAPP(hAPP(c_Orderings_Oord__class_Omax(X6168),X6167),X6166))=X6167), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__absorb])])). 6.97/7.23 fof(c_0_8644, plain, ![X742, X743, X744]:(~class_Orderings_Olinorder(X744)|X743=hAPP(hAPP(c_Orderings_Oord__class_Omax(X744),X743),hAPP(hAPP(c_Orderings_Oord__class_Omin(X744),X743),X742))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup__inf__absorb])])])). 6.97/7.23 fof(c_0_8645, plain, ![X17026, X17027]:(~hBOOL(hAPP(c_List_Odistinct(X17027),X17026))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17027)),X17026)=hAPP(c_Finite__Set_Ocard(X17027),hAPP(c_List_Oset(X17027),X17026))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__card])])). 6.97/7.23 fof(c_0_8646, plain, ![X14406, X14407]:(~class_Rings_Olinordered__idom(X14407)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14407),c_Groups_Osgn__class_Osgn(X14407,X14406)),hAPP(c_Groups_Oabs__class_Oabs(X14407),X14406))=X14406), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__sgn__abs])])). 6.97/7.23 fof(c_0_8647, plain, ![X4834, X4835]:(~class_Orderings_Olinorder(X4835)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4835,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X4835),X4834))=hAPP(c_SetInterval_Oord__class_OatMost(X4835),X4834)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__greaterThan])])). 6.97/7.23 fof(c_0_8648, plain, ![X9319, X9320]:(~class_Orderings_Olinorder(X9320)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9320,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X9320),X9319))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X9320),X9319)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Compl__atMost])])])). 6.97/7.23 fof(c_0_8649, plain, ![X5141, X5142]:(~class_Orderings_Olinorder(X5142)|hAPP(c_SetInterval_Oord__class_OlessThan(X5142),X5141)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5142,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X5142),X5141))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Compl__atLeast])])])). 6.97/7.23 fof(c_0_8650, plain, ![X11021, X11022]:(~class_Orderings_Olinorder(X11022)|hAPP(c_SetInterval_Oord__class_OatLeast(X11022),X11021)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11022,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X11022),X11021))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Compl__lessThan])])])). 6.97/7.23 fof(c_0_8651, plain, ![X13686, X13687, X13688]:(~c_Equiv__Relations_Oequiv(X13688,X13687,X13686)|c_Complete__Lattice_OSup__class_OSup(tc_fun(X13688,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(X13688),X13687),X13686))=X13687), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Union__quotient])])). 6.97/7.23 fof(c_0_8652, plain, ![X13836, X13837]:(~class_Groups_Oordered__ab__group__add__abs(X13837)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13837),c_Groups_Ozero__class_Ozero(X13837)),hAPP(c_Groups_Oabs__class_Oabs(X13837),X13836)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__ge__zero])])])). 6.97/7.23 fof(c_0_8653, plain, ![X4127, X4128]:(~class_Rings_Olinordered__semidom(X4128)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4128),c_Groups_Ozero__class_Ozero(X4128)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4128),X4127)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__le__imp__of__nat])])])). 6.97/7.23 cnf(c_0_8654, 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_5414])). 6.97/7.23 fof(c_0_8655, plain, ![X10252, X10253, X10254, X10255]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10255),X10254))|hBOOL(hAPP(c_Finite__Set_Ofinite(X10253),hAPP(c_Set_Oimage(X10255,X10253,X10252),X10254)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__imageI])])])). 6.97/7.23 fof(c_0_8656, plain, ![X2076, X2077, X2078, X2079, X2080, X2081]:(~hBOOL(hAPP(hAPP(c_member(X2081),X2080),X2079))|hAPP(X2076,X2080)=hAPP(c_Fun_Ooverride__on(X2081,X2078,X2077,X2076,X2079),X2080)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_override__on__apply__in])])). 6.97/7.23 fof(c_0_8657, plain, ![X16646, X16647, X16648]:(~hBOOL(hAPP(c_List_Odistinct(X16648),X16647))|hBOOL(hAPP(c_List_Odistinct(X16648),hAPP(hAPP(c_List_Odrop(X16648),X16646),X16647)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__drop])])). 6.97/7.23 fof(c_0_8658, plain, ![X2772, X2773, X2774]:(~hBOOL(hAPP(c_List_Odistinct(X2774),X2773))|hBOOL(hAPP(c_List_Odistinct(X2774),hAPP(hAPP(c_List_Otake(X2774),X2772),X2773)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__take])])). 6.97/7.23 fof(c_0_8659, plain, ![X2015, X2016, X2017]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X2017),hAPP(hAPP(c_Set_Oinsert(X2017),X2016),X2015)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X2017),X2015)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2017),X2015))|hBOOL(hAPP(c_Finite__Set_Ofinite(X2017),hAPP(hAPP(c_Set_Oinsert(X2017),X2016),X2015))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__insert])])). 6.97/7.23 fof(c_0_8660, plain, ![X4793, X4794, X4795]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X4795),X4793))|hBOOL(hAPP(c_Finite__Set_Ofinite(X4795),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4795,tc_HOL_Obool)),X4793),X4794)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4795),X4794)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4795),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4795,tc_HOL_Obool)),X4793),X4794)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X4795),X4793))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4795),X4794)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__Diff2])])])])). 6.97/7.23 fof(c_0_8661, plain, ![X12678, X12679, X12680, X12681]:(~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X12681,X12680),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X12679),X12678)))|X12679=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X12681),X12680)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__eq])])])). 6.97/7.23 fof(c_0_8662, plain, ![X14274, X14275, X14276]:((hBOOL(hAPP(X14275,esk486_3(X14274,X14275,X14276)))|c_Orderings_Oord__class_OLeast(X14276,X14275)=X14274|~hBOOL(hAPP(X14275,X14274))|~class_Orderings_Oorder(X14276))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14276),X14274),esk486_3(X14274,X14275,X14276)))|c_Orderings_Oord__class_OLeast(X14276,X14275)=X14274|~hBOOL(hAPP(X14275,X14274))|~class_Orderings_Oorder(X14276))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Least__equality])])])])])). 6.97/7.23 fof(c_0_8663, plain, ![X6192, X6193]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X6193),X6192))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X6193,tc_HOL_Obool)),hAPP(c_Set_OPow(X6193),X6192))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X6193,tc_HOL_Obool)),hAPP(c_Set_OPow(X6193),X6192)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X6193),X6192)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Pow__iff])])). 6.97/7.23 fof(c_0_8664, plain, ![X3026, X3027, X3028]:((c_Orderings_Obot__class_Obot(tc_fun(X3028,tc_HOL_Obool))!=c_SetInterval_Oord__class_OgreaterThanAtMost(X3028,X3027,X3026)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3028),X3027),X3026))|~class_Orderings_Oorder(X3028))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3028),X3027),X3026))|c_Orderings_Obot__class_Obot(tc_fun(X3028,tc_HOL_Obool))=c_SetInterval_Oord__class_OgreaterThanAtMost(X3028,X3027,X3026)|~class_Orderings_Oorder(X3028))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_greaterThanAtMost__empty__iff2])])])])). 6.97/7.23 fof(c_0_8665, plain, ![X17379, X17380, X17381]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17381)),X17379)),X17380))|hAPP(hAPP(c_List_Odrop(X17381),X17380),X17379)=c_List_Olist_ONil(X17381))&(hAPP(hAPP(c_List_Odrop(X17381),X17380),X17379)!=c_List_Olist_ONil(X17381)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17381)),X17379)),X17380)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__eq__Nil])])). 6.97/7.23 fof(c_0_8666, plain, ![X832, X833, X835, X836, X837]:((c_Orderings_Obot__class_Obot(tc_fun(X833,tc_HOL_Obool))=X832|hBOOL(hAPP(hAPP(c_member(X833),esk24_2(X832,X833)),X832)))&(~hBOOL(hAPP(hAPP(c_member(X836),X837),X835))|c_Orderings_Obot__class_Obot(tc_fun(X836,tc_HOL_Obool))!=X835)), 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])])])])])). 6.97/7.23 fof(c_0_8667, plain, ![X14841, X14842, X14843]:(~class_Orderings_Olinorder(X14843)|(~hBOOL(hAPP(hAPP(c_member(X14843),X14842),hAPP(c_List_Oset(X14843),X14841)))|X14841=c_List_Olinorder__class_Oinsort__insert__key(X14843,X14843,c_COMBI(X14843),X14842,X14841))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insort__insert__triv])])])). 6.97/7.23 fof(c_0_8668, plain, ![X12030, X12031, X12032, X12033, X12034]:((X12030!=c_Orderings_Obot__class_Obot(tc_fun(X12031,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(X12031),X12032),X12030)))&(hBOOL(hAPP(hAPP(c_member(X12034),esk401_2(X12033,X12034)),X12033))|X12033=c_Orderings_Obot__class_Obot(tc_fun(X12034,tc_HOL_Obool)))), 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])])])])])])). 6.97/7.23 cnf(c_0_8669, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))|c_List_Oupt(X1,X2)!=c_List_Olist_ONil(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_5415])). 6.97/7.23 fof(c_0_8670, plain, ![X14374, X14375, X14376]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14376)),X14375)),X14374))|hAPP(hAPP(c_List_Odrop(X14376),X14374),X14375)=c_List_Olist_ONil(X14376)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__all])])). 6.97/7.23 cnf(c_0_8671, plain, (X3=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3)=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Omult__zero(X2)|~class_Rings_Ono__zero__divisors(X2)|~class_Rings_Ozero__neq__one(X2)|~class_Power_Opower(X2)), inference(split_conjunct,[status(thm)],[c_0_5416])). 6.97/7.23 fof(c_0_8672, plain, ![X1023, X1024, X1025]:(~class_Groups_Ocomm__monoid__mult(X1025)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1024,X1025),X1023),c_Orderings_Obot__class_Obot(tc_fun(X1024,tc_HOL_Obool)))=c_Groups_Oone__class_Oone(X1025)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__empty])])])). 6.97/7.23 fof(c_0_8673, plain, ![X2622, X2623, X2624]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X2624,X2623)),X2622))|hBOOL(hAPP(c_Finite__Set_Ofinite(X2624),hAPP(c_Relation_ODomain(X2624,X2623),X2622)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Domain])])). 6.97/7.23 fof(c_0_8674, plain, ![X16323, X16324]:((X16323!=c_Orderings_Obot__class_Obot(tc_fun(X16324,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16324,tc_HOL_Obool)),X16323),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X16324,tc_HOL_Obool)),X16323))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16324,tc_HOL_Obool)),X16323),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X16324,tc_HOL_Obool)),X16323)))|X16323=c_Orderings_Obot__class_Obot(tc_fun(X16324,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__Compl__self__eq])])). 6.97/7.23 cnf(c_0_8675, plain, (hBOOL(hAPP(X2,esk56_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_5417])). 6.97/7.23 fof(c_0_8676, plain, ![X6911, X6912, X6913]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X6913,X6912)),X6911))|hBOOL(hAPP(c_Finite__Set_Ofinite(X6912),hAPP(c_Relation_ORange(X6913,X6912),X6911)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Range])])). 6.97/7.23 fof(c_0_8677, plain, ![X7724, X7725]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7725),hAPP(c_Nat_OSuc,X7724)))|(X7724=X7725|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7725),X7724))))&((X7724!=X7725|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7725),hAPP(c_Nat_OSuc,X7724))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7725),X7724))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7725),hAPP(c_Nat_OSuc,X7724)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq])])])). 6.97/7.23 fof(c_0_8678, plain, ![X9494, X9495]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X9495),X9494))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9495),hAPP(c_Nat_OSuc,X9494))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9495),hAPP(c_Nat_OSuc,X9494)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X9495),X9494)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le])])). 6.97/7.23 fof(c_0_8679, plain, ![X7276, X7277, X7278, X7279, X7280]:((hAPP(c_Set_Oimage(X7280,X7279,X7278),X7277)!=hAPP(c_Set_Oimage(X7280,X7279,X7278),X7276)|X7277=X7276|~c_Fun_Oinj__on(X7280,X7279,X7278,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7280,tc_HOL_Obool)),X7277),X7276)))&(X7277!=X7276|hAPP(c_Set_Oimage(X7280,X7279,X7278),X7277)=hAPP(c_Set_Oimage(X7280,X7279,X7278),X7276)|~c_Fun_Oinj__on(X7280,X7279,X7278,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7280,tc_HOL_Obool)),X7277),X7276)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__Un__image__eq__iff])])])])). 6.97/7.23 fof(c_0_8680, plain, ![X9143, X9144, X9145, X9146, X9147]:(~c_Fun_Oinj__on(X9147,X9146,X9145,X9144)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9147,tc_HOL_Obool)),X9143),X9144))|c_Fun_Oinj__on(X9147,X9146,X9145,X9143))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_subset__inj__on])])])). 6.97/7.23 cnf(c_0_8681, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=X1|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)!=c_Groups_Oone__class_Oone(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_4405])). 6.97/7.23 fof(c_0_8682, plain, ![X5191, X5192]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5192),X5191))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5192),hAPP(c_Nat_OSuc,X5191)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__SucI])])])). 6.97/7.23 cnf(c_0_8683, 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_5401])). 6.97/7.23 fof(c_0_8684, plain, ![X16455, X16456, X16457, X16458, X16460, X16461, X16462, X16463, X16464]:((~hBOOL(hAPP(c_Predicate_ORangeP(X16458,X16457,X16456),X16455))|hBOOL(hAPP(hAPP(X16456,esk548_2(X16455,X16456)),X16455)))&(~hBOOL(hAPP(hAPP(X16461,X16462),X16460))|hBOOL(hAPP(c_Predicate_ORangeP(X16464,X16463,X16461),X16460)))), 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])])])])])). 6.97/7.23 fof(c_0_8685, plain, ![X7099, X7100, X7101, X7102, X7104, X7105, X7106, X7107, X7108]:((~hBOOL(hAPP(c_Predicate_ODomainP(X7102,X7101,X7100),X7099))|hBOOL(hAPP(hAPP(X7100,X7099),esk228_2(X7099,X7100))))&(~hBOOL(hAPP(hAPP(X7105,X7104),X7106))|hBOOL(hAPP(c_Predicate_ODomainP(X7108,X7107,X7105),X7104)))), 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])])])])])). 6.97/7.23 fof(c_0_8686, plain, ![X12667, X12668, X12669, X12670, X12671]:((X12668!=X12667|hAPP(c_Set_Oimage(X12671,X12670,X12669),X12668)=hAPP(c_Set_Oimage(X12671,X12670,X12669),X12667)|~c_Fun_Oinj__on(X12671,X12670,X12669,c_Orderings_Otop__class_Otop(tc_fun(X12671,tc_HOL_Obool))))&(hAPP(c_Set_Oimage(X12671,X12670,X12669),X12668)!=hAPP(c_Set_Oimage(X12671,X12670,X12669),X12667)|X12668=X12667|~c_Fun_Oinj__on(X12671,X12670,X12669,c_Orderings_Otop__class_Otop(tc_fun(X12671,tc_HOL_Obool))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__image__eq__iff])])])). 6.97/7.23 cnf(c_0_8687, plain, (c_List_Olinorder__class_Osorted(X1,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk454_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_5212])). 6.97/7.23 cnf(c_0_8688, 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_5386])). 6.97/7.23 fof(c_0_8689, plain, ![X17626, X17627, X17628]:(hAPP(hAPP(c_Set_Oinsert(X17628),X17627),c_Orderings_Obot__class_Obot(tc_fun(X17628,tc_HOL_Obool)))!=hAPP(hAPP(c_Set_Oinsert(X17628),X17626),c_Orderings_Obot__class_Obot(tc_fun(X17628,tc_HOL_Obool)))|X17627=X17626), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__inject])])). 6.97/7.23 fof(c_0_8690, plain, ![X2229, X2230, X2231, X2232]:((~hBOOL(hAPP(X2231,X2230))|~c_List_Olist__all(X2232,X2231,X2229)|c_List_Olist__all(X2232,X2231,hAPP(hAPP(c_List_Olist_OCons(X2232),X2230),X2229)))&((hBOOL(hAPP(X2231,X2230))|~c_List_Olist__all(X2232,X2231,hAPP(hAPP(c_List_Olist_OCons(X2232),X2230),X2229)))&(c_List_Olist__all(X2232,X2231,X2229)|~c_List_Olist__all(X2232,X2231,hAPP(hAPP(c_List_Olist_OCons(X2232),X2230),X2229))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__simps_I1_J])])])). 6.97/7.23 cnf(c_0_8691, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=X1|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)!=c_Groups_Oone__class_Oone(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_4405])). 6.97/7.23 fof(c_0_8692, plain, ![X905, X906]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X906),hAPP(c_Nat_OSuc,X905)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X906),X905))|X906=X905)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__SucE])])])). 6.97/7.23 fof(c_0_8693, plain, ![X5902, X5903, X5904, X5905]:((hBOOL(hAPP(X5905,X5904))|c_List_Olist_ONil(X5903)=hAPP(c_List_Ofilter(X5903,X5905),c_List_Oreplicate(X5903,X5902,X5904)))&(~hBOOL(hAPP(X5905,X5904))|hAPP(c_List_Ofilter(X5903,X5905),c_List_Oreplicate(X5903,X5902,X5904))=c_List_Oreplicate(X5903,X5902,X5904))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_filter__replicate])])])). 6.97/7.23 cnf(c_0_8694, 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_5302])). 6.97/7.23 cnf(c_0_8695, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=X1|X1=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)!=c_Groups_Oone__class_Oone(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_4405])). 6.97/7.23 cnf(c_0_8696, 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_5378])). 6.97/7.23 fof(c_0_8697, plain, ![X6616, X6617]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6617),X6616))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X6617)),hAPP(c_Nat_OSuc,X6616))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X6617)),hAPP(c_Nat_OSuc,X6616)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6617),X6616)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__eq])])). 6.97/7.23 cnf(c_0_8698, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=X1|X2=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)!=c_Groups_Oone__class_Oone(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_4405])). 6.97/7.23 cnf(c_0_8699, 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_5379])). 6.97/7.23 fof(c_0_8700, plain, ![X14061, X14062, X14063, X14064, X14065]:(hAPP(hAPP(c_List_Odrop(X14065),X14064),X14063)!=hAPP(hAPP(c_List_Olist_OCons(X14065),X14062),X14061)|X14062=hAPP(hAPP(c_List_Onth(X14065),X14063),X14064)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__via__drop])])])). 6.97/7.23 fof(c_0_8701, plain, ![X4564, X4565, X4566]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X4566,X4566),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4565),X4564)))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X4566|c_Groups_Oone__class_Oone(tc_Int_Oint)=X4565)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_self__quotient])])])). 6.97/7.23 fof(c_0_8702, plain, ![X5853, X5854, X5855]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X5855,X5855),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X5854),X5853)))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X5855|X5853=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])])])). 6.97/7.23 fof(c_0_8703, plain, ![X11574, X11575, X11576, X11577]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X11577,X11576),tc_HOL_Obool)),X11575),X11574))|(~c_Relation_Osingle__valued(X11577,X11576,X11574)|c_Relation_Osingle__valued(X11577,X11576,X11575))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__subset])])). 6.97/7.23 fof(c_0_8704, plain, ![X2165, X2166, X2167, X2168]:((~hBOOL(hAPP(c_List_Odistinct(X2167),c_List_Olinorder__class_Osort__key(X2167,X2168,X2166,X2165)))|hBOOL(hAPP(c_List_Odistinct(X2167),X2165))|~class_Orderings_Olinorder(X2168))&(~hBOOL(hAPP(c_List_Odistinct(X2167),X2165))|hBOOL(hAPP(c_List_Odistinct(X2167),c_List_Olinorder__class_Osort__key(X2167,X2168,X2166,X2165)))|~class_Orderings_Olinorder(X2168))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__sort])])])])). 6.97/7.23 cnf(c_0_8705, 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_5418])). 6.97/7.23 cnf(c_0_8706, plain, (X2=c_Transitive__Closure_Otrancl(X1,X2)|~c_Relation_Otrans(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5419])). 6.97/7.23 fof(c_0_8707, plain, ![X2847, X2848, X2849, X2850]:(((c_List_Olist__all(X2850,X2849,X2847)|~c_List_Olist__all(X2850,X2849,hAPP(hAPP(c_List_Oappend(X2850),X2848),X2847)))&(c_List_Olist__all(X2850,X2849,X2848)|~c_List_Olist__all(X2850,X2849,hAPP(hAPP(c_List_Oappend(X2850),X2848),X2847))))&(~c_List_Olist__all(X2850,X2849,X2847)|~c_List_Olist__all(X2850,X2849,X2848)|c_List_Olist__all(X2850,X2849,hAPP(hAPP(c_List_Oappend(X2850),X2848),X2847)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__append])])])). 6.97/7.23 cnf(c_0_8708, 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),X1),X2)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_5420])). 6.97/7.23 cnf(c_0_8709, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|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))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)), inference(split_conjunct,[status(thm)],[c_0_5400])). 6.97/7.23 fof(c_0_8710, plain, ![X11686, X11687]:(~class_Rings_Osemiring__1(X11687)|hBOOL(hAPP(hAPP(c_member(X11687),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X11687),X11686)),c_Nat_Osemiring__1__class_ONats(X11687)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__in__Nats])])). 6.97/7.23 fof(c_0_8711, plain, ![X9952, X9953]:(~class_Rings_Oring__1(X9953)|hBOOL(hAPP(hAPP(c_member(X9953),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X9953),X9952)),c_Int_Oring__1__class_OInts(X9953)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Ints__of__nat])])])). 6.97/7.23 fof(c_0_8712, plain, ![X6209, X6210]:(~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X6210),c_Int_OInteg))|(~hBOOL(hAPP(X6209,hAPP(c_Int_ORep__Integ,esk208_2(X6209,X6210))))|hBOOL(hAPP(X6209,X6210)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Rep__Integ__induct])])])])). 6.97/7.23 fof(c_0_8713, plain, ![X3627, X3628, X3629, X3630]:(~hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3630,tc_HOL_Obool)),X3629),X3628),X3627))|(hBOOL(hAPP(X3629,X3627))|hBOOL(hAPP(X3628,X3627)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup1E])])])). 6.97/7.23 cnf(c_0_8714, 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_Oring__char__0(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_5344])). 6.97/7.23 fof(c_0_8715, plain, ![X7013, X7014]:(~class_Rings_Oring__1(X7014)|hBOOL(hAPP(hAPP(c_member(X7014),hAPP(c_Int_Oring__1__class_Oof__int(X7014),X7013)),c_Int_Oring__1__class_OInts(X7014)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__of__int])])). 6.97/7.23 fof(c_0_8716, plain, ![X577, X578]:(~class_Int_Onumber__ring(X578)|hBOOL(hAPP(hAPP(c_member(X578),hAPP(c_Int_Onumber__class_Onumber__of(X578),X577)),c_Int_Oring__1__class_OInts(X578)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Ints__number__of])])])). 6.97/7.23 cnf(c_0_8717, plain, (c_List_Olist__all(tc_Nat_Onat,X1,c_List_Oupt(X2,X3))|~c_List_Oall__interval__nat(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_5421])). 6.97/7.23 cnf(c_0_8718, plain, (X2=X1|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))|~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_5422])). 6.97/7.23 cnf(c_0_8719, plain, (c_Groups_Ozero__class_Ozero(X1)=X3|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=c_Groups_Ozero__class_Ozero(X1)|X3!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber(X1)), inference(split_conjunct,[status(thm)],[c_0_5423])). 6.97/7.23 fof(c_0_8720, plain, ![X17329, X17330]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17330),c_Groups_Ozero__class_Ozero(X17330)),X17329))|c_Groups_Oone__class_Oone(X17330)=c_Groups_Osgn__class_Osgn(X17330,X17329)|~class_Rings_Olinordered__idom(X17330))&(c_Groups_Oone__class_Oone(X17330)!=c_Groups_Osgn__class_Osgn(X17330,X17329)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17330),c_Groups_Ozero__class_Ozero(X17330)),X17329))|~class_Rings_Olinordered__idom(X17330))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__1__pos])])])). 6.97/7.23 fof(c_0_8721, plain, ![X381, X382, X383]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X381,tc_HOL_Obool)),X383),X382))|X383!=X382)&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X381,tc_HOL_Obool)),X382),X383))|X383!=X382))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X381,tc_HOL_Obool)),X383),X382))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X381,tc_HOL_Obool)),X382),X383))|X383=X382)), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__eq__subset])])])). 6.97/7.23 fof(c_0_8722, plain, ![X15535, X15536, X15537]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15537,tc_HOL_Obool)),X15536),X15535))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15537,tc_HOL_Obool)),X15536),X15535)=X15535)&(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15537,tc_HOL_Obool)),X15536),X15535)!=X15535|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15537,tc_HOL_Obool)),X15536),X15535)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__Un__eq])])). 6.97/7.23 fof(c_0_8723, plain, ![X16372, X16373, X16374]:(~class_Orderings_Owellorder(X16374)|(~hBOOL(hAPP(X16373,X16372))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16374),c_Orderings_Oord__class_OLeast(X16374,X16373)),X16372)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Least__le])])])). 6.97/7.23 fof(c_0_8724, plain, ![X8501, X8502, X8503]:(~class_Divides_Osemiring__div(X8503)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8503),c_Divides_Odiv__class_Omod(X8503,X8502,X8501)),X8501)=c_Groups_Ozero__class_Ozero(X8503)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__div__trivial])])])). 6.97/7.23 fof(c_0_8725, plain, ![X5303, X5304, X5305]:(~class_Divides_Osemiring__div(X5305)|c_Divides_Odiv__class_Omod(X5305,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5305),X5304),X5303),X5304)=c_Groups_Ozero__class_Ozero(X5305)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__mult__self1__is__0])])])). 6.97/7.23 fof(c_0_8726, plain, ![X15586, X15587, X15588]:(~class_Divides_Osemiring__div(X15588)|c_Groups_Ozero__class_Ozero(X15588)=c_Divides_Odiv__class_Omod(X15588,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15588),X15587),X15586),X15586)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__mult__self2__is__0])])])). 6.97/7.23 fof(c_0_8727, plain, ![X15284, X15285]:(~class_Groups_Ogroup__add(X15285)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15285),hAPP(c_Groups_Ouminus__class_Ouminus(X15285),X15284)),X15284)=c_Groups_Ozero__class_Ozero(X15285)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_left__minus])])])). 6.97/7.23 fof(c_0_8728, plain, ![X8487, X8488]:(~class_Groups_Oab__group__add(X8488)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8488),hAPP(c_Groups_Ouminus__class_Ouminus(X8488),X8487)),X8487)=c_Groups_Ozero__class_Ozero(X8488)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__left__minus])])). 6.97/7.23 fof(c_0_8729, plain, ![X2818, X2819]:(~class_Lattices_Oboolean__algebra(X2819)|c_Orderings_Otop__class_Otop(X2819)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2819),hAPP(c_Groups_Ouminus__class_Ouminus(X2819),X2818)),X2818)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_compl__sup__top])])])). 6.97/7.23 fof(c_0_8730, plain, ![X10998, X10999]:(~class_Lattices_Oboolean__algebra(X10999)|c_Orderings_Obot__class_Obot(X10999)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10999),hAPP(c_Groups_Ouminus__class_Ouminus(X10999),X10998)),X10998)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_compl__inf__bot])])])). 6.97/7.23 fof(c_0_8731, plain, ![X16900, X16901, X16902]:(X16902=c_List_Olist_ONil(X16901)|c_List_Olast(X16901,hAPP(hAPP(c_List_Oappend(X16901),X16900),X16902))=c_List_Olast(X16901,X16902)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_last__appendR])])])). 6.97/7.23 fof(c_0_8732, plain, ![X13531, X13532]:(~class_Groups_Ogroup__add(X13532)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13532),X13531),hAPP(c_Groups_Ouminus__class_Ouminus(X13532),X13531))=c_Groups_Ozero__class_Ozero(X13532)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus])])). 6.97/7.23 fof(c_0_8733, plain, ![X6487, X6488]:(~class_Lattices_Oboolean__algebra(X6488)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6488),X6487),hAPP(c_Groups_Ouminus__class_Ouminus(X6488),X6487))=c_Orderings_Obot__class_Obot(X6488)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__compl__bot])])). 6.97/7.23 fof(c_0_8734, plain, ![X10735, X10736]:(~class_Lattices_Oboolean__algebra(X10736)|c_Orderings_Otop__class_Otop(X10736)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10736),X10735),hAPP(c_Groups_Ouminus__class_Ouminus(X10736),X10735))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__compl__top])])])). 6.97/7.23 fof(c_0_8735, plain, ![X7982, X7983, X7984]:((c_List_Olist_ONil(X7983)!=X7984|X7982=c_List_Olast(X7983,hAPP(hAPP(c_List_Olist_OCons(X7983),X7982),X7984)))&(X7984=c_List_Olist_ONil(X7983)|c_List_Olast(X7983,X7984)=c_List_Olast(X7983,hAPP(hAPP(c_List_Olist_OCons(X7983),X7982),X7984)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_last_Osimps])])])). 6.97/7.23 fof(c_0_8736, plain, ![X3193, X3194, X3195]:(~class_Orderings_Oorder(X3195)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3195),X3194),X3193))|hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X3195,X3193),X3194)=c_Orderings_Obot__class_Obot(tc_fun(X3195,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__empty])])])). 6.97/7.23 fof(c_0_8737, plain, ![X12038, X12039, X12040, X12041]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X12041),hAPP(c_Set_Oimage(X12040,X12041,X12039),X12038))),hAPP(c_Finite__Set_Ocard(X12040),X12038)))|~c_Fun_Oinj__on(X12040,X12041,X12039,X12038)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pigeonhole])])])). 6.97/7.23 fof(c_0_8738, plain, ![X8937, X8938, X8939, X8940]:(~c_Hoare__Mirabelle_Ohoare__derivs(X8940,X8939,X8938)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X8940),tc_HOL_Obool)),X8937),X8938))|c_Hoare__Mirabelle_Ohoare__derivs(X8940,X8939,X8937))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_weaken])])). 6.97/7.23 fof(c_0_8739, plain, ![X16480, X16481, X16482, X16483, X16484]:(~hBOOL(hAPP(hAPP(c_member(X16484),X16483),X16482))|hAPP(c_Quotient_OBabs(X16484,X16481,X16482,X16480),X16483)=hAPP(X16480,X16483)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Babs__def])])). 6.97/7.23 cnf(c_0_8740, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)=c_Divides_Odivmod__int(X2,X1)|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_4449])). 6.97/7.23 fof(c_0_8741, plain, ![X7069]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7069))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X7069)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X7069))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7069)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less])])). 6.97/7.23 fof(c_0_8742, plain, ![X1482, X1483, X1484, X1485, X1486]:((~hBOOL(hAPP(hAPP(X1484,X1482),X1483))|hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1486,X1485,X1484),X1483),X1482)))&(~hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1486,X1485,X1484),X1483),X1482))|hBOOL(hAPP(hAPP(X1484,X1482),X1483)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep__iff])])). 6.97/7.23 cnf(c_0_8743, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))))), inference(rw,[status(thm)],[c_0_5424, c_0_4565])). 6.97/7.23 fof(c_0_8744, plain, ![X11941, X11942, X11943]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11943)),X11942)),X11941))|hAPP(hAPP(c_List_Otake(X11943),X11941),X11942)=X11942), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__all])])). 6.97/7.23 fof(c_0_8745, plain, ![X15047, X15048, X15049, X15050]:(~class_Orderings_Olinorder(X15050)|hAPP(c_List_Oset(X15049),c_List_Olinorder__class_Osort__key(X15049,X15050,X15048,X15047))=hAPP(c_List_Oset(X15049),X15047)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_set__sort])])])). 6.97/7.23 fof(c_0_8746, plain, ![X2429, X2430]:(~class_Rings_Olinordered__idom(X2430)|hAPP(c_Groups_Oabs__class_Oabs(X2430),X2429)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2430),X2429),c_Groups_Osgn__class_Osgn(X2430,X2429))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__sgn])])])). 6.97/7.23 fof(c_0_8747, plain, ![X2144, X2145, X2146, X2147]:(~hBOOL(hAPP(X2147,X2146))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2145,tc_HOL_Obool)),X2147),X2144))|hBOOL(hAPP(X2144,X2146)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate1D])])). 6.97/7.23 fof(c_0_8748, plain, ![X2851, X2852]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2852),X2851))|X2852=X2851|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2852),X2851)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2852),X2851))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2852),X2851)))&(X2852!=X2851|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2852),X2851))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])])). 6.97/7.23 fof(c_0_8749, plain, ![X1165, X1166]:(~class_Orderings_Olinorder(X1166)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1166),X1165))|hAPP(c_Finite__Set_Ofold1(X1166,c_Orderings_Oord__class_Omin(X1166)),X1165)=c_Big__Operators_Olattice_OInf__fin(X1166,c_Orderings_Oord__class_Omin(X1166),X1165))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_OF__eq])])])). 6.97/7.23 fof(c_0_8750, plain, ![X10733, X10734]:(~class_Complete__Lattice_Ocomplete__lattice(X10734)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10734),X10733))|(c_Orderings_Obot__class_Obot(tc_fun(X10734,tc_HOL_Obool))=X10733|c_Big__Operators_Olattice__class_OSup__fin(X10734,X10733)=c_Complete__Lattice_OSup__class_OSup(X10734,X10733)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin__Sup])])])). 6.97/7.23 fof(c_0_8751, plain, ![X8050, X8051]:(~class_Complete__Lattice_Ocomplete__lattice(X8051)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8051),X8050))|(c_Orderings_Obot__class_Obot(tc_fun(X8051,tc_HOL_Obool))=X8050|c_Complete__Lattice_OInf__class_OInf(X8051,X8050)=c_Big__Operators_Olattice__class_OInf__fin(X8051,X8050)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin__Inf])])). 6.97/7.23 cnf(c_0_8752, plain, (c_List_Oupt(X2,X1)=c_List_Olist_ONil(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5415])). 6.97/7.23 fof(c_0_8753, plain, ![X5271, X5272]:(~class_Orderings_Olinorder(X5272)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5272),X5271))|c_Big__Operators_Olattice_OSup__fin(X5272,c_Orderings_Oord__class_Omax(X5272),X5271)=hAPP(c_Finite__Set_Ofold1(X5272,c_Orderings_Oord__class_Omax(X5272)),X5271))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_OF__eq])])])). 6.97/7.23 cnf(c_0_8754, plain, (hBOOL(hAPP(X2,X1))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))|~hBOOL(hAPP(X2,hAPP(c_Code__Numeral_Onat__of,esk573_2(X2,X1))))), inference(split_conjunct,[status(thm)],[c_0_5425])). 6.97/7.23 fof(c_0_8755, plain, ![X811, X812, X813]:(~hBOOL(hAPP(c_List_Odistinct(X813),X812))|c_List_Oremove1(X813,X811,c_List_Oremdups(X813,X812))=c_List_Oremdups(X813,c_List_Oremove1(X813,X811,X812))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_remove1__remdups])])])). 6.97/7.23 cnf(c_0_8756, 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_5292])). 6.97/7.23 fof(c_0_8757, plain, ![X16331, X16332]:(~class_Groups_Oordered__ab__group__add__abs(X16332)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16332),X16331),hAPP(c_Groups_Oabs__class_Oabs(X16332),X16331)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__ge__self])])])). 6.97/7.23 fof(c_0_8758, plain, ![X9038, X9039]:((hBOOL(hAPP(hAPP(X9038,esk299_2(X9038,X9039)),esk299_2(X9038,X9039)))|~c_Equiv__Relations_Opart__equivp(X9039,X9038))&((c_Predicate_Osymp(X9039,X9038)|~c_Equiv__Relations_Opart__equivp(X9039,X9038))&(c_Predicate_Otransp(X9039,X9038)|~c_Equiv__Relations_Opart__equivp(X9039,X9038)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_part__equivpE])])])])])). 6.97/7.23 fof(c_0_8759, plain, ![X5135, X5136, X5138, X5139, X5140]:((((c_Predicate_Otransp(X5136,X5135)|~c_Equiv__Relations_Opart__equivp(X5136,X5135))&(c_Predicate_Osymp(X5136,X5135)|~c_Equiv__Relations_Opart__equivp(X5136,X5135)))&(hBOOL(hAPP(hAPP(X5135,esk167_2(X5135,X5136)),esk167_2(X5135,X5136)))|~c_Equiv__Relations_Opart__equivp(X5136,X5135)))&(~c_Predicate_Otransp(X5139,X5138)|~c_Predicate_Osymp(X5139,X5138)|~hBOOL(hAPP(hAPP(X5138,X5140),X5140))|c_Equiv__Relations_Opart__equivp(X5139,X5138))), 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_part__equivp__refl__symp__transp])])])])])])). 6.97/7.23 fof(c_0_8760, plain, ![X15855, X15856]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15856))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15856),X15855))|c_Divides_Odiv__class_Omod(tc_Int_Oint,X15856,X15855)=X15856)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__pos__pos__trivial])])])). 6.97/7.23 fof(c_0_8761, plain, ![X15155, X15156]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15156),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15155),X15156))|c_Divides_Odiv__class_Omod(tc_Int_Oint,X15156,X15155)=X15156)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__neg__neg__trivial])])])). 6.97/7.23 fof(c_0_8762, plain, ![X7435, X7436, X7437]:((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7435),X7436)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7437),X7436)|(X7437=X7435|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X7436))&((X7437!=X7435|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7435),X7436)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7437),X7436))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X7436|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7435),X7436)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7437),X7436)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel2])])])). 6.97/7.23 fof(c_0_8763, plain, ![X11578, X11579]:((hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X11579)!=hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X11578)|X11578=X11579|~c_Nat__Transfer_Onat__set(X11578)|~c_Nat__Transfer_Onat__set(X11579))&(X11578!=X11579|hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X11579)=hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X11578)|~c_Nat__Transfer_Onat__set(X11578)|~c_Nat__Transfer_Onat__set(X11579))), 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_I3_J])])])])). 6.97/7.23 fof(c_0_8764, plain, ![X1681, X1682, X1683]:((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1683)),X1682)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1683)),X1681)|X1682=X1681)&(X1682!=X1681|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1683)),X1682)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1683)),X1681))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__cancel1])])). 6.97/7.23 fof(c_0_8765, plain, ![X6638, X6639, X6640, X6641, X6642]:(~c_Fun_Obij__betw(X6642,X6641,X6640,X6639,X6638)|c_Fun_Obij__betw(X6641,X6642,c_Fun_Othe__inv__into(X6642,X6641,X6639,X6640),X6638,X6639)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bij__betw__the__inv__into])])])). 6.97/7.23 fof(c_0_8766, plain, ![X9384, X9385, X9386, X9387, X9388]:(~c_Fun_Obij__betw(X9388,X9387,X9386,X9385,X9384)|c_Fun_Obij__betw(X9387,X9388,c_Hilbert__Choice_Oinv__into(X9388,X9387,X9385,X9386),X9384,X9385)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__inv__into])])). 6.97/7.23 fof(c_0_8767, plain, ![X9586, X9587, X9588]:(((X9588!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9588),X9586)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9588),X9587))&(X9587!=X9586|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9588),X9586)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9588),X9587)))&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9588),X9586)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9588),X9587)|(X9588=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X9587=X9586))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel__disj])])])). 6.97/7.23 fof(c_0_8768, plain, ![X1791, X1792]:((~c_Wellfounded_Owf(X1792,hAPP(hAPP(c_Relation_Orel__comp(X1792,X1792,X1792),X1791),X1791))|c_Wellfounded_Owf(X1792,X1791))&(~c_Wellfounded_Owf(X1792,X1791)|c_Wellfounded_Owf(X1792,hAPP(hAPP(c_Relation_Orel__comp(X1792,X1792,X1792),X1791),X1791)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__comp__self])])). 6.97/7.23 fof(c_0_8769, plain, ![X5633, X5634]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5634,tc_HOL_Obool)),X5633),c_Orderings_Obot__class_Obot(tc_fun(X5634,tc_HOL_Obool))))|c_Orderings_Obot__class_Obot(tc_fun(X5634,tc_HOL_Obool))=X5633)&(c_Orderings_Obot__class_Obot(tc_fun(X5634,tc_HOL_Obool))!=X5633|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5634,tc_HOL_Obool)),X5633),c_Orderings_Obot__class_Obot(tc_fun(X5634,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__empty])])). 6.97/7.23 fof(c_0_8770, plain, ![X12874, X12875, X12876]:(~hBOOL(hAPP(c_List_Odistinct(X12876),X12875))|hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X12876)),c_Enum_On__lists(X12876,X12874,X12875)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__n__lists])])])). 6.97/7.23 fof(c_0_8771, plain, ![X4134, X4135, X4136]:(~hBOOL(hAPP(c_List_Odistinct(X4136),X4135))|hBOOL(hAPP(c_List_Odistinct(X4136),hAPP(c_List_Ofilter(X4136,X4134),X4135)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__filter])])])). 6.97/7.23 fof(c_0_8772, plain, ![X5819, X5820]:(X5820=c_List_Olist_ONil(X5819)|(~hBOOL(hAPP(c_List_Odistinct(X5819),X5820))|hBOOL(hAPP(c_List_Odistinct(X5819),c_List_Obutlast(X5819,X5820))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__butlast])])). 6.97/7.23 fof(c_0_8773, plain, ![X3008, X3009, X3010, X3011]:((hBOOL(hAPP(hAPP(X3010,X3008),X3009))|~hBOOL(hAPP(hAPP(X3010,X3009),X3008))|c_Partial__Function_Omk__less(X3011,X3010,X3009,X3008))&((~hBOOL(hAPP(hAPP(X3010,X3008),X3009))|~c_Partial__Function_Omk__less(X3011,X3010,X3009,X3008))&(hBOOL(hAPP(hAPP(X3010,X3009),X3008))|~c_Partial__Function_Omk__less(X3011,X3010,X3009,X3008)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mk__less__def])])])])). 6.97/7.23 fof(c_0_8774, plain, ![X10712, X10713]:(~class_Groups_Ogroup__add(X10713)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10713),c_Groups_Ozero__class_Ozero(X10713)),X10712)=hAPP(c_Groups_Ouminus__class_Ouminus(X10713),X10712)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__0])])])). 6.97/7.23 fof(c_0_8775, plain, ![X6708]:(~class_Orderings_Olinorder(X6708)|c_Orderings_Oord_Omin(X6708,hAPP(c_COMBC(X6708,X6708,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X6708)))=c_Orderings_Oord__class_Omax(X6708)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dual__min])])])). 6.97/7.23 fof(c_0_8776, plain, ![X918]:(~class_Orderings_Olinorder(X918)|c_Orderings_Oord__class_Omin(X918)=c_Orderings_Oord_Omax(X918,hAPP(c_COMBC(X918,X918,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X918)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dual__max])])). 6.97/7.23 fof(c_0_8777, plain, ![X17471, X17472, X17473, X17474]:(~c_Equiv__Relations_Opart__equivp(X17474,X17473)|(~hBOOL(hAPP(hAPP(X17473,X17472),X17471))|hBOOL(hAPP(hAPP(X17473,X17471),X17472)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_part__equivp__symp])])])). 6.97/7.23 fof(c_0_8778, plain, ![X8133, X8134, X8135, X8136]:(~c_Predicate_Osymp(X8136,X8135)|(~hBOOL(hAPP(hAPP(X8135,X8134),X8133))|hBOOL(hAPP(hAPP(X8135,X8133),X8134)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sympE])])])). 6.97/7.23 fof(c_0_8779, plain, ![X16229, X16230]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X16230,X16230)),X16229))|hBOOL(hAPP(c_Finite__Set_Ofinite(X16230),hAPP(c_Relation_OField(X16230),X16229)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__Field])])])). 6.97/7.23 fof(c_0_8780, plain, ![X6584, X6585, X6586, X6587]:(~c_Equiv__Relations_Oequivp(X6587,X6586)|(~hBOOL(hAPP(hAPP(X6586,X6585),X6584))|hBOOL(hAPP(hAPP(X6586,X6584),X6585)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equivp__symp])])])). 6.97/7.23 fof(c_0_8781, plain, ![X5300, X5301, X5302]:(~class_Lattices_Osemilattice__inf(X5302)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5302),X5301),X5300))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5302),X5300),X5301)=X5301)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__absorb2])])])). 6.97/7.23 fof(c_0_8782, plain, ![X2028, X2029, X2030]:(~class_Lattices_Osemilattice__sup(X2030)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2030),X2029),X2028))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2030),X2029),X2028)=X2028)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__absorb2])])). 6.97/7.23 cnf(c_0_8783, plain, (hBOOL(hAPP(X1,esk307_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_5426])). 6.97/7.23 fof(c_0_8784, plain, ![X6533, X6534, X6535]:((X6534!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6535),X6534),X6533)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6535),X6534),X6533))|~class_Lattices_Osemilattice__inf(X6535))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6535),X6534),X6533))|X6534=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6535),X6534),X6533)|~class_Lattices_Osemilattice__inf(X6535))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__inf])])])). 6.97/7.23 fof(c_0_8785, plain, ![X11370, X11371, X11372]:(~class_Lattices_Osemilattice__sup(X11372)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11372),X11371),X11370))|X11370=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X11372),X11370),X11371))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__absorb1])])])). 6.97/7.23 fof(c_0_8786, plain, ![X11356, X11357]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X11357,X11357)),X11356))|c_Nitpick_Ounknown(tc_HOL_Obool)|~c_Nitpick_Owf_H(X11357,X11356))&(c_Wellfounded_Oacyclic(X11357,X11356)|~c_Nitpick_Owf_H(X11357,X11356)))&((~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X11357,X11357)),X11356))|~c_Wellfounded_Oacyclic(X11357,X11356)|c_Nitpick_Owf_H(X11357,X11356))&(~c_Nitpick_Ounknown(tc_HOL_Obool)|~c_Wellfounded_Oacyclic(X11357,X11356)|c_Nitpick_Owf_H(X11357,X11356)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Owf_H__def])])])). 6.97/7.23 fof(c_0_8787, plain, ![X11160, X11161, X11162, X11163]:((~c_Fun_Oinj__on(X11163,X11161,X11160,X11162)|hAPP(c_Finite__Set_Ocard(X11161),hAPP(c_Set_Oimage(X11163,X11161,X11160),X11162))=hAPP(c_Finite__Set_Ocard(X11163),X11162)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11163),X11162)))&(hAPP(c_Finite__Set_Ocard(X11161),hAPP(c_Set_Oimage(X11163,X11161,X11160),X11162))!=hAPP(c_Finite__Set_Ocard(X11163),X11162)|c_Fun_Oinj__on(X11163,X11161,X11160,X11162)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11163),X11162)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__iff__eq__card])])])])). 6.97/7.23 fof(c_0_8788, plain, ![X2268, X2269, X2270, X2271]:(~c_Relation_Otrans(X2271,X2270)|(~c_Relation_Otrans(X2269,X2268)|c_Relation_Otrans(tc_prod(X2271,X2269),c_Wellfounded_Olex__prod(X2271,X2269,X2270,X2268)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_trans__lex__prod])])])). 6.97/7.23 cnf(c_0_8789, plain, (hBOOL(hAPP(X1,esk77_1(X1)))|hAPP(c_Set_OCollect(X2),X1)=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5427])). 6.97/7.23 fof(c_0_8790, plain, ![X3888, X3889]:(~class_Lattices_Olattice(X3889)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3889),X3888))|hAPP(c_Finite__Set_Ofold1(X3889,c_Lattices_Osemilattice__sup__class_Osup(X3889)),X3888)=c_Big__Operators_Olattice__class_OSup__fin(X3889,X3888))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_OF__eq])])])). 6.97/7.23 fof(c_0_8791, plain, ![X9633, X9634]:(~class_Orderings_Olinorder(X9634)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9634),X9633))|c_Big__Operators_Olinorder__class_OMax(X9634,X9633)=hAPP(c_Finite__Set_Ofold1(X9634,c_Orderings_Oord__class_Omax(X9634)),X9633))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max_OF__eq])])])). 6.97/7.23 fof(c_0_8792, plain, ![X14001, X14002]:(~class_Orderings_Olinorder(X14002)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14002),X14001))|c_Big__Operators_Olinorder__class_OMin(X14002,X14001)=hAPP(c_Finite__Set_Ofold1(X14002,c_Orderings_Oord__class_Omin(X14002)),X14001))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min_OF__eq])])])). 6.97/7.23 fof(c_0_8793, plain, ![X13441, X13442]:(~class_Lattices_Olattice(X13442)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13442),X13441))|c_Big__Operators_Olattice__class_OInf__fin(X13442,X13441)=hAPP(c_Finite__Set_Ofold1(X13442,c_Lattices_Osemilattice__inf__class_Oinf(X13442)),X13441))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_OF__eq])])])). 6.97/7.23 fof(c_0_8794, plain, ![X8706, X8707, X8708, X8709]:(~c_Wellfounded_Owf(X8709,X8708)|(~c_Wellfounded_Owf(X8707,X8706)|c_Wellfounded_Owf(tc_prod(X8709,X8707),c_Wellfounded_Olex__prod(X8709,X8707,X8708,X8706)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__lex__prod])])])). 6.97/7.23 fof(c_0_8795, plain, ![X13930, X13931]:(~class_Groups_Oordered__ab__group__add__abs(X13931)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13931),c_Groups_Ozero__class_Ozero(X13931)),X13930))|hAPP(c_Groups_Oabs__class_Oabs(X13931),X13930)=X13930)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__of__pos])])])). 6.97/7.23 fof(c_0_8796, plain, ![X11421, X11422]:(~class_Groups_Oordered__ab__group__add__abs(X11422)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11422),c_Groups_Ozero__class_Ozero(X11422)),X11421))|X11421=hAPP(c_Groups_Oabs__class_Oabs(X11422),X11421))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__of__nonneg])])])). 6.97/7.23 cnf(c_0_8797, plain, (c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))=esk81_3(X1,X3,X2)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1|hAPP(c_Finite__Set_Ocard(X2),X3)!=hAPP(c_Nat_OSuc,X1)), inference(split_conjunct,[status(thm)],[c_0_5303])). 6.97/7.23 cnf(c_0_8798, plain, (hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|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_5428])). 6.97/7.23 cnf(c_0_8799, 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_5429])). 6.97/7.23 fof(c_0_8800, plain, ![X2756, X2757, X2758]:(~class_Groups_Ogroup__add(X2758)|(c_Groups_Ozero__class_Ozero(X2758)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2758),X2757),X2756)|hAPP(c_Groups_Ouminus__class_Ouminus(X2758),X2757)=X2756)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__unique])])])). 6.97/7.23 fof(c_0_8801, plain, ![X6430, X6431, X6432]:((c_Groups_Ozero__class_Ozero(X6432)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6432),X6431),X6430)|hAPP(c_Groups_Ouminus__class_Ouminus(X6432),X6430)=X6431|~class_Groups_Ogroup__add(X6432))&(hAPP(c_Groups_Ouminus__class_Ouminus(X6432),X6430)!=X6431|c_Groups_Ozero__class_Ozero(X6432)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6432),X6431),X6430)|~class_Groups_Ogroup__add(X6432))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__neg__iff__add__eq__0])])])])). 6.97/7.23 cnf(c_0_8802, 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_5430])). 6.97/7.23 fof(c_0_8803, plain, ![X16754]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X16754))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X16754)))|~c_Nat__Transfer_Onat__set(X16754))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X16754)))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X16754))|~c_Nat__Transfer_Onat__set(X16754))), 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_I1_J])])])])). 6.97/7.23 cnf(c_0_8804, plain, (~class_Int_Onumber__ring(X1)|~class_Int_Oring__char__0(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(X2)))), inference(split_conjunct,[status(thm)],[c_0_5431])). 6.97/7.23 fof(c_0_8805, plain, ![X14944, X14945]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X14945,X14945)),X14944))|(~c_Wellfounded_Oacyclic(X14945,X14944)|c_Wellfounded_Owf(X14945,hAPP(c_Relation_Oconverse(X14945,X14945),X14944)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__acyclic__wf__converse])])])). 6.97/7.23 cnf(c_0_8806, plain, (X2=c_List_Oremdups(X1,X2)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oremdups(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5432])). 6.97/7.23 cnf(c_0_8807, 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_5433]), ['final']). 6.97/7.23 fof(c_0_8808, plain, ![X3109, X3110]:(~c_Nat__Transfer_Onat__set(X3110)|(~c_Nat__Transfer_Onat__set(X3109)|c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X3110),X3109)))), 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])])])). 6.97/7.23 fof(c_0_8809, plain, ![X11464, X11465]:(~c_Nat__Transfer_Onat__set(X11465)|(~c_Nat__Transfer_Onat__set(X11464)|c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X11465),X11464)))), 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])])])). 6.97/7.23 fof(c_0_8810, plain, ![X11151, X11152, X11153]:(~class_Orderings_Olinorder(X11153)|(~c_List_Olinorder__class_Osorted(X11153,X11152)|c_List_Olinorder__class_Osorted(X11153,c_List_Olinorder__class_Oinsort__insert__key(X11153,X11153,c_COMBI(X11153),X11151,X11152)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__insort__insert])])])). 6.97/7.23 fof(c_0_8811, plain, ![X8575, X8576, X8577]:(~c_Wellfounded_Oacyclic(X8577,X8576)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X8577,X8577),tc_HOL_Obool)),X8575),X8576))|c_Wellfounded_Oacyclic(X8577,X8575))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclic__subset])])). 6.97/7.23 fof(c_0_8812, plain, ![X10500, X10501, X10502]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10502,X10502),tc_HOL_Obool)),X10501),X10500))|(~c_Relation_Oantisym(X10502,X10500)|c_Relation_Oantisym(X10502,X10501))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_antisym__subset])])). 6.97/7.23 fof(c_0_8813, plain, ![X11023, X11024, X11025]:(~c_Wellfounded_Owf(X11025,X11024)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X11025,X11025),tc_HOL_Obool)),X11023),X11024))|c_Wellfounded_Owf(X11025,X11023))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__subset])])). 6.97/7.23 fof(c_0_8814, plain, ![X646, X647, X648, X649]:(((~hBOOL(hAPP(X648,X647))|c_List_Olist__ex(X649,X648,hAPP(hAPP(c_List_Olist_OCons(X649),X647),X646)))&(~c_List_Olist__ex(X649,X648,X646)|c_List_Olist__ex(X649,X648,hAPP(hAPP(c_List_Olist_OCons(X649),X647),X646))))&(~c_List_Olist__ex(X649,X648,hAPP(hAPP(c_List_Olist_OCons(X649),X647),X646))|(hBOOL(hAPP(X648,X647))|c_List_Olist__ex(X649,X648,X646)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ex__simps_I1_J])])])). 6.97/7.23 fof(c_0_8815, plain, ![X8363, X8364, X8365]:(~c_Wellfounded_OwfP(X8365,X8364)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8365,tc_fun(X8365,tc_HOL_Obool))),X8363),X8364))|c_Wellfounded_OwfP(X8365,X8363))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wfP__subset])])])). 6.97/7.23 fof(c_0_8816, plain, ![X12610, X12611, X12612, X12613]:(~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X12613,X12612),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X12611),X12610)))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12613,X12612)=X12610), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__eq])])])). 6.97/7.23 fof(c_0_8817, plain, ![X7902]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X7902))|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)),X7902))))&(~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)),X7902)))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X7902)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I1_J])])). 6.97/7.23 fof(c_0_8818, plain, ![X16030, X16031, X16032, X16033, X16034, X16035]:((X16035=X16034|hAPP(X16031,X16035)=hAPP(c_Fun_Ofun__upd(X16033,X16032,X16031,X16034,X16030),X16035))&(X16034!=X16035|X16030=hAPP(c_Fun_Ofun__upd(X16033,X16032,X16031,X16034,X16030),X16035))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__upd__def])])])). 6.97/7.23 cnf(c_0_8819, 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_5339])). 6.97/7.23 fof(c_0_8820, plain, ![X1539, X1540, X1541, X1542]:(((~c_List_Olist__ex(X1542,X1541,X1540)|c_List_Olist__ex(X1542,X1541,hAPP(hAPP(c_List_Oappend(X1542),X1540),X1539)))&(~c_List_Olist__ex(X1542,X1541,X1539)|c_List_Olist__ex(X1542,X1541,hAPP(hAPP(c_List_Oappend(X1542),X1540),X1539))))&(~c_List_Olist__ex(X1542,X1541,hAPP(hAPP(c_List_Oappend(X1542),X1540),X1539))|(c_List_Olist__ex(X1542,X1541,X1540)|c_List_Olist__ex(X1542,X1541,X1539)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ex__append])])])). 6.97/7.23 fof(c_0_8821, plain, ![X14346, X14347]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X14347)),X14346))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14347),X14346))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Suc__lessD])])])). 6.97/7.23 fof(c_0_8822, plain, ![X13432, X13433, X13434]:(~c_Relation_Orefl__on(X13434,X13433,X13432)|c_Relation_Orefl__on(tc_List_Olist(X13434),c_List_Olists(X13434,X13433),c_List_Olistrel(X13434,X13432))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel__refl__on])])])). 6.97/7.23 fof(c_0_8823, plain, ![X14591, X14592, X14593]:(~c_Equiv__Relations_Oequiv(X14593,X14592,X14591)|c_Equiv__Relations_Oequiv(tc_List_Olist(X14593),c_List_Olists(X14593,X14592),c_List_Olistrel(X14593,X14591))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__listrel])])). 6.97/7.23 fof(c_0_8824, plain, ![X8526, X8527, X8528, X8529]:(hAPP(c_Product__Type_Ofst(X8529,X8528),X8526)!=hAPP(c_Product__Type_Ofst(X8529,X8528),X8527)|(hAPP(c_Product__Type_Osnd(X8529,X8528),X8526)!=hAPP(c_Product__Type_Osnd(X8529,X8528),X8527)|X8527=X8526)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_prod__eqI])])])). 6.97/7.23 fof(c_0_8825, plain, ![X10120, X10121, X10122, X10123]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10123),hAPP(c_Set_Oimage(X10122,X10123,X10121),X10120)))|(~c_Fun_Oinj__on(X10122,X10123,X10121,X10120)|hBOOL(hAPP(c_Finite__Set_Ofinite(X10122),X10120)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__imageD])])])). 6.97/7.23 fof(c_0_8826, plain, ![X14251, X14252]:((X14251!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(X14252),c_Groups_Ozero__class_Ozero(X14252)),X14251)=c_Groups_Oone__class_Oone(X14252)|(~class_Power_Opower(X14252)|~class_Rings_Osemiring__0(X14252)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X14251|hAPP(hAPP(c_Power_Opower__class_Opower(X14252),c_Groups_Ozero__class_Ozero(X14252)),X14251)=c_Groups_Ozero__class_Ozero(X14252)|(~class_Power_Opower(X14252)|~class_Rings_Osemiring__0(X14252)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__0__left])])])])). 6.97/7.23 fof(c_0_8827, plain, ![X3428, X3429, X3430]:((hAPP(hAPP(c_Orderings_Oord__class_Omin(X3430),X3429),X3428)!=X3429|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3430),X3429),X3428))|~class_Orderings_Olinorder(X3430))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3430),X3429),X3428))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X3430),X3429),X3428)=X3429|~class_Orderings_Olinorder(X3430))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ole__iff__inf])])])])). 6.97/7.23 fof(c_0_8828, plain, ![X4578, X4579, X4580]:(~class_Orderings_Olinorder(X4580)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4580),X4579),X4578))|X4579=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4580),X4578),X4579))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oinf__absorb2])])])). 6.97/7.23 fof(c_0_8829, plain, ![X5591, X5592]:(~class_Groups_Oordered__ab__group__add__abs(X5592)|hAPP(c_Groups_Oabs__class_Oabs(X5592),X5591)=hAPP(c_Groups_Oabs__class_Oabs(X5592),hAPP(c_Groups_Ouminus__class_Ouminus(X5592),X5591))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__minus__cancel])])])). 6.97/7.23 fof(c_0_8830, plain, ![X1529, X1530, X1531]:(~class_Orderings_Olinorder(X1531)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1531),X1530),X1529))|X1529=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1531),X1530),X1529))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup__absorb2])])])). 6.97/7.23 fof(c_0_8831, plain, ![X11934, X11935, X11936]:(~class_Orderings_Olinorder(X11936)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11936),X11935),X11934))|X11934=hAPP(hAPP(c_Orderings_Oord__class_Omax(X11936),X11934),X11935))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup__absorb1])])])). 6.97/7.23 fof(c_0_8832, plain, ![X14012, X14013, X14014, X14015, X14016]:(~c_List_Olist__all2(X14016,X14015,X14014,X14013,X14012)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14016)),X14013)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14015)),X14012)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__lengthD])])). 6.97/7.23 fof(c_0_8833, plain, ![X3024, X3025]:(c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3025),X3024)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,X3025,X3024)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zminus1__not__zero])])). 6.97/7.23 fof(c_0_8834, plain, ![X6106, X6107, X6108, X6109]:(~hBOOL(hAPP(hAPP(c_member(X6109),X6108),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6109,tc_HOL_Obool)),X6107),X6106)))|~hBOOL(hAPP(hAPP(c_member(X6109),X6108),X6106))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_DiffD2])])])). 6.97/7.23 fof(c_0_8835, plain, ![X9389, X9390, X9391, X9392, X9393]:(~hBOOL(hAPP(hAPP(X9393,X9392),X9391))|hBOOL(hAPP(c_Predicate_ORangeP(X9390,X9389,X9393),X9391))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_RangeP_Ointros])])])). 6.97/7.23 cnf(c_0_8836, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)), inference(split_conjunct,[status(thm)],[c_0_5400])). 6.97/7.23 cnf(c_0_8837, 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_5135])). 6.97/7.23 fof(c_0_8838, plain, ![X10581, X10582, X10583]:(~hBOOL(hAPP(hAPP(c_member(X10583),X10582),hAPP(c_List_Oset(X10583),X10581)))|X10581=c_List_Oinsert(X10583,X10582,X10581)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_in__set__insert])])])). 6.97/7.23 fof(c_0_8839, plain, ![X11050, X11051]:(~class_Rings_Olinordered__idom(X11051)|hAPP(c_Groups_Oabs__class_Oabs(X11051),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X11051),X11050))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X11051),X11050)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nat])])). 6.97/7.23 fof(c_0_8840, plain, ![X13987, X13988]:(~class_Groups_Ocomm__monoid__add(X13988)|hAPP(c_List_Omonoid__add__class_Olistsum(X13988),X13987)=hAPP(c_List_Omonoid__add__class_Olistsum(X13988),hAPP(c_List_Orev(X13988),X13987))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__rev])])])). 6.97/7.23 fof(c_0_8841, plain, ![X4037, X4038]:(~class_Groups_Oordered__ab__group__add__abs(X4038)|hAPP(c_Groups_Oabs__class_Oabs(X4038),X4037)=hAPP(c_Groups_Oabs__class_Oabs(X4038),hAPP(c_Groups_Oabs__class_Oabs(X4038),X4037))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__idempotent])])])). 6.97/7.23 fof(c_0_8842, plain, ![X1188, X1189, X1190]:(~class_Orderings_Oorder(X1190)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1190),X1189),X1188))|c_Orderings_Obot__class_Obot(tc_fun(X1190,tc_HOL_Obool))=c_SetInterval_Oord__class_OatLeastAtMost(X1190,X1188,X1189))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastatMost__empty])])])). 6.97/7.23 fof(c_0_8843, plain, ![X11215, X11216, X11217]:(~class_Divides_Osemiring__div(X11217)|c_Divides_Odiv__class_Omod(X11217,c_Divides_Odiv__class_Omod(X11217,X11216,X11215),X11215)=c_Divides_Odiv__class_Omod(X11217,X11216,X11215)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mod__trivial])])). 6.97/7.23 fof(c_0_8844, plain, ![X8048, X8049]:((X8049!=X8048|hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X8049)=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X8048))&(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X8049)!=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X8048)|X8049=X8048)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I3_J])])). 6.97/7.23 cnf(c_0_8845, 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_5434, c_0_5435]), c_0_5435])). 6.97/7.23 fof(c_0_8846, plain, ![X17439, X17440]:(~class_Rings_Oring__1(X17440)|hAPP(c_Int_Oring__1__class_Oof__int(X17440),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17439))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X17440),X17439)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__of__nat__eq])])). 6.97/7.23 fof(c_0_8847, plain, ![X11674, X11675]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11675),X11674)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11675),X11674)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11675),X11674))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11675),X11674)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq])])). 6.97/7.23 fof(c_0_8848, plain, ![X16585, X16586]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16586),X16585))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X16586),X16585)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__less])])). 6.97/7.23 cnf(c_0_8849, 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)!=esk457_2(X1,X2)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X2), inference(split_conjunct,[status(thm)],[c_0_5259])). 6.97/7.23 fof(c_0_8850, plain, ![X1859]:(~class_Nat_Osemiring__char__0(X1859)|c_Fun_Oinj__on(tc_Nat_Onat,X1859,c_Nat_Osemiring__1__class_Oof__nat(X1859),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])])])). 6.97/7.23 fof(c_0_8851, plain, ![X2217, X2218, X2219, X2220, X2221]:(~c_Typedef_Otype__definition(X2221,X2220,X2219,X2218,X2217)|c_Orderings_Otop__class_Otop(tc_fun(X2221,tc_HOL_Obool))=hAPP(c_Set_Oimage(X2220,X2221,X2218),X2217)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_type__definition_OAbs__image])])])). 6.97/7.23 fof(c_0_8852, plain, ![X10972, X10973]:(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),X10973),X10972))|c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X10973)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__zmult__eq__1])])). 6.97/7.23 fof(c_0_8853, plain, ![X15287]:(~class_Rings_Olinordered__semidom(X15287)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15287),c_Groups_Ozero__class_Ozero(X15287)),c_Groups_Oone__class_Oone(X15287)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__one])])). 6.97/7.23 fof(c_0_8854, plain, ![X3743]:(~class_Rings_Olinordered__semidom(X3743)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3743),c_Groups_Ozero__class_Ozero(X3743)),c_Groups_Oone__class_Oone(X3743)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__one])])). 6.97/7.23 fof(c_0_8855, plain, ![X6381, X6382, X6383]:(~class_Orderings_Oorder(X6383)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6383),X6382),X6381))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6383),X6381),X6382))|X6381=X6382))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__antisym])])])). 6.97/7.23 fof(c_0_8856, plain, ![X11134, X11135]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X11135),X11134)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X11135),X11134))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__ge__0__finite])])])). 6.97/7.23 fof(c_0_8857, plain, ![X5177, X5178, X5179, X5180]:(~c_FunDef_Oreduction__pair(X5180,X5179)|c_FunDef_Oreduction__pair(X5178,hAPP(hAPP(c_FunDef_Orp__inv__image(X5180,X5178),X5179),X5177))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rp__inv__image__rp])])). 6.97/7.23 fof(c_0_8858, plain, ![X16708, X16709, X16710, X16711]:(~c_Relation_Otrans(X16711,X16710)|c_Relation_Otrans(X16709,hAPP(hAPP(c_Relation_Oinv__image(X16711,X16709),X16710),X16708))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__inv__image])])). 6.97/7.23 fof(c_0_8859, plain, ![X7698, X7699, X7700, X7701]:(~c_Relation_Osym(X7701,X7700)|c_Relation_Osym(X7699,hAPP(hAPP(c_Relation_Oinv__image(X7701,X7699),X7700),X7698))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__inv__image])])). 6.97/7.23 fof(c_0_8860, plain, ![X14096, X14097]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14097),X14096)|(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14096),X14097)|X14096=X14097)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diffs0__imp__equal])])])). 6.97/7.23 fof(c_0_8861, plain, ![X13321, X13322, X13323, X13324]:(~c_Wellfounded_Owf(X13324,X13323)|c_Wellfounded_Owf(X13322,hAPP(hAPP(c_Relation_Oinv__image(X13324,X13322),X13323),X13321))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__inv__image])])). 6.97/7.23 fof(c_0_8862, plain, ![X6402, X6403, X6404]:(~c_Wellfounded_Owf(X6404,X6403)|hBOOL(hAPP(hAPP(c_member(X6404),X6402),c_Wellfounded_Oacc(X6404,X6403)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__wfD])])). 6.97/7.23 fof(c_0_8863, plain, ![X3896, X3897]:(c_List_Olist_ONil(X3896)=X3897|c_List_Olast(X3896,X3897)=hAPP(c_List_Ohd(X3896),hAPP(c_List_Orev(X3896),X3897))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_hd__rev])])])). 6.97/7.23 fof(c_0_8864, plain, ![X13517]:(~class_Groups_Omonoid__add(X13517)|c_List_Ofoldl(X13517,X13517,c_Groups_Oplus__class_Oplus(X13517),c_Groups_Ozero__class_Ozero(X13517))=c_List_Omonoid__add__class_Olistsum(X13517)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__foldl])])])). 6.97/7.23 fof(c_0_8865, plain, ![X9216, X9217, X9218]:(~class_Orderings_Olinorder(X9218)|(~c_List_Olinorder__class_Osorted(X9218,X9217)|c_List_Olinorder__class_Osorted(X9218,hAPP(hAPP(c_List_Odrop(X9218),X9216),X9217)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__drop])])). 6.97/7.23 fof(c_0_8866, plain, ![X8158, X8159, X8160]:(~class_Orderings_Olinorder(X8160)|(~c_List_Olinorder__class_Osorted(X8160,X8159)|c_List_Olinorder__class_Osorted(X8160,hAPP(hAPP(c_List_Otake(X8160),X8158),X8159)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__take])])])). 6.97/7.23 cnf(c_0_8867, plain, (X3=X4|X1!=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X2),X1)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X3),X4)|~class_Groups_Oab__group__add(X5)), inference(split_conjunct,[status(thm)],[c_0_5436])). 6.97/7.23 fof(c_0_8868, plain, ![X9457, X9458, X9459]:(~hBOOL(hAPP(c_List_Odistinct(X9459),X9458))|hBOOL(hAPP(c_List_Odistinct(X9459),c_List_Osublist(X9459,X9458,X9457)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__sublistI])])])). 6.97/7.23 fof(c_0_8869, plain, ![X4131, X4132, X4133]:(~hBOOL(hAPP(c_List_Odistinct(X4133),X4132))|hBOOL(hAPP(c_List_Odistinct(X4133),c_List_Oremove1(X4133,X4131,X4132)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__remove1])])). 6.97/7.23 fof(c_0_8870, plain, ![X15550, X15551, X15552]:(~hBOOL(hAPP(c_List_Odistinct(X15552),X15551))|hBOOL(hAPP(c_List_Odistinct(X15552),c_List_Oinsert(X15552,X15550,X15551)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__insert])])])). 6.97/7.23 fof(c_0_8871, plain, ![X8093, X8094, X8095]:(~hBOOL(hAPP(hAPP(c_member(X8095),X8094),hAPP(hAPP(c_Set_Oinsert(X8095),X8093),c_Orderings_Obot__class_Obot(tc_fun(X8095,tc_HOL_Obool)))))|X8094=X8093), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_singletonE])])])). 6.97/7.23 fof(c_0_8872, plain, ![X8964, X8965, X8966]:(~hBOOL(hAPP(c_List_Odistinct(X8966),X8965))|hBOOL(hAPP(c_List_Odistinct(X8966),c_List_OtakeWhile(X8966,X8964,X8965)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__takeWhile])])). 6.97/7.23 fof(c_0_8873, plain, ![X14867, X14868]:(~hBOOL(hAPP(c_List_Odistinct(X14868),X14867))|hBOOL(hAPP(c_List_Odistinct(X14868),hAPP(c_List_Otl(X14868),X14867)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__tl])])])). 6.97/7.23 fof(c_0_8874, plain, ![X15387, X15388]:((~hBOOL(hAPP(c_List_Odistinct(X15388),hAPP(c_List_Orotate1(X15388),X15387)))|hBOOL(hAPP(c_List_Odistinct(X15388),X15387)))&(~hBOOL(hAPP(c_List_Odistinct(X15388),X15387))|hBOOL(hAPP(c_List_Odistinct(X15388),hAPP(c_List_Orotate1(X15388),X15387))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct1__rotate])])). 6.97/7.23 fof(c_0_8875, plain, ![X2503, X2504]:((~hBOOL(hAPP(c_List_Odistinct(X2504),X2503))|hBOOL(hAPP(c_List_Odistinct(X2504),hAPP(c_List_Orev(X2504),X2503))))&(~hBOOL(hAPP(c_List_Odistinct(X2504),hAPP(c_List_Orev(X2504),X2503)))|hBOOL(hAPP(c_List_Odistinct(X2504),X2503)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__rev])])). 6.97/7.23 fof(c_0_8876, plain, ![X4523, X4524, X4525]:((X4523!=c_Orderings_Obot__class_Obot(tc_fun(X4525,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X4525,tc_HOL_Obool))!=X4524|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4525,tc_HOL_Obool)),X4524),X4523)=c_Orderings_Obot__class_Obot(tc_fun(X4525,tc_HOL_Obool)))&((X4523=c_Orderings_Obot__class_Obot(tc_fun(X4525,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4525,tc_HOL_Obool)),X4524),X4523)!=c_Orderings_Obot__class_Obot(tc_fun(X4525,tc_HOL_Obool)))&(c_Orderings_Obot__class_Obot(tc_fun(X4525,tc_HOL_Obool))=X4524|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4525,tc_HOL_Obool)),X4524),X4523)!=c_Orderings_Obot__class_Obot(tc_fun(X4525,tc_HOL_Obool))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__empty])])])). 6.97/7.23 fof(c_0_8877, plain, ![X11729, X11730, X11731]:(~class_Orderings_Oorder(X11731)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11731),X11730),X11729))|c_Orderings_Obot__class_Obot(tc_fun(X11731,tc_HOL_Obool))=c_SetInterval_Oord__class_OgreaterThanLessThan(X11731,X11729,X11730))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_greaterThanLessThan__empty])])])). 6.97/7.23 fof(c_0_8878, plain, ![X7681, X7682, X7683]:(~class_Orderings_Oorder(X7683)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7683),X7682),X7681))|c_Orderings_Obot__class_Obot(tc_fun(X7683,tc_HOL_Obool))=c_SetInterval_Oord__class_OgreaterThanAtMost(X7683,X7681,X7682))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__empty])])). 6.97/7.23 cnf(c_0_8879, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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_5437])). 6.97/7.23 cnf(c_0_8880, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_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(split_conjunct,[status(thm)],[c_0_5438])). 6.97/7.23 fof(c_0_8881, plain, ![X15934]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15934),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X15934)=X15934)&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15934),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X15934)=hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X15934))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zabs__def])])])). 6.97/7.23 fof(c_0_8882, plain, ![X11625, X11626]:(((hBOOL(hAPP(c_List_Odistinct(X11626),c_List_Olinorder__class_Osorted__list__of__set(X11626,X11625)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11626),X11625))|~class_Orderings_Olinorder(X11626))&(c_List_Olinorder__class_Osorted(X11626,c_List_Olinorder__class_Osorted__list__of__set(X11626,X11625))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11626),X11625))|~class_Orderings_Olinorder(X11626)))&(X11625=hAPP(c_List_Oset(X11626),c_List_Olinorder__class_Osorted__list__of__set(X11626,X11625))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11626),X11625))|~class_Orderings_Olinorder(X11626))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__list__of__set])])])])). 6.97/7.23 cnf(c_0_8883, plain, (hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X1)))|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_5164])). 6.97/7.23 cnf(c_0_8884, 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)|hAPP(c_Int_Onat,X1)!=X2), inference(split_conjunct,[status(thm)],[c_0_5439])). 6.97/7.23 fof(c_0_8885, plain, ![X6716]:(~class_Int_Onumber__ring(X6716)|~class_Rings_Olinordered__idom(X6716)|c_Groups_Oone__class_Oone(X6716)=hAPP(c_Groups_Oabs__class_Oabs(X6716),hAPP(c_Int_Onumber__class_Onumber__of(X6716),c_Int_OMin))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__minus__one])])])). 6.97/7.23 fof(c_0_8886, plain, ![X11087, X11088, X11089, X11090]:(((X11088=X11089|hAPP(hAPP(c_Set_Oinsert(X11090),X11087),c_Orderings_Obot__class_Obot(tc_fun(X11090,tc_HOL_Obool)))!=c_SetInterval_Oord__class_OatLeastAtMost(X11090,X11089,X11088)|~class_Orderings_Oorder(X11090))&(X11088=X11087|hAPP(hAPP(c_Set_Oinsert(X11090),X11087),c_Orderings_Obot__class_Obot(tc_fun(X11090,tc_HOL_Obool)))!=c_SetInterval_Oord__class_OatLeastAtMost(X11090,X11089,X11088)|~class_Orderings_Oorder(X11090)))&(X11088!=X11089|X11088!=X11087|hAPP(hAPP(c_Set_Oinsert(X11090),X11087),c_Orderings_Obot__class_Obot(tc_fun(X11090,tc_HOL_Obool)))=c_SetInterval_Oord__class_OatLeastAtMost(X11090,X11089,X11088)|~class_Orderings_Oorder(X11090))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton__iff])])])). 6.97/7.23 fof(c_0_8887, plain, ![X10464, X10465, X10466]:(~class_Rings_Ono__zero__divisors(X10466)|(c_Groups_Ozero__class_Ozero(X10466)=X10465|(X10464=c_Groups_Ozero__class_Ozero(X10466)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10466),X10465),X10464)!=c_Groups_Ozero__class_Ozero(X10466)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_no__zero__divisors])])])). 6.97/7.23 fof(c_0_8888, plain, ![X13906, X13907]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13907)),X13906)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))|hAPP(c_List_Orotate1(X13907),X13906)=X13906), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate1__length01])])). 6.97/7.23 fof(c_0_8889, plain, ![X2822, X2823]:(X2823=c_List_Olist_ONil(X2822)|hAPP(c_List_Ohd(X2822),X2823)=hAPP(hAPP(c_List_Onth(X2822),X2823),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_hd__conv__nth])])])). 6.97/7.23 fof(c_0_8890, plain, ![X5863, X5864, X5865]:((hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5865),X5864),X5863)!=X5863|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5865),X5864),X5863))|~class_Lattices_Osemilattice__sup(X5865))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5865),X5864),X5863))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5865),X5864),X5863)=X5863|~class_Lattices_Osemilattice__sup(X5865))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__iff__sup])])])])). 6.97/7.23 fof(c_0_8891, plain, ![X3763, X3764]:(X3764=c_List_Olist_ONil(X3763)|hAPP(c_List_Ohd(X3763),X3764)=c_List_Olast(X3763,hAPP(c_List_Orev(X3763),X3764))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_last__rev])])])). 6.97/7.23 cnf(c_0_8892, 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_4715])). 6.97/7.23 fof(c_0_8893, plain, ![X7769, X7770]:(~class_Rings_Olinordered__idom(X7770)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7770),c_Groups_Ozero__class_Ozero(X7770)),X7769))|c_Groups_Oone__class_Oone(X7770)=c_Groups_Osgn__class_Osgn(X7770,X7769))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__pos])])). 6.97/7.23 fof(c_0_8894, plain, ![X13952]:(~class_Orderings_Olinorder(X13952)|c_Finite__Set_Ofun__left__comm(X13952,tc_List_Olist(X13952),c_List_Olinorder__class_Oinsort__key(X13952,X13952,c_COMBI(X13952)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm__insort])])])). 6.97/7.23 cnf(c_0_8895, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)=c_Groups_Oone__class_Oone(X2)|X1!=c_Groups_Oone__class_Oone(X2)|~class_Rings_Oring__1__no__zero__divisors(X2)), inference(split_conjunct,[status(thm)],[c_0_5412])). 6.97/7.23 fof(c_0_8896, plain, ![X12268]:(~class_Rings_Osemiring__1(X12268)|hBOOL(hAPP(hAPP(c_member(X12268),c_Groups_Oone__class_Oone(X12268)),c_Nat_Osemiring__1__class_ONats(X12268)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__1])])). 6.97/7.23 fof(c_0_8897, plain, ![X17198]:(~class_Rings_Oring__1(X17198)|hBOOL(hAPP(hAPP(c_member(X17198),c_Groups_Oone__class_Oone(X17198)),c_Int_Oring__1__class_OInts(X17198)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Ints__1])])])). 6.97/7.23 fof(c_0_8898, plain, ![X1927]:(~class_Rings_Osemiring__1(X1927)|hBOOL(hAPP(hAPP(c_member(X1927),c_Groups_Ozero__class_Ozero(X1927)),c_Nat_Osemiring__1__class_ONats(X1927)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nats__0])])])). 6.97/7.23 fof(c_0_8899, plain, ![X9913]:(~class_Rings_Oring__1(X9913)|hBOOL(hAPP(hAPP(c_member(X9913),c_Groups_Ozero__class_Ozero(X9913)),c_Int_Oring__1__class_OInts(X9913)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__0])])). 6.97/7.23 cnf(c_0_8900, plain, (hBOOL(hAPP(X1,hAPP(c_Int_Onat,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,esk116_2(X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_5339])). 6.97/7.23 fof(c_0_8901, plain, ![X4186, X4187]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4187),X4186))|c_Nat__Transfer_Otsub(X4186,X4187)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4186),X4187))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4187),X4186))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Nat__Transfer_Otsub(X4186,X4187))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_tsub__def])])])). 6.97/7.23 fof(c_0_8902, plain, ![X6198, X6199]:(~class_Orderings_Olinorder(X6199)|c_List_Olinorder__class_Osorted(X6199,hAPP(hAPP(c_List_Olist_OCons(X6199),X6198),c_List_Olist_ONil(X6199)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__single])])])). 6.97/7.23 fof(c_0_8903, plain, ![X7192, X7193]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7193),X7192))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7192),X7193))|X7193=X7192)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__antisym])])). 6.97/7.23 fof(c_0_8904, plain, ![X12608, X12609]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X12609),X12608))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X12608),X12609))|X12609=X12608)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__antisym])])])). 6.97/7.23 cnf(c_0_8905, plain, (c_Fun_Obij__betw(X1,X2,X3,X4,X5)|~c_Fun_Oinj__on(X1,X2,X3,X4)|hAPP(c_Set_Oimage(X1,X2,X3),X4)!=X5), inference(split_conjunct,[status(thm)],[c_0_5440])). 6.97/7.23 cnf(c_0_8906, plain, (~c_List_Olist__ex(tc_Nat_Onat,X1,c_List_Oupt(X2,X3))|~c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),X1),X2,X3)), inference(split_conjunct,[status(thm)],[c_0_5320])). 6.97/7.23 cnf(c_0_8907, 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_5441])). 6.97/7.23 fof(c_0_8908, plain, ![X9639, X9640, X9641]:(~c_Wellfounded_Owf(X9641,X9640)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X9641,X9641)),hAPP(hAPP(c_Product__Type_OPair(X9641,X9641),X9639),X9639)),X9640))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__not__refl])])])). 6.97/7.23 cnf(c_0_8909, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Rings_Oring__no__zero__divisors(X1)), inference(split_conjunct,[status(thm)],[c_0_5442])). 6.97/7.23 fof(c_0_8910, plain, ![X16829, X16830, X16831]:(~hBOOL(hAPP(hAPP(c_member(X16831),X16830),X16829))|X16829=hAPP(hAPP(c_Set_Oinsert(X16831),X16830),X16829)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__absorb])])). 6.97/7.23 cnf(c_0_8911, plain, (hBOOL(hAPP(X1,hAPP(c_Int_Onat,esk55_1(X1))))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5417])). 6.97/7.23 fof(c_0_8912, plain, ![X494, X495]:((X495!=X494|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X494),hAPP(c_Nat_OSuc,X495)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X495),X494)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X494),hAPP(c_Nat_OSuc,X495)))|X495=X494|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X495),X494)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__less__Suc__eq])])])])). 6.97/7.23 fof(c_0_8913, plain, ![X8096, X8097, X8098]:((~hBOOL(hAPP(hAPP(X8097,X8096),X8096))|hBOOL(hAPP(c_Quotient_ORespects(X8098,X8097),X8096)))&(~hBOOL(hAPP(c_Quotient_ORespects(X8098,X8097),X8096))|hBOOL(hAPP(hAPP(X8097,X8096),X8096)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Respects__def])])). 6.97/7.23 cnf(c_0_8914, plain, (c_Groups_Ozero__class_Ozero(X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1)|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Oring__no__zero__divisors(X2)), inference(split_conjunct,[status(thm)],[c_0_5442])). 6.97/7.23 fof(c_0_8915, plain, ![X16423, X16424]:(~class_Rings_Ocomm__semiring__1(X16424)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16424),c_Groups_Ozero__class_Ozero(X16424)),X16423)=c_Groups_Ozero__class_Ozero(X16424)), 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])])])). 6.97/7.23 fof(c_0_8916, plain, ![X15370, X15371]:(~class_Rings_Odivision__ring(X15371)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15371),c_Groups_Ozero__class_Ozero(X15371)),X15370)=c_Groups_Ozero__class_Ozero(X15371)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__zero__left])])). 6.97/7.23 fof(c_0_8917, plain, ![X6391, X6392]:(~class_Lattices_Obounded__lattice__top(X6392)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6392),c_Orderings_Otop__class_Otop(X6392)),X6391)=c_Orderings_Otop__class_Otop(X6392)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__top__left])])])). 6.97/7.23 fof(c_0_8918, plain, ![X12725, X12726]:(~class_Groups_Omonoid__mult(X12726)|c_Groups_Oone__class_Oone(X12726)=hAPP(hAPP(c_Power_Opower__class_Opower(X12726),c_Groups_Oone__class_Oone(X12726)),X12725)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one])])). 6.97/7.23 fof(c_0_8919, plain, ![X13741, X13742, X13743]:(~class_Orderings_Owellorder(X13742)|(~hBOOL(hAPP(X13741,X13743))|hBOOL(hAPP(X13741,c_Orderings_Oord__class_OLeast(X13742,X13741))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_LeastI__ex])])])])). 6.97/7.23 fof(c_0_8920, plain, ![X9763, X9764]:(X9764=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X9763,X9764),c_Divides_Odivmod__int(X9763,X9764)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__int__correct])])])). 6.97/7.23 fof(c_0_8921, plain, ![X2829, X2830]:(~class_Divides_Osemiring__div(X2830)|c_Groups_Ozero__class_Ozero(X2830)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X2830),c_Groups_Ozero__class_Ozero(X2830)),X2829)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__0])])). 6.97/7.23 fof(c_0_8922, plain, ![X14059, X14060]:(~class_Rings_Omult__zero(X14060)|c_Groups_Ozero__class_Ozero(X14060)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14060),c_Groups_Ozero__class_Ozero(X14060)),X14059)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__left])])). 6.97/7.23 fof(c_0_8923, plain, ![X15819, X15820]:(~class_Lattices_Obounded__lattice__bot(X15820)|c_Orderings_Obot__class_Obot(X15820)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15820),c_Orderings_Obot__class_Obot(X15820)),X15819)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__bot__left])])). 6.97/7.23 fof(c_0_8924, plain, ![X10893, X10894]:(~class_Divides_Osemiring__div(X10894)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X10894),X10893),c_Groups_Ozero__class_Ozero(X10894))=c_Groups_Ozero__class_Ozero(X10894)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__by__0])])). 6.97/7.23 fof(c_0_8925, plain, ![X12836, X12837, X12838]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12838),X12837),X12836))|X12836=hAPP(hAPP(c_Orderings_Oord__class_Omax(X12838),X12837),X12836)|~class_Orderings_Olinorder(X12838))&(X12836!=hAPP(hAPP(c_Orderings_Oord__class_Omax(X12838),X12837),X12836)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12838),X12837),X12836))|~class_Orderings_Olinorder(X12838))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__iff__sup])])])). 6.97/7.23 fof(c_0_8926, plain, ![X1671, X1672]:(~class_Rings_Omult__zero(X1672)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1672),X1671),c_Groups_Ozero__class_Ozero(X1672))=c_Groups_Ozero__class_Ozero(X1672)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__right])])). 6.97/7.23 fof(c_0_8927, plain, ![X4944, X4945]:(~class_Rings_Ocomm__semiring__1(X4945)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4945),X4944),c_Groups_Ozero__class_Ozero(X4945))=c_Groups_Ozero__class_Ozero(X4945)), 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])])])). 6.97/7.23 fof(c_0_8928, plain, ![X10623, X10624]:(~class_Lattices_Obounded__lattice__top(X10624)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10624),X10623),c_Orderings_Otop__class_Otop(X10624))=c_Orderings_Otop__class_Otop(X10624)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__top__right])])])). 6.97/7.23 fof(c_0_8929, plain, ![X9981, X9982]:(~class_Rings_Odivision__ring__inverse__zero(X9982)|c_Groups_Ozero__class_Ozero(X9982)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9982),X9981),c_Groups_Ozero__class_Ozero(X9982))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__zero])])])). 6.97/7.23 fof(c_0_8930, plain, ![X5314, X5315]:(~class_Lattices_Obounded__lattice__bot(X5315)|c_Orderings_Obot__class_Obot(X5315)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5315),X5314),c_Orderings_Obot__class_Obot(X5315))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__bot__right])])). 6.97/7.23 fof(c_0_8931, plain, ![X1940, X1941, X1942, X1943]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X1943,X1942)),c_Sum__Type_OPlus(X1943,X1942,X1941,X1940)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X1943),X1941))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I1_J])])). 6.97/7.23 fof(c_0_8932, plain, ![X9767, X9768, X9769, X9770]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X9770,X9769)),c_Sum__Type_OPlus(X9770,X9769,X9768,X9767)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X9769),X9767))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I2_J])])). 6.97/7.23 fof(c_0_8933, plain, ![X16251, X16252, X16253, X16254, X16255, X16256, X16257]:(~c_Finite__Set_Ofolding__image__simple__idem(X16257,X16256,X16255,X16254,X16253,X16252)|X16251=hAPP(hAPP(X16255,X16251),X16251)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oidem])])). 6.97/7.23 fof(c_0_8934, plain, ![X13876, X13877]:((c_Groups_Ozero__class_Ozero(X13877)!=X13876|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13877),X13876),X13876)=c_Groups_Ozero__class_Ozero(X13877)|~class_Rings_Odivision__ring__inverse__zero(X13877))&(c_Groups_Ozero__class_Ozero(X13877)=X13876|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13877),X13876),X13876)=c_Groups_Oone__class_Oone(X13877)|~class_Rings_Odivision__ring__inverse__zero(X13877))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__self__if])])])])). 6.97/7.23 cnf(c_0_8935, 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,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_4612])). 6.97/7.23 fof(c_0_8936, plain, ![X12914, X12915, X12916]:(~hBOOL(hAPP(hAPP(c_member(X12916),X12915),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X12916,tc_HOL_Obool)),X12914)))|~hBOOL(hAPP(hAPP(c_member(X12916),X12915),X12914))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ComplD])])])). 6.97/7.23 fof(c_0_8937, plain, ![X13711, X13712, X13713]:((~c_Relation_Ototal__on(X13713,X13712,X13711)|c_Relation_Ototal__on(X13713,X13712,hAPP(c_Relation_Oconverse(X13713,X13713),X13711)))&(~c_Relation_Ototal__on(X13713,X13712,hAPP(c_Relation_Oconverse(X13713,X13713),X13711))|c_Relation_Ototal__on(X13713,X13712,X13711))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_total__on__converse])])). 6.97/7.23 cnf(c_0_8938, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)|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_4953])). 6.97/7.23 fof(c_0_8939, plain, ![X2099]:(~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X2099),c_Int_OInteg))|X2099=hAPP(c_Int_ORep__Integ,esk64_1(X2099))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Rep__Integ__cases])])])). 6.97/7.23 fof(c_0_8940, plain, ![X1424, X1425, X1426]:((~c_Relation_Orefl__on(X1426,X1425,hAPP(c_Relation_Oconverse(X1426,X1426),X1424))|c_Relation_Orefl__on(X1426,X1425,X1424))&(~c_Relation_Orefl__on(X1426,X1425,X1424)|c_Relation_Orefl__on(X1426,X1425,hAPP(c_Relation_Oconverse(X1426,X1426),X1424)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__converse])])). 6.97/7.23 cnf(c_0_8941, plain, (X1=X2|hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X1),X3)!=c_List_Oupt(X2,X4)), inference(split_conjunct,[status(thm)],[c_0_4593])). 6.97/7.23 fof(c_0_8942, plain, ![X8539, X8540, X8541, X8542]:((X8541!=X8539|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8542),X8541),X8540)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8542),X8539),X8540)|~class_Groups_Ocancel__semigroup__add(X8542))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8542),X8541),X8540)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8542),X8539),X8540)|X8541=X8539|~class_Groups_Ocancel__semigroup__add(X8542))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__right__cancel])])])])). 6.97/7.23 fof(c_0_8943, plain, ![X2447, X2448]:(~class_Divides_Osemiring__div(X2448)|(c_Groups_Ozero__class_Ozero(X2448)=X2447|c_Groups_Oone__class_Oone(X2448)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X2448),X2447),X2447))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__self])])])). 6.97/7.23 fof(c_0_8944, plain, ![X4796, X4797]:(~class_Orderings_Obot(X4797)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4797),c_Orderings_Obot__class_Obot(X4797)),X4796))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bot__least])])])). 6.97/7.23 fof(c_0_8945, plain, ![X14689]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14689))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X14689)))&(hBOOL(hAPP(c_Nat__Numeral_Oneg,X14689))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14689)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__neg__eq__ge__0])])])). 6.97/7.23 fof(c_0_8946, plain, ![X7751, X7752, X7753, X7754]:(~class_Groups_Ocancel__ab__semigroup__add(X7754)|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7754),X7753),X7751)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7754),X7753),X7752)|X7751=X7752)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__imp__eq])])). 6.97/7.23 fof(c_0_8947, plain, ![X4639, X4640, X4641, X4642]:(~class_Groups_Ocancel__semigroup__add(X4642)|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4642),X4641),X4639)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4642),X4641),X4640)|X4639=X4640)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__left__imp__eq])])])). 6.97/7.23 fof(c_0_8948, plain, ![X13564, X13565]:(~class_Rings_Odivision__ring(X13565)|(c_Groups_Ozero__class_Ozero(X13565)=X13564|c_Groups_Oone__class_Oone(X13565)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13565),X13564),X13564))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__self])])). 6.97/7.23 fof(c_0_8949, plain, ![X2853, X2854]:(~class_Rings_Ocomm__semiring__1(X2854)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2854),X2853),c_Groups_Ozero__class_Ozero(X2854)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__0__right])])). 6.97/7.23 fof(c_0_8950, plain, ![X6796, X6797]:(~class_Orderings_Otop(X6797)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6797),X6796),c_Orderings_Otop__class_Otop(X6797)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__greatest])])). 6.97/7.23 fof(c_0_8951, plain, ![X12317, X12318]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12318),X12317)!=X12318|(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X12318|c_Groups_Oone__class_Oone(tc_Nat_Onat)=X12317)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__eq__self__implies__10])])])). 6.97/7.23 fof(c_0_8952, plain, ![X10770, X10771, X10772]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X10772|X10770=hAPP(c_List_Ohd(X10771),c_List_Oreplicate(X10771,X10772,X10770))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__replicate])])). 6.97/7.23 fof(c_0_8953, plain, ![X5949, X5950, X5951]:(~c_Wellfounded_Owf(X5951,X5950)|c_Wellfounded_Owf(tc_List_Olist(X5951),hAPP(c_List_Olexn(X5951,X5950),X5949))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__lexn])])])). 6.97/7.23 fof(c_0_8954, plain, ![X10866, X10867]:(hAPP(c_Finite__Set_Ocard(X10867),hAPP(c_List_Oset(X10867),X10866))!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10867)),X10866)|hBOOL(hAPP(c_List_Odistinct(X10867),X10866))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__distinct])])])). 6.97/7.23 cnf(c_0_8955, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),X1),X2)=c_Groups_Ozero__class_Ozero(X3)|X1!=X2|~class_Groups_Oab__group__add(X3)), inference(split_conjunct,[status(thm)],[c_0_5443])). 6.97/7.23 fof(c_0_8956, plain, ![X13611, X13612, X13613, X13614, X13615]:(~c_Fun_Oinj__on(X13615,X13614,X13613,c_Orderings_Otop__class_Otop(tc_fun(X13615,tc_HOL_Obool)))|(hAPP(X13613,X13611)!=hAPP(X13613,X13612)|X13612=X13611)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_injD])])). 6.97/7.23 fof(c_0_8957, plain, ![X2082, X2083]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2083),X2082))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2083),X2082)))&(X2083!=X2082|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2083),X2082)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le])])])). 6.97/7.23 fof(c_0_8958, plain, ![X10344]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X10344)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X10344=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(X10344!=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),X10344)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__le__0__conv])])). 6.97/7.23 fof(c_0_8959, plain, ![X584, X585, X586, X587, X588, X589]:((X585=X587|hAPP(hAPP(c_Product__Type_OPair(X589,X588),X587),X586)!=hAPP(hAPP(c_Product__Type_OPair(X589,X588),X585),X584))&(X586=X584|hAPP(hAPP(c_Product__Type_OPair(X589,X588),X587),X586)!=hAPP(hAPP(c_Product__Type_OPair(X589,X588),X585),X584))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__inject])])])). 6.97/7.23 fof(c_0_8960, plain, ![X13128, X13129, X13130, X13131, X13132, X13133]:((X13128!=X13130|X13131!=X13129|hAPP(hAPP(c_Product__Type_OPair(X13133,X13132),X13131),X13130)=hAPP(hAPP(c_Product__Type_OPair(X13133,X13132),X13129),X13128))&((X13128=X13130|hAPP(hAPP(c_Product__Type_OPair(X13133,X13132),X13131),X13130)!=hAPP(hAPP(c_Product__Type_OPair(X13133,X13132),X13129),X13128))&(X13131=X13129|hAPP(hAPP(c_Product__Type_OPair(X13133,X13132),X13131),X13130)!=hAPP(hAPP(c_Product__Type_OPair(X13133,X13132),X13129),X13128)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__eq])])])). 6.97/7.23 fof(c_0_8961, plain, ![X1156, X1157]:(~class_Power_Opower(X1157)|hAPP(hAPP(c_Power_Opower__class_Opower(X1157),X1156),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(X1157)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0])])). 6.97/7.23 cnf(c_0_8962, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2)=X3|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)), inference(split_conjunct,[status(thm)],[c_0_5444])). 6.97/7.23 fof(c_0_8963, plain, ![X16220, X16221]:(~class_Orderings_Olinorder(X16221)|(c_List_Olist_ONil(X16221)=X16220|(~c_List_Olinorder__class_Osorted(X16221,X16220)|c_List_Olinorder__class_Osorted(X16221,c_List_Obutlast(X16221,X16220))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__butlast])])). 6.97/7.23 fof(c_0_8964, plain, ![X8874, X8875]:(~class_Rings_Ocomm__semiring__1(X8875)|c_Groups_Oone__class_Oone(X8875)=hAPP(hAPP(c_Power_Opower__class_Opower(X8875),X8874),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J])])). 6.97/7.23 fof(c_0_8965, plain, ![X5168, X5169, X5170]:((hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5170),X5168),X5169)!=c_Groups_Oone__class_Oone(X5170)|X5169=X5168|X5169=c_Groups_Ozero__class_Ozero(X5170)|~class_Rings_Odivision__ring(X5170))&(X5169!=X5168|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5170),X5168),X5169)=c_Groups_Oone__class_Oone(X5170)|X5169=c_Groups_Ozero__class_Ozero(X5170)|~class_Rings_Odivision__ring(X5170))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__inverse__eq])])])). 6.97/7.23 fof(c_0_8966, plain, ![X13960, X13961]:(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X13961,X13961),tc_HOL_Obool))!=hAPP(hAPP(c_Relation_Orel__comp(X13961,X13961,X13961),X13960),X13960)|c_Wellfounded_Owf(X13961,X13960)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__no__loop])])). 6.97/7.23 cnf(c_0_8967, 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_5374])). 6.97/7.23 cnf(c_0_8968, plain, (c_Predicate_Otransp(X1,X2)|~c_Relation_Otrans(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_5372])). 6.97/7.23 cnf(c_0_8969, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X1),X2))|X1!=X2|~class_Orderings_Oorder(X3)), inference(split_conjunct,[status(thm)],[c_0_5112])). 6.97/7.23 fof(c_0_8970, plain, ![X1312, X1313]:(((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1312|hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1313))!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1312))&(X1313=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1313))!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1312)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1312|X1313!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1313))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1312))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negative__eq__positive])])])). 6.97/7.23 cnf(c_0_8971, plain, (c_Predicate_Osymp(X1,X2)|~c_Relation_Osym(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_5373])). 6.97/7.23 fof(c_0_8972, plain, ![X8376, X8377, X8378, X8379]:(~hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8379,tc_HOL_Obool)),X8378),X8377),X8376))|hBOOL(hAPP(X8378,X8376))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1D1])])). 6.97/7.23 fof(c_0_8973, plain, ![X15553, X15554, X15555, X15556]:(~hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15556,tc_HOL_Obool)),X15555),X15554),X15553))|hBOOL(hAPP(X15554,X15553))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1D2])])). 6.97/7.23 fof(c_0_8974, plain, ![X13305, X13306, X13307, X13308, X13309, X13310]:(~c_Typedef_Otype__definition(X13310,X13309,X13308,X13307,X13306)|X13305=hAPP(X13307,hAPP(X13308,X13305))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__inverse])])). 6.97/7.23 cnf(c_0_8975, 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_5445])). 6.97/7.23 cnf(c_0_8976, plain, (X1=c_Int_OMin|c_Int_OBit1(X1)!=c_Int_OMin), inference(split_conjunct,[status(thm)],[c_0_5446])). 6.97/7.23 fof(c_0_8977, plain, ![X617, X618, X619, X620, X621]:(~hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X621,X620,X619),X618),X617))|hBOOL(hAPP(hAPP(X619,X617),X618))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_conversepD])])])). 6.97/7.23 cnf(c_0_8978, plain, (hAPP(X3,X2)=X2|~class_Complete__Lattice_Ocomplete__lattice(X1)|X2!=c_Inductive_Ocomplete__lattice__class_Olfp(X1,X3)|~c_Orderings_Oorder__class_Omono(X1,X1,X3)), inference(split_conjunct,[status(thm)],[c_0_5447])). 6.97/7.23 fof(c_0_8979, plain, ![X15414, X15415, X15416]:((~hBOOL(hAPP(X15414,X15416))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X15415),X15414))|~class_Enum_Oenum(X15415))&(~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X15415),X15414))|hBOOL(hAPP(X15414,esk518_2(X15414,X15415)))|~class_Enum_Oenum(X15415))), 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])])])])])). 6.97/7.23 fof(c_0_8980, plain, ![X7291, X7292, X7293]:((~hBOOL(hAPP(X7291,X7293))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X7292),X7291))|~class_Enum_Oenum(X7292))&(~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X7292),X7291))|hBOOL(hAPP(X7291,esk234_2(X7291,X7292)))|~class_Enum_Oenum(X7292))), 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_exists__code])])])])])])). 6.97/7.23 cnf(c_0_8981, plain, (hAPP(X3,X2)=X2|~class_Complete__Lattice_Ocomplete__lattice(X1)|X2!=c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X3)|~c_Orderings_Oorder__class_Omono(X1,X1,X3)), inference(split_conjunct,[status(thm)],[c_0_5448])). 6.97/7.23 cnf(c_0_8982, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(X1),X2)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5366])). 6.97/7.23 fof(c_0_8983, plain, ![X3206, X3207, X3208, X3209, X3210]:(~c_Fun_Obij__betw(X3210,X3209,X3208,X3207,X3206)|hAPP(c_Finite__Set_Ocard(X3209),X3206)=hAPP(c_Finite__Set_Ocard(X3210),X3207)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bij__betw__same__card])])])). 6.97/7.23 fof(c_0_8984, plain, ![X5413, X5414, X5415, X5416]:(~c_Fun_Obij__betw(X5416,X5415,X5414,X5413,c_Orderings_Obot__class_Obot(tc_fun(X5415,tc_HOL_Obool)))|c_Orderings_Obot__class_Obot(tc_fun(X5416,tc_HOL_Obool))=X5413), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__empty2])])). 6.97/7.23 fof(c_0_8985, plain, ![X17107, X17108]:(~class_Groups_Omonoid__add(X17108)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17108),c_Groups_Ozero__class_Ozero(X17108)),X17107)=X17107), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])])). 6.97/7.23 fof(c_0_8986, plain, ![X11845, X11846]:(~class_Rings_Ocomm__semiring__1(X11846)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11846),c_Groups_Ozero__class_Ozero(X11846)),X11845)=X11845), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])])])). 6.97/7.23 fof(c_0_8987, plain, ![X16674, X16675]:(~class_Groups_Ocomm__monoid__add(X16675)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16675),c_Groups_Ozero__class_Ozero(X16675)),X16674)=X16674), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__0])])])). 6.97/7.23 fof(c_0_8988, plain, ![X9841, X9842]:(~class_Lattices_Obounded__lattice__top(X9842)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X9842),c_Orderings_Otop__class_Otop(X9842)),X9841)=X9841), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__top__left])])). 6.97/7.23 fof(c_0_8989, plain, ![X4389, X4390, X4391, X4392]:(~c_Fun_Obij__betw(X4392,X4391,X4390,c_Orderings_Obot__class_Obot(tc_fun(X4392,tc_HOL_Obool)),X4389)|X4389=c_Orderings_Obot__class_Obot(tc_fun(X4391,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__empty1])])). 6.97/7.23 fof(c_0_8990, plain, ![X5596, X5597, X5598, X5599, X5600, X5601]:(~c_Finite__Set_Ofolding__image__simple(X5601,X5600,X5599,X5598,X5597,X5596)|X5598=hAPP(X5596,c_Orderings_Obot__class_Obot(tc_fun(X5600,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oempty])])). 6.97/7.23 fof(c_0_8991, plain, ![X15807, X15808]:(~class_Groups_Omonoid__mult(X15808)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15808),c_Groups_Oone__class_Oone(X15808)),X15807)=X15807), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__left])])). 6.97/7.23 fof(c_0_8992, plain, ![X17458, X17459]:(~class_Groups_Ocomm__monoid__mult(X17459)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17459),c_Groups_Oone__class_Oone(X17459)),X17458)=X17458), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1])])). 6.97/7.23 fof(c_0_8993, plain, ![X14870, X14871]:(~class_Lattices_Obounded__lattice__bot(X14871)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X14871),c_Orderings_Obot__class_Obot(X14871)),X14870)=X14870), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__bot__left])])). 6.97/7.23 fof(c_0_8994, plain, ![X8643, X8644]:(~class_Rings_Ocomm__semiring__1(X8644)|X8643=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8644),c_Groups_Oone__class_Oone(X8644)),X8643)), 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])])])). 6.97/7.23 fof(c_0_8995, plain, ![X444, X445, X446]:(~class_Orderings_Opreorder(X446)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X446),X445),X444))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X446),X444),X445)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__asym])])])). 6.97/7.23 fof(c_0_8996, plain, ![X7601, X7602, X7603]:(~class_Orderings_Oorder(X7603)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7603),X7602),X7601))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7603),X7601),X7602)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_xt1_I9_J])])])). 6.97/7.23 fof(c_0_8997, plain, ![X11340, X11341]:(~class_Divides_Osemiring__div(X11341)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X11341),X11340),c_Groups_Oone__class_Oone(X11341))=X11340), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__by__1])])])). 6.97/7.23 fof(c_0_8998, plain, ![X17651, X17652]:(~class_Groups_Omonoid__mult(X17652)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17652),X17651),c_Groups_Oone__class_Oone(X17652))=X17651), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__1__right])])])). 6.97/7.23 fof(c_0_8999, plain, ![X2466, X2467]:(~class_Rings_Ocomm__semiring__1(X2467)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2467),X2466),c_Groups_Oone__class_Oone(X2467))=X2466), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J])])). 6.97/7.23 fof(c_0_9000, plain, ![X9262, X9263, X9264]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9264),X9263),X9262))|(X9262=X9263|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9264),X9262),X9263)))|~class_Orderings_Olinorder(X9264))&((X9262!=X9263|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9264),X9263),X9262))|~class_Orderings_Olinorder(X9264))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9264),X9262),X9263))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9264),X9263),X9262))|~class_Orderings_Olinorder(X9264)))), 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])])])])). 6.97/7.23 fof(c_0_9001, plain, ![X1954, X1955, X1956, X1957]:(~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1957,X1956),X1955))|(~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1957,X1956),X1954))|X1955=X1954)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__nat__rel__unique])])])). 6.97/7.23 fof(c_0_9002, plain, ![X6865, X6866, X6867]:((hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6867,tc_HOL_Obool)),X6866)!=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6867,tc_HOL_Obool)),X6865)|X6866=X6865)&(X6866!=X6865|hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6867,tc_HOL_Obool)),X6866)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6867,tc_HOL_Obool)),X6865))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__eq__Compl__iff])])). 6.97/7.23 cnf(c_0_9003, plain, (X2=X1|c_Int_OBit0(X1)!=c_Int_OBit0(X2)), inference(split_conjunct,[status(thm)],[c_0_5449])). 6.97/7.23 cnf(c_0_9004, plain, (c_Groups_Ozero__class_Ozero(X2)=X3|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_5375])). 6.97/7.23 fof(c_0_9005, plain, ![X9413, X9414]:(~class_Lattices_Oboolean__algebra(X9414)|hAPP(c_Groups_Ouminus__class_Ouminus(X9414),hAPP(c_Groups_Ouminus__class_Ouminus(X9414),X9413))=X9413), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_double__compl])])])). 6.97/7.23 fof(c_0_9006, plain, ![X2151, X2152]:(~class_Groups_Ogroup__add(X2152)|X2151=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2152),X2151),c_Groups_Ozero__class_Ozero(X2152))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0__right])])). 6.97/7.23 fof(c_0_9007, plain, ![X6247, X6248]:(~class_Groups_Omonoid__add(X6248)|X6247=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6248),X6247),c_Groups_Ozero__class_Ozero(X6248))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])])). 6.97/7.23 fof(c_0_9008, plain, ![X9022, X9023]:(~class_Rings_Ocomm__semiring__1(X9023)|X9022=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9023),X9022),c_Groups_Ozero__class_Ozero(X9023))), 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])])])). 6.97/7.23 fof(c_0_9009, plain, ![X353, X354, X355]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X353),X354)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X355),X354)|X355=X353)&(X355!=X353|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X353),X354)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X355),X354))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])])). 6.97/7.23 fof(c_0_9010, plain, ![X4043, X4044, X4045]:((X4043!=X4044|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4045),X4044)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4045),X4043))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4045),X4044)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4045),X4043)|X4043=X4044)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])])). 6.97/7.23 fof(c_0_9011, plain, ![X5817, X5818]:(~class_Groups_Ocomm__monoid__add(X5818)|X5817=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5818),X5817),c_Groups_Ozero__class_Ozero(X5818))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add_Ocomm__neutral])])])). 6.97/7.23 fof(c_0_9012, plain, ![X3716, X3717]:(~class_Lattices_Obounded__lattice__top(X3717)|X3716=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3717),X3716),c_Orderings_Otop__class_Otop(X3717))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__top__right])])])). 6.97/7.23 fof(c_0_9013, plain, ![X4804, X4805]:(~class_Groups_Ocomm__monoid__mult(X4805)|X4804=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4805),X4804),c_Groups_Oone__class_Oone(X4805))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult_Ocomm__neutral])])])). 6.97/7.23 fof(c_0_9014, plain, ![X7726, X7727]:(~class_Rings_Odivision__ring(X7727)|X7726=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7727),X7726),c_Groups_Oone__class_Oone(X7727))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__1])])])). 6.97/7.23 fof(c_0_9015, plain, ![X7137, X7138]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X7138),X7137))|X7137=c_Quickcheck_Obeyond(X7138,X7137))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X7138),X7137))|c_Quickcheck_Obeyond(X7138,X7137)=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_beyond__def])])])). 6.97/7.23 fof(c_0_9016, plain, ![X6768, X6769]:(~class_Lattices_Obounded__lattice__bot(X6769)|X6768=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6769),X6768),c_Orderings_Obot__class_Obot(X6769))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__bot__right])])])). 6.97/7.23 fof(c_0_9017, plain, ![X3506, X3507]:(~class_Groups_Omonoid__mult(X3507)|X3506=hAPP(hAPP(c_Power_Opower__class_Opower(X3507),X3506),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__right])])). 6.97/7.23 fof(c_0_9018, plain, ![X15859, X15860]:(~class_Rings_Ocomm__semiring__1(X15860)|X15859=hAPP(hAPP(c_Power_Opower__class_Opower(X15860),X15859),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J])])). 6.97/7.23 fof(c_0_9019, plain, ![X10001, X10002, X10003, X10004]:(~c_Equiv__Relations_Oequivp(X10004,X10003)|c_Quotient_OBabs(X10004,X10002,c_Quotient_ORespects(X10004,X10003),X10001)=X10001), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_babs__reg__eqv])])])). 6.97/7.23 cnf(c_0_9020, plain, (X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1)!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Omult__zero(X2)|~class_Rings_Ono__zero__divisors(X2)|~class_Rings_Ozero__neq__one(X2)|~class_Power_Opower(X2)), inference(split_conjunct,[status(thm)],[c_0_5416])). 6.97/7.23 cnf(c_0_9021, plain, (X3=hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1)|X1!=hAPP(c_Groups_Ouminus__class_Ouminus(X2),X3)|~class_Groups_Ogroup__add(X2)), inference(split_conjunct,[status(thm)],[c_0_5450])). 6.97/7.23 fof(c_0_9022, plain, ![X16594, X16595]:(~class_Orderings_Olinorder(X16595)|c_List_Olinorder__class_Osorted(X16595,c_List_Olinorder__class_Osort__key(X16595,X16595,c_COMBI(X16595),X16594))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__sort])])])). 6.97/7.23 fof(c_0_9023, plain, ![X11506, X11507]:(~c_Nat__Transfer_Ois__nat(X11507)|(~c_Nat__Transfer_Ois__nat(X11506)|c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11507),X11506)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Divides_Otransfer__int__nat__function__closures_I1_J])])])). 6.97/7.23 fof(c_0_9024, plain, ![X8852, X8853]:(~c_Nat__Transfer_Ois__nat(X8853)|(~c_Nat__Transfer_Ois__nat(X8852)|c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X8853),X8852)))), 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])])])). 6.97/7.23 fof(c_0_9025, plain, ![X2966, X2967]:(~c_Nat__Transfer_Ois__nat(X2967)|(~c_Nat__Transfer_Ois__nat(X2966)|c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2967),X2966)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J])])). 6.97/7.23 fof(c_0_9026, plain, ![X6709, X6710, X6711]:((c_List_Olist_ONil(X6711)!=hAPP(hAPP(c_List_Otake(X6711),X6710),X6709)|(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X6710|c_List_Olist_ONil(X6711)=X6709))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X6710|c_List_Olist_ONil(X6711)=hAPP(hAPP(c_List_Otake(X6711),X6710),X6709))&(c_List_Olist_ONil(X6711)!=X6709|c_List_Olist_ONil(X6711)=hAPP(hAPP(c_List_Otake(X6711),X6710),X6709)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__eq__Nil])])])). 6.97/7.23 fof(c_0_9027, plain, ![X13099, X13100]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13100),X13099)|(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X13099|X13100=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X13099|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13100),X13099))&(X13100!=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),X13100),X13099)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__is__0])])])). 6.97/7.23 fof(c_0_9028, plain, ![X9212, X9213]:((X9213=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_List_Olist_ONil(tc_List_Olist(X9212))=c_Enum_On__lists(X9212,X9213,c_List_Olist_ONil(X9212)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X9213|hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X9212)),c_List_Olist_ONil(X9212)),c_List_Olist_ONil(tc_List_Olist(X9212)))=c_Enum_On__lists(X9212,X9213,c_List_Olist_ONil(X9212)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_n__lists__Nil])])])). 6.97/7.23 fof(c_0_9029, plain, ![X565, X566, X567]:((~c_List_Olist__all(X567,X566,hAPP(c_List_Orev(X567),X565))|c_List_Olist__all(X567,X566,X565))&(~c_List_Olist__all(X567,X566,X565)|c_List_Olist__all(X567,X566,hAPP(c_List_Orev(X567),X565)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__rev])])). 6.97/7.23 fof(c_0_9030, plain, ![X16090, X16091, X16092]:((~c_List_Olist__ex(X16092,X16091,hAPP(c_List_Orev(X16092),X16090))|c_List_Olist__ex(X16092,X16091,X16090))&(~c_List_Olist__ex(X16092,X16091,X16090)|c_List_Olist__ex(X16092,X16091,hAPP(c_List_Orev(X16092),X16090)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ex__rev])])). 6.97/7.23 fof(c_0_9031, plain, ![X361, X362, X363]:((~hBOOL(hAPP(X361,X362))|hBOOL(hAPP(hAPP(c_member(X363),X362),X361)))&(~hBOOL(hAPP(hAPP(c_member(X363),X362),X361))|hBOOL(hAPP(X361,X362)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])])). 6.97/7.23 fof(c_0_9032, plain, ![X3242, X3243, X3244]:(~hBOOL(hAPP(X3244,X3243))|hBOOL(hAPP(X3244,c_Hilbert__Choice_OEps(X3242,X3244)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_someI])])). 6.97/7.23 fof(c_0_9033, plain, ![X14498, X14499, X14500, X14501, X14502]:((~hBOOL(hAPP(X14499,X14500))|hBOOL(hAPP(X14499,c_Hilbert__Choice_OEps(X14498,X14499))))&(~hBOOL(hAPP(X14502,c_Hilbert__Choice_OEps(X14501,X14502)))|hBOOL(hAPP(X14502,esk489_2(X14501,X14502))))), 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])])])])])). 6.97/7.23 fof(c_0_9034, plain, ![X4350, X4351, X4352, X4353]:(~c_Finite__Set_Ofolding(X4353,X4352,X4351,X4350)|c_Fun_Oid(X4352)=hAPP(X4350,c_Orderings_Obot__class_Obot(tc_fun(X4353,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Oempty])])])). 6.97/7.23 cnf(c_0_9035, 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_5451])). 6.97/7.23 fof(c_0_9036, plain, ![X5753, X5754, X5755, X5756, X5757, X5758]:(~c_Fun_Oinj__on(X5758,X5757,hAPP(c_Fun_Ocomp(X5756,X5757,X5758,X5755),X5754),X5753)|c_Fun_Oinj__on(X5758,X5756,X5754,X5753)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__imageI2])])])). 6.97/7.23 cnf(c_0_9037, 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_5452])). 6.97/7.23 fof(c_0_9038, plain, ![X1414, X1415, X1416]:(~class_Orderings_Obot(X1416)|hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1415,X1416)),X1414)=c_Orderings_Obot__class_Obot(X1416)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bot__apply])])])). 6.97/7.23 fof(c_0_9039, plain, ![X7883, X7884, X7885]:(~class_Orderings_Otop(X7885)|c_Orderings_Otop__class_Otop(X7885)=hAPP(c_Orderings_Otop__class_Otop(tc_fun(X7884,X7885)),X7883)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_top__apply])])])). 6.97/7.23 fof(c_0_9040, plain, ![X16735, X16736]:(~class_Groups_Ogroup__add(X16736)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X16736),X16735),X16735)=c_Groups_Ozero__class_Ozero(X16736)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__self])])])). 6.97/7.23 fof(c_0_9041, plain, ![X4901, X4902, X4903, X4904, X4905]:(((X4904!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X4904!=X4902|c_List_Oreplicate(X4905,X4904,X4903)=c_List_Oreplicate(X4905,X4902,X4901))&(X4903!=X4901|X4904!=X4902|c_List_Oreplicate(X4905,X4904,X4903)=c_List_Oreplicate(X4905,X4902,X4901)))&((X4904=X4902|c_List_Oreplicate(X4905,X4904,X4903)!=c_List_Oreplicate(X4905,X4902,X4901))&(X4904=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X4903=X4901|c_List_Oreplicate(X4905,X4904,X4903)!=c_List_Oreplicate(X4905,X4902,X4901)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_replicate__eq__replicate])])])])). 6.97/7.23 fof(c_0_9042, plain, ![X5803, X5804, X5805, X5806, X5807]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X5806),X5803))|hBOOL(hAPP(c_Finite__Set_Ofinite(X5807),X5804))|~c_Fun_Obij__betw(X5807,X5806,X5805,X5804,X5803))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5807),X5804))|hBOOL(hAPP(c_Finite__Set_Ofinite(X5806),X5803))|~c_Fun_Obij__betw(X5807,X5806,X5805,X5804,X5803))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__finite])])])). 6.97/7.23 fof(c_0_9043, plain, ![X4450, X4451]:(~class_Rings_Olinordered__ring(X4451)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4451),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4451),X4450),X4450)),c_Groups_Ozero__class_Ozero(X4451)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__square__less__zero])])])). 6.97/7.23 fof(c_0_9044, plain, ![X5311, X5312, X5313]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X5313),tc_HOL_Obool)),X5312),X5311))|c_Hoare__Mirabelle_Ohoare__derivs(X5313,X5311,X5312)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_asm])])])). 6.97/7.23 fof(c_0_9045, plain, ![X529, X530]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X530))|c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X530,X529))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__function__closures])])])). 6.97/7.23 fof(c_0_9046, plain, ![X3203, X3204, X3205]:(X3205=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X3203=c_List_Olast(X3204,c_List_Oreplicate(X3204,X3205,X3203))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__replicate])])). 6.97/7.23 cnf(c_0_9047, plain, (c_List_Oall__interval__nat(X1,X2,X3)|~c_List_Olist__all(tc_Nat_Onat,X1,c_List_Oupt(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_5421])). 6.97/7.23 cnf(c_0_9048, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(c_Int_Onat,esk18_1(X1))))), inference(split_conjunct,[status(thm)],[c_0_5403])). 6.97/7.23 fof(c_0_9049, plain, ![X12895, X12896, X12897, X12898, X12899]:(((X12898=X12896|hAPP(hAPP(c_List_Olist_OCons(X12899),X12896),X12895)!=hAPP(hAPP(c_List_Olist_OCons(X12899),X12898),X12897))&(X12895=X12897|hAPP(hAPP(c_List_Olist_OCons(X12899),X12896),X12895)!=hAPP(hAPP(c_List_Olist_OCons(X12899),X12898),X12897)))&(X12898!=X12896|X12895!=X12897|hAPP(hAPP(c_List_Olist_OCons(X12899),X12896),X12895)=hAPP(hAPP(c_List_Olist_OCons(X12899),X12898),X12897))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list_Oinject])])])). 6.97/7.23 fof(c_0_9050, plain, ![X7928, X7929]:(~class_Complete__Lattice_Ocomplete__lattice(X7929)|X7928=c_Inductive_Ocomplete__lattice__class_Olfp(X7929,hAPP(c_COMBK(X7929,X7929),X7928))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lfp__const])])). 6.97/7.23 fof(c_0_9051, plain, ![X12821, X12822]:(~class_Orderings_Opreorder(X12822)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12822),X12821),X12821))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])])). 6.97/7.23 fof(c_0_9052, plain, ![X9559, X9560]:(~c_Wellfounded_Owf(X9560,X9559)|c_Wellfounded_Owf(tc_fun(X9560,tc_HOL_Obool),c_Wellfounded_Omin__ext(X9560,X9559))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__ext__wf])])). 6.97/7.23 fof(c_0_9053, plain, ![X16894, X16895]:(~c_Wellfounded_Owf(X16895,X16894)|c_Wellfounded_Owf(tc_fun(X16895,tc_HOL_Obool),c_Wellfounded_Omax__ext(X16895,X16894))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ext__wf])])). 6.97/7.23 fof(c_0_9054, plain, ![X910, X911, X912, X913]:((hAPP(hAPP(c_List_Oappend(X913),X910),X911)!=hAPP(hAPP(c_List_Oappend(X913),X912),X911)|X910=X912)&(X910!=X912|hAPP(hAPP(c_List_Oappend(X913),X910),X911)=hAPP(hAPP(c_List_Oappend(X913),X912),X911))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__same__eq])])). 6.97/7.23 fof(c_0_9055, plain, ![X1152, X1153, X1154, X1155]:((X1152!=X1153|hAPP(hAPP(c_List_Oappend(X1155),X1154),X1152)=hAPP(hAPP(c_List_Oappend(X1155),X1154),X1153))&(hAPP(hAPP(c_List_Oappend(X1155),X1154),X1152)!=hAPP(hAPP(c_List_Oappend(X1155),X1154),X1153)|X1152=X1153)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__append__eq])])). 6.97/7.23 fof(c_0_9056, plain, ![X7274, X7275]:((~c_Wellfounded_Oacyclic(X7275,hAPP(c_Relation_Oconverse(X7275,X7275),X7274))|c_Wellfounded_Oacyclic(X7275,X7274))&(~c_Wellfounded_Oacyclic(X7275,X7274)|c_Wellfounded_Oacyclic(X7275,hAPP(c_Relation_Oconverse(X7275,X7275),X7274)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclic__converse])])). 6.97/7.23 cnf(c_0_9057, 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_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_5453])). 6.97/7.23 cnf(c_0_9058, 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_Onat,X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_5454])). 6.97/7.23 fof(c_0_9059, plain, ![X6368, X6369]:((~c_Relation_Oantisym(X6369,hAPP(c_Relation_Oconverse(X6369,X6369),X6368))|c_Relation_Oantisym(X6369,X6368))&(~c_Relation_Oantisym(X6369,X6368)|c_Relation_Oantisym(X6369,hAPP(c_Relation_Oconverse(X6369,X6369),X6368)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_antisym__converse])])). 6.97/7.23 fof(c_0_9060, plain, ![X4139, X4140]:((~c_Relation_Otrans(X4140,hAPP(c_Relation_Oconverse(X4140,X4140),X4139))|c_Relation_Otrans(X4140,X4139))&(~c_Relation_Otrans(X4140,X4139)|c_Relation_Otrans(X4140,hAPP(c_Relation_Oconverse(X4140,X4140),X4139)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__converse])])). 6.97/7.23 fof(c_0_9061, plain, ![X2790, X2791]:((~c_Relation_Osym(X2791,X2790)|c_Relation_Osym(X2791,hAPP(c_Relation_Oconverse(X2791,X2791),X2790)))&(~c_Relation_Osym(X2791,hAPP(c_Relation_Oconverse(X2791,X2791),X2790))|c_Relation_Osym(X2791,X2790))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__converse])])). 6.97/7.23 fof(c_0_9062, plain, ![X10655, X10656, X10657]:(~class_Orderings_Olinorder(X10657)|c_List_Olist_ONil(X10656)=c_List_Olinorder__class_Osort__key(X10656,X10657,X10655,c_List_Olist_ONil(X10656))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sort__key__simps_I1_J])])])). 6.97/7.23 cnf(c_0_9063, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onat,X1)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(split_conjunct,[status(thm)],[c_0_5455])). 6.97/7.23 fof(c_0_9064, plain, ![X10450, X10451, X10452, X10453, X10454]:((X10450!=X10451|hAPP(X10452,X10450)=hAPP(X10452,X10451)|~c_Orderings_Oorder__class_Ostrict__mono(X10453,X10454,X10452)|(~class_Orderings_Olinorder(X10453)|~class_Orderings_Oorder(X10454)))&(hAPP(X10452,X10450)!=hAPP(X10452,X10451)|X10450=X10451|~c_Orderings_Oorder__class_Ostrict__mono(X10453,X10454,X10452)|(~class_Orderings_Olinorder(X10453)|~class_Orderings_Oorder(X10454)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_strict__mono__eq])])])])). 6.97/7.23 fof(c_0_9065, plain, ![X16359, X16360, X16361, X16362, X16363, X16364]:(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X16364,X16363,X16362,X16361,X16360),X16359))|hBOOL(hAPP(c_Finite__Set_Ofinite(X16364),X16360))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__graph__imp__finite])])). 6.97/7.23 fof(c_0_9066, plain, ![X14173, X14174, X14175]:((X14173!=hAPP(c_Nat_OSuc,X14174)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14173)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14175))|X14175=hAPP(c_Nat_OSuc,esk483_1(X14175)))), 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])])])])])). 6.97/7.23 fof(c_0_9067, plain, ![X670]:(~class_Power_Opower(X670)|c_Power_Opower__class_Opower(X670)=c_Power_Opower_Opower(X670,c_Groups_Oone__class_Oone(X670),c_Groups_Otimes__class_Otimes(X670))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__power__power])])])). 6.97/7.23 fof(c_0_9068, plain, ![X17355]:(~class_Complete__Lattice_Ocomplete__lattice(X17355)|c_Complete__Lattice_OSup__class_OSup(X17355,c_Orderings_Otop__class_Otop(tc_fun(X17355,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(X17355)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__UNIV])])])). 6.97/7.23 fof(c_0_9069, plain, ![X907]:(~class_Complete__Lattice_Ocomplete__lattice(X907)|c_Complete__Lattice_OSup__class_OSup(X907,c_Orderings_Obot__class_Obot(tc_fun(X907,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(X907)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__empty])])). 6.97/7.23 fof(c_0_9070, plain, ![X16593]:(~class_Complete__Lattice_Ocomplete__lattice(X16593)|c_Complete__Lattice_OInf__class_OInf(X16593,c_Orderings_Obot__class_Obot(tc_fun(X16593,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(X16593)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__empty])])). 6.97/7.23 fof(c_0_9071, plain, ![X9270]:(~class_Orderings_Olinorder(X9270)|c_List_Olist_ONil(X9270)=c_List_Olinorder__class_Osorted__list__of__set(X9270,c_Orderings_Obot__class_Obot(tc_fun(X9270,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__empty])])). 6.97/7.23 cnf(c_0_9072, 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_5388])). 6.97/7.23 fof(c_0_9073, plain, ![X16216, X16217, X16218, X16219]:(~c_Finite__Set_Ofolding__one__idem(X16219,X16218,X16217)|hAPP(hAPP(X16218,X16216),X16216)=X16216), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oidem])])). 6.97/7.23 fof(c_0_9074, plain, ![X15446, X15447]:(~class_Orderings_Olinorder(X15447)|(~c_List_Olinorder__class_Osorted(X15447,X15446)|c_List_Olinorder__class_Osorted(X15447,hAPP(c_List_Otl(X15447),X15446)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__tl])])). 6.97/7.23 fof(c_0_9075, plain, ![X9801]:(~class_Complete__Lattice_Ocomplete__lattice(X9801)|c_Orderings_Obot__class_Obot(X9801)=c_Complete__Lattice_OInf__class_OInf(X9801,c_Orderings_Otop__class_Otop(tc_fun(X9801,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__UNIV])])). 6.97/7.23 fof(c_0_9076, plain, ![X12642, X12643, X12644]:(((X12642=c_Orderings_Otop__class_Otop(X12644)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X12644),X12643),X12642)!=c_Orderings_Otop__class_Otop(X12644)|~class_Lattices_Obounded__lattice__top(X12644))&(c_Orderings_Otop__class_Otop(X12644)=X12643|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X12644),X12643),X12642)!=c_Orderings_Otop__class_Otop(X12644)|~class_Lattices_Obounded__lattice__top(X12644)))&(X12642!=c_Orderings_Otop__class_Otop(X12644)|c_Orderings_Otop__class_Otop(X12644)!=X12643|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X12644),X12643),X12642)=c_Orderings_Otop__class_Otop(X12644)|~class_Lattices_Obounded__lattice__top(X12644))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__eq__top__iff])])])])). 6.97/7.23 fof(c_0_9077, plain, ![X13068]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,X13068))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13068),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13068),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X13068)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__def])])). 6.97/7.23 cnf(c_0_9078, 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_5164])). 6.97/7.23 fof(c_0_9079, plain, ![X3548, X3549, X3550, X3551]:(~class_Orderings_Oorder(X3551)|~class_Orderings_Olinorder(X3550)|(~c_Orderings_Oorder__class_Ostrict__mono(X3550,X3551,X3549)|c_Fun_Oinj__on(X3550,X3551,X3549,X3548))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_strict__mono__imp__inj__on])])])). 6.97/7.23 fof(c_0_9080, plain, ![X12466, X12467, X12468, X12469, X12470]:(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X12470,X12469,X12468,X12467,c_Orderings_Obot__class_Obot(tc_fun(X12470,tc_HOL_Obool))),X12466))|X12466=X12467), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_empty__fold__graphE])])). 6.97/7.23 fof(c_0_9081, plain, ![X1816, X1817, X1818]:(~c_Wellfounded_Owf(X1818,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1818,X1818),tc_HOL_Obool),X1817),X1816))|c_Wellfounded_Owf(X1818,X1816)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__exp])])). 6.97/7.23 fof(c_0_9082, plain, ![X8986, X8987, X8989, X8990, X8991]:((~hBOOL(hAPP(hAPP(c_member(X8987),esk294_2(X8986,X8987)),c_Wellfounded_Oacc(X8987,X8986)))|c_Wellfounded_Owf(X8987,X8986))&(~c_Wellfounded_Owf(X8990,X8989)|hBOOL(hAPP(hAPP(c_member(X8990),X8991),c_Wellfounded_Oacc(X8990,X8989))))), 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])])])])])). 6.97/7.23 fof(c_0_9083, plain, ![X2018, X2019, X2020]:((X2019!=X2018|hAPP(c_Int_Onumber__class_Onumber__of(X2020),X2019)=hAPP(c_Int_Onumber__class_Onumber__of(X2020),X2018)|(~class_Int_Oring__char__0(X2020)|~class_Int_Onumber__ring(X2020)))&(hAPP(c_Int_Onumber__class_Onumber__of(X2020),X2019)!=hAPP(c_Int_Onumber__class_Onumber__of(X2020),X2018)|X2019=X2018|(~class_Int_Oring__char__0(X2020)|~class_Int_Onumber__ring(X2020)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of])])])). 6.97/7.23 fof(c_0_9084, plain, ![X8165, X8166, X8167]:(~c_Wellfounded_OwfP(X8167,X8166)|hBOOL(hAPP(c_Wellfounded_Oaccp(X8167,X8166),X8165))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__wfPD])])). 6.97/7.23 fof(c_0_9085, plain, ![X17573]:(X17573=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X17573),X17573)=c_Groups_Oone__class_Oone(tc_Int_Oint)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__self])])])). 6.97/7.23 fof(c_0_9086, plain, ![X15340, X15341]:(~class_Lattices_Olattice(X15341)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15341),X15340),X15340)=X15340), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oidem])])])). 6.97/7.23 fof(c_0_9087, plain, ![X13884, X13885, X13886]:(~c_Predicate_Oreflp(X13886,X13885)|hBOOL(hAPP(hAPP(X13885,X13884),X13884))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_reflpE])])])). 6.97/7.23 fof(c_0_9088, plain, ![X3160, X3161, X3162]:(~c_Equiv__Relations_Oequivp(X3162,X3161)|hBOOL(hAPP(hAPP(X3161,X3160),X3160))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__reflp])])). 6.97/7.23 fof(c_0_9089, plain, ![X14471, X14472]:(~class_Lattices_Olattice(X14472)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X14472),X14471),X14471)=X14471), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oidem])])). 6.97/7.23 fof(c_0_9090, plain, ![X797, X798]:(~class_Lattices_Osemilattice__inf(X798)|X797=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X798),X797),X797)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__idem])])])). 6.97/7.23 fof(c_0_9091, plain, ![X10806, X10807]:(~class_Lattices_Oab__semigroup__idem__mult(X10807)|X10806=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10807),X10806),X10806)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__idem])])])). 6.97/7.23 fof(c_0_9092, plain, ![X1799, X1800, X1802]:((~hBOOL(hAPP(X1799,esk54_2(X1799,X1800)))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1800),X1799))|~class_Enum_Oenum(X1800))&(~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1800),X1799))|hBOOL(hAPP(X1799,X1802))|~class_Enum_Oenum(X1800))), 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])])])])])])). 6.97/7.23 fof(c_0_9093, plain, ![X9245]:(~class_Int_Onumber__ring(X9245)|hAPP(c_Int_Onumber__class_Onumber__of(X9245),c_Int_OMin)=hAPP(c_Groups_Ouminus__class_Ouminus(X9245),c_Groups_Oone__class_Oone(X9245))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_arith__simps_I31_J])])])). 6.97/7.23 fof(c_0_9094, plain, ![X10889, X10890]:(~class_Lattices_Osemilattice__sup(X10890)|X10889=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10890),X10889),X10889)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup_Oidem])])])). 6.97/7.23 fof(c_0_9095, plain, ![X7604, X7605, X7606]:(~hBOOL(hAPP(hAPP(X7605,X7606),X7606))|(~c_Predicate_Osymp(X7604,X7605)|(~c_Predicate_Otransp(X7604,X7605)|c_Equiv__Relations_Opart__equivp(X7604,X7605)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_part__equivpI])])])])). 6.97/7.23 fof(c_0_9096, plain, ![X4591, X4592, X4593]:(~class_Orderings_Olinorder(X4593)|(~c_List_Olinorder__class_Osorted(X4593,X4592)|c_List_Olinorder__class_Osorted(X4593,c_List_Oremove1(X4593,X4591,X4592)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__remove1])])])). 6.97/7.23 fof(c_0_9097, plain, ![X372, X373, X374]:(~class_Orderings_Olinorder(X374)|(~c_List_Olinorder__class_Osorted(X374,X373)|c_List_Olinorder__class_Osorted(X374,c_List_OtakeWhile(X374,X372,X373)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__takeWhile])])])). 6.97/7.23 fof(c_0_9098, plain, ![X7847, X7848]:(~c_Nat__Transfer_Ois__nat(X7848)|c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X7848),X7847))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J])])])). 6.97/7.23 fof(c_0_9099, plain, ![X6808, X6809, X6810, X6811, X6812, X6813, X6814]:((hAPP(X6812,X6809)!=hAPP(X6812,X6808)|X6809=X6808|~c_Typedef_Otype__definition(X6814,X6813,X6812,X6811,X6810))&(X6809!=X6808|hAPP(X6812,X6809)=hAPP(X6812,X6808)|~c_Typedef_Otype__definition(X6814,X6813,X6812,X6811,X6810))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__inject])])])). 6.97/7.23 fof(c_0_9100, plain, ![X15925, X15926, X15928]:((~hBOOL(hAPP(X15925,esk538_2(X15925,X15926)))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X15926),X15925))|~class_Enum_Oenum(X15926))&(~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X15926),X15925))|hBOOL(hAPP(X15925,X15928))|~class_Enum_Oenum(X15926))), 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__code])])])])])])). 6.97/7.23 fof(c_0_9101, plain, ![X3999]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3999),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onat,X3999)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__0])])). 6.97/7.23 fof(c_0_9102, plain, ![X5075, X5076, X5077]:(((c_Orderings_Obot__class_Obot(X5077)=X5075|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5077),X5076),X5075)!=c_Orderings_Obot__class_Obot(X5077)|~class_Lattices_Obounded__lattice__bot(X5077))&(X5076=c_Orderings_Obot__class_Obot(X5077)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5077),X5076),X5075)!=c_Orderings_Obot__class_Obot(X5077)|~class_Lattices_Obounded__lattice__bot(X5077)))&(c_Orderings_Obot__class_Obot(X5077)!=X5075|X5076!=c_Orderings_Obot__class_Obot(X5077)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5077),X5076),X5075)=c_Orderings_Obot__class_Obot(X5077)|~class_Lattices_Obounded__lattice__bot(X5077))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__eq__bot__iff])])])). 6.97/7.23 fof(c_0_9103, plain, ![X11368, X11369]:(~class_Rings_Olinordered__idom(X11369)|c_Groups_Osgn__class_Osgn(X11369,X11368)=c_Groups_Osgn__class_Osgn(X11369,c_Groups_Osgn__class_Osgn(X11369,X11368))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__sgn])])). 6.97/7.23 fof(c_0_9104, plain, ![X4171, X4172]:(~hBOOL(X4172)|hBOOL(hAPP(hAPP(c_fconj,X4172),X4171))|~hBOOL(X4171)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fconj__1])])). 6.97/7.23 fof(c_0_9105, plain, ![X11187, X11188, X11189]:((~c_List_Oall__interval__int(X11189,X11188,X11187)|c_List_Olist__all(tc_Int_Oint,X11189,c_List_Oupto(X11188,X11187)))&(~c_List_Olist__all(tc_Int_Oint,X11189,c_List_Oupto(X11188,X11187))|c_List_Oall__interval__int(X11189,X11188,X11187))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__iff__all__interval__int])])). 6.97/7.23 fof(c_0_9106, plain, ![X14903, X14904, X14905]:(~class_Rings_Oring__1__no__zero__divisors(X14905)|(X14904=c_Groups_Ozero__class_Ozero(X14905)|c_Groups_Ozero__class_Ozero(X14905)!=hAPP(hAPP(c_Power_Opower__class_Opower(X14905),X14904),X14903))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__power__not__zero])])). 6.97/7.23 fof(c_0_9107, plain, ![X8834, X8835]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8835),X8834))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X8835),X8834),X8834)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X8835,X8834))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8835),X8834))|X8835=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X8835,X8834))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__if])])])). 6.97/7.23 fof(c_0_9108, plain, ![X10143, X10144]:(~class_Divides_Osemiring__div(X10144)|c_Divides_Odiv__class_Omod(X10144,c_Groups_Ozero__class_Ozero(X10144),X10143)=c_Groups_Ozero__class_Ozero(X10144)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__0])])])). 6.97/7.23 fof(c_0_9109, plain, ![X13947, X13948]:(~class_Divides_Osemiring__div(X13948)|c_Divides_Odiv__class_Omod(X13948,X13947,c_Groups_Oone__class_Oone(X13948))=c_Groups_Ozero__class_Ozero(X13948)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__by__1])])). 6.97/7.23 fof(c_0_9110, plain, ![X10154, X10155]:((~c_Relation_Osym(X10155,X10154)|hAPP(c_Relation_Oconverse(X10155,X10155),X10154)=X10154)&(hAPP(c_Relation_Oconverse(X10155,X10155),X10154)!=X10154|c_Relation_Osym(X10155,X10154))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__conv__converse__eq])])). 6.97/7.23 fof(c_0_9111, plain, ![X4666, X4667, X4668]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4668),X4666),X4667))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4668),X4667),X4666))|~class_Orderings_Olinorder(X4668))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4668),X4667),X4666))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4668),X4666),X4667))|~class_Orderings_Olinorder(X4668))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__not__le])])])])). 6.97/7.23 cnf(c_0_9112, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(c_Code__Numeral_Oof__nat,esk488_2(X2,X1))))), inference(split_conjunct,[status(thm)],[c_0_5456])). 6.97/7.23 fof(c_0_9113, plain, ![X4855, X4856]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4856,X4856)),X4855))|(~c_Wellfounded_Oacyclic(X4856,X4855)|c_Wellfounded_Owf(X4856,X4855))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__acyclic__wf])])). 6.97/7.23 fof(c_0_9114, plain, ![X12564, X12565]:(~class_Rings_Olinordered__semidom(X12565)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12565),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X12565),X12564)),c_Groups_Ozero__class_Ozero(X12565)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__less__0__iff])])])). 6.97/7.23 fof(c_0_9115, plain, ![X13051, X13052]:(~class_Groups_Oordered__ab__group__add__abs(X13052)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13052),hAPP(c_Groups_Oabs__class_Oabs(X13052),X13051)),c_Groups_Ozero__class_Ozero(X13052)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__not__less__zero])])])). 6.97/7.23 fof(c_0_9116, plain, ![X13829, X13830, X13831]:((hAPP(c_Nat_Osemiring__1__class_Oof__nat(X13831),X13830)!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X13831),X13829)|X13829=X13830|~class_Nat_Osemiring__char__0(X13831))&(X13829!=X13830|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X13831),X13830)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X13831),X13829)|~class_Nat_Osemiring__char__0(X13831))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__eq__iff])])])). 6.97/7.23 fof(c_0_9117, plain, ![X15176, X15177, X15178]:(~class_Rings_Osemiring__1(X15178)|c_Nat_Osemiring__1__class_Oof__nat__aux(X15178,X15177,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15176)=X15176), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__aux_Osimps_I1_J])])])). 6.97/7.23 fof(c_0_9118, plain, ![X1813, X1814]:(~class_Orderings_Olinorder(X1814)|X1813=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1814),X1813),X1813)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup_Oidem])])])). 6.97/7.23 fof(c_0_9119, plain, ![X11479, X11480, X11481]:((X11479!=X11480|hAPP(c_Int_Oring__1__class_Oof__int(X11481),X11480)=hAPP(c_Int_Oring__1__class_Oof__int(X11481),X11479)|~class_Int_Oring__char__0(X11481))&(hAPP(c_Int_Oring__1__class_Oof__int(X11481),X11480)!=hAPP(c_Int_Oring__1__class_Oof__int(X11481),X11479)|X11479=X11480|~class_Int_Oring__char__0(X11481))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__eq__iff])])])). 6.97/7.23 fof(c_0_9120, plain, ![X6226, X6227, X6228]:((X6227!=X6226|hAPP(c_Groups_Ouminus__class_Ouminus(X6228),X6227)=hAPP(c_Groups_Ouminus__class_Ouminus(X6228),X6226)|~class_Groups_Ogroup__add(X6228))&(hAPP(c_Groups_Ouminus__class_Ouminus(X6228),X6227)!=hAPP(c_Groups_Ouminus__class_Ouminus(X6228),X6226)|X6227=X6226|~class_Groups_Ogroup__add(X6228))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__equal__iff__equal])])])])). 6.97/7.23 fof(c_0_9121, plain, ![X13953, X13954, X13955]:((hAPP(c_Groups_Ouminus__class_Ouminus(X13955),X13954)!=hAPP(c_Groups_Ouminus__class_Ouminus(X13955),X13953)|X13954=X13953|~class_Lattices_Oboolean__algebra(X13955))&(X13954!=X13953|hAPP(c_Groups_Ouminus__class_Ouminus(X13955),X13954)=hAPP(c_Groups_Ouminus__class_Ouminus(X13955),X13953)|~class_Lattices_Oboolean__algebra(X13955))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__eq__compl__iff])])])). 6.97/7.23 fof(c_0_9122, plain, ![X1354, X1355]:(~class_Orderings_Olinorder(X1355)|X1354=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1355),X1354),X1354)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oidem])])). 6.97/7.23 fof(c_0_9123, plain, ![X8358, X8359]:(~class_Int_Onumber__ring(X8359)|hAPP(c_Int_Oring__1__class_Oof__int(X8359),X8358)=hAPP(c_Int_Onumber__class_Onumber__of(X8359),X8358)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_number__of__eq])])])). 6.97/7.23 fof(c_0_9124, plain, ![X12586, X12587, X12588]:(~class_Orderings_Owellorder(X12588)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12588),X12587),c_Orderings_Oord__class_OLeast(X12588,X12586)))|~hBOOL(hAPP(X12586,X12587)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__less__Least])])])). 6.97/7.23 fof(c_0_9125, plain, ![X15253, X15254]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15254),X15253))|c_List_Oupto(X15253,X15254)=c_List_Olist_ONil(tc_Int_Oint)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_upto__empty])])])). 6.97/7.23 fof(c_0_9126, plain, ![X7758, X7759]:(hAPP(X7759,esk253_2(X7758,X7759))!=hAPP(X7758,esk253_2(X7758,X7759))|X7758=X7759), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])])). 6.97/7.23 fof(c_0_9127, plain, ![X4688, X4689]:(~class_Groups_Oordered__ab__group__add(X4689)|c_Fun_Oinj__on(X4689,X4689,c_Groups_Ouminus__class_Ouminus(X4689),X4688)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__uminus])])])). 6.97/7.23 fof(c_0_9128, plain, ![X6620, X6621]:(hBOOL(X6621)|hBOOL(hAPP(hAPP(c_fimplies,X6621),X6620))), inference(variable_rename,[status(thm)],[help_c__fimplies__1])). 6.97/7.23 fof(c_0_9129, plain, ![X10794, X10795]:(~c_Relation_Otrans(X10795,X10794)|c_Relation_Otrans(tc_List_Olist(X10795),c_List_Olistrel(X10795,X10794))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__trans])])). 6.97/7.23 fof(c_0_9130, plain, ![X809, X810]:(~c_Relation_Otrans(X810,X809)|c_Relation_Otrans(tc_List_Olist(X810),c_List_Olexord(X810,X809))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__transI])])). 6.97/7.23 fof(c_0_9131, plain, ![X1296]:(~class_Lattices_Oboolean__algebra(X1296)|hAPP(c_Groups_Ouminus__class_Ouminus(X1296),c_Orderings_Otop__class_Otop(X1296))=c_Orderings_Obot__class_Obot(X1296)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__top__eq])])). 6.97/7.23 fof(c_0_9132, plain, ![X5236, X5237]:(~c_Relation_Osym(X5237,X5236)|c_Relation_Osym(tc_List_Olist(X5237),c_List_Olistrel(X5237,X5236))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel__sym])])])). 6.97/7.23 fof(c_0_9133, plain, ![X8901, X8902]:(~c_Wellfounded_Owf(X8902,X8901)|c_Wellfounded_Owf(tc_List_Olist(X8902),c_List_Olenlex(X8902,X8901))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lenlex])])). 6.97/7.23 fof(c_0_9134, plain, ![X15373, X15374]:(~c_Wellfounded_Owf(X15374,X15373)|c_Wellfounded_Owf(tc_List_Olist(X15374),c_List_Olex(X15374,X15373))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lex])])). 6.97/7.23 fof(c_0_9135, plain, ![X2614, X2615, X2616]:((((c_Relation_Osym(X2616,X2614)|~c_Equiv__Relations_Oequiv(X2616,X2615,X2614))&(c_Relation_Otrans(X2616,X2614)|~c_Equiv__Relations_Oequiv(X2616,X2615,X2614)))&(c_Relation_Orefl__on(X2616,X2615,X2614)|~c_Equiv__Relations_Oequiv(X2616,X2615,X2614)))&(~c_Relation_Osym(X2616,X2614)|~c_Relation_Otrans(X2616,X2614)|~c_Relation_Orefl__on(X2616,X2615,X2614)|c_Equiv__Relations_Oequiv(X2616,X2615,X2614))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__def])])])). 6.97/7.23 fof(c_0_9136, plain, ![X10932, X10933]:(~c_Wellfounded_Owf(X10933,X10932)|c_Wellfounded_OwfP(X10933,c_FunDef_Oin__rel(X10933,X10933,X10932))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__in__rel])])). 6.97/7.23 fof(c_0_9137, plain, ![X4029, X4030, X4031]:(~c_Wellfounded_Owf(X4031,X4030)|c_Wellfounded_Owf(X4031,c_Wellfounded_Omlex__prod(X4031,X4029,X4030))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__mlex])])). 6.97/7.23 fof(c_0_9138, plain, ![X14053]:(~class_Groups_Ogroup__add(X14053)|hAPP(c_Groups_Ouminus__class_Ouminus(X14053),c_Groups_Ozero__class_Ozero(X14053))=c_Groups_Ozero__class_Ozero(X14053)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__zero])])). 6.97/7.23 fof(c_0_9139, plain, ![X12172, X12173, X12174, X12175]:(~c_Hoare__Mirabelle_Ohoare__derivs(X12175,X12174,X12173)|(~c_Hoare__Mirabelle_Ohoare__derivs(X12175,X12172,X12174)|c_Hoare__Mirabelle_Ohoare__derivs(X12175,X12172,X12173))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_cut])])])). 6.97/7.23 fof(c_0_9140, plain, ![X2600]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X2600|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2600),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2600),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2600)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__0__eq])])). 6.97/7.23 fof(c_0_9141, plain, ![X4431]:(~class_Lattices_Oboolean__algebra(X4431)|c_Orderings_Otop__class_Otop(X4431)=hAPP(c_Groups_Ouminus__class_Ouminus(X4431),c_Orderings_Obot__class_Obot(X4431))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__bot__eq])])). 6.97/7.23 fof(c_0_9142, plain, ![X1106, X1107]:(((X1106=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1107),X1106)!=c_Groups_Oone__class_Oone(tc_Nat_Onat))&(X1107=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1107),X1106)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)))&(X1106!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X1107!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1107),X1106)=c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff])])])). 6.97/7.23 fof(c_0_9143, plain, ![X13518, X13519]:(((X13519=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),X13519),X13518))&(c_Groups_Oone__class_Oone(tc_Nat_Onat)=X13518|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13519),X13518)))&(X13519!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=X13518|c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13519),X13518))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__1__iff])])])). 6.97/7.23 fof(c_0_9144, plain, ![X11225]:(~class_Rings_Olinordered__idom(X11225)|c_Groups_Oone__class_Oone(X11225)=hAPP(c_Groups_Oabs__class_Oabs(X11225),c_Groups_Oone__class_Oone(X11225))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__one])])). 6.97/7.23 fof(c_0_9145, plain, ![X6387, X6388, X6389, X6390]:((hAPP(hAPP(c_List_Olist__update(X6390,X6389),X6388),X6387)!=c_List_Olist_ONil(X6390)|c_List_Olist_ONil(X6390)=X6389)&(c_List_Olist_ONil(X6390)!=X6389|hAPP(hAPP(c_List_Olist__update(X6390,X6389),X6388),X6387)=c_List_Olist_ONil(X6390))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__nonempty])])). 6.97/7.23 fof(c_0_9146, plain, ![X6208]:(~class_Groups_Omonoid__add(X6208)|c_Groups_Ozero__class_Ozero(X6208)=hAPP(c_List_Omonoid__add__class_Olistsum(X6208),c_List_Olist_ONil(X6208))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__simps_I1_J])])])). 6.97/7.23 fof(c_0_9147, plain, ![X15032, X15033, X15034, X15035]:((X15032!=c_List_Olist_ONil(X15035)|hAPP(hAPP(c_List_Omap(X15035,X15034),X15033),X15032)=c_List_Olist_ONil(X15034))&(hAPP(hAPP(c_List_Omap(X15035,X15034),X15033),X15032)!=c_List_Olist_ONil(X15034)|X15032=c_List_Olist_ONil(X15035))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__is__Nil__conv])])). 6.97/7.23 fof(c_0_9148, plain, ![X5506, X5507, X5508]:((X5507!=X5506|hAPP(c_SetInterval_Oord__class_OgreaterThan(X5508),X5507)=hAPP(c_SetInterval_Oord__class_OgreaterThan(X5508),X5506)|~class_Orderings_Olinorder(X5508))&(hAPP(c_SetInterval_Oord__class_OgreaterThan(X5508),X5507)!=hAPP(c_SetInterval_Oord__class_OgreaterThan(X5508),X5506)|X5507=X5506|~class_Orderings_Olinorder(X5508))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__eq__iff])])])). 6.97/7.23 fof(c_0_9149, plain, ![X12526, X12527, X12528]:((X12527!=X12526|hAPP(c_SetInterval_Oord__class_OlessThan(X12528),X12526)=hAPP(c_SetInterval_Oord__class_OlessThan(X12528),X12527)|~class_Orderings_Olinorder(X12528))&(hAPP(c_SetInterval_Oord__class_OlessThan(X12528),X12526)!=hAPP(c_SetInterval_Oord__class_OlessThan(X12528),X12527)|X12527=X12526|~class_Orderings_Olinorder(X12528))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lessThan__eq__iff])])])])). 6.97/7.23 fof(c_0_9150, plain, ![X16848]:(~class_Groups_Oordered__ab__group__add__abs(X16848)|c_Groups_Ozero__class_Ozero(X16848)=hAPP(c_Groups_Oabs__class_Oabs(X16848),c_Groups_Ozero__class_Ozero(X16848))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__zero])])). 6.97/7.23 fof(c_0_9151, plain, ![X15610, X15611, X15612]:((X15610!=X15611|hAPP(c_SetInterval_Oord__class_OatLeast(X15612),X15610)=hAPP(c_SetInterval_Oord__class_OatLeast(X15612),X15611)|~class_Orderings_Olinorder(X15612))&(hAPP(c_SetInterval_Oord__class_OatLeast(X15612),X15610)!=hAPP(c_SetInterval_Oord__class_OatLeast(X15612),X15611)|X15610=X15611|~class_Orderings_Olinorder(X15612))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeast__eq__iff])])])])). 6.97/7.23 fof(c_0_9152, plain, ![X10760, X10761, X10762]:((X10760!=X10761|hAPP(c_SetInterval_Oord__class_OatMost(X10762),X10760)=hAPP(c_SetInterval_Oord__class_OatMost(X10762),X10761)|~class_Orderings_Olinorder(X10762))&(hAPP(c_SetInterval_Oord__class_OatMost(X10762),X10760)!=hAPP(c_SetInterval_Oord__class_OatMost(X10762),X10761)|X10760=X10761|~class_Orderings_Olinorder(X10762))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__eq__iff])])])). 6.97/7.23 fof(c_0_9153, plain, ![X6053, X6054]:(~class_Orderings_Olinorder(X6054)|(~c_List_Olinorder__class_Osorted(X6054,X6053)|c_List_Olinorder__class_Osorted(X6054,c_List_Oremdups(X6054,X6053)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__remdups])])])). 6.97/7.23 fof(c_0_9154, plain, ![X9089, X9090]:(~class_Divides_Osemiring__div(X9090)|c_Divides_Odiv__class_Omod(X9090,X9089,c_Groups_Ozero__class_Ozero(X9090))=X9089), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__by__0])])). 6.97/7.23 fof(c_0_9155, plain, ![X3260, X3261, X3262]:((X3261!=X3260|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3262),X3261),X3260)=c_Groups_Ozero__class_Ozero(X3262)|~class_Groups_Ogroup__add(X3262))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3262),X3261),X3260)!=c_Groups_Ozero__class_Ozero(X3262)|X3261=X3260|~class_Groups_Ogroup__add(X3262))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_right__minus__eq])])])])). 6.97/7.23 cnf(c_0_9156, plain, (c_Groups_Ozero__class_Ozero(X2)=hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)|X1!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~class_Int_Oring__char__0(X2)), inference(split_conjunct,[status(thm)],[c_0_5457])). 6.97/7.23 fof(c_0_9157, plain, ![X11638, X11639]:(hBOOL(hAPP(hAPP(c_fimplies,X11638),X11639))|~hBOOL(X11639)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fimplies__2])])). 6.97/7.23 fof(c_0_9158, plain, ![X1593, X1594]:(hBOOL(hAPP(hAPP(c_fdisj,X1594),X1593))|~hBOOL(X1594)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fdisj__1])])). 6.97/7.23 fof(c_0_9159, plain, ![X11607, X11608]:(~hBOOL(X11608)|hBOOL(hAPP(hAPP(c_fdisj,X11607),X11608))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fdisj__2])])). 6.97/7.23 cnf(c_0_9160, 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_5458])). 6.97/7.23 fof(c_0_9161, plain, ![X13474, X13475, X13476, X13477, X13478, X13479]:(((X13476=X13474|c_Nitpick_Opair__box_OPairBox(X13479,X13478,X13475,X13474)!=c_Nitpick_Opair__box_OPairBox(X13479,X13478,X13477,X13476))&(X13477=X13475|c_Nitpick_Opair__box_OPairBox(X13479,X13478,X13475,X13474)!=c_Nitpick_Opair__box_OPairBox(X13479,X13478,X13477,X13476)))&(X13476!=X13474|X13477!=X13475|c_Nitpick_Opair__box_OPairBox(X13479,X13478,X13475,X13474)=c_Nitpick_Opair__box_OPairBox(X13479,X13478,X13477,X13476))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__box_Oinject])])])). 6.97/7.23 fof(c_0_9162, plain, ![X7670, X7671]:((c_Groups_Ozero__class_Ozero(X7671)!=hAPP(c_Groups_Oabs__class_Oabs(X7671),X7670)|c_Groups_Ozero__class_Ozero(X7671)=X7670|~class_Groups_Oordered__ab__group__add__abs(X7671))&(c_Groups_Ozero__class_Ozero(X7671)!=X7670|c_Groups_Ozero__class_Ozero(X7671)=hAPP(c_Groups_Oabs__class_Oabs(X7671),X7670)|~class_Groups_Oordered__ab__group__add__abs(X7671))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__eq__0])])])). 6.97/7.23 fof(c_0_9163, plain, ![X5900, X5901]:((c_Groups_Ozero__class_Ozero(X5901)!=X5900|c_Groups_Ozero__class_Ozero(X5901)=hAPP(c_Groups_Ouminus__class_Ouminus(X5901),X5900)|~class_Groups_Ogroup__add(X5901))&(c_Groups_Ozero__class_Ozero(X5901)!=hAPP(c_Groups_Ouminus__class_Ouminus(X5901),X5900)|c_Groups_Ozero__class_Ozero(X5901)=X5900|~class_Groups_Ogroup__add(X5901))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__0__iff__equal])])])). 6.97/7.23 fof(c_0_9164, plain, ![X2021, X2022]:(~c_Nat__Transfer_Ois__nat(X2022)|(~c_Nat__Transfer_Ois__nat(X2021)|c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X2022,X2021)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Divides_Otransfer__int__nat__function__closures_I2_J])])])). 6.97/7.23 fof(c_0_9165, plain, ![X12212, X12213, X12215, X12216, X12217]:((~hBOOL(hAPP(c_Wellfounded_Oaccp(X12213,X12212),esk407_2(X12212,X12213)))|c_Wellfounded_OwfP(X12213,X12212))&(~c_Wellfounded_OwfP(X12216,X12215)|hBOOL(hAPP(c_Wellfounded_Oaccp(X12216,X12215),X12217)))), 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])])])])])). 6.97/7.23 cnf(c_0_9166, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)=X2|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_5459])). 6.97/7.23 fof(c_0_9167, plain, ![X15922, X15923, X15924]:((X15923!=c_List_Olist_ONil(X15924)|c_List_Olist_ONil(X15924)!=X15922|c_List_Olist_ONil(X15924)=hAPP(hAPP(c_List_Oappend(X15924),X15923),X15922))&((X15923=c_List_Olist_ONil(X15924)|c_List_Olist_ONil(X15924)!=hAPP(hAPP(c_List_Oappend(X15924),X15923),X15922))&(c_List_Olist_ONil(X15924)=X15922|c_List_Olist_ONil(X15924)!=hAPP(hAPP(c_List_Oappend(X15924),X15923),X15922)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__is__Nil__conv])])])). 6.97/7.23 fof(c_0_9168, plain, ![X14613, X14614, X14615]:(((c_List_Olist_ONil(X14615)=X14614|c_List_Olist_ONil(X14615)!=hAPP(hAPP(c_List_Oappend(X14615),X14614),X14613))&(X14613=c_List_Olist_ONil(X14615)|c_List_Olist_ONil(X14615)!=hAPP(hAPP(c_List_Oappend(X14615),X14614),X14613)))&(c_List_Olist_ONil(X14615)!=X14614|X14613!=c_List_Olist_ONil(X14615)|c_List_Olist_ONil(X14615)=hAPP(hAPP(c_List_Oappend(X14615),X14614),X14613))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nil__is__append__conv])])])). 6.97/7.23 fof(c_0_9169, plain, ![X10162, X10163]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X10162|X10163!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10163),X10162))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X10162|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10163),X10162))&(X10163=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10163),X10162)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__is__0])])])). 6.97/7.23 fof(c_0_9170, plain, ![X6837, X6838]:(~hBOOL(hAPP(hAPP(c_fdisj,X6838),X6837))|hBOOL(X6837)|hBOOL(X6838)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fdisj__3])])). 6.97/7.23 fof(c_0_9171, plain, ![X10566]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10566))|c_Nat__Transfer_Ois__nat(X10566))&(~c_Nat__Transfer_Ois__nat(X10566)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10566)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_is__nat__def])])). 6.97/7.23 fof(c_0_9172, plain, ![X5916]:(~class_Rings_Olinordered__semidom(X5916)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5916),c_Groups_Oone__class_Oone(X5916)),c_Groups_Ozero__class_Ozero(X5916)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__one__less__zero])])])). 6.97/7.23 fof(c_0_9173, plain, ![X15609]:(~class_Rings_Olinordered__semidom(X15609)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15609),c_Groups_Oone__class_Oone(X15609)),c_Groups_Ozero__class_Ozero(X15609)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__one__le__zero])])])). 6.97/7.23 fof(c_0_9174, plain, ![X5832, X5833]:(~class_Divides_Osemiring__div(X5833)|c_Divides_Odiv__class_Omod(X5833,X5832,X5832)=c_Groups_Ozero__class_Ozero(X5833)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__self])])). 6.97/7.23 fof(c_0_9175, plain, ![X14341, X14342, X14343]:((X14342!=X14341|hAPP(c_List_Orev(X14343),X14342)=hAPP(c_List_Orev(X14343),X14341))&(hAPP(c_List_Orev(X14343),X14342)!=hAPP(c_List_Orev(X14343),X14341)|X14342=X14341)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__is__rev__conv])])). 6.97/7.23 fof(c_0_9176, plain, ![X15375]:(~class_Rings_Oring__1(X15375)|c_Groups_Oone__class_Oone(X15375)=hAPP(c_Int_Oring__1__class_Oof__int(X15375),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])])])). 6.97/7.23 fof(c_0_9177, plain, ![X9100, X9101]:((X9101!=X9100|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X9100)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X9101))&(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X9100)!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X9101)|X9101=X9100)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__int__eq])])). 6.97/7.23 cnf(c_0_9178, plain, (c_Groups_Ozero__class_Ozero(X1)=c_Groups_Osgn__class_Osgn(X1,X2)|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_5460])). 6.97/7.23 fof(c_0_9179, plain, ![X13648, X13649, X13650]:(~class_Orderings_Oorder(X13650)|~class_Orderings_Oorder(X13649)|(~c_Orderings_Oorder__class_Ostrict__mono(X13649,X13650,X13648)|c_Orderings_Oorder__class_Omono(X13649,X13650,X13648))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_strict__mono__mono])])])). 6.97/7.23 fof(c_0_9180, plain, ![X1609, X1610, X1611, X1612]:((~c_List_Olist__all2(X1612,X1611,X1610,c_List_Olist_ONil(X1612),X1609)|c_List_Olist_ONil(X1611)=X1609)&(c_List_Olist_ONil(X1611)!=X1609|c_List_Olist__all2(X1612,X1611,X1610,c_List_Olist_ONil(X1612),X1609))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__Nil])])). 6.97/7.23 fof(c_0_9181, plain, ![X9798, X9799, X9800]:((X9800!=hAPP(hAPP(c_List_Oappend(X9799),X9800),X9798)|c_List_Olist_ONil(X9799)=X9798)&(c_List_Olist_ONil(X9799)!=X9798|X9800=hAPP(hAPP(c_List_Oappend(X9799),X9800),X9798))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__append__conv])])). 6.97/7.23 fof(c_0_9182, plain, ![X3718, X3719, X3720]:((X3718!=hAPP(hAPP(c_List_Oappend(X3720),X3719),X3718)|X3719=c_List_Olist_ONil(X3720))&(X3719!=c_List_Olist_ONil(X3720)|X3718=hAPP(hAPP(c_List_Oappend(X3720),X3719),X3718))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__self__conv2])])). 6.97/7.23 fof(c_0_9183, plain, ![X15122, X15123]:((X15122!=c_List_Olist_ONil(X15123)|c_Orderings_Obot__class_Obot(tc_fun(X15123,tc_HOL_Obool))=hAPP(c_List_Oset(X15123),X15122))&(c_Orderings_Obot__class_Obot(tc_fun(X15123,tc_HOL_Obool))!=hAPP(c_List_Oset(X15123),X15122)|X15122=c_List_Olist_ONil(X15123))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__empty2])])). 6.97/7.23 fof(c_0_9184, plain, ![X13037, X13038]:(X13038!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13038),X13037)|X13037=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])])). 6.97/7.23 fof(c_0_9185, plain, ![X8771, X8772]:(~class_Finite__Set_Ofinite(X8772)|hBOOL(hAPP(c_Finite__Set_Ofinite(X8772),X8771))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__code])])). 6.97/7.23 fof(c_0_9186, plain, ![X8887, X8888]:(~c_Wellfounded_Oacyclic(X8888,X8887)|c_Relation_Oantisym(X8888,c_Transitive__Closure_Ortrancl(X8888,X8887))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_acyclic__impl__antisym__rtrancl])])])). 6.97/7.23 fof(c_0_9187, plain, ![X3898, X3899, X3900, X3901, X3902]:(((X3898=X3900|c_Lazy__Sequence_Olazy__sequence_OInsert(X3902,X3899,X3898)!=c_Lazy__Sequence_Olazy__sequence_OInsert(X3902,X3901,X3900))&(X3899=X3901|c_Lazy__Sequence_Olazy__sequence_OInsert(X3902,X3899,X3898)!=c_Lazy__Sequence_Olazy__sequence_OInsert(X3902,X3901,X3900)))&(X3898!=X3900|X3899!=X3901|c_Lazy__Sequence_Olazy__sequence_OInsert(X3902,X3899,X3898)=c_Lazy__Sequence_Olazy__sequence_OInsert(X3902,X3901,X3900))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lazy__sequence_Oinject])])])). 6.97/7.23 fof(c_0_9188, plain, ![X11702, X11703]:(~c_Relation_Osym(X11703,X11702)|c_Relation_Osym(X11703,c_Transitive__Closure_Ortrancl(X11703,X11702))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__rtrancl])])). 6.97/7.23 fof(c_0_9189, plain, ![X9857, X9858]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9858)),X9857)|c_List_Olist_ONil(X9858)=X9857)&(c_List_Olist_ONil(X9858)!=X9857|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9858)),X9857))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__0__conv])])). 6.97/7.23 fof(c_0_9190, plain, ![X7245]:(~class_Orderings_Oord(X7245)|c_Orderings_Oord_Omin(X7245,c_Orderings_Oord__class_Oless__eq(X7245))=c_Orderings_Oord__class_Omin(X7245)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__ord__min])])). 6.97/7.23 fof(c_0_9191, plain, ![X15055]:(~class_Groups_Osgn__if(X15055)|c_Groups_Osgn__class_Osgn(X15055,c_Groups_Ozero__class_Ozero(X15055))=c_Groups_Ozero__class_Ozero(X15055)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sgn0])])])). 6.97/7.23 fof(c_0_9192, plain, ![X8247, X8248]:(~c_Nat__Transfer_Ois__nat(X8248)|c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X8248,X8247))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SetInterval_Otransfer__int__nat__set__function__closures])])])). 6.97/7.23 fof(c_0_9193, plain, ![X5682]:(~class_Orderings_Olinorder(X5682)|c_Finite__Set_Ofun__left__comm__idem(X5682,X5682,c_Orderings_Oord__class_Omax(X5682))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofun__left__comm__idem__sup])])). 6.97/7.23 fof(c_0_9194, plain, ![X11663]:(~class_Orderings_Olinorder(X11663)|c_Finite__Set_Ofun__left__comm__idem(X11663,X11663,c_Orderings_Oord__class_Omin(X11663))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ofun__left__comm__idem__inf])])])). 6.97/7.23 cnf(c_0_9195, plain, (~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|X3!=X2), inference(split_conjunct,[status(thm)],[c_0_5461])). 6.97/7.23 fof(c_0_9196, plain, ![X11676]:(~class_Orderings_Oord(X11676)|c_Orderings_Oord__class_Omax(X11676)=c_Orderings_Oord_Omax(X11676,c_Orderings_Oord__class_Oless__eq(X11676))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ord__max])])). 6.97/7.23 fof(c_0_9197, plain, ![X12503]:(~class_Lattices_Osemilattice__inf(X12503)|c_Finite__Set_Ofun__left__comm__idem(X12503,X12503,c_Lattices_Osemilattice__inf__class_Oinf(X12503))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__inf])])). 6.97/7.23 fof(c_0_9198, plain, ![X2043]:(~class_Lattices_Oab__semigroup__idem__mult(X2043)|c_Finite__Set_Ofun__left__comm__idem(X2043,X2043,c_Groups_Otimes__class_Otimes(X2043))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm__idem])])])). 6.97/7.23 fof(c_0_9199, plain, ![X6932]:(~class_Lattices_Osemilattice__sup(X6932)|c_Finite__Set_Ofun__left__comm__idem(X6932,X6932,c_Lattices_Osemilattice__sup__class_Osup(X6932))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm__idem__sup])])])). 6.97/7.23 fof(c_0_9200, plain, ![X2696]:(~class_Groups_Oab__semigroup__mult(X2696)|c_Finite__Set_Ofun__left__comm(X2696,X2696,c_Groups_Otimes__class_Otimes(X2696))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm])])])). 6.97/7.23 cnf(c_0_9201, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|X3!=X2|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5462])). 6.97/7.23 fof(c_0_9202, plain, ![X1815]:((~c_List_Onat__list(X1815)|c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X1815)))&(~c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X1815))|c_List_Onat__list(X1815))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__list__def])])). 6.97/7.23 fof(c_0_9203, plain, ![X8431, X8432]:((~hBOOL(hAPP(c_List_Odistinct(X8432),X8431))|X8431=c_List_Oremdups(X8432,X8431))&(X8431!=c_List_Oremdups(X8432,X8431)|hBOOL(hAPP(c_List_Odistinct(X8432),X8431)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remdups__id__iff__distinct])])). 6.97/7.23 fof(c_0_9204, plain, ![X14771, X14772]:(~class_Lazy__Sequence_Osmall__lazy(X14772)|~class_Lazy__Sequence_Osmall__lazy(X14771)|class_Lazy__Sequence_Osmall__lazy(tc_prod(X14772,X14771))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Lazy__Sequence_Osmall__lazy])])). 6.97/7.23 fof(c_0_9205, plain, ![X7262, X7263]:(~c_Nat__Transfer_Ois__nat(X7263)|(~c_Nat__Transfer_Ois__nat(X7262)|c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X7263,X7262)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J])])])). 6.97/7.23 fof(c_0_9206, plain, ![X8660, X8661]:(~class_Finite__Set_Ofinite(X8660)|~class_Finite__Set_Ofinite(X8661)|class_Finite__Set_Ofinite(tc_sum(X8661,X8660))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_sum__Finite__Set_Ofinite])])). 6.97/7.23 fof(c_0_9207, plain, ![X14493, X14494]:(~class_Finite__Set_Ofinite(X14493)|~class_Finite__Set_Ofinite(X14494)|class_Finite__Set_Ofinite(tc_prod(X14494,X14493))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_prod__Finite__Set_Ofinite])])])). 6.97/7.23 fof(c_0_9208, plain, ![X1392, X1393]:(~class_Finite__Set_Ofinite(X1393)|~class_Finite__Set_Ofinite(X1392)|class_Finite__Set_Ofinite(tc_fun(X1393,X1392))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Finite__Set_Ofinite])])])). 6.97/7.23 fof(c_0_9209, plain, ![X17005, X17006]:(~class_Enum_Oenum(X17006)|~class_Enum_Oenum(X17005)|class_Enum_Oenum(tc_sum(X17006,X17005))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_sum__Enum_Oenum])])])). 6.97/7.23 cnf(c_0_9210, plain, (c_Int_OPls=X1|c_Int_OPls!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)), inference(rw,[status(thm)],[c_0_5463, c_0_4410])). 6.97/7.23 fof(c_0_9211, plain, ![X15740, X15741]:(~class_Enum_Oenum(X15740)|~class_Enum_Oenum(X15741)|class_Enum_Oenum(tc_prod(X15741,X15740))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_prod__Enum_Oenum])])])). 6.97/7.23 fof(c_0_9212, plain, ![X15692, X15693]:(~class_Enum_Oenum(X15693)|~class_Enum_Oenum(X15692)|class_Enum_Oenum(tc_fun(X15693,X15692))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Enum_Oenum])])). 6.97/7.23 fof(c_0_9213, plain, ![X3251, X3252, X3253, X3254, X3255]:(~class_Orderings_Olinorder(X3255)|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X3254,X3255,X3253),X3252),X3251)!=c_List_Olist_ONil(X3254)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__not__Nil])])). 6.97/7.23 fof(c_0_9214, plain, ![X3694]:(~class_Rings_Osemiring__1(X3694)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3694),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(X3694)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__1])])])). 6.97/7.23 fof(c_0_9215, plain, ![X13155, X13156]:(hBOOL(X13155)|~hBOOL(X13156)|~hBOOL(hAPP(hAPP(c_fimplies,X13156),X13155))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fimplies__3])])). 6.97/7.23 fof(c_0_9216, plain, ![X8592, X8593]:((~c_Predicate_Oreflp(X8593,X8592)|~c_Predicate_Osymp(X8593,X8592)|~c_Predicate_Otransp(X8593,X8592)|c_Equiv__Relations_Oequivp(X8593,X8592))&(((c_Predicate_Oreflp(X8593,X8592)|~c_Equiv__Relations_Oequivp(X8593,X8592))&(c_Predicate_Osymp(X8593,X8592)|~c_Equiv__Relations_Oequivp(X8593,X8592)))&(c_Predicate_Otransp(X8593,X8592)|~c_Equiv__Relations_Oequivp(X8593,X8592)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__reflp__symp__transp])])])). 6.97/7.23 fof(c_0_9217, plain, ![X8547]:(~class_Rings_Oring__1(X8547)|hAPP(c_Int_Oring__1__class_Oof__int(X8547),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(X8547)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__0])])). 6.97/7.23 fof(c_0_9218, plain, ![X16350]:(~class_Rings_Osemiring__1(X16350)|c_Groups_Ozero__class_Ozero(X16350)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X16350),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__0])])). 6.97/7.23 fof(c_0_9219, plain, ![X7281, X7282, X7283]:((c_List_Oreplicate(X7283,X7282,X7281)!=c_List_Olist_ONil(X7283)|X7282=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(X7282!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_List_Oreplicate(X7283,X7282,X7281)=c_List_Olist_ONil(X7283))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_replicate__empty])])). 6.97/7.23 fof(c_0_9220, plain, ![X4614, X4615]:((c_List_Olist_ONil(X4615)!=X4614|c_List_Olist_ONil(X4615)=hAPP(c_List_Orotate1(X4615),X4614))&(c_List_Olist_ONil(X4615)!=hAPP(c_List_Orotate1(X4615),X4614)|c_List_Olist_ONil(X4615)=X4614)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate1__is__Nil__conv])])). 6.97/7.23 fof(c_0_9221, plain, ![X10490, X10491]:((hAPP(c_List_Orev(X10491),X10490)!=c_List_Olist_ONil(X10491)|X10490=c_List_Olist_ONil(X10491))&(X10490!=c_List_Olist_ONil(X10491)|hAPP(c_List_Orev(X10491),X10490)=c_List_Olist_ONil(X10491))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nil__is__rev__conv])])). 6.97/7.23 fof(c_0_9222, plain, ![X6423]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6423)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X6423)&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X6423|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6423))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__eq__0__conv])])). 6.97/7.23 fof(c_0_9223, plain, ![X2119]:(hBOOL(X2119)|hBOOL(hAPP(c_fNot,X2119))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fNot__2])])). 6.97/7.23 fof(c_0_9224, plain, ![X14881, X14882, X14883]:((~c_Fun_Obij__betw(X14883,X14883,c_Fun_Oid(X14883),X14882,X14881)|X14882=X14881)&(X14882!=X14881|c_Fun_Obij__betw(X14883,X14883,c_Fun_Oid(X14883),X14882,X14881))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__id__iff])])). 6.97/7.23 fof(c_0_9225, plain, ![X4371, X4372]:((hAPP(c_Code__Numeral_Onat__of,X4371)!=hAPP(c_Code__Numeral_Onat__of,X4372)|X4372=X4371)&(X4372!=X4371|hAPP(c_Code__Numeral_Onat__of,X4371)=hAPP(c_Code__Numeral_Onat__of,X4372))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral_Onat__of__inject])])). 6.97/7.23 fof(c_0_9226, plain, ![X10529, X10530]:(hAPP(c_Nat_OSuc,X10530)!=hAPP(c_Nat_OSuc,X10529)|X10529=X10530), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Suc__inject])])])). 6.97/7.23 fof(c_0_9227, plain, ![X8736, X8737]:((hAPP(c_Int_ORep__Integ,X8737)!=hAPP(c_Int_ORep__Integ,X8736)|X8736=X8737)&(X8736!=X8737|hAPP(c_Int_ORep__Integ,X8737)=hAPP(c_Int_ORep__Integ,X8736))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Rep__Integ__inject])])). 6.97/7.23 fof(c_0_9228, plain, ![X3266, X3267]:(X3266=X3267|~hBOOL(hAPP(hAPP(c_fequal,X3267),X3266))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fequal__1])])). 6.97/7.23 fof(c_0_9229, plain, ![X4293, X4294]:(~class_Orderings_Opreorder(X4294)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4294),X4293),X4293))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__irrefl])])])). 6.97/7.23 cnf(c_0_9230, plain, (X1=X2|hAPP(c_Code__Numeral_Oof__nat,X1)!=hAPP(c_Code__Numeral_Oof__nat,X2)), inference(split_conjunct,[status(thm)],[c_0_5464])). 6.97/7.23 fof(c_0_9231, plain, ![X9620, X9621]:(~class_Orderings_Otop(X9621)|class_Orderings_Otop(tc_fun(X9620,X9621))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Orderings_Otop])])])). 6.97/7.23 fof(c_0_9232, plain, ![X8311, X8312]:(~class_Lattices_Obounded__lattice(X8312)|class_Lattices_Obounded__lattice__bot(tc_fun(X8311,X8312))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice__bot])])). 6.97/7.23 fof(c_0_9233, plain, ![X7827, X7828]:(~class_Groups_Ominus(X7828)|class_Groups_Ominus(tc_fun(X7827,X7828))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ominus])])). 6.97/7.23 fof(c_0_9234, plain, ![X9377, X9378]:(~class_Groups_Ouminus(X9378)|class_Groups_Ouminus(tc_fun(X9377,X9378))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Groups_Ouminus])])])). 6.97/7.23 fof(c_0_9235, plain, ![X1736, X1737]:(~class_Lattices_Obounded__lattice(X1737)|class_Lattices_Obounded__lattice(tc_fun(X1736,X1737))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice])])). 6.97/7.23 fof(c_0_9236, plain, ![X11287, X11288]:(~class_Orderings_Obot(X11288)|class_Orderings_Obot(tc_fun(X11287,X11288))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Orderings_Obot])])])). 6.97/7.23 fof(c_0_9237, plain, ![X15248, X15249]:(~class_Lattices_Oboolean__algebra(X15249)|class_Lattices_Oboolean__algebra(tc_fun(X15248,X15249))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Lattices_Oboolean__algebra])])])). 6.97/7.23 fof(c_0_9238, plain, ![X13063, X13064]:(~class_Orderings_Oord(X13064)|class_Orderings_Oord(tc_fun(X13063,X13064))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])])). 6.97/7.23 fof(c_0_9239, plain, ![X13870, X13871]:(~class_Lattices_Obounded__lattice(X13871)|class_Lattices_Obounded__lattice__top(tc_fun(X13870,X13871))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice__top])])). 6.97/7.23 fof(c_0_9240, plain, ![X6019, X6020]:(~class_Lattices_Olattice(X6020)|class_Lattices_Osemilattice__inf(tc_fun(X6019,X6020))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Lattices_Osemilattice__inf])])])). 6.97/7.23 fof(c_0_9241, plain, ![X14344, X14345]:(~class_Complete__Lattice_Ocomplete__lattice(X14345)|class_Complete__Lattice_Ocomplete__lattice(tc_fun(X14344,X14345))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Complete__Lattice_Ocomplete__lattice])])])). 6.97/7.23 fof(c_0_9242, plain, ![X16077, X16078]:(~class_Lattices_Olattice(X16078)|class_Lattices_Osemilattice__sup(tc_fun(X16077,X16078))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Lattices_Osemilattice__sup])])])). 6.97/7.23 fof(c_0_9243, plain, ![X2324, X2325]:(~class_Orderings_Opreorder(X2325)|class_Orderings_Opreorder(tc_fun(X2324,X2325))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Orderings_Opreorder])])])). 6.97/7.23 fof(c_0_9244, plain, ![X12991, X12992]:(~class_Orderings_Oorder(X12992)|class_Orderings_Oorder(tc_fun(X12991,X12992))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Orderings_Oorder])])])). 6.97/7.23 fof(c_0_9245, plain, ![X15548, X15549]:(~class_Lattices_Odistrib__lattice(X15549)|class_Lattices_Odistrib__lattice(tc_fun(X15548,X15549))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Odistrib__lattice])])). 6.97/7.23 fof(c_0_9246, plain, ![X7402, X7403]:(hBOOL(X7403)|~hBOOL(hAPP(hAPP(c_fconj,X7403),X7402))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fconj__2])])). 6.97/7.23 fof(c_0_9247, plain, ![X16039, X16040]:(hBOOL(X16039)|~hBOOL(hAPP(hAPP(c_fconj,X16040),X16039))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fconj__3])])). 6.97/7.23 fof(c_0_9248, plain, ![X12045, X12046]:(~class_Lattices_Olattice(X12046)|class_Lattices_Olattice(tc_fun(X12045,X12046))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Lattices_Olattice])])])). 6.97/7.23 fof(c_0_9249, plain, ![X13049]:(~class_Orderings_Olinorder(X13049)|c_List_Olinorder__class_Osorted(X13049,c_List_Olist_ONil(X13049))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted_ONil])])). 6.97/7.23 fof(c_0_9250, plain, ![X7381]:(~class_Rings_Osemiring__1(X7381)|c_Int_Oiszero(X7381,c_Groups_Ozero__class_Ozero(X7381))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_iszero__0])])])). 6.97/7.23 fof(c_0_9251, plain, ![X300, X301]:((~c_Int_Oiszero(X301,X300)|c_Groups_Ozero__class_Ozero(X301)=X300|~class_Rings_Osemiring__1(X301))&(c_Groups_Ozero__class_Ozero(X301)!=X300|c_Int_Oiszero(X301,X300)|~class_Rings_Osemiring__1(X301))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__def])])])). 6.97/7.23 cnf(c_0_9252, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_5465])). 6.97/7.23 fof(c_0_9253, plain, ![X13345, X13346]:((c_List_Olist_ONil(X13346)!=c_List_Oremdups(X13346,X13345)|X13345=c_List_Olist_ONil(X13346))&(X13345!=c_List_Olist_ONil(X13346)|c_List_Olist_ONil(X13346)=c_List_Oremdups(X13346,X13345))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remdups__eq__nil__right__iff])])). 6.97/7.23 fof(c_0_9254, plain, ![X16471]:(~class_Int_Onumber__ring(X16471)|~c_Int_Oiszero(X16471,hAPP(c_Int_Onumber__class_Onumber__of(X16471),c_Int_OMin))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nonzero__number__of__Min])])])). 6.97/7.23 fof(c_0_9255, plain, ![X14448]:(~class_Orderings_Olinorder(X14448)|~class_Lattices_Osemilattice__sup(X14448)|c_Lattices_Osemilattice__sup__class_Osup(X14448)=c_Orderings_Oord__class_Omax(X14448)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__max])])])). 6.97/7.23 fof(c_0_9256, plain, ![X7973]:(~class_Orderings_Olinorder(X7973)|~class_Lattices_Osemilattice__inf(X7973)|c_Lattices_Osemilattice__inf__class_Oinf(X7973)=c_Orderings_Oord__class_Omin(X7973)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__min])])). 6.97/7.23 fof(c_0_9257, plain, ![X15444, X15445]:(~c_Equiv__Relations_Oequivp(X15445,X15444)|c_Equiv__Relations_Opart__equivp(X15445,X15444)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equivp__implies__part__equivp])])])). 6.97/7.23 fof(c_0_9258, plain, ![X2104, X2105]:((c_Predicate_Oreflp(X2105,X2104)|~c_Equiv__Relations_Oequivp(X2105,X2104))&((c_Predicate_Osymp(X2105,X2104)|~c_Equiv__Relations_Oequivp(X2105,X2104))&(c_Predicate_Otransp(X2105,X2104)|~c_Equiv__Relations_Oequivp(X2105,X2104)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equivpE])])])])). 6.97/7.23 fof(c_0_9259, plain, ![X7736, X7737]:(~c_Wellfounded_Owf(X7737,X7736)|c_Wellfounded_Oacyclic(X7737,X7736)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__acyclic])])). 6.97/7.23 fof(c_0_9260, plain, ![X2200]:(~class_Lazy__Sequence_Osmall__lazy(X2200)|class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X2200))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_List__Olist__Lazy__Sequence_Osmall__lazy])])])). 6.97/7.23 fof(c_0_9261, plain, ![X7935]:(~class_Finite__Set_Ofinite(X7935)|class_Finite__Set_Ofinite(tc_Option_Ooption(X7935))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Option__Ooption__Finite__Set_Ofinite])])])). 6.97/7.23 fof(c_0_9262, plain, ![X8110]:(~class_Enum_Oenum(X8110)|class_Enum_Oenum(tc_Option_Ooption(X8110))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Option__Ooption__Enum_Oenum])])])). 6.97/7.23 fof(c_0_9263, plain, ![X12267]:(~hBOOL(X12267)|~hBOOL(hAPP(c_fNot,X12267))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fNot__1])])). 6.97/7.23 fof(c_0_9264, plain, ![X9907]:(~class_Rings_Osemiring__1(X9907)|~c_Int_Oiszero(X9907,c_Groups_Oone__class_Oone(X9907))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__iszero__1])])])). 6.97/7.23 fof(c_0_9265, plain, ![X13060]:(~class_Rings_Ozero__neq__one(X13060)|c_Groups_Ozero__class_Ozero(X13060)!=c_Groups_Oone__class_Oone(X13060)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_one__neq__zero])])])). 6.97/7.23 cnf(c_0_9266, 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_5466])). 6.97/7.23 cnf(c_0_9267, 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_5467])). 6.97/7.23 fof(c_0_9268, plain, ![X2946, X2947, X2948]:~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2948),tc_List_Olist(X2948))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2948),tc_List_Olist(X2948)),c_List_Olist_ONil(X2948)),X2947)),c_List_Olex(X2948,X2946))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nil__notin__lex])])). 6.97/7.23 fof(c_0_9269, plain, ![X1404, X1405, X1406]:~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1406),tc_List_Olist(X1406))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1406),tc_List_Olist(X1406)),c_List_Olist_ONil(X1406)),X1405)),c_List_Olistrel1(X1406,X1404))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__Nil__listrel1])])). 6.97/7.23 fof(c_0_9270, plain, ![X1479, X1480, X1481]:~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1481),tc_List_Olist(X1481))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1481),tc_List_Olist(X1481)),X1480),c_List_Olist_ONil(X1481))),c_List_Olex(X1481,X1479))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nil2__notin__lex])])). 6.97/7.23 fof(c_0_9271, plain, ![X6186, X6187, X6188]:~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6188),tc_List_Olist(X6188))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6188),tc_List_Olist(X6188)),X6187),c_List_Olist_ONil(X6188))),c_List_Olistrel1(X6188,X6186))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__listrel1__Nil])])). 6.97/7.23 fof(c_0_9272, plain, ![X10517, X10518, X10519]:~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10519),tc_List_Olist(X10519))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10519),tc_List_Olist(X10519)),X10518),c_List_Olist_ONil(X10519))),c_List_Olexord(X10519,X10517))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lexord__Nil__right])])). 6.97/7.23 fof(c_0_9273, plain, ![X8703, X8704, X8705]:~hBOOL(hAPP(hAPP(c_member(tc_prod(X8705,X8705)),hAPP(hAPP(c_Product__Type_OPair(X8705,X8705),X8704),X8703)),c_List_Omeasures(X8705,c_List_Olist_ONil(tc_fun(X8705,tc_Nat_Onat))))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_in__measures_I1_J])])). 6.97/7.23 cnf(c_0_9274, plain, (c_Int_OBit1(X1)!=c_Int_OBit0(X2)), inference(split_conjunct,[status(thm)],[c_0_5468])). 6.97/7.23 fof(c_0_9275, plain, ![X11047]:~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,X11047))))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__zle__0__negative])])). 6.97/7.23 fof(c_0_9276, plain, ![X16140, X16141]:~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X16141)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X16140)))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__int__zless__negative])])). 6.97/7.23 cnf(c_0_9277, 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_5331])). 6.97/7.23 cnf(c_0_9278, 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))|hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=X1), inference(split_conjunct,[status(thm)],[c_0_5411])). 6.97/7.23 cnf(c_0_9279, plain, (c_Int_OPls!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(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_5469, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.23 fof(c_0_9280, plain, ![X4387, X4388]:~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4388),X4387)),X4388)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__add__less1])])). 6.97/7.23 fof(c_0_9281, plain, ![X664, X665]:~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X665),X664)),X664)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__add__less2])])). 6.97/7.23 fof(c_0_9282, plain, ![X11045, X11046]:~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X11046,tc_HOL_Obool)),X11045),c_Orderings_Obot__class_Obot(tc_fun(X11046,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__psubset__empty])])). 6.97/7.23 fof(c_0_9283, plain, ![X2807]:~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2807)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_int__less__0__conv])])). 6.97/7.23 fof(c_0_9284, plain, ![X5688, X5689, X5690]:hAPP(c_Set_OPow(X5689),X5688)!=hAPP(c_Set_Oimage(X5689,tc_fun(X5689,tc_HOL_Obool),X5690),X5688), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cantors__paradox])])). 6.97/7.23 fof(c_0_9285, plain, ![X2549, X2550, X2551, X2552]:~hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2552,tc_fun(X2551,tc_HOL_Obool))),X2550),X2549)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bot2E])])). 6.97/7.23 fof(c_0_9286, plain, ![X8688]:~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X8688)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X8688),tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_infinite__UNIV__listI])])). 6.97/7.23 cnf(c_0_9287, plain, (X1!=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool)),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_4570])). 6.97/7.23 cnf(c_0_9288, plain, (hAPP(c_Set_OCollect(X1),X2)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_5427])). 6.97/7.23 fof(c_0_9289, plain, ![X6661, X6662, X6663]:~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X6663,X6662,c_Orderings_Obot__class_Obot(tc_fun(X6663,tc_HOL_Obool))),X6661)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_empty__fold1SetE])])). 6.97/7.23 cnf(c_0_9290, 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_5470, c_0_5435])). 6.97/7.23 fof(c_0_9291, 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])). 6.97/7.23 fof(c_0_9292, 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])). 6.97/7.23 fof(c_0_9293, plain, ![X2821]:~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2821),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__zeroE])])). 6.97/7.23 cnf(c_0_9294, plain, (X1!=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5471])). 6.97/7.23 fof(c_0_9295, plain, ![X2526, X2527, X2528]:hAPP(hAPP(c_Set_Oinsert(X2528),X2527),X2526)!=c_Orderings_Obot__class_Obot(tc_fun(X2528,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_insert__not__empty])). 6.97/7.23 fof(c_0_9296, 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])). 6.97/7.23 cnf(c_0_9297, 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_5472])). 6.97/7.23 cnf(c_0_9298, 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_5473])). 6.97/7.23 cnf(c_0_9299, 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_5474])). 6.97/7.23 fof(c_0_9300, plain, ![X7418, X7419]:c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X7419,tc_HOL_Obool),tc_HOL_Obool))!=hAPP(c_Set_OPow(X7419),X7418), inference(variable_rename,[status(thm)],[fact_Pow__not__empty])). 6.97/7.23 fof(c_0_9301, plain, ![X5662]:~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5662))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__neg__int])])). 6.97/7.23 cnf(c_0_9302, plain, (c_Int_OMin!=c_Int_OBit0(X1)), inference(split_conjunct,[status(thm)],[c_0_5475])). 6.97/7.23 fof(c_0_9303, plain, ![X713]:~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X713),X713)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat])])). 6.97/7.23 fof(c_0_9304, plain, ![X9168, X9169, X9170]:hAPP(hAPP(c_List_Olist_OCons(X9170),X9169),X9168)!=c_List_Olist_ONil(X9170), inference(variable_rename,[status(thm)],[fact_list_Osimps_I3_J])). 6.97/7.23 fof(c_0_9305, plain, ![X14632]:c_Orderings_Obot__class_Obot(tc_fun(X14632,tc_HOL_Obool))!=c_Orderings_Otop__class_Otop(tc_fun(X14632,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_UNIV__not__empty])). 6.97/7.23 fof(c_0_9306, plain, ![X14437, X14438, X14439]:X14439!=hAPP(hAPP(c_List_Olist_OCons(X14438),X14437),X14439), inference(variable_rename,[status(thm)],[fact_not__Cons__self])). 6.97/7.23 fof(c_0_9307, plain, ![X2989, X2990, X2991]:c_Lazy__Sequence_Olazy__sequence_OEmpty(X2991)!=c_Lazy__Sequence_Olazy__sequence_OInsert(X2991,X2990,X2989), inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osimps_I2_J])). 6.97/7.23 fof(c_0_9308, plain, ~hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(fof_simplification,[status(thm)],[fact_not__neg__1])). 6.97/7.23 fof(c_0_9309, plain, ~hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(fof_simplification,[status(thm)],[fact_not__neg__0])). 6.97/7.23 fof(c_0_9310, plain, ![X17374, X17375]:~c_List_Olist__ex1(X17375,X17374,c_List_Olist_ONil(X17375)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__ex1__simps_I1_J])])). 6.97/7.23 fof(c_0_9311, plain, ![X6517, X6518]:~c_List_Olist__ex(X6518,X6517,c_List_Olist_ONil(X6518)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__ex__simps_I2_J])])). 6.97/7.23 fof(c_0_9312, plain, ![X10721]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,X10721), inference(variable_rename,[status(thm)],[fact_Suc__not__Zero])). 6.97/7.23 fof(c_0_9313, plain, ![X3033]:hAPP(c_Nat_OSuc,X3033)!=X3033, inference(variable_rename,[status(thm)],[fact_Suc__n__not__n])). 6.97/7.23 cnf(c_0_9314, plain, (c_Int_OPls!=c_Int_OMin), inference(split_conjunct,[status(thm)],[fact_rel__simps_I40_J])). 6.97/7.23 fof(c_0_9315, plain, ~hBOOL(c_fFalse), inference(fof_simplification,[status(thm)],[help_c__fFalse__1])). 6.97/7.23 fof(c_0_9316, negated_conjecture, ~c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts), inference(fof_simplification,[status(thm)],[c_0_5476])). 6.97/7.24 cnf(c_0_9317, 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_5477, c_0_5174]), c_0_5174])). 6.97/7.24 cnf(c_0_9318, 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_5478, c_0_4471]), c_0_4471])). 6.97/7.24 cnf(c_0_9319, plain, (hAPP(X1,hAPP(c_Set_OCollect(X2),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3,X2),tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OEx(tc_fun(X3,X2))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3,X2),tc_HOL_Obool),tc_fun(tc_fun(X3,X2),tc_HOL_Obool),X2),hAPP(c_COMBS(tc_fun(X3,X2),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X3,X2)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X3,X2),tc_fun(tc_fun(X3,X2),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X3,X2))),X4)))),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_fun(X3,X2),X2),tc_fun(tc_fun(X3,X2),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X3,X2),X2),tc_fun(tc_fun(X3,X2),tc_HOL_Obool)),X2),c_COMBB(X2,tc_HOL_Obool,tc_fun(X3,X2))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X3,X2),X3,X2),c_COMBI(tc_fun(X3,X2))),X5))))))=c_Partial__Function_Ofun__lub(X2,X6,X3,X1,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_5479])). 6.97/7.24 fof(c_0_9320, plain, ![X6268, X6269, X6270, X6271, X6272, X6273]:hAPP(hAPP(c_Product__Type_OSigma(X6272,X6271),hAPP(c_Set_Oimage(X6273,X6272,X6270),X6268)),hAPP(hAPP(c_COMBB(tc_fun(X6273,tc_HOL_Obool),tc_fun(X6271,tc_HOL_Obool),X6272),c_Set_Oimage(X6273,X6271,X6269)),hAPP(hAPP(c_COMBC(X6272,tc_fun(X6273,tc_HOL_Obool),tc_fun(X6273,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6273,tc_HOL_Obool),tc_fun(tc_fun(X6273,tc_HOL_Obool),tc_fun(X6273,tc_HOL_Obool)),X6272),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6273,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X6272,tc_HOL_Obool),tc_fun(X6273,tc_HOL_Obool),X6272),c_Set_Ovimage(X6273,X6272,X6270)),hAPP(hAPP(c_COMBC(X6272,tc_fun(X6272,tc_HOL_Obool),tc_fun(X6272,tc_HOL_Obool)),c_Set_Oinsert(X6272)),c_Orderings_Obot__class_Obot(tc_fun(X6272,tc_HOL_Obool)))))),X6268)))=hAPP(c_Set_Oimage(X6273,tc_prod(X6272,X6271),hAPP(hAPP(c_COMBS(X6273,X6271,tc_prod(X6272,X6271)),hAPP(hAPP(c_COMBB(X6272,tc_fun(X6271,tc_prod(X6272,X6271)),X6273),c_Product__Type_OPair(X6272,X6271)),X6270)),X6269)),X6268), inference(variable_rename,[status(thm)],[fact_image__split__eq__Sigma])). 6.97/7.24 cnf(c_0_9321, plain, (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),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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),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),X2),X3)))),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_5480])). 6.97/7.24 cnf(c_0_9322, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[c_0_5481, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.24 cnf(c_0_9323, 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_5482])). 6.97/7.24 fof(c_0_9324, plain, ![X440, X441, X442, X443]:hAPP(hAPP(c_List_Omap(tc_prod(X443,tc_Nat_Onat),X443),c_Product__Type_Ofst(X443,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X443,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X443,tc_Nat_Onat)),X442),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(X443,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(X443,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(X443,tc_Nat_Onat),X441),X440)))=hAPP(hAPP(c_List_Omap(tc_prod(X443,tc_Nat_Onat),X443),c_Product__Type_Ofst(X443,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X443,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X443,tc_Nat_Onat)),X442),c_Product__Type_Osnd(X443,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(X443,tc_Nat_Onat),X441),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),X440)))), inference(variable_rename,[status(thm)],[fact_sublist__shift__lemma__Suc])). 6.97/7.24 cnf(c_0_9325, plain, (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),X1),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)))), inference(rw,[status(thm)],[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_5483, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.24 fof(c_0_9326, plain, ![X11957, X11958, X11959, X11960, X11961, X11962, X11963, X11964, X11965]:hAPP(hAPP(c_Product__Type_Oscomp(X11965,X11964,X11963,X11962),hAPP(hAPP(c_Product__Type_Oscomp(X11965,X11961,X11960,tc_prod(X11964,X11963)),X11959),X11958)),X11957)=hAPP(hAPP(c_Product__Type_Oscomp(X11965,X11961,X11960,X11962),X11959),hAPP(hAPP(c_COMBC(X11961,tc_fun(X11964,tc_fun(X11963,X11962)),tc_fun(X11960,X11962)),hAPP(hAPP(c_COMBB(tc_fun(X11960,tc_prod(X11964,X11963)),tc_fun(tc_fun(X11964,tc_fun(X11963,X11962)),tc_fun(X11960,X11962)),X11961),c_Product__Type_Oscomp(X11960,X11964,X11963,X11962)),X11958)),X11957)), inference(variable_rename,[status(thm)],[fact_scomp__scomp])). 6.97/7.24 fof(c_0_9327, plain, ![X302, X303, X304, X305, X306]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X306,tc_fun(X305,tc_HOL_Obool)),X304),hAPP(hAPP(c_COMBS(X306,tc_fun(X305,tc_HOL_Obool),tc_fun(X305,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X305,tc_HOL_Obool),tc_fun(tc_fun(X305,tc_HOL_Obool),tc_fun(X305,tc_HOL_Obool)),X306),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X305,tc_HOL_Obool))),X303)),X302))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X305,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X306,tc_fun(X305,tc_HOL_Obool)),X304),X303)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X306,tc_fun(X305,tc_HOL_Obool)),X304),X302)), inference(variable_rename,[status(thm)],[fact_INT__Int__distrib])). 6.97/7.24 cnf(c_0_9328, plain, (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),X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),X2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X3)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),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),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2))))), inference(split_conjunct,[status(thm)],[c_0_5484])). 6.97/7.24 fof(c_0_9329, plain, ![X7030, X7031, X7032, X7033, X7034]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7034,tc_fun(X7033,tc_HOL_Obool)),X7032),hAPP(hAPP(c_COMBS(X7034,tc_fun(X7033,tc_HOL_Obool),tc_fun(X7033,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7033,tc_HOL_Obool),tc_fun(tc_fun(X7033,tc_HOL_Obool),tc_fun(X7033,tc_HOL_Obool)),X7034),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7033,tc_HOL_Obool))),X7031)),X7030))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7033,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7034,tc_fun(X7033,tc_HOL_Obool)),X7032),X7031)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7034,tc_fun(X7033,tc_HOL_Obool)),X7032),X7030)), inference(variable_rename,[status(thm)],[fact_UN__Un__distrib])). 6.97/7.24 fof(c_0_9330, plain, ![X13103, X13104, X13105, X13106, X13107]:hAPP(hAPP(c_Product__Type_OSigma(X13107,X13106),X13105),hAPP(hAPP(c_COMBS(X13107,tc_fun(X13106,tc_HOL_Obool),tc_fun(X13106,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13106,tc_HOL_Obool),tc_fun(tc_fun(X13106,tc_HOL_Obool),tc_fun(X13106,tc_HOL_Obool)),X13107),c_Groups_Ominus__class_Ominus(tc_fun(X13106,tc_HOL_Obool))),X13104)),X13103))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X13107,X13106),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X13107,X13106),X13105),X13104)),hAPP(hAPP(c_Product__Type_OSigma(X13107,X13106),X13105),X13103)), inference(variable_rename,[status(thm)],[fact_Sigma__Diff__distrib2])). 6.97/7.24 fof(c_0_9331, plain, ![X4891, X4892, X4893, X4894, X4895]:hAPP(hAPP(c_Product__Type_OSigma(X4895,X4894),X4893),hAPP(hAPP(c_COMBS(X4895,tc_fun(X4894,tc_HOL_Obool),tc_fun(X4894,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4894,tc_HOL_Obool),tc_fun(tc_fun(X4894,tc_HOL_Obool),tc_fun(X4894,tc_HOL_Obool)),X4895),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4894,tc_HOL_Obool))),X4892)),X4891))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4895,X4894),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X4895,X4894),X4893),X4892)),hAPP(hAPP(c_Product__Type_OSigma(X4895,X4894),X4893),X4891)), inference(variable_rename,[status(thm)],[fact_Sigma__Int__distrib2])). 6.97/7.24 fof(c_0_9332, plain, ![X11146, X11147, X11148, X11149, X11150]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X11150,X11149),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X11150,X11149),X11148),X11147)),hAPP(hAPP(c_Product__Type_OSigma(X11150,X11149),X11148),X11146))=hAPP(hAPP(c_Product__Type_OSigma(X11150,X11149),X11148),hAPP(hAPP(c_COMBS(X11150,tc_fun(X11149,tc_HOL_Obool),tc_fun(X11149,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X11149,tc_HOL_Obool),tc_fun(tc_fun(X11149,tc_HOL_Obool),tc_fun(X11149,tc_HOL_Obool)),X11150),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11149,tc_HOL_Obool))),X11147)),X11146)), inference(variable_rename,[status(thm)],[fact_Sigma__Un__distrib2])). 6.97/7.24 cnf(c_0_9333, 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_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_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)))), inference(rw,[status(thm)],[c_0_5485, c_0_4632])). 6.97/7.24 cnf(c_0_9334, 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_5486, c_0_4978]), ['final']). 6.97/7.24 cnf(c_0_9335, 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_5487])). 6.97/7.24 cnf(c_0_9336, plain, (hAPP(hAPP(c_Product__Type_OSigma(X2,X8),X5),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X2),X6))=hAPP(c_Set_Oimage(tc_prod(X1,X7),tc_prod(X2,X8),c_Product__Type_Omap__pair(X1,X2,X7,X8,X3,X9)),hAPP(hAPP(c_Product__Type_OSigma(X1,X7),X4),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X1),X10)))|hAPP(c_Set_Oimage(X1,X2,X3),X4)!=X5|X6!=hAPP(c_Set_Oimage(X7,X8,X9),X10)), inference(split_conjunct,[status(thm)],[c_0_5488])). 6.97/7.24 cnf(c_0_9337, 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_5489])). 6.97/7.24 cnf(c_0_9338, plain, (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))))=hAPP(c_Set_OCollect(X2),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),hAPP(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))),hAPP(c_Product__Type_OPair(X1,X2),X4))),X3))), inference(split_conjunct,[status(thm)],[c_0_5490])). 6.97/7.24 cnf(c_0_9339, plain, (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),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,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)),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,X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4))),X3)), inference(split_conjunct,[status(thm)],[c_0_5491])). 6.97/7.24 cnf(c_0_9340, 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_5492])). 6.97/7.24 cnf(c_0_9341, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[c_0_5493, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.24 cnf(c_0_9342, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[c_0_5494, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.24 cnf(c_0_9343, 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_5495, c_0_4645]), c_0_4645])). 6.97/7.24 cnf(c_0_9344, plain, (c_List_Ofoldr(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5),X6)=hAPP(hAPP(X3,X4),c_List_Ofoldr(X1,X2,X3,X5,X6))), inference(split_conjunct,[status(thm)],[c_0_5496])). 6.97/7.24 cnf(c_0_9345, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),hAPP(X3,hAPP(c_Product__Type_Ofst(X4,X5),X6))),hAPP(X7,hAPP(c_Product__Type_Osnd(X4,X5),X6)))=hAPP(c_Product__Type_Oapsnd(X5,X2,X1,X7),hAPP(c_Product__Type_Oapfst(X4,X1,X5,X3),X6))), inference(split_conjunct,[status(thm)],[c_0_5497])). 6.97/7.24 cnf(c_0_9346, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),hAPP(X3,hAPP(c_Product__Type_Ofst(X4,X5),X6))),hAPP(X7,hAPP(c_Product__Type_Osnd(X4,X5),X6)))=hAPP(c_Product__Type_Oapfst(X4,X1,X2,X3),hAPP(c_Product__Type_Oapsnd(X5,X2,X4,X7),X6))), inference(split_conjunct,[status(thm)],[c_0_5498])). 6.97/7.24 cnf(c_0_9347, plain, (hAPP(c_Product__Type_Oapsnd(X1,X2,X3,X4),hAPP(c_Product__Type_Oapfst(X5,X3,X1,X6),X7))=hAPP(c_Product__Type_Oapfst(X5,X3,X2,X6),hAPP(c_Product__Type_Oapsnd(X1,X2,X5,X4),X7))), inference(split_conjunct,[status(thm)],[c_0_5499])). 6.97/7.24 fof(c_0_9348, plain, ![X4475, X4476, X4477, X4478, X4479, X4480, X4481]:hAPP(hAPP(c_List_Ozip(X4481,X4480),hAPP(hAPP(c_List_Olist__update(X4481,X4479),X4478),X4477)),hAPP(hAPP(c_List_Olist__update(X4480,X4476),X4478),X4475))=hAPP(hAPP(c_List_Olist__update(tc_prod(X4481,X4480),hAPP(hAPP(c_List_Ozip(X4481,X4480),X4479),X4476)),X4478),hAPP(hAPP(c_Product__Type_OPair(X4481,X4480),X4477),X4475)), inference(variable_rename,[status(thm)],[fact_zip__update])). 6.97/7.24 fof(c_0_9349, plain, ![X11435, X11436, X11437, X11438, X11439, X11440, X11441, X11442, X11443, X11444, X11445]:hAPP(c_Product__Type_Omap__pair(X11445,X11444,X11443,X11442,X11441,X11440),hAPP(c_Product__Type_Omap__pair(X11439,X11445,X11438,X11443,X11437,X11436),X11435))=hAPP(c_Product__Type_Omap__pair(X11439,X11444,X11438,X11442,hAPP(c_Fun_Ocomp(X11445,X11444,X11439,X11441),X11437),hAPP(c_Fun_Ocomp(X11443,X11442,X11438,X11440),X11436)),X11435), inference(variable_rename,[status(thm)],[fact_map__pair_Ocompositionality])). 6.97/7.24 cnf(c_0_9350, 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_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[c_0_5500, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411])). 6.97/7.24 cnf(c_0_9351, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))), inference(split_conjunct,[status(thm)],[c_0_5501]), ['final']). 6.97/7.24 cnf(c_0_9352, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_Orotate(X1,X4),X5))=hAPP(c_List_Orotate(X2,X4),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5))), inference(split_conjunct,[status(thm)],[c_0_5502])). 6.97/7.24 cnf(c_0_9353, 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_5503])). 6.97/7.24 cnf(c_0_9354, 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_5504])). 6.97/7.24 cnf(c_0_9355, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),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),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5505, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.24 cnf(c_0_9356, 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_5506])). 6.97/7.24 fof(c_0_9357, plain, ![X3127, X3128, X3129, X3130, X3131, X3132]:hAPP(hAPP(c_List_Ozip(X3132,X3131),hAPP(hAPP(c_List_Olist_OCons(X3132),X3130),X3129)),hAPP(hAPP(c_List_Olist_OCons(X3131),X3128),X3127))=hAPP(hAPP(c_List_Olist_OCons(tc_prod(X3132,X3131)),hAPP(hAPP(c_Product__Type_OPair(X3132,X3131),X3130),X3128)),hAPP(hAPP(c_List_Ozip(X3132,X3131),X3129),X3127)), inference(variable_rename,[status(thm)],[fact_zip__Cons__Cons])). 6.97/7.24 cnf(c_0_9358, 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_5507])). 6.97/7.24 fof(c_0_9359, plain, ![X3054, X3055, X3056]: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)),X3056)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3055),X3054))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3055),X3056)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3054),X3056)), inference(variable_rename,[status(thm)],[fact_image__add__atLeastLessThan])). 6.97/7.24 fof(c_0_9360, plain, ![X8252, X8253, X8254, X8255, X8256, X8257]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8255,tc_fun(X8256,tc_HOL_Obool)),X8253),hAPP(hAPP(c_COMBB(X8257,tc_fun(X8256,tc_HOL_Obool),X8255),X8252),X8254))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8257,tc_fun(X8256,tc_HOL_Obool)),hAPP(c_Set_Oimage(X8255,X8257,X8254),X8253)),X8252), inference(variable_rename,[status(thm)],[fact_INT__simps_I10_J])). 6.97/7.24 fof(c_0_9361, plain, ![X2518, X2519, X2520, X2521, X2522, X2523]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2521,tc_fun(X2522,tc_HOL_Obool)),X2519),hAPP(hAPP(c_COMBB(X2523,tc_fun(X2522,tc_HOL_Obool),X2521),X2518),X2520))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2523,tc_fun(X2522,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2521,X2523,X2520),X2519)),X2518), inference(variable_rename,[status(thm)],[fact_UN__simps_I10_J])). 6.97/7.24 fof(c_0_9362, plain, ![X6827, X6828, X6829, X6830, X6831]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6830,tc_HOL_Obool)),hAPP(X6827,X6829)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6831,tc_fun(X6830,tc_HOL_Obool)),X6828),X6827))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6831,tc_fun(X6830,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X6831),X6829),X6828)),X6827), inference(variable_rename,[status(thm)],[fact_INT__insert])). 6.97/7.24 fof(c_0_9363, plain, ![X3423, X3424, X3425, X3426, X3427]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3426,tc_HOL_Obool)),hAPP(X3423,X3425)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3427,tc_fun(X3426,tc_HOL_Obool)),X3424),X3423))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3427,tc_fun(X3426,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X3427),X3425),X3424)),X3423), inference(variable_rename,[status(thm)],[fact_UN__insert])). 6.97/7.24 fof(c_0_9364, plain, ![X16119, X16120, X16121, X16122, X16123, X16124, X16125]:hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X16125,X16124,X16123),hAPP(c_Fun_Ocomp(X16122,tc_fun(X16124,X16123),X16125,X16121),X16120)),X16119)=hAPP(hAPP(X16121,hAPP(X16120,hAPP(c_Product__Type_Ofst(X16125,X16124),X16119))),hAPP(c_Product__Type_Osnd(X16125,X16124),X16119)), inference(variable_rename,[status(thm)],[fact_split__comp])). 6.97/7.24 fof(c_0_9365, plain, ![X15144, X15145, X15146, X15147, X15148, X15149]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15146,tc_fun(X15148,tc_HOL_Obool)),hAPP(c_Set_Oimage(X15149,X15146,X15144),X15147)),X15145)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15149,tc_fun(X15148,tc_HOL_Obool)),X15147),hAPP(c_Fun_Ocomp(X15146,tc_fun(X15148,tc_HOL_Obool),X15149,X15145),X15144)), inference(variable_rename,[status(thm)],[fact_UN__o])). 6.97/7.24 fof(c_0_9366, plain, ![X6292, X6293, X6294]: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)),X6294)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X6293,X6292))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6293),X6294),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6292),X6294)), inference(variable_rename,[status(thm)],[fact_image__add__atLeastAtMost])). 6.97/7.24 fof(c_0_9367, plain, ![X17059, X17060, X17061, X17062, X17063, X17064]:hAPP(c_Fun_Ocomp(tc_prod(X17064,X17063),X17064,tc_prod(X17062,X17061),c_Product__Type_Ofst(X17064,X17063)),c_Product__Type_Omap__pair(X17062,X17064,X17061,X17063,X17060,X17059))=hAPP(c_Fun_Ocomp(X17062,X17064,tc_prod(X17062,X17061),X17060),c_Product__Type_Ofst(X17062,X17061)), inference(variable_rename,[status(thm)],[fact_fst__comp__map__pair])). 6.97/7.24 fof(c_0_9368, plain, ![X9007, X9008, X9009, X9010, X9011, X9012]:hAPP(c_Fun_Ocomp(X9009,X9011,tc_prod(X9010,X9009),X9007),c_Product__Type_Osnd(X9010,X9009))=hAPP(c_Fun_Ocomp(tc_prod(X9012,X9011),X9011,tc_prod(X9010,X9009),c_Product__Type_Osnd(X9012,X9011)),c_Product__Type_Omap__pair(X9010,X9012,X9009,X9011,X9008,X9007)), inference(variable_rename,[status(thm)],[fact_snd__comp__map__pair])). 6.97/7.24 fof(c_0_9369, plain, ![X7965, X7966, X7967, X7968, X7969]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7969)),hAPP(c_List_Ofilter(X7969,X7968),hAPP(hAPP(c_List_Omap(X7967,X7969),X7966),X7965)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7967)),hAPP(c_List_Ofilter(X7967,hAPP(c_Fun_Ocomp(X7969,tc_HOL_Obool,X7967,X7968),X7966)),X7965)), inference(variable_rename,[status(thm)],[fact_length__filter__map])). 6.97/7.24 fof(c_0_9370, plain, ![X2336, X2337, X2338, X2339]:c_List_Otranspose(X2339,hAPP(hAPP(c_List_Omap(tc_List_Olist(X2338),tc_List_Olist(X2339)),hAPP(c_List_Omap(X2338,X2339),X2337)),X2336))=hAPP(hAPP(c_List_Omap(tc_List_Olist(X2338),tc_List_Olist(X2339)),hAPP(c_List_Omap(X2338,X2339),X2337)),c_List_Otranspose(X2338,X2336)), inference(variable_rename,[status(thm)],[fact_transpose__map__map])). 6.97/7.24 fof(c_0_9371, plain, ![X3751, X3752, X3753, X3754]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3754,tc_HOL_Obool)),X3752),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3754,tc_HOL_Obool)),X3753),X3751))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3754,tc_HOL_Obool)),X3753),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3754,tc_HOL_Obool)),X3752),X3751)), inference(variable_rename,[status(thm)],[fact_Int__left__commute])). 6.97/7.24 fof(c_0_9372, plain, ![X12446, X12447, X12448, X12449]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12449,tc_HOL_Obool)),X12447),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12449,tc_HOL_Obool)),X12448),X12446))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12449,tc_HOL_Obool)),X12448),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12449,tc_HOL_Obool)),X12447),X12446)), inference(variable_rename,[status(thm)],[fact_Un__left__commute])). 6.97/7.24 fof(c_0_9373, plain, ![X8996, X8997]:hAPP(hAPP(c_List_Omap(X8997,tc_prod(X8997,X8997)),hAPP(hAPP(c_COMBS(X8997,X8997,tc_prod(X8997,X8997)),c_Product__Type_OPair(X8997,X8997)),c_COMBI(X8997))),X8996)=hAPP(hAPP(c_List_Ozip(X8997,X8997),X8996),X8996), inference(variable_rename,[status(thm)],[fact_zip__same__conv__map])). 6.97/7.24 cnf(c_0_9374, plain, (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))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oconcat(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5508])). 6.97/7.24 fof(c_0_9375, plain, ![X17587, X17588, X17589, X17590, X17591, X17592]:hAPP(hAPP(c_List_Omap(X17592,X17591),X17590),hAPP(hAPP(c_List_Olist__update(X17592,X17589),X17588),X17587))=hAPP(hAPP(c_List_Olist__update(X17591,hAPP(hAPP(c_List_Omap(X17592,X17591),X17590),X17589)),X17588),hAPP(X17590,X17587)), inference(variable_rename,[status(thm)],[fact_map__update])). 6.97/7.24 cnf(c_0_9376, 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_5509])). 6.97/7.24 cnf(c_0_9377, 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_5510])). 6.97/7.24 cnf(c_0_9378, 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_5511])). 6.97/7.24 cnf(c_0_9379, plain, (hAPP(c_Relation_ORange(X1,X2),hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3)))=hAPP(c_Set_OCollect(X2),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(split_conjunct,[status(thm)],[c_0_5512])). 6.97/7.24 fof(c_0_9380, plain, ![X8060, X8061, X8062, X8063, X8064, X8065, X8066]:c_Fun_Ofun__upd(X8064,X8065,hAPP(c_Fun_Ocomp(X8066,X8065,X8064,X8063),X8062),X8061,hAPP(X8063,X8060))=hAPP(c_Fun_Ocomp(X8066,X8065,X8064,X8063),c_Fun_Ofun__upd(X8064,X8066,X8062,X8061,X8060)), inference(variable_rename,[status(thm)],[fact_fun__upd__comp])). 6.97/7.24 fof(c_0_9381, plain, ![X1094, X1095, X1096, X1097, X1098, X1099, X1100]:hAPP(c_Fun_Ocomp(X1096,X1099,X1098,hAPP(c_Fun_Ocomp(X1100,X1099,X1096,X1097),X1095)),X1094)=hAPP(c_Fun_Ocomp(X1100,X1099,X1098,X1097),hAPP(c_Fun_Ocomp(X1096,X1100,X1098,X1095),X1094)), inference(variable_rename,[status(thm)],[fact_o__assoc])). 6.97/7.24 fof(c_0_9382, plain, ![X4918, X4919, X4920]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X4920,tc_HOL_Obool),tc_fun(X4920,tc_HOL_Obool)),X4918),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4920,tc_HOL_Obool)),X4919))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4920,tc_HOL_Obool)),X4919),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4920,tc_HOL_Obool),X4918)), inference(variable_rename,[status(thm)],[fact_Un__Inter])). 6.97/7.24 fof(c_0_9383, plain, ![X16263, X16264, X16265]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X16265,tc_HOL_Obool),tc_fun(X16265,tc_HOL_Obool)),X16263),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16265,tc_HOL_Obool)),X16264))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16265,tc_HOL_Obool)),X16264),c_Complete__Lattice_OSup__class_OSup(tc_fun(X16265,tc_HOL_Obool),X16263)), inference(variable_rename,[status(thm)],[fact_Int__Union])). 6.97/7.24 fof(c_0_9384, plain, ![X13514, X13515, X13516]:hAPP(c_Relation_ODomain(X13516,X13515),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X13516,X13515),tc_HOL_Obool),X13514))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X13516,X13515),tc_HOL_Obool),tc_fun(X13516,tc_HOL_Obool)),X13514),c_Relation_ODomain(X13516,X13515)), inference(variable_rename,[status(thm)],[fact_Domain__Union])). 6.97/7.24 fof(c_0_9385, plain, ![X5238, X5239, X5240]:hAPP(c_Relation_ORange(X5240,X5239),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X5240,X5239),tc_HOL_Obool),X5238))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X5240,X5239),tc_HOL_Obool),tc_fun(X5239,tc_HOL_Obool)),X5238),c_Relation_ORange(X5240,X5239)), inference(variable_rename,[status(thm)],[fact_Range__Union])). 6.97/7.24 fof(c_0_9386, plain, ![X2601, X2602, X2603, X2604, X2605]:hAPP(hAPP(c_List_Omap(X2605,X2604),X2603),hAPP(hAPP(c_List_Olist_OCons(X2605),X2602),X2601))=hAPP(hAPP(c_List_Olist_OCons(X2604),hAPP(X2603,X2602)),hAPP(hAPP(c_List_Omap(X2605,X2604),X2603),X2601)), inference(variable_rename,[status(thm)],[fact_map_Osimps_I2_J])). 6.97/7.24 fof(c_0_9387, plain, ![X14851, X14852, X14853, X14854]:hAPP(c_Set_Oimage(X14854,X14853,X14852),c_Complete__Lattice_OSup__class_OSup(tc_fun(X14854,tc_HOL_Obool),X14851))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X14854,tc_HOL_Obool),tc_fun(X14853,tc_HOL_Obool)),X14851),c_Set_Oimage(X14854,X14853,X14852)), inference(variable_rename,[status(thm)],[fact_image__Union])). 6.97/7.24 fof(c_0_9388, plain, ![X12081, X12082, X12083, X12084, X12085]:hAPP(hAPP(c_Set_Oinsert(X12084),hAPP(X12083,X12082)),hAPP(c_Set_Oimage(X12085,X12084,X12083),X12081))=hAPP(c_Set_Oimage(X12085,X12084,X12083),hAPP(hAPP(c_Set_Oinsert(X12085),X12082),X12081)), inference(variable_rename,[status(thm)],[fact_image__insert])). 6.97/7.24 fof(c_0_9389, plain, ![X8466, X8467, X8468, X8469]:hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X8469)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(X8469),X8468))=hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(X8469),X8468),X8467),X8466), inference(variable_rename,[status(thm)],[fact_Random__Sequence_Osingle__def])). 6.97/7.24 cnf(c_0_9390, plain, (hAPP(c_Relation_OField(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X2))=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))), inference(split_conjunct,[status(thm)],[c_0_5513])). 6.97/7.24 fof(c_0_9391, plain, ![X653, X654, X655, X656, X657]:hAPP(hAPP(c_List_Omap(X655,X657),X654),hAPP(hAPP(c_List_Odrop(X655),X656),X653))=hAPP(hAPP(c_List_Odrop(X657),X656),hAPP(hAPP(c_List_Omap(X655,X657),X654),X653)), inference(variable_rename,[status(thm)],[fact_drop__map])). 6.97/7.24 fof(c_0_9392, plain, ![X4262, X4263, X4264, X4265, X4266]:hAPP(hAPP(c_List_Otake(X4266),X4265),hAPP(hAPP(c_List_Omap(X4264,X4266),X4263),X4262))=hAPP(hAPP(c_List_Omap(X4264,X4266),X4263),hAPP(hAPP(c_List_Otake(X4264),X4265),X4262)), inference(variable_rename,[status(thm)],[fact_take__map])). 6.97/7.24 cnf(c_0_9393, 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),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)],[c_0_5514, c_0_4410]), c_0_4410])). 6.97/7.24 cnf(c_0_9394, plain, (hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_Set_Ovimage(X2,X4,X5),X6))=hAPP(c_Set_Ovimage(X1,X4,hAPP(c_Fun_Ocomp(X2,X4,X1,X5),X3)),X6)), inference(split_conjunct,[status(thm)],[c_0_5515])). 6.97/7.24 fof(c_0_9395, plain, ![X5330, X5331, X5332, X5333, X5334, X5335]:hAPP(c_Set_Oimage(X5333,X5334,X5332),hAPP(c_Set_Oimage(X5335,X5333,X5331),X5330))=hAPP(c_Set_Oimage(X5335,X5334,hAPP(c_Fun_Ocomp(X5333,X5334,X5335,X5332),X5331)),X5330), inference(variable_rename,[status(thm)],[fact_image__compose])). 6.97/7.24 fof(c_0_9396, plain, ![X15170, X15171, X15172, X15173, X15174, X15175]:hAPP(c_List_Ofoldl(X15175,X15174,X15173,X15172),hAPP(hAPP(c_List_Olist_OCons(X15174),X15171),X15170))=hAPP(c_List_Ofoldl(X15175,X15174,X15173,hAPP(hAPP(X15173,X15172),X15171)),X15170), inference(variable_rename,[status(thm)],[fact_foldl__Cons])). 6.97/7.24 cnf(c_0_9397, plain, (hAPP(c_Set_OPow(X1),X2)=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))), inference(split_conjunct,[status(thm)],[c_0_5516])). 6.97/7.24 fof(c_0_9398, plain, ![X17533, X17534, X17535, X17536, X17537]:c_List_Omaps(X17537,X17536,X17535,hAPP(hAPP(c_List_Olist_OCons(X17537),X17534),X17533))=hAPP(hAPP(c_List_Oappend(X17536),hAPP(X17535,X17534)),c_List_Omaps(X17537,X17536,X17535,X17533)), inference(variable_rename,[status(thm)],[fact_maps__simps_I1_J])). 6.97/7.24 fof(c_0_9399, plain, ![X3632, X3633, X3634, X3635, X3636]:hAPP(hAPP(X3634,X3633),hAPP(hAPP(c_Power_Opower_Opower(X3636,X3635,X3634),X3633),X3632))=hAPP(hAPP(c_Power_Opower_Opower(X3636,X3635,X3634),X3633),hAPP(c_Nat_OSuc,X3632)), inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__Suc])). 6.97/7.24 cnf(c_0_9400, 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_5517])). 6.97/7.24 fof(c_0_9401, plain, ![X10953, X10954, X10955, X10956]:hAPP(c_Relation_Oconverse(X10956,X10956),hAPP(hAPP(c_Relation_Oinv__image(X10955,X10956),X10954),X10953))=hAPP(hAPP(c_Relation_Oinv__image(X10955,X10956),hAPP(c_Relation_Oconverse(X10955,X10955),X10954)),X10953), inference(variable_rename,[status(thm)],[fact_converse__inv__image])). 6.97/7.24 cnf(c_0_9402, plain, (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))=c_Divides_Odivmod__nat(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5518])). 6.97/7.24 cnf(c_0_9403, 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_5519])). 6.97/7.24 fof(c_0_9404, plain, ![X8368, X8369, X8370, X8371, X8372, X8373]:hAPP(hAPP(hAPP(X8370,X8369),X8368),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X8373,X8372,X8371,X8370,X8368))=c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X8373,X8372,X8371,X8370,c_Lazy__Sequence_Olazy__sequence_OInsert(X8372,X8369,X8368)), inference(variable_rename,[status(thm)],[fact_lazy__sequence_Orecs_I2_J])). 6.97/7.24 fof(c_0_9405, plain, ![X4814, X4815, X4816, X4817, X4818]:hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4818,X4817,X4816),X4815),X4814)=hAPP(hAPP(X4815,hAPP(c_Product__Type_Ofst(X4818,X4817),X4814)),hAPP(c_Product__Type_Osnd(X4818,X4817),X4814)), inference(variable_rename,[status(thm)],[fact_prod__case__beta])). 6.97/7.24 fof(c_0_9406, plain, ![X13242, X13243, X13244, X13245]:hAPP(hAPP(c_Set_Oinsert(X13245),X13244),hAPP(hAPP(c_Set_Oinsert(X13245),X13243),X13242))=hAPP(hAPP(c_Set_Oinsert(X13245),X13243),hAPP(hAPP(c_Set_Oinsert(X13245),X13244),X13242)), inference(variable_rename,[status(thm)],[fact_insert__commute])). 6.97/7.24 fof(c_0_9407, plain, ![X12392, X12393, X12394, X12395, X12396]:c_List_Olist_Olist__size(X12396,X12395,hAPP(hAPP(c_List_Omap(X12394,X12396),X12393),X12392))=c_List_Olist_Olist__size(X12394,hAPP(c_Fun_Ocomp(X12396,tc_Nat_Onat,X12394,X12395),X12393),X12392), inference(variable_rename,[status(thm)],[fact_list__size__map])). 6.97/7.24 cnf(c_0_9408, plain, (c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X1,X2,X3,hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X4))))=hAPP(hAPP(X3,X4),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X1,X2,X3,X4))), inference(rw,[status(thm)],[c_0_5520, c_0_5435])). 6.97/7.24 fof(c_0_9409, plain, ![X5115, X5116, X5117, X5118]:(hAPP(c_List_Orotate1(X5117),hAPP(hAPP(c_List_Olist_OCons(X5117),X5116),X5115))=hAPP(hAPP(c_List_Oappend(X5117),X5115),hAPP(hAPP(c_List_Olist_OCons(X5117),X5116),c_List_Olist_ONil(X5117)))&hAPP(c_List_Orotate1(X5118),c_List_Olist_ONil(X5118))=c_List_Olist_ONil(X5118)), inference(variable_rename,[status(thm)],[fact_rotate__simps])). 6.97/7.24 fof(c_0_9410, plain, ![X9225, X9226, X9227, X9228]:hAPP(c_List_Otl(X9227),hAPP(hAPP(c_List_Omap(X9228,X9227),X9226),X9225))=hAPP(hAPP(c_List_Omap(X9228,X9227),X9226),hAPP(c_List_Otl(X9228),X9225)), inference(variable_rename,[status(thm)],[fact_map__tl])). 6.97/7.24 fof(c_0_9411, plain, ![X15142, X15143]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15143),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X15142),X15143))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X15142),c_Divides_Odiv__class_Omod(tc_Int_Oint,X15142,X15143)), inference(variable_rename,[status(thm)],[fact_zmult__div__cancel])). 6.97/7.24 fof(c_0_9412, plain, ![X2026, X2027]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2026),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2026,X2027))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2027),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2026),X2027)), inference(variable_rename,[status(thm)],[fact_mult__div__cancel])). 6.97/7.24 cnf(c_0_9413, plain, (hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X2,X3,X4),X1),X5)=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),X2),c_List_Olist_ONil(X3)),X5)|X1!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[c_0_5521])). 6.97/7.24 fof(c_0_9414, plain, ![X4258, X4259, X4260, X4261]:hAPP(hAPP(c_List_Omap(X4261,X4260),hAPP(c_COMBK(X4260,X4261),X4259)),X4258)=c_List_Oreplicate(X4260,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4261)),X4258),X4259), inference(variable_rename,[status(thm)],[fact_map__replicate__const])). 6.97/7.24 fof(c_0_9415, plain, ![X6169, X6170, X6171, X6172]:hAPP(c_Set_Oimage(X6171,X6172,X6170),hAPP(c_List_Oset(X6171),X6169))=hAPP(c_List_Oset(X6172),hAPP(hAPP(c_List_Omap(X6171,X6172),X6170),X6169)), inference(variable_rename,[status(thm)],[fact_set__map])). 6.97/7.24 fof(c_0_9416, plain, ![X17155, X17156, X17157]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X17156),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X17157),X17155))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X17157),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X17156),X17155)), inference(variable_rename,[status(thm)],[fact_zadd__left__commute])). 6.97/7.24 fof(c_0_9417, plain, ![X13273, X13274, X13275]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13274),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13275),X13273))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13275),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13274),X13273)), inference(variable_rename,[status(thm)],[fact_nat__add__left__commute])). 6.97/7.24 fof(c_0_9418, plain, ![X8729, X8730, X8731, X8732, X8733]:c_Lazy__Sequence_Omap(X8733,X8732,X8731,c_Lazy__Sequence_Olazy__sequence_OInsert(X8733,X8730,X8729))=c_Lazy__Sequence_Olazy__sequence_OInsert(X8732,hAPP(X8731,X8730),c_Lazy__Sequence_Omap(X8733,X8732,X8731,X8729)), inference(variable_rename,[status(thm)],[fact__06])). 6.97/7.24 fof(c_0_9419, plain, ![X16920, X16921, X16922]:c_Random__Sequence_Oempty(X16922,X16921,X16920)=hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X16922)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X16922)), inference(variable_rename,[status(thm)],[fact_Random__Sequence_Oempty__def])). 6.97/7.24 fof(c_0_9420, plain, ![X6362, X6363, X6364, X6365]:hAPP(c_Nat_Onat_Onat__rec(X6365,X6364,X6363),hAPP(c_Nat_OSuc,X6362))=hAPP(hAPP(X6363,X6362),hAPP(c_Nat_Onat_Onat__rec(X6365,X6364,X6363),X6362)), inference(variable_rename,[status(thm)],[fact_nat__rec__Suc])). 6.97/7.24 cnf(c_0_9421, 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_5522])). 6.97/7.24 fof(c_0_9422, plain, ![X13456, X13457, X13458, X13459]:c_List_Obutlast(X13458,hAPP(hAPP(c_List_Omap(X13459,X13458),X13457),X13456))=hAPP(hAPP(c_List_Omap(X13459,X13458),X13457),c_List_Obutlast(X13459,X13456)), inference(variable_rename,[status(thm)],[fact_map__butlast])). 6.97/7.24 fof(c_0_9423, plain, ![X14293, X14294]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X14294)),X14293)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14293),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14294),X14293)), inference(variable_rename,[status(thm)],[fact_mult__Suc])). 6.97/7.24 fof(c_0_9424, plain, ![X10478, X10479, X10480, X10481, X10482, X10483]:hAPP(hAPP(hAPP(c_COMBS(X10483,X10482,X10481),X10480),X10479),X10478)=hAPP(hAPP(X10480,X10478),hAPP(X10479,X10478)), inference(variable_rename,[status(thm)],[help_c__COMBS__1])). 6.97/7.24 fof(c_0_9425, plain, ![X11583, X11584]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11584),hAPP(c_Nat_OSuc,X11583))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11584),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11584),X11583)), inference(variable_rename,[status(thm)],[fact_mult__Suc__right])). 6.97/7.24 fof(c_0_9426, plain, ![X9698, X9699]:c_List_Opartition(X9699,X9698,c_List_Olist_ONil(X9699))=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X9699),tc_List_Olist(X9699)),c_List_Olist_ONil(X9699)),c_List_Olist_ONil(X9699)), inference(variable_rename,[status(thm)],[fact_partition_Osimps_I1_J])). 6.97/7.24 fof(c_0_9427, plain, ![X3239, X3240, X3241]:hAPP(c_List_Orev(X3241),hAPP(c_List_Ofilter(X3241,X3240),X3239))=hAPP(c_List_Ofilter(X3241,X3240),hAPP(c_List_Orev(X3241),X3239)), inference(variable_rename,[status(thm)],[fact_rev__filter])). 6.97/7.24 fof(c_0_9428, plain, ![X8091, X8092]:c_Enum_On__lists(X8092,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X8091)=hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X8092)),c_List_Olist_ONil(X8092)),c_List_Olist_ONil(tc_List_Olist(X8092))), inference(variable_rename,[status(thm)],[fact_n__lists_Osimps_I1_J])). 6.97/7.24 fof(c_0_9429, plain, ![X8336, X8337, X8338, X8339]:c_List_Oremove1(X8339,X8337,c_List_Oremove1(X8339,X8338,X8336))=c_List_Oremove1(X8339,X8338,c_List_Oremove1(X8339,X8337,X8336)), inference(variable_rename,[status(thm)],[fact_remove1__commute])). 6.97/7.24 fof(c_0_9430, plain, ![X10374, X10375]:hAPP(c_Product__Type_Oprod_Oprod__case(X10375,X10374,tc_prod(X10375,X10374)),c_Product__Type_OPair(X10375,X10374))=c_Fun_Oid(tc_prod(X10375,X10374)), inference(variable_rename,[status(thm)],[fact_split__Pair])). 6.97/7.24 fof(c_0_9431, plain, ![X553, X554, X555, X556]:hAPP(c_New__DSequence_Opos__union(X556,X555,X554),X553)=c_Lazy__Sequence_Oappend(X556,hAPP(X555,X553),hAPP(X554,X553)), inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__union__def])). 6.97/7.24 fof(c_0_9432, plain, ![X6433, X6434]:hAPP(c_List_Olexn(X6434,X6433),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(X6434),tc_List_Olist(X6434)),tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_lexn_Osimps_I1_J])). 6.97/7.24 fof(c_0_9433, plain, ![X13384]:hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X13384)),c_List_Olist_ONil(X13384)),c_List_Olist_ONil(tc_List_Olist(X13384)))=c_Enum_Osublists(X13384,c_List_Olist_ONil(X13384)), inference(variable_rename,[status(thm)],[fact_sublists_Osimps_I1_J])). 6.97/7.24 cnf(c_0_9434, 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_5523])). 6.97/7.24 cnf(c_0_9435, 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_5524])). 6.97/7.24 fof(c_0_9436, plain, ![X16351, X16352]:c_FunDef_Orp__inv__image(X16352,X16351)=hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(X16352,X16352),tc_HOL_Obool),tc_fun(tc_prod(X16352,X16352),tc_HOL_Obool),tc_fun(tc_fun(X16351,X16352),tc_prod(tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool),tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(X16352,X16352),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X16352,X16352),tc_HOL_Obool),tc_fun(tc_fun(X16351,X16352),tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X16352,X16352),tc_HOL_Obool),tc_fun(tc_fun(X16351,X16352),tc_prod(tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool),tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(X16351,X16352),tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool)),tc_fun(tc_fun(X16351,X16352),tc_prod(tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool),tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(X16352,X16352),tc_HOL_Obool),tc_fun(tc_fun(X16351,X16352),tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X16352,X16352),tc_HOL_Obool),tc_fun(tc_fun(X16351,X16352),tc_prod(tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool),tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool))))),tc_fun(tc_prod(X16352,X16352),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(X16351,X16352),tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool)),tc_fun(tc_fun(X16351,X16352),tc_prod(tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool),tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool))),tc_fun(tc_prod(X16352,X16352),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X16351,X16352),tc_fun(tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool),tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(X16351,X16352),tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool)),tc_fun(tc_fun(X16351,X16352),tc_prod(tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool),tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool)))),tc_fun(tc_prod(X16352,X16352),tc_HOL_Obool)),c_COMBS(tc_fun(X16351,X16352),tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool),tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X16351,X16352),tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool)),tc_fun(tc_fun(X16351,X16352),tc_fun(tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool),tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool)))),tc_fun(tc_prod(X16352,X16352),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool),tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool))),tc_fun(X16351,X16352)),c_Product__Type_OPair(tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool),tc_fun(tc_prod(X16351,X16351),tc_HOL_Obool)))),c_Relation_Oinv__image(X16352,X16351))))),c_Relation_Oinv__image(X16352,X16351))), inference(variable_rename,[status(thm)],[fact_rp__inv__image__def])). 6.97/7.24 cnf(c_0_9437, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X4),X5)=hAPP(c_Set_OCollect(tc_prod(X1,X3)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X3,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(X2,tc_HOL_Obool)),tc_fun(X3,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X3),c_HOL_OEx(X2))),hAPP(hAPP(c_COMBC(X1,tc_fun(X3,tc_fun(X2,tc_HOL_Obool)),tc_fun(X3,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(X3,tc_fun(X2,tc_HOL_Obool)),tc_fun(X3,tc_fun(X2,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X3)),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(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(X3,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,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(X2,tc_HOL_Obool)),X3),c_COMBC(X2,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X2,X3)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(c_COMBB(tc_prod(X2,X3),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X2,X3)))),hAPP(c_COMBC(X2,X3,tc_prod(X2,X3)),c_Product__Type_OPair(X2,X3))))),X5)))))), inference(split_conjunct,[status(thm)],[c_0_5525])). 6.97/7.24 cnf(c_0_9438, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5526, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.24 fof(c_0_9439, plain, ![X392]: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,X392)),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),X392), inference(variable_rename,[status(thm)],[fact_minus__int__def])). 6.97/7.24 fof(c_0_9440, plain, ![X3345, X3346, X3347, X3348]:c_List_Opartition(X3348,X3347,hAPP(hAPP(c_List_Olist_OCons(X3348),X3346),X3345))=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X3348),tc_List_Olist(X3348),tc_prod(tc_List_Olist(X3348),tc_List_Olist(X3348))),hAPP(hAPP(c_COMBS(tc_List_Olist(X3348),tc_fun(tc_List_Olist(X3348),tc_prod(tc_List_Olist(X3348),tc_List_Olist(X3348))),tc_fun(tc_List_Olist(X3348),tc_prod(tc_List_Olist(X3348),tc_List_Olist(X3348)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X3348),tc_fun(tc_prod(tc_List_Olist(X3348),tc_List_Olist(X3348)),tc_prod(tc_List_Olist(X3348),tc_List_Olist(X3348)))),tc_fun(tc_fun(tc_List_Olist(X3348),tc_prod(tc_List_Olist(X3348),tc_List_Olist(X3348))),tc_fun(tc_List_Olist(X3348),tc_prod(tc_List_Olist(X3348),tc_List_Olist(X3348)))),tc_List_Olist(X3348)),c_COMBS(tc_List_Olist(X3348),tc_prod(tc_List_Olist(X3348),tc_List_Olist(X3348)),tc_prod(tc_List_Olist(X3348),tc_List_Olist(X3348)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X3348),tc_prod(tc_List_Olist(X3348),tc_List_Olist(X3348))),tc_fun(tc_List_Olist(X3348),tc_fun(tc_prod(tc_List_Olist(X3348),tc_List_Olist(X3348)),tc_prod(tc_List_Olist(X3348),tc_List_Olist(X3348)))),tc_List_Olist(X3348)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X3348),tc_List_Olist(X3348)),tc_fun(tc_prod(tc_List_Olist(X3348),tc_List_Olist(X3348)),tc_prod(tc_List_Olist(X3348),tc_List_Olist(X3348))),tc_List_Olist(X3348)),hAPP(c_If(tc_prod(tc_List_Olist(X3348),tc_List_Olist(X3348))),hAPP(X3347,X3346)))),hAPP(hAPP(c_COMBB(tc_List_Olist(X3348),tc_fun(tc_List_Olist(X3348),tc_prod(tc_List_Olist(X3348),tc_List_Olist(X3348))),tc_List_Olist(X3348)),c_Product__Type_OPair(tc_List_Olist(X3348),tc_List_Olist(X3348))),hAPP(c_List_Olist_OCons(X3348),X3346))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X3348),tc_fun(tc_List_Olist(X3348),tc_List_Olist(X3348)),tc_fun(tc_List_Olist(X3348),tc_prod(tc_List_Olist(X3348),tc_List_Olist(X3348)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X3348),tc_prod(tc_List_Olist(X3348),tc_List_Olist(X3348))),tc_fun(tc_fun(tc_List_Olist(X3348),tc_List_Olist(X3348)),tc_fun(tc_List_Olist(X3348),tc_prod(tc_List_Olist(X3348),tc_List_Olist(X3348)))),tc_List_Olist(X3348)),c_COMBB(tc_List_Olist(X3348),tc_prod(tc_List_Olist(X3348),tc_List_Olist(X3348)),tc_List_Olist(X3348))),c_Product__Type_OPair(tc_List_Olist(X3348),tc_List_Olist(X3348)))),hAPP(c_List_Olist_OCons(X3348),X3346)))),c_List_Opartition(X3348,X3347,X3345)), inference(variable_rename,[status(thm)],[fact_partition_Osimps_I2_J])). 6.97/7.24 cnf(c_0_9441, 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_5527])). 6.97/7.24 cnf(c_0_9442, plain, (hAPP(c_Set_OPow(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2))=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)))))), inference(split_conjunct,[status(thm)],[c_0_5528])). 6.97/7.24 cnf(c_0_9443, 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_5529])). 6.97/7.24 cnf(c_0_9444, plain, (c_Nitpick_Oplus__frac(X1,X2,X3)=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)))), 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_5530, c_0_4921]), c_0_4921]), c_0_4921]), c_0_4921]), c_0_4922]), c_0_4922])). 6.97/7.24 fof(c_0_9445, plain, ![X7992, X7993, X7994, X7995]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7995,tc_fun(tc_prod(X7995,X7994),tc_HOL_Obool)),X7993),hAPP(hAPP(c_COMBS(X7995,tc_fun(X7994,tc_fun(tc_prod(X7995,X7994),tc_HOL_Obool)),tc_fun(tc_prod(X7995,X7994),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7994,tc_HOL_Obool),tc_fun(tc_fun(X7994,tc_fun(tc_prod(X7995,X7994),tc_HOL_Obool)),tc_fun(tc_prod(X7995,X7994),tc_HOL_Obool)),X7995),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7994,tc_fun(tc_prod(X7995,X7994),tc_HOL_Obool))),X7992)),hAPP(hAPP(c_COMBC(X7995,tc_fun(tc_prod(X7995,X7994),tc_HOL_Obool),tc_fun(X7994,tc_fun(tc_prod(X7995,X7994),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7994,tc_fun(tc_fun(tc_prod(X7995,X7994),tc_HOL_Obool),tc_fun(tc_prod(X7995,X7994),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X7995,X7994),tc_HOL_Obool),tc_fun(X7994,tc_fun(tc_prod(X7995,X7994),tc_HOL_Obool))),X7995),c_COMBC(X7994,tc_fun(tc_prod(X7995,X7994),tc_HOL_Obool),tc_fun(tc_prod(X7995,X7994),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7994,tc_prod(X7995,X7994)),tc_fun(X7994,tc_fun(tc_fun(tc_prod(X7995,X7994),tc_HOL_Obool),tc_fun(tc_prod(X7995,X7994),tc_HOL_Obool))),X7995),hAPP(c_COMBB(tc_prod(X7995,X7994),tc_fun(tc_fun(tc_prod(X7995,X7994),tc_HOL_Obool),tc_fun(tc_prod(X7995,X7994),tc_HOL_Obool)),X7994),c_Set_Oinsert(tc_prod(X7995,X7994)))),c_Product__Type_OPair(X7995,X7994)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7995,X7994),tc_HOL_Obool)))))=hAPP(hAPP(c_Product__Type_OSigma(X7995,X7994),X7993),X7992), inference(variable_rename,[status(thm)],[fact_Sigma__def])). 6.97/7.24 cnf(c_0_9446, 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),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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),X3)),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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))),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)],[c_0_5531, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.24 cnf(c_0_9447, 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_5532])). 6.97/7.24 cnf(c_0_9448, plain, (hAPP(c_List_Oset(X1),c_List_Osublist(X1,X2,X3))=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)))))), inference(split_conjunct,[status(thm)],[c_0_5533])). 6.97/7.24 cnf(c_0_9449, plain, (hAPP(hAPP(c_Relation_Oinv__image(X1,X2),X3),X4)=hAPP(c_Set_OCollect(tc_prod(X2,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X2,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,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(X2,tc_HOL_Obool)),X2),c_COMBC(X2,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X1)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X1)))),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,X1),tc_fun(X2,tc_prod(X1,X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(tc_fun(X2,X1),tc_fun(X2,tc_prod(X1,X1))),X2),c_COMBB(X1,tc_prod(X1,X1),X2)),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,tc_prod(X1,X1)),X2),c_Product__Type_OPair(X1,X1)),X4))),X4)))),X3)))), inference(split_conjunct,[status(thm)],[c_0_5534])). 6.97/7.24 cnf(c_0_9450, 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_5535, c_0_4645]), c_0_4645])). 6.97/7.24 cnf(c_0_9451, 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_5536, c_0_5537]), c_0_5538]), c_0_5539]), c_0_5065]), ['final']). 6.97/7.24 cnf(c_0_9452, 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_5540, c_0_5537]), c_0_5538]), c_0_5539]), c_0_5065]), ['final']). 6.97/7.24 fof(c_0_9453, plain, ![X11205, X11206, X11207]:c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X11207,tc_Lazy__Sequence_Olazy__sequence(X11207)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X11207,tc_Lazy__Sequence_Olazy__sequence(X11207),tc_Nat_Onat),hAPP(hAPP(c_COMBC(X11207,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X11207),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X11207),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X11207),tc_Nat_Onat)),X11207),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X11207),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X11207),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X11207),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),X11207),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X11207)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(X11207,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X11207),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X11207),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X11207),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X11207),tc_Nat_Onat)),X11207),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(X11207))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),X11207),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X11206))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X11207,X11206))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(X11207),X11205))=hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X11207,X11206),X11205), inference(variable_rename,[status(thm)],[fact_lazy__sequence__size__code])). 6.97/7.24 fof(c_0_9454, plain, ![X14684, X14685, X14686, X14687, X14688]:hAPP(hAPP(c_List_Ozip(X14688,X14687),X14686),hAPP(hAPP(c_List_Olist_OCons(X14687),X14685),X14684))=hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X14688,X14687)),X14688,c_List_Olist_ONil(tc_prod(X14688,X14687)),hAPP(hAPP(c_COMBC(X14688,tc_fun(tc_List_Olist(X14688),tc_List_Olist(tc_prod(X14688,X14687))),tc_fun(tc_List_Olist(X14688),tc_List_Olist(tc_prod(X14688,X14687)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X14688,X14687)),tc_List_Olist(tc_prod(X14688,X14687))),tc_fun(tc_fun(tc_List_Olist(X14688),tc_List_Olist(tc_prod(X14688,X14687))),tc_fun(tc_List_Olist(X14688),tc_List_Olist(tc_prod(X14688,X14687)))),X14688),c_COMBB(tc_List_Olist(tc_prod(X14688,X14687)),tc_List_Olist(tc_prod(X14688,X14687)),tc_List_Olist(X14688))),hAPP(hAPP(c_COMBB(tc_prod(X14688,X14687),tc_fun(tc_List_Olist(tc_prod(X14688,X14687)),tc_List_Olist(tc_prod(X14688,X14687))),X14688),c_List_Olist_OCons(tc_prod(X14688,X14687))),hAPP(hAPP(c_COMBC(X14688,X14687,tc_prod(X14688,X14687)),c_Product__Type_OPair(X14688,X14687)),X14685)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X14688),tc_List_Olist(X14687),tc_List_Olist(tc_prod(X14688,X14687))),c_List_Ozip(X14688,X14687)),X14684))),X14686), inference(variable_rename,[status(thm)],[fact_zip__Cons])). 6.97/7.24 fof(c_0_9455, plain, ![X5244, X5245, X5246, X5247, X5248, X5249, X5250, X5251]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(X5251,X5250),tc_fun(tc_prod(X5249,X5248),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5251,X5250),X5247),hAPP(c_COMBK(tc_fun(X5250,tc_HOL_Obool),X5251),X5246))),hAPP(c_Product__Type_Oprod_Oprod__case(X5251,X5250,tc_fun(tc_prod(X5249,X5248),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X5251,tc_fun(X5250,tc_fun(X5249,tc_fun(X5248,tc_HOL_Obool))),tc_fun(X5250,tc_fun(tc_prod(X5249,X5248),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5249,tc_fun(X5248,tc_HOL_Obool)),tc_fun(tc_prod(X5249,X5248),tc_HOL_Obool)),tc_fun(tc_fun(X5250,tc_fun(X5249,tc_fun(X5248,tc_HOL_Obool))),tc_fun(X5250,tc_fun(tc_prod(X5249,X5248),tc_HOL_Obool))),X5251),c_COMBB(tc_fun(X5249,tc_fun(X5248,tc_HOL_Obool)),tc_fun(tc_prod(X5249,X5248),tc_HOL_Obool),X5250)),hAPP(hAPP(c_COMBB(tc_fun(X5249,tc_HOL_Obool),tc_fun(tc_fun(X5249,tc_fun(X5248,tc_HOL_Obool)),tc_fun(tc_prod(X5249,X5248),tc_HOL_Obool)),X5251),c_Product__Type_OSigma(X5249,X5248)),X5245))),hAPP(hAPP(c_COMBB(tc_fun(X5248,tc_HOL_Obool),tc_fun(X5249,tc_fun(X5248,tc_HOL_Obool)),X5250),c_COMBK(tc_fun(X5248,tc_HOL_Obool),X5249)),X5244))))=hAPP(hAPP(c_Product__Type_OSigma(X5249,X5248),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5251,tc_fun(X5249,tc_HOL_Obool)),X5247),X5245)),hAPP(c_COMBK(tc_fun(X5248,tc_HOL_Obool),X5249),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5250,tc_fun(X5248,tc_HOL_Obool)),X5246),X5244))), inference(variable_rename,[status(thm)],[fact_UN__Times__distrib])). 6.97/7.24 cnf(c_0_9456, plain, (hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4)),X5))=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)),hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),X5))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,X1),tc_Int_Oint),X3),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,X2,X3)),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)))))), inference(rw,[status(thm)],[c_0_5541, c_0_4565])). 6.97/7.24 cnf(c_0_9457, plain, (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)))))=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)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5542, c_0_4632]), c_0_4632])). 6.97/7.24 cnf(c_0_9458, plain, (hAPP(c_List_Oset(X1),X2)=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)))))), inference(split_conjunct,[status(thm)],[c_0_5543])). 6.97/7.24 fof(c_0_9459, plain, ![X9968, X9969, X9970, X9971, X9972, X9973, X9974]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9974,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9973,tc_fun(X9974,tc_HOL_Obool)),X9972),X9971)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9970,tc_fun(X9974,tc_HOL_Obool)),X9969),X9968))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9973,tc_fun(X9974,tc_HOL_Obool)),X9972),hAPP(hAPP(c_COMBB(tc_fun(X9970,tc_fun(X9974,tc_HOL_Obool)),tc_fun(X9974,tc_HOL_Obool),X9973),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9970,tc_fun(X9974,tc_HOL_Obool)),X9969)),hAPP(hAPP(c_COMBC(X9973,tc_fun(X9970,tc_fun(X9974,tc_HOL_Obool)),tc_fun(X9970,tc_fun(X9974,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X9974,tc_HOL_Obool),tc_fun(X9974,tc_HOL_Obool)),tc_fun(tc_fun(X9970,tc_fun(X9974,tc_HOL_Obool)),tc_fun(X9970,tc_fun(X9974,tc_HOL_Obool))),X9973),c_COMBB(tc_fun(X9974,tc_HOL_Obool),tc_fun(X9974,tc_HOL_Obool),X9970)),hAPP(hAPP(c_COMBB(tc_fun(X9974,tc_HOL_Obool),tc_fun(tc_fun(X9974,tc_HOL_Obool),tc_fun(X9974,tc_HOL_Obool)),X9973),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9974,tc_HOL_Obool))),X9971))),X9968))), inference(variable_rename,[status(thm)],[fact_Int__UN__distrib2])). 6.97/7.24 fof(c_0_9460, plain, ![X3059, X3060, X3061, X3062, X3063, X3064, X3065]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3065,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3064,tc_fun(X3065,tc_HOL_Obool)),X3063),X3062)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3061,tc_fun(X3065,tc_HOL_Obool)),X3060),X3059))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3064,tc_fun(X3065,tc_HOL_Obool)),X3063),hAPP(hAPP(c_COMBB(tc_fun(X3061,tc_fun(X3065,tc_HOL_Obool)),tc_fun(X3065,tc_HOL_Obool),X3064),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3061,tc_fun(X3065,tc_HOL_Obool)),X3060)),hAPP(hAPP(c_COMBC(X3064,tc_fun(X3061,tc_fun(X3065,tc_HOL_Obool)),tc_fun(X3061,tc_fun(X3065,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3065,tc_HOL_Obool),tc_fun(X3065,tc_HOL_Obool)),tc_fun(tc_fun(X3061,tc_fun(X3065,tc_HOL_Obool)),tc_fun(X3061,tc_fun(X3065,tc_HOL_Obool))),X3064),c_COMBB(tc_fun(X3065,tc_HOL_Obool),tc_fun(X3065,tc_HOL_Obool),X3061)),hAPP(hAPP(c_COMBB(tc_fun(X3065,tc_HOL_Obool),tc_fun(tc_fun(X3065,tc_HOL_Obool),tc_fun(X3065,tc_HOL_Obool)),X3064),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3065,tc_HOL_Obool))),X3062))),X3059))), inference(variable_rename,[status(thm)],[fact_Un__INT__distrib2])). 6.97/7.24 cnf(c_0_9461, plain, (c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),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(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2)),c_fequal)),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_5544])). 6.97/7.24 cnf(c_0_9462, 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_OCollect(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X2,tc_HOL_Obool)),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),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(tc_fun(X2,tc_HOL_Obool),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)),tc_fun(X2,tc_HOL_Obool)),c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1)),c_fequal)),X4)))))), inference(split_conjunct,[status(thm)],[c_0_5545])). 6.97/7.24 fof(c_0_9463, plain, ![X10398, X10399, X10400, X10401, X10402]:hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X10402,X10401)),X10401,c_List_Olist_ONil(tc_prod(X10402,X10401)),hAPP(hAPP(c_COMBC(X10401,tc_fun(tc_List_Olist(X10401),tc_List_Olist(tc_prod(X10402,X10401))),tc_fun(tc_List_Olist(X10401),tc_List_Olist(tc_prod(X10402,X10401)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X10402,X10401)),tc_List_Olist(tc_prod(X10402,X10401))),tc_fun(tc_fun(tc_List_Olist(X10401),tc_List_Olist(tc_prod(X10402,X10401))),tc_fun(tc_List_Olist(X10401),tc_List_Olist(tc_prod(X10402,X10401)))),X10401),c_COMBB(tc_List_Olist(tc_prod(X10402,X10401)),tc_List_Olist(tc_prod(X10402,X10401)),tc_List_Olist(X10401))),hAPP(hAPP(c_COMBB(tc_prod(X10402,X10401),tc_fun(tc_List_Olist(tc_prod(X10402,X10401)),tc_List_Olist(tc_prod(X10402,X10401))),X10401),c_List_Olist_OCons(tc_prod(X10402,X10401))),hAPP(c_Product__Type_OPair(X10402,X10401),X10400)))),hAPP(c_List_Ozip(X10402,X10401),X10399))),X10398)=hAPP(hAPP(c_List_Ozip(X10402,X10401),hAPP(hAPP(c_List_Olist_OCons(X10402),X10400),X10399)),X10398), inference(variable_rename,[status(thm)],[fact_zip__Cons1])). 6.97/7.24 cnf(c_0_9464, 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_5546])). 6.97/7.24 cnf(c_0_9465, 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_5547])). 6.97/7.24 cnf(c_0_9466, 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_5548])). 6.97/7.24 cnf(c_0_9467, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),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)))),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))))), inference(split_conjunct,[status(thm)],[c_0_5549])). 6.97/7.24 cnf(c_0_9468, 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_5550])). 6.97/7.24 cnf(c_0_9469, 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)), inference(split_conjunct,[status(thm)],[c_0_5551]), ['final']). 6.97/7.24 fof(c_0_9470, plain, ![X16912, X16913, X16914, X16915, X16916, X16917, X16918, X16919]:hAPP(hAPP(c_List_Omap(tc_prod(X16919,X16918),X16917),X16916),hAPP(hAPP(c_List_Ozip(X16919,X16918),X16915),hAPP(hAPP(c_List_Omap(X16914,X16918),X16913),X16912)))=hAPP(hAPP(c_List_Omap(tc_prod(X16919,X16914),X16917),hAPP(c_Product__Type_Oprod_Oprod__case(X16919,X16914,X16917),hAPP(hAPP(c_COMBB(tc_fun(X16914,tc_prod(X16919,X16918)),tc_fun(X16914,X16917),X16919),hAPP(c_COMBB(tc_prod(X16919,X16918),X16917,X16914),X16916)),hAPP(hAPP(c_COMBC(X16919,tc_fun(X16914,X16918),tc_fun(X16914,tc_prod(X16919,X16918))),hAPP(hAPP(c_COMBB(tc_fun(X16918,tc_prod(X16919,X16918)),tc_fun(tc_fun(X16914,X16918),tc_fun(X16914,tc_prod(X16919,X16918))),X16919),c_COMBB(X16918,tc_prod(X16919,X16918),X16914)),c_Product__Type_OPair(X16919,X16918))),X16913)))),hAPP(hAPP(c_List_Ozip(X16919,X16914),X16915),X16912)), inference(variable_rename,[status(thm)],[fact_map__zip__map2])). 6.97/7.24 cnf(c_0_9471, 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_5552, c_0_4565])). 6.97/7.24 cnf(c_0_9472, 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_5553])). 6.97/7.24 cnf(c_0_9473, 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_5554])). 6.97/7.24 cnf(c_0_9474, 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_5555]), ['final']). 6.97/7.24 cnf(c_0_9475, 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_5556, c_0_4565])). 6.97/7.24 cnf(c_0_9476, 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_5557, c_0_4798]), c_0_4467])). 6.97/7.24 cnf(c_0_9477, plain, (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))=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))))), inference(rw,[status(thm)],[c_0_5558, c_0_4565])). 6.97/7.24 cnf(c_0_9478, 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_5559, c_0_5560])). 6.97/7.24 cnf(c_0_9479, 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_5561])). 6.97/7.24 cnf(c_0_9480, 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_5562, c_0_4565])). 6.97/7.24 cnf(c_0_9481, 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_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))))=c_FunDef_Omax__weak), inference(split_conjunct,[status(thm)],[fact_max__weak__def])). 6.97/7.24 cnf(c_0_9482, plain, (c_FunDef_Omin__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_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))))), inference(split_conjunct,[status(thm)],[fact_min__weak__def])). 6.97/7.24 cnf(c_0_9483, plain, (c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)=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_OEx(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_fconj),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))))), inference(split_conjunct,[status(thm)],[c_0_5563])). 6.97/7.24 cnf(c_0_9484, plain, (c_Nitpick_Otimes__frac(X1,X2,X3)=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)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5564, c_0_4921]), c_0_4921]), c_0_4922]), c_0_4922])). 6.97/7.24 cnf(c_0_9485, 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)),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_Orderings_Oord__class_Omax(tc_Nat_Onat),X2)),c_Int_Onat))))=hAPP(hAPP(c_Orderings_Oord__class_Omax(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_5565, c_0_4565])). 6.97/7.24 cnf(c_0_9486, plain, (c_Enum_On__lists(X1,hAPP(c_Nat_OSuc,X2),X3)=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)))),X3)),c_Enum_On__lists(X1,X2,X3)))), inference(rw,[status(thm)],[c_0_5566, c_0_4645])). 6.97/7.24 cnf(c_0_9487, 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_5567, c_0_4565])). 6.97/7.24 fof(c_0_9488, plain, ![X7350, X7351, X7352, X7353, X7354, X7355]:hAPP(hAPP(c_List_Omap(tc_prod(X7355,X7352),tc_prod(X7355,X7354)),hAPP(c_Product__Type_Oprod_Oprod__case(X7355,X7352,tc_prod(X7355,X7354)),hAPP(hAPP(c_COMBC(X7355,tc_fun(X7352,X7354),tc_fun(X7352,tc_prod(X7355,X7354))),hAPP(hAPP(c_COMBB(tc_fun(X7354,tc_prod(X7355,X7354)),tc_fun(tc_fun(X7352,X7354),tc_fun(X7352,tc_prod(X7355,X7354))),X7355),c_COMBB(X7354,tc_prod(X7355,X7354),X7352)),c_Product__Type_OPair(X7355,X7354))),X7351))),hAPP(hAPP(c_List_Ozip(X7355,X7352),X7353),X7350))=hAPP(hAPP(c_List_Ozip(X7355,X7354),X7353),hAPP(hAPP(c_List_Omap(X7352,X7354),X7351),X7350)), inference(variable_rename,[status(thm)],[fact_zip__map2])). 6.97/7.24 cnf(c_0_9489, plain, (c_Relation_OId__on(X1,X2)=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))))), inference(split_conjunct,[status(thm)],[c_0_5568])). 6.97/7.24 cnf(c_0_9490, 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_5569, c_0_4467])). 6.97/7.24 cnf(c_0_9491, 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_5570, c_0_4467]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_9492, 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_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),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X3)))),hAPP(c_COMBC(X2,X1,tc_HOL_Obool),X4))))=hAPP(c_Relation_OImage(X2,X1,hAPP(c_Set_OCollect(tc_prod(X2,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X2,X1,tc_HOL_Obool),X4))),X3)), inference(split_conjunct,[status(thm)],[c_0_5571])). 6.97/7.24 cnf(c_0_9493, 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_5572, c_0_4471])). 6.97/7.24 fof(c_0_9494, plain, ![X13061, X13062]:c_Fun_Oinj__on(tc_fun(X13062,X13061),tc_fun(tc_prod(X13062,X13061),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X13062,X13061),tc_HOL_Obool),tc_fun(tc_prod(X13062,X13061),tc_HOL_Obool),tc_fun(X13062,X13061)),c_Set_OCollect(tc_prod(X13062,X13061))),hAPP(hAPP(c_COMBB(tc_fun(X13062,tc_fun(X13061,tc_HOL_Obool)),tc_fun(tc_prod(X13062,X13061),tc_HOL_Obool),tc_fun(X13062,X13061)),c_Product__Type_Oprod_Oprod__case(X13062,X13061,tc_HOL_Obool)),hAPP(c_COMBB(X13061,tc_fun(X13061,tc_HOL_Obool),X13062),hAPP(c_COMBC(X13061,X13061,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X13062,X13061),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_inj__graph])). 6.97/7.24 fof(c_0_9495, plain, ![X11069, X11070, X11071, X11072, X11073, X11074, X11075]:hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(X11075,X11074,X11073,X11072),X11071),X11070),X11069)=c_New__DSequence_Oneg__bind(X11075,X11074,hAPP(hAPP(hAPP(X11073,X11071),X11070),X11069),hAPP(hAPP(c_COMBC(X11075,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(X11074)))),hAPP(hAPP(c_COMBC(X11075,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(X11074))))),hAPP(hAPP(c_COMBC(X11075,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(X11074)))))),X11072),X11071)),X11070)),X11069)), inference(variable_rename,[status(thm)],[fact_neg__bind__def])). 6.97/7.24 fof(c_0_9496, plain, ![X3490, X3491, X3492, X3493, X3494, X3495, X3496, X3497]:hAPP(hAPP(c_List_Omap(tc_prod(X3493,X3496),X3495),hAPP(c_Product__Type_Oprod_Oprod__case(X3493,X3496,X3495),hAPP(hAPP(c_COMBB(tc_fun(X3496,tc_prod(X3497,X3496)),tc_fun(X3496,X3495),X3493),hAPP(c_COMBB(tc_prod(X3497,X3496),X3495,X3496),X3494)),hAPP(hAPP(c_COMBB(X3497,tc_fun(X3496,tc_prod(X3497,X3496)),X3493),c_Product__Type_OPair(X3497,X3496)),X3492)))),hAPP(hAPP(c_List_Ozip(X3493,X3496),X3491),X3490))=hAPP(hAPP(c_List_Omap(tc_prod(X3497,X3496),X3495),X3494),hAPP(hAPP(c_List_Ozip(X3497,X3496),hAPP(hAPP(c_List_Omap(X3493,X3497),X3492),X3491)),X3490)), inference(variable_rename,[status(thm)],[fact_map__zip__map])). 6.97/7.24 fof(c_0_9497, plain, ![X16564, X16565, X16566]:hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(X16566)),tc_List_Olist(tc_List_Olist(X16566))),c_Enum_Osublists(X16566,X16564)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(X16566)),tc_List_Olist(tc_List_Olist(X16566)),tc_List_Olist(tc_List_Olist(X16566))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(X16566)),tc_fun(tc_List_Olist(tc_List_Olist(X16566)),tc_List_Olist(tc_List_Olist(X16566))),tc_List_Olist(tc_List_Olist(X16566))),c_List_Oappend(tc_List_Olist(X16566))),hAPP(c_List_Omap(tc_List_Olist(X16566),tc_List_Olist(X16566)),hAPP(c_List_Olist_OCons(X16566),X16565)))),c_COMBI(tc_List_Olist(tc_List_Olist(X16566)))))=c_Enum_Osublists(X16566,hAPP(hAPP(c_List_Olist_OCons(X16566),X16565),X16564)), inference(variable_rename,[status(thm)],[fact_sublists_Osimps_I2_J])). 6.97/7.24 cnf(c_0_9498, plain, (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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))=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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[c_0_5573, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.24 fof(c_0_9499, plain, ![X16079, X16080, X16081, X16082]:c_Lazy__Sequence_Oproduct(X16082,X16081,X16080,X16079)=hAPP(c_Lazy__Sequence_Obind(X16082,tc_prod(X16082,X16081),X16080),hAPP(hAPP(c_COMBB(tc_fun(X16081,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X16082,X16081))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X16082,X16081)),X16082),c_Lazy__Sequence_Obind(X16081,tc_prod(X16082,X16081),X16079)),hAPP(hAPP(c_COMBB(tc_fun(X16081,tc_prod(X16082,X16081)),tc_fun(X16081,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X16082,X16081))),X16082),hAPP(c_COMBB(tc_prod(X16082,X16081),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X16082,X16081)),X16081),c_Lazy__Sequence_Osingle(tc_prod(X16082,X16081)))),c_Product__Type_OPair(X16082,X16081)))), inference(variable_rename,[status(thm)],[fact_])). 6.97/7.24 cnf(c_0_9500, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)=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))))), inference(split_conjunct,[status(thm)],[c_0_5574])). 6.97/7.24 cnf(c_0_9501, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)=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))))), inference(split_conjunct,[status(thm)],[c_0_5575])). 6.97/7.24 fof(c_0_9502, plain, ![X11038, X11039, X11040, X11041, X11042, X11043, X11044]:hAPP(hAPP(c_Relation_Orel__comp(X11044,X11043,X11042),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11041,tc_fun(tc_prod(X11044,X11043),tc_HOL_Obool)),X11040),X11039)),X11038)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11041,tc_fun(tc_prod(X11044,X11042),tc_HOL_Obool)),X11040),hAPP(hAPP(c_COMBC(X11041,tc_fun(tc_prod(X11043,X11042),tc_HOL_Obool),tc_fun(tc_prod(X11044,X11042),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X11044,X11043),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X11043,X11042),tc_HOL_Obool),tc_fun(tc_prod(X11044,X11042),tc_HOL_Obool)),X11041),c_Relation_Orel__comp(X11044,X11043,X11042)),X11039)),X11038)), inference(variable_rename,[status(thm)],[fact_rel__comp__UNION__distrib2])). 6.97/7.24 fof(c_0_9503, plain, ![X9114, X9115, X9116, X9117, X9118, X9119, X9120]:c_New__DSequence_Oneg__decr__bind(X9120,X9119,hAPP(hAPP(hAPP(X9118,X9116),X9115),X9114),hAPP(hAPP(c_COMBC(X9120,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(X9119)))),hAPP(hAPP(c_COMBC(X9120,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(X9119))))),hAPP(hAPP(c_COMBC(X9120,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(X9119)))))),X9117),X9116)),X9115)),X9114))=c_New__Random__Sequence_Oneg__decr__bind(X9120,X9119,X9118,X9117,X9116,X9115,X9114), inference(variable_rename,[status(thm)],[fact_New__Random__Sequence_Oneg__decr__bind__def])). 6.97/7.24 fof(c_0_9504, plain, ![X8143, X8144, X8145, X8146, X8147, X8148, X8149]:c_New__DSequence_Opos__bind(X8149,X8148,hAPP(hAPP(hAPP(X8147,X8145),X8144),X8143),hAPP(hAPP(c_COMBC(X8149,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X8148))),hAPP(hAPP(c_COMBC(X8149,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(X8148)))),hAPP(hAPP(c_COMBC(X8149,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(X8148))))),X8146),X8145)),X8144)),X8143))=hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(X8149,X8148,X8147,X8146),X8145),X8144),X8143), inference(variable_rename,[status(thm)],[fact_pos__bind__def])). 6.97/7.24 fof(c_0_9505, plain, ![X3121, X3122, X3123, X3124, X3125, X3126]:hAPP(hAPP(c_Product__Type_OSigma(X3126,X3125),hAPP(hAPP(c_Set_Oinsert(X3126),X3124),X3123)),hAPP(c_COMBK(tc_fun(X3125,tc_HOL_Obool),X3126),hAPP(hAPP(c_Set_Oinsert(X3125),X3122),X3121)))=hAPP(hAPP(c_Set_Oinsert(tc_prod(X3126,X3125)),hAPP(hAPP(c_Product__Type_OPair(X3126,X3125),X3124),X3122)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3126,X3125),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X3126,X3125),X3123),hAPP(c_COMBK(tc_fun(X3125,tc_HOL_Obool),X3126),hAPP(hAPP(c_Set_Oinsert(X3125),X3122),X3121)))),hAPP(hAPP(c_Product__Type_OSigma(X3126,X3125),hAPP(hAPP(c_Set_Oinsert(X3126),X3124),X3123)),hAPP(c_COMBK(tc_fun(X3125,tc_HOL_Obool),X3126),X3121)))), inference(variable_rename,[status(thm)],[fact_insert__times__insert])). 6.97/7.24 cnf(c_0_9506, 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_5576])). 6.97/7.24 cnf(c_0_9507, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),c_Int_OMin))=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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_5577, c_0_4409]), c_0_4409]), c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.24 fof(c_0_9508, plain, ![X7789, X7790, X7791, X7792, X7793, X7794, X7795]:c_New__Random__Sequence_Opos__decr__bind(X7795,X7794,X7793,X7792,X7791,X7790,X7789)=c_New__DSequence_Opos__decr__bind(X7795,X7794,hAPP(hAPP(hAPP(X7793,X7791),X7790),X7789),hAPP(hAPP(c_COMBC(X7795,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X7794))),hAPP(hAPP(c_COMBC(X7795,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(X7794)))),hAPP(hAPP(c_COMBC(X7795,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(X7794))))),X7792),X7791)),X7790)),X7789)), inference(variable_rename,[status(thm)],[fact_New__Random__Sequence_Opos__decr__bind__def])). 6.97/7.24 cnf(c_0_9509, 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_5578])). 6.97/7.24 cnf(c_0_9510, 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_5579])). 6.97/7.24 cnf(c_0_9511, 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))), inference(split_conjunct,[status(thm)],[c_0_5580]), ['final']). 6.97/7.24 cnf(c_0_9512, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[c_0_5581, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.24 cnf(c_0_9513, 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))),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))), inference(split_conjunct,[status(thm)],[c_0_5582])). 6.97/7.24 cnf(c_0_9514, 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_5583]), ['final']). 6.97/7.24 cnf(c_0_9515, 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_5584, c_0_4565])). 6.97/7.24 fof(c_0_9516, plain, ![X492, X493]:c_Relation_OId__on(X493,X492)=hAPP(c_Product__Type_Oprod_Oprod__case(X493,X493,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X493,tc_HOL_Obool,tc_fun(X493,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X493,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(X493,tc_HOL_Obool)),X493),c_COMBC(X493,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X493,tc_HOL_Obool),tc_fun(X493,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X493),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X493),c_fconj)),c_fequal))),X492)), inference(variable_rename,[status(thm)],[fact_Id__on__def_H])). 6.97/7.24 fof(c_0_9517, plain, ![X14749, X14750, X14751, X14752, X14753, X14754]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X14751,tc_fun(X14753,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14754,tc_fun(X14751,tc_HOL_Obool)),X14752),X14750)),X14749)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X14754,tc_fun(X14753,tc_HOL_Obool)),X14752),hAPP(hAPP(c_COMBC(X14754,tc_fun(X14751,tc_fun(X14753,tc_HOL_Obool)),tc_fun(X14753,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14751,tc_HOL_Obool),tc_fun(tc_fun(X14751,tc_fun(X14753,tc_HOL_Obool)),tc_fun(X14753,tc_HOL_Obool)),X14754),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X14751,tc_fun(X14753,tc_HOL_Obool))),X14750)),X14749)), inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I9_J])). 6.97/7.24 cnf(c_0_9518, 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_5585])). 6.97/7.24 fof(c_0_9519, plain, ![X6229, X6230]:hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),X6230),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(X6230,tc_List_Olist(tc_fun(X6230,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X6230,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(X6230,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),X6230),c_List_Omap(tc_fun(X6230,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(X6230,tc_Nat_Onat),X6230,tc_Nat_Onat),c_COMBI(tc_fun(X6230,tc_Nat_Onat))))),X6229))=c_List_Omeasures(X6230,X6229), inference(variable_rename,[status(thm)],[fact_measures__def])). 6.97/7.24 fof(c_0_9520, plain, ![X4742, X4743]: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(X4743,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,X4743),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X4743)),X4742)))),hAPP(hAPP(c_COMBB(X4743,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X4743,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X4743,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(X4743,X4742)))=c_Random_Oselect__weight(X4743,X4742), inference(variable_rename,[status(thm)],[fact_select__weight__def])). 6.97/7.24 cnf(c_0_9521, plain, (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))))=c_List_Olenlex(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5586])). 6.97/7.24 cnf(c_0_9522, 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)), inference(split_conjunct,[status(thm)],[c_0_5587]), ['final']). 6.97/7.24 cnf(c_0_9523, plain, (c_Random_Oselect(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_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)))), inference(split_conjunct,[status(thm)],[c_0_5588])). 6.97/7.24 cnf(c_0_9524, 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_5589])). 6.97/7.24 fof(c_0_9525, plain, ![X11746, X11747]:c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X11747,tc_Lazy__Sequence_Olazy__sequence(X11747)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X11747,tc_Lazy__Sequence_Olazy__sequence(X11747),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X11747),tc_Nat_Onat),X11747),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X11747),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(X11747)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X11747)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(X11747),X11746))=hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X11747)),X11746), inference(variable_rename,[status(thm)],[fact_size__code])). 6.97/7.24 cnf(c_0_9526, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[c_0_5590, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.24 cnf(c_0_9527, 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_5591])). 6.97/7.24 fof(c_0_9528, plain, ![X13229]:c_Finite__Set_Ofun__left__comm__idem(X13229,tc_fun(X13229,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X13229,tc_HOL_Obool),tc_fun(tc_fun(X13229,tc_HOL_Obool),tc_fun(X13229,tc_HOL_Obool)),X13229),hAPP(c_COMBC(tc_fun(X13229,tc_HOL_Obool),tc_fun(X13229,tc_HOL_Obool),tc_fun(X13229,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X13229,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X13229,tc_fun(X13229,tc_HOL_Obool),tc_fun(X13229,tc_HOL_Obool)),c_Set_Oinsert(X13229)),c_Orderings_Obot__class_Obot(tc_fun(X13229,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[fact_fun__left__comm__idem__remove])). 6.97/7.24 cnf(c_0_9529, plain, (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))=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)))), inference(split_conjunct,[status(thm)],[c_0_5592])). 6.97/7.24 cnf(c_0_9530, 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_5593])). 6.97/7.24 fof(c_0_9531, plain, ![X6030, X6031, X6032, X6033, X6034]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6034,tc_fun(X6033,tc_HOL_Obool)),X6032),hAPP(hAPP(c_COMBC(X6034,tc_fun(X6033,tc_HOL_Obool),tc_fun(X6033,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6033,tc_HOL_Obool),tc_fun(tc_fun(X6033,tc_HOL_Obool),tc_fun(X6033,tc_HOL_Obool)),X6034),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6033,tc_HOL_Obool))),X6031)),X6030))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6033,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6034,tc_fun(X6033,tc_HOL_Obool)),X6032),X6031)),X6030), inference(variable_rename,[status(thm)],[fact_INT__simps_I6_J])). 6.97/7.24 fof(c_0_9532, plain, ![X9500, X9501, X9502, X9503, X9504]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9503,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9504,tc_fun(X9503,tc_HOL_Obool)),X9502),X9501)),X9500)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9504,tc_fun(X9503,tc_HOL_Obool)),X9502),hAPP(hAPP(c_COMBC(X9504,tc_fun(X9503,tc_HOL_Obool),tc_fun(X9503,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9503,tc_HOL_Obool),tc_fun(tc_fun(X9503,tc_HOL_Obool),tc_fun(X9503,tc_HOL_Obool)),X9504),c_Groups_Ominus__class_Ominus(tc_fun(X9503,tc_HOL_Obool))),X9501)),X9500)), inference(variable_rename,[status(thm)],[fact_UN__simps_I6_J])). 6.97/7.24 fof(c_0_9533, plain, ![X867, X868, X869, X870, X871]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X870,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X871,tc_fun(X870,tc_HOL_Obool)),X869),X868)),X867)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X871,tc_fun(X870,tc_HOL_Obool)),X869),hAPP(hAPP(c_COMBC(X871,tc_fun(X870,tc_HOL_Obool),tc_fun(X870,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X870,tc_HOL_Obool),tc_fun(tc_fun(X870,tc_HOL_Obool),tc_fun(X870,tc_HOL_Obool)),X871),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X870,tc_HOL_Obool))),X868)),X867)), inference(variable_rename,[status(thm)],[fact_UN__simps_I4_J])). 6.97/7.24 cnf(c_0_9534, 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(hAPP(c_Set_Oinsert(tc_List_Olist(X1)),X4),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)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X1),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_5594])). 6.97/7.24 fof(c_0_9535, plain, ![X4411, X4412, X4413, X4414]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X4414,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4413,tc_fun(tc_fun(X4414,tc_HOL_Obool),tc_HOL_Obool)),X4412),hAPP(hAPP(c_COMBB(tc_fun(X4414,tc_HOL_Obool),tc_fun(tc_fun(X4414,tc_HOL_Obool),tc_HOL_Obool),X4413),c_Set_OPow(X4414)),X4411))),hAPP(c_Set_OPow(X4414),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4413,tc_fun(X4414,tc_HOL_Obool)),X4412),X4411)))), inference(variable_rename,[status(thm)],[fact_UN__Pow__subset])). 6.97/7.24 fof(c_0_9536, plain, ![X6682, X6683, X6684, X6685]:hAPP(hAPP(c_Product__Type_OSigma(X6684,X6685),X6682),hAPP(c_COMBK(tc_fun(X6685,tc_HOL_Obool),X6684),X6683))=hAPP(c_Set_Oimage(tc_prod(X6685,X6684),tc_prod(X6684,X6685),hAPP(c_Product__Type_Oprod_Oprod__case(X6685,X6684,tc_prod(X6684,X6685)),hAPP(c_COMBC(X6684,X6685,tc_prod(X6684,X6685)),c_Product__Type_OPair(X6684,X6685)))),hAPP(hAPP(c_Product__Type_OSigma(X6685,X6684),X6683),hAPP(c_COMBK(tc_fun(X6684,tc_HOL_Obool),X6685),X6682))), inference(variable_rename,[status(thm)],[fact_swap__product])). 6.97/7.24 fof(c_0_9537, plain, ![X6508, X6509, X6510, X6511, X6512]:hAPP(hAPP(c_List_Oappend(tc_prod(X6512,X6511)),hAPP(hAPP(c_List_Ozip(X6512,X6511),hAPP(hAPP(c_List_Otake(X6512),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6511)),X6509)),X6510)),X6509)),hAPP(hAPP(c_List_Ozip(X6512,X6511),hAPP(hAPP(c_List_Odrop(X6512),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6511)),X6509)),X6510)),X6508))=hAPP(hAPP(c_List_Ozip(X6512,X6511),X6510),hAPP(hAPP(c_List_Oappend(X6511),X6509),X6508)), inference(variable_rename,[status(thm)],[fact_zip__append2])). 6.97/7.24 fof(c_0_9538, plain, ![X722, X723, X724, X725, X726]:hAPP(hAPP(c_List_Oappend(tc_prod(X726,X725)),hAPP(hAPP(c_List_Ozip(X726,X725),X724),hAPP(hAPP(c_List_Otake(X725),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X726)),X724)),X722))),hAPP(hAPP(c_List_Ozip(X726,X725),X723),hAPP(hAPP(c_List_Odrop(X725),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X726)),X724)),X722)))=hAPP(hAPP(c_List_Ozip(X726,X725),hAPP(hAPP(c_List_Oappend(X726),X724),X723)),X722), inference(variable_rename,[status(thm)],[fact_zip__append1])). 6.97/7.24 cnf(c_0_9539, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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),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)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_5595, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.24 cnf(c_0_9540, 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_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))),c_Int_OMin)=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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_5596, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4565]), c_0_4565])). 6.97/7.24 fof(c_0_9541, plain, ![X1269, X1270, X1271, X1272, X1273, X1274]:hAPP(hAPP(c_List_Omap(tc_prod(X1272,X1273),tc_prod(X1274,X1273)),hAPP(c_Product__Type_Oprod_Oprod__case(X1272,X1273,tc_prod(X1274,X1273)),hAPP(hAPP(c_COMBB(X1274,tc_fun(X1273,tc_prod(X1274,X1273)),X1272),c_Product__Type_OPair(X1274,X1273)),X1271))),hAPP(hAPP(c_List_Ozip(X1272,X1273),X1270),X1269))=hAPP(hAPP(c_List_Ozip(X1274,X1273),hAPP(hAPP(c_List_Omap(X1272,X1274),X1271),X1270)),X1269), inference(variable_rename,[status(thm)],[fact_zip__map1])). 6.97/7.24 cnf(c_0_9542, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))),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)],[inference(rw,[status(thm)],[c_0_5597, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.24 cnf(c_0_9543, 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)),hAPP(hAPP(c_COMBC(X2,tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_COMBB(X1,tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_OCons(X1)),X3)),c_List_Olist_ONil(X1))),X4))=hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)), inference(rw,[status(thm)],[c_0_5598, c_0_4645])). 6.97/7.24 fof(c_0_9544, plain, ![X15649, X15650, X15651, X15652, X15653, X15654]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15654,tc_HOL_Obool)),hAPP(c_Relation_OImage(X15653,X15654,X15652),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X15651,tc_fun(X15653,tc_HOL_Obool)),X15650),X15649))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X15651,tc_fun(X15654,tc_HOL_Obool)),X15650),hAPP(hAPP(c_COMBB(tc_fun(X15653,tc_HOL_Obool),tc_fun(X15654,tc_HOL_Obool),X15651),c_Relation_OImage(X15653,X15654,X15652)),X15649)))), inference(variable_rename,[status(thm)],[fact_Image__INT__subset])). 6.97/7.24 cnf(c_0_9545, plain, (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),X2)),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(split_conjunct,[status(thm)],[c_0_5599])). 6.97/7.24 cnf(c_0_9546, plain, (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),X2)),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(split_conjunct,[status(thm)],[c_0_5600])). 6.97/7.24 cnf(c_0_9547, 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_5601])). 6.97/7.24 cnf(c_0_9548, 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_5602, c_0_5560]), c_0_5174])). 6.97/7.24 cnf(c_0_9549, 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_5603, c_0_5560]), ['final']). 6.97/7.24 fof(c_0_9550, plain, ![X10422, X10423]:hAPP(c_List_Orotate1(X10423),X10422)=hAPP(c_List_Olist_Olist__case(tc_List_Olist(X10423),X10423,c_List_Olist_ONil(X10423),hAPP(hAPP(c_COMBB(tc_List_Olist(X10423),tc_fun(tc_List_Olist(X10423),tc_List_Olist(X10423)),X10423),hAPP(c_COMBC(tc_List_Olist(X10423),tc_List_Olist(X10423),tc_List_Olist(X10423)),c_List_Oappend(X10423))),hAPP(hAPP(c_COMBC(X10423,tc_List_Olist(X10423),tc_List_Olist(X10423)),c_List_Olist_OCons(X10423)),c_List_Olist_ONil(X10423)))),X10422), inference(variable_rename,[status(thm)],[fact_rotate1__def])). 6.97/7.24 fof(c_0_9551, plain, ![X17247, X17248, X17249, X17250, X17251, X17252, X17253]:hAPP(c_List_Ofoldl(X17253,X17252,X17251,X17250),hAPP(hAPP(c_List_Omap(X17249,X17252),X17248),X17247))=hAPP(c_List_Ofoldl(X17253,X17249,hAPP(hAPP(c_COMBC(X17253,tc_fun(X17249,X17252),tc_fun(X17249,X17253)),hAPP(hAPP(c_COMBB(tc_fun(X17252,X17253),tc_fun(tc_fun(X17249,X17252),tc_fun(X17249,X17253)),X17253),c_COMBB(X17252,X17253,X17249)),X17251)),X17248),X17250),X17247), inference(variable_rename,[status(thm)],[fact_foldl__map])). 6.97/7.24 fof(c_0_9552, plain, ![X14186, X14187, X14188, X14189, X14190, X14191, X14192]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14188,tc_fun(tc_prod(X14192,X14190),tc_HOL_Obool)),X14187),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X14191,X14190),tc_HOL_Obool),tc_fun(tc_prod(X14192,X14190),tc_HOL_Obool),X14188),hAPP(c_Relation_Orel__comp(X14192,X14191,X14190),X14189)),X14186))=hAPP(hAPP(c_Relation_Orel__comp(X14192,X14191,X14190),X14189),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14188,tc_fun(tc_prod(X14191,X14190),tc_HOL_Obool)),X14187),X14186)), inference(variable_rename,[status(thm)],[fact_rel__comp__UNION__distrib])). 6.97/7.24 fof(c_0_9553, plain, ![X15493, X15494, X15495, X15496, X15497, X15498]:hAPP(hAPP(c_COMBS(tc_prod(X15498,X15497),X15497,X15496),hAPP(hAPP(c_COMBB(X15495,tc_fun(X15497,X15496),tc_prod(X15498,X15497)),X15494),hAPP(hAPP(c_COMBB(X15498,X15495,tc_prod(X15498,X15497)),X15493),c_Product__Type_Ofst(X15498,X15497)))),c_Product__Type_Osnd(X15498,X15497))=hAPP(c_Product__Type_Oprod_Oprod__case(X15498,X15497,X15496),hAPP(hAPP(c_COMBB(X15495,tc_fun(X15497,X15496),X15498),X15494),X15493)), inference(variable_rename,[status(thm)],[fact_split__comp__eq])). 6.97/7.24 fof(c_0_9554, plain, ![X11709, X11710, X11711, X11712, X11713, X11714, X11715, X11716]:hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X11716,X11715,X11714),X11713),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X11712,X11711,tc_prod(X11716,X11715)),X11710),X11709))=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X11712,X11711,X11714),hAPP(hAPP(c_COMBB(tc_fun(X11711,tc_prod(X11716,X11715)),tc_fun(X11711,X11714),X11712),hAPP(c_COMBB(tc_prod(X11716,X11715),X11714,X11711),hAPP(c_Product__Type_Oprod_Oprod__case(X11716,X11715,X11714),X11713))),X11710)),X11709), inference(variable_rename,[status(thm)],[fact_split__twice])). 6.97/7.24 cnf(c_0_9555, 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),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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),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_5604, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.24 cnf(c_0_9556, 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),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),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5605, c_0_5606]), c_0_5606]), ['final']). 6.97/7.24 cnf(c_0_9557, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),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)],[inference(rw,[status(thm)],[c_0_5607, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.24 cnf(c_0_9558, 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_5608])). 6.97/7.24 cnf(c_0_9559, plain, (hAPP(c_List_Orotate(X1,X2),hAPP(c_List_Orev(X1),X3))=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)),X3)),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_5609])). 6.97/7.24 fof(c_0_9560, plain, ![X10640, X10641, X10642, X10643, X10644]:hAPP(hAPP(c_List_Olist__update(X10644,hAPP(hAPP(c_List_Olist_OCons(X10644),X10643),X10642)),X10641),X10640)=c_Nat_Onat_Onat__case(tc_List_Olist(X10644),hAPP(hAPP(c_List_Olist_OCons(X10644),X10640),X10642),hAPP(hAPP(c_COMBB(tc_List_Olist(X10644),tc_List_Olist(X10644),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X10644),X10643)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X10644,tc_List_Olist(X10644)),c_List_Olist__update(X10644,X10642)),X10640)),X10641), inference(variable_rename,[status(thm)],[fact_list__update_Osimps_I2_J])). 6.97/7.24 cnf(c_0_9561, 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_5610, c_0_4921]), c_0_4922])). 6.97/7.24 cnf(c_0_9562, plain, (hAPP(hAPP(c_Set_Oinsert(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),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))), inference(split_conjunct,[status(thm)],[c_0_5611])). 6.97/7.24 cnf(c_0_9563, 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_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))=X1), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5612, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.24 fof(c_0_9564, plain, ![X17119, X17120, X17121, X17122]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X17122,tc_HOL_Obool),tc_fun(tc_prod(X17122,X17121),tc_HOL_Obool)),X17120),hAPP(hAPP(c_COMBC(tc_fun(X17122,tc_HOL_Obool),tc_fun(X17122,tc_fun(X17121,tc_HOL_Obool)),tc_fun(tc_prod(X17122,X17121),tc_HOL_Obool)),c_Product__Type_OSigma(X17122,X17121)),X17119))=hAPP(hAPP(c_Product__Type_OSigma(X17122,X17121),c_Complete__Lattice_OSup__class_OSup(tc_fun(X17122,tc_HOL_Obool),X17120)),X17119), inference(variable_rename,[status(thm)],[fact_Sigma__Union])). 6.97/7.24 cnf(c_0_9565, 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_5613])). 6.97/7.24 fof(c_0_9566, plain, ![X11775, X11776, X11777, X11778]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X11778,tc_HOL_Obool),tc_fun(X11777,tc_HOL_Obool)),X11776),hAPP(hAPP(c_COMBC(tc_fun(X11778,tc_HOL_Obool),tc_fun(X11778,tc_fun(X11777,tc_HOL_Obool)),tc_fun(X11777,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11778,tc_fun(X11777,tc_HOL_Obool))),X11775))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11778,tc_fun(X11777,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X11778,tc_HOL_Obool),X11776)),X11775), inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I8_J])). 6.97/7.24 fof(c_0_9567, plain, ![X745, X746, X747, X748]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X748,tc_fun(X747,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X748,tc_HOL_Obool),X746)),X745)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X748,tc_HOL_Obool),tc_fun(X747,tc_HOL_Obool)),X746),hAPP(hAPP(c_COMBC(tc_fun(X748,tc_HOL_Obool),tc_fun(X748,tc_fun(X747,tc_HOL_Obool)),tc_fun(X747,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X748,tc_fun(X747,tc_HOL_Obool))),X745)), inference(variable_rename,[status(thm)],[fact_INT__simps_I8_J])). 6.97/7.24 cnf(c_0_9568, 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_5614])). 6.97/7.24 fof(c_0_9569, plain, ![X9609, X9610, X9611, X9612, X9613]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9613,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9613,tc_HOL_Obool)),hAPP(c_Set_Oimage(X9612,X9613,X9611),X9610)),hAPP(c_Set_Oimage(X9612,X9613,X9611),X9609))),hAPP(c_Set_Oimage(X9612,X9613,X9611),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9612,tc_HOL_Obool)),X9610),X9609)))), inference(variable_rename,[status(thm)],[fact_image__diff__subset])). 6.97/7.24 fof(c_0_9570, plain, ![X1745, X1746, X1747, X1748, X1749]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1749,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1748,X1749,X1747),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1748,tc_HOL_Obool)),X1746),X1745))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1749,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1748,X1749,X1747),X1746)),hAPP(c_Set_Oimage(X1748,X1749,X1747),X1745)))), inference(variable_rename,[status(thm)],[fact_image__Int__subset])). 6.97/7.24 fof(c_0_9571, plain, ![X4990, X4991, X4992, X4993, X4994]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4994,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4993,X4994,X4992),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4993,tc_HOL_Obool)),X4991),X4990))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4994,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4993,X4994,X4992),X4991)),hAPP(c_Relation_OImage(X4993,X4994,X4992),X4990)))), inference(variable_rename,[status(thm)],[fact_Image__Int__subset])). 6.97/7.24 cnf(c_0_9572, 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_5615])). 6.97/7.24 cnf(c_0_9573, 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(c_List_Orotate(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_5616])). 6.97/7.24 cnf(c_0_9574, 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_5617, c_0_5618])). 6.97/7.24 cnf(c_0_9575, 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_5619, c_0_5002]), c_0_5002]), c_0_5002]), ['final']). 6.97/7.24 fof(c_0_9576, plain, ![X3709, X3710, X3711, X3712, X3713]:hAPP(c_Relation_Oconverse(X3713,X3712),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3711,tc_fun(tc_prod(X3713,X3712),tc_HOL_Obool)),X3710),X3709))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3711,tc_fun(tc_prod(X3712,X3713),tc_HOL_Obool)),X3710),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X3713,X3712),tc_HOL_Obool),tc_fun(tc_prod(X3712,X3713),tc_HOL_Obool),X3711),c_Relation_Oconverse(X3713,X3712)),X3709)), inference(variable_rename,[status(thm)],[fact_converse__INTER])). 6.97/7.24 fof(c_0_9577, plain, ![X14440, X14441, X14442, X14443, X14444]:hAPP(c_Relation_Oconverse(X14444,X14443),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14442,tc_fun(tc_prod(X14444,X14443),tc_HOL_Obool)),X14441),X14440))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14442,tc_fun(tc_prod(X14443,X14444),tc_HOL_Obool)),X14441),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X14444,X14443),tc_HOL_Obool),tc_fun(tc_prod(X14443,X14444),tc_HOL_Obool),X14442),c_Relation_Oconverse(X14444,X14443)),X14440)), inference(variable_rename,[status(thm)],[fact_converse__UNION])). 6.97/7.24 fof(c_0_9578, plain, ![X5068, X5069, X5070, X5071]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5071,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5071,X5070),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5071,X5070),tc_HOL_Obool)),X5069),X5068))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5071,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5071,X5070),X5069)),hAPP(c_Relation_ODomain(X5071,X5070),X5068)))), inference(variable_rename,[status(thm)],[fact_Domain__Int__subset])). 6.97/7.24 fof(c_0_9579, plain, ![X9750, X9751, X9752, X9753]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9753,tc_HOL_Obool)),hAPP(c_Relation_ORange(X9752,X9753),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X9752,X9753),tc_HOL_Obool)),X9751),X9750))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9753,tc_HOL_Obool)),hAPP(c_Relation_ORange(X9752,X9753),X9751)),hAPP(c_Relation_ORange(X9752,X9753),X9750)))), inference(variable_rename,[status(thm)],[fact_Range__Int__subset])). 6.97/7.24 fof(c_0_9580, plain, ![X15411, X15412, X15413]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15413,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X15413,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X15413,tc_HOL_Obool),tc_HOL_Obool)),X15412),X15411))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15413,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X15413,tc_HOL_Obool),X15412)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X15413,tc_HOL_Obool),X15411)))), inference(variable_rename,[status(thm)],[fact_Union__Int__subset])). 6.97/7.24 cnf(c_0_9581, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[inference(rw,[status(thm)],[c_0_5620, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.24 fof(c_0_9582, plain, ![X9363, X9364, X9365, X9366]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9366,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9366,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X9366,X9365),X9364)),hAPP(c_Relation_ODomain(X9366,X9365),X9363))),hAPP(c_Relation_ODomain(X9366,X9365),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X9366,X9365),tc_HOL_Obool)),X9364),X9363)))), inference(variable_rename,[status(thm)],[fact_Domain__Diff__subset])). 6.97/7.24 fof(c_0_9583, plain, ![X3676, X3677, X3678, X3679]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3679,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3679,tc_HOL_Obool)),hAPP(c_Relation_ORange(X3678,X3679),X3677)),hAPP(c_Relation_ORange(X3678,X3679),X3676))),hAPP(c_Relation_ORange(X3678,X3679),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X3678,X3679),tc_HOL_Obool)),X3677),X3676)))), inference(variable_rename,[status(thm)],[fact_Range__Diff__subset])). 6.97/7.24 fof(c_0_9584, plain, ![X6733, X6734, X6735]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6735,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6735,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X6735,tc_HOL_Obool),X6734)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X6735,tc_HOL_Obool),X6733))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X6735,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X6735,tc_HOL_Obool),tc_HOL_Obool)),X6734),X6733)))), inference(variable_rename,[status(thm)],[fact_Inter__Un__subset])). 6.97/7.24 fof(c_0_9585, plain, ![X16803, X16804, X16805, X16806, X16807, X16808]:hAPP(hAPP(c_List_Ozip(X16808,X16807),hAPP(hAPP(c_List_Olist__update(X16808,X16806),X16804),hAPP(c_Product__Type_Ofst(X16808,X16807),X16803))),hAPP(hAPP(c_List_Olist__update(X16807,X16805),X16804),hAPP(c_Product__Type_Osnd(X16808,X16807),X16803)))=hAPP(hAPP(c_List_Olist__update(tc_prod(X16808,X16807),hAPP(hAPP(c_List_Ozip(X16808,X16807),X16806),X16805)),X16804),X16803), inference(variable_rename,[status(thm)],[fact_update__zip])). 6.97/7.24 fof(c_0_9586, plain, ![X4034, X4035, X4036]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X4036,X4035),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X4036,X4035),X4034),hAPP(c_COMBK(tc_fun(X4035,tc_HOL_Obool),X4036),c_Orderings_Otop__class_Otop(tc_fun(X4035,tc_HOL_Obool)))))=hAPP(hAPP(c_Product__Type_OSigma(X4036,X4035),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4036,tc_HOL_Obool)),X4034)),hAPP(c_COMBK(tc_fun(X4035,tc_HOL_Obool),X4036),c_Orderings_Otop__class_Otop(tc_fun(X4035,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_Compl__Times__UNIV2])). 6.97/7.24 fof(c_0_9587, plain, ![X17294, X17295, X17296]:hAPP(hAPP(c_Product__Type_OSigma(X17296,X17295),c_Orderings_Otop__class_Otop(tc_fun(X17296,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X17295,tc_HOL_Obool),X17296),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X17295,tc_HOL_Obool)),X17294)))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X17296,X17295),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X17296,X17295),c_Orderings_Otop__class_Otop(tc_fun(X17296,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X17295,tc_HOL_Obool),X17296),X17294))), inference(variable_rename,[status(thm)],[fact_Compl__Times__UNIV1])). 6.97/7.24 cnf(c_0_9588, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))=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))), inference(rw,[status(thm)],[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_5621, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.24 cnf(c_0_9589, 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),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))),c_Int_OMin)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5622, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4565]), c_0_4565])). 6.97/7.24 cnf(c_0_9590, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))),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))), inference(rw,[status(thm)],[c_0_5623, c_0_5624]), ['final']). 6.97/7.24 fof(c_0_9591, plain, ![X8933, X8934, X8935, X8936]:hAPP(hAPP(c_List_Otake(X8936),X8935),hAPP(hAPP(c_List_Olist_OCons(X8936),X8934),X8933))=c_Nat_Onat_Onat__case(tc_List_Olist(X8936),c_List_Olist_ONil(X8936),hAPP(hAPP(c_COMBB(tc_List_Olist(X8936),tc_List_Olist(X8936),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X8936),X8934)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X8936),tc_List_Olist(X8936)),c_List_Otake(X8936)),X8933)),X8935), inference(variable_rename,[status(thm)],[fact_take__Cons])). 6.97/7.24 fof(c_0_9592, plain, ![X3744, X3745, X3746]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3746),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3745),X3744))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3746),c_Divides_Odiv__class_Omod(tc_Int_Oint,X3745,X3744))),X3744))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3746),X3745)),X3744), inference(variable_rename,[status(thm)],[fact_zdiv__zmult1__eq])). 6.97/7.24 fof(c_0_9593, plain, ![X16190, X16191, X16192]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16192),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X16191),X16190))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16192),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X16191,X16190))),X16190))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16192),X16191)),X16190), inference(variable_rename,[status(thm)],[fact_div__mult1__eq])). 6.97/7.24 fof(c_0_9594, plain, ![X12844, X12845, X12846, X12847]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X12846,X12847),tc_HOL_Obool)),hAPP(c_Set_Oimage(X12847,tc_prod(X12846,X12847),esk420_4(X12844,X12845,X12846,X12847)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12846,tc_fun(X12847,tc_HOL_Obool)),X12845),X12844))),hAPP(hAPP(c_Product__Type_OSigma(X12846,X12847),X12845),X12844)))&c_Fun_Oinj__on(X12847,tc_prod(X12846,X12847),esk420_4(X12844,X12845,X12846,X12847),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12846,tc_fun(X12847,tc_HOL_Obool)),X12845),X12844))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact_Ex__inj__on__UNION__Sigma])])). 6.97/7.24 cnf(c_0_9595, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[c_0_5625, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.24 fof(c_0_9596, plain, ![X1280]: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)),X1280),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])). 6.97/7.24 fof(c_0_9597, plain, ![X13592, X13593, X13594]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X13594,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X13594,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X13594),X13593)),hAPP(c_Set_OPow(X13594),X13592))),hAPP(c_Set_OPow(X13594),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13594,tc_HOL_Obool)),X13593),X13592)))), inference(variable_rename,[status(thm)],[fact_Un__Pow__subset])). 6.97/7.24 cnf(c_0_9598, 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_5626])). 6.97/7.24 cnf(c_0_9599, plain, (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))))=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_5627])). 6.97/7.24 fof(c_0_9600, plain, ![X13949, X13950, X13951]:hAPP(c_List_Otl(X13951),hAPP(hAPP(c_List_Oappend(X13951),X13950),X13949))=hAPP(c_List_Olist_Olist__case(tc_List_Olist(X13951),X13951,hAPP(c_List_Otl(X13951),X13949),hAPP(c_COMBK(tc_fun(tc_List_Olist(X13951),tc_List_Olist(X13951)),X13951),hAPP(hAPP(c_COMBC(tc_List_Olist(X13951),tc_List_Olist(X13951),tc_List_Olist(X13951)),c_List_Oappend(X13951)),X13949))),X13950), inference(variable_rename,[status(thm)],[fact_tl__append])). 6.97/7.24 fof(c_0_9601, plain, ![X17371, X17372, X17373]:c_HOL_OThe(tc_prod(X17373,X17372),hAPP(hAPP(c_COMBS(tc_prod(X17373,X17372),X17372,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X17373,tc_fun(X17372,tc_HOL_Obool),tc_prod(X17373,X17372)),X17371),c_Product__Type_Ofst(X17373,X17372))),c_Product__Type_Osnd(X17373,X17372)))=c_HOL_OThe(tc_prod(X17373,X17372),hAPP(c_Product__Type_Oprod_Oprod__case(X17373,X17372,tc_HOL_Obool),X17371)), inference(variable_rename,[status(thm)],[fact_The__split])). 6.97/7.24 fof(c_0_9602, plain, ![X7766, X7767, X7768]:c_Hilbert__Choice_OEps(tc_prod(X7768,X7767),hAPP(c_Product__Type_Oprod_Oprod__case(X7768,X7767,tc_HOL_Obool),X7766))=c_Hilbert__Choice_OEps(tc_prod(X7768,X7767),hAPP(hAPP(c_COMBS(tc_prod(X7768,X7767),X7767,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X7768,tc_fun(X7767,tc_HOL_Obool),tc_prod(X7768,X7767)),X7766),c_Product__Type_Ofst(X7768,X7767))),c_Product__Type_Osnd(X7768,X7767))), inference(variable_rename,[status(thm)],[fact_Eps__split])). 6.97/7.24 fof(c_0_9603, plain, ![X9476, X9477, X9478, X9479, X9480]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9478,tc_fun(X9480,tc_HOL_Obool)),X9477),hAPP(hAPP(c_COMBB(tc_fun(X9480,tc_HOL_Obool),tc_fun(X9480,tc_HOL_Obool),X9478),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9480,tc_HOL_Obool)),X9479)),X9476))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9480,tc_HOL_Obool)),X9479),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9478,tc_fun(X9480,tc_HOL_Obool)),X9477),X9476)), inference(variable_rename,[status(thm)],[fact_Int__UN__distrib])). 6.97/7.24 fof(c_0_9604, plain, ![X6677, X6678, X6679, X6680, X6681]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6680,tc_HOL_Obool)),X6678),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6681,tc_fun(X6680,tc_HOL_Obool)),X6679),X6677))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6681,tc_fun(X6680,tc_HOL_Obool)),X6679),hAPP(hAPP(c_COMBB(tc_fun(X6680,tc_HOL_Obool),tc_fun(X6680,tc_HOL_Obool),X6681),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6680,tc_HOL_Obool)),X6678)),X6677)), inference(variable_rename,[status(thm)],[fact_UN__simps_I7_J])). 6.97/7.24 fof(c_0_9605, plain, ![X12617, X12618, X12619, X12620, X12621]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12620,tc_HOL_Obool)),X12618),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12621,tc_fun(X12620,tc_HOL_Obool)),X12619),X12617))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12621,tc_fun(X12620,tc_HOL_Obool)),X12619),hAPP(hAPP(c_COMBB(tc_fun(X12620,tc_HOL_Obool),tc_fun(X12620,tc_HOL_Obool),X12621),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12620,tc_HOL_Obool)),X12618)),X12617)), inference(variable_rename,[status(thm)],[fact_INT__simps_I7_J])). 6.97/7.24 cnf(c_0_9606, plain, (c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),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)],[inference(rw,[status(thm)],[c_0_5628, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.24 fof(c_0_9607, plain, ![X11522, X11523, X11524]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X11524,X11524),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X11524,X11524),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X11524,X11523)),c_Transitive__Closure_Ortrancl(X11524,X11522))),c_Transitive__Closure_Ortrancl(X11524,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X11524,X11524),tc_HOL_Obool)),X11523),X11522)))), inference(variable_rename,[status(thm)],[fact_rtrancl__Un__subset])). 6.97/7.24 fof(c_0_9608, plain, ![X17430, X17431, X17432, X17433, X17434, X17435]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X17435,X17433),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X17435,X17434,X17433),X17432),X17430)),hAPP(hAPP(c_Relation_Orel__comp(X17435,X17434,X17433),X17431),X17430))=hAPP(hAPP(c_Relation_Orel__comp(X17435,X17434,X17433),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X17435,X17434),tc_HOL_Obool)),X17432),X17431)),X17430), inference(variable_rename,[status(thm)],[fact_rel__comp__distrib2])). 6.97/7.24 fof(c_0_9609, plain, ![X3440, X3441, X3442, X3443, X3444, X3445]:hAPP(hAPP(c_Relation_Orel__comp(X3445,X3444,X3443),X3442),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3444,X3443),tc_HOL_Obool)),X3441),X3440))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3445,X3443),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X3445,X3444,X3443),X3442),X3441)),hAPP(hAPP(c_Relation_Orel__comp(X3445,X3444,X3443),X3442),X3440)), inference(variable_rename,[status(thm)],[fact_rel__comp__distrib])). 6.97/7.24 cnf(c_0_9610, 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_5629])). 6.97/7.24 cnf(c_0_9611, plain, (hAPP(hAPP(c_Set_Oinsert(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))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),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(split_conjunct,[status(thm)],[c_0_5630])). 6.97/7.24 fof(c_0_9612, plain, ![X1803, X1804, X1805, X1806, X1807, X1808, X1809, X1810, X1811, X1812]:hAPP(c_Fun_Ocomp(tc_prod(X1812,X1811),tc_prod(X1810,X1809),tc_prod(X1808,X1807),c_Product__Type_Omap__pair(X1812,X1810,X1811,X1809,X1806,X1805)),c_Product__Type_Omap__pair(X1808,X1812,X1807,X1811,X1804,X1803))=c_Product__Type_Omap__pair(X1808,X1810,X1807,X1809,hAPP(c_Fun_Ocomp(X1812,X1810,X1808,X1806),X1804),hAPP(c_Fun_Ocomp(X1811,X1809,X1807,X1805),X1803)), inference(variable_rename,[status(thm)],[fact_map__pair_Ocomp])). 6.97/7.24 fof(c_0_9613, plain, ![X9455, X9456]:c_Transitive__Closure_Ortrancl(X9456,X9455)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X9456,X9456),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(X9456,X9456),tc_HOL_Obool),tc_fun(tc_prod(X9456,X9456),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X9456,X9456),tc_HOL_Obool)),X9455)), inference(variable_rename,[status(thm)],[fact_rtrancl__is__UN__rel__pow])). 6.97/7.24 fof(c_0_9614, plain, ![X16477, X16478, X16479]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X16479,tc_HOL_Obool),tc_fun(X16479,tc_HOL_Obool)),X16478),hAPP(hAPP(c_COMBC(tc_fun(X16479,tc_HOL_Obool),tc_fun(X16479,tc_HOL_Obool),tc_fun(X16479,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16479,tc_HOL_Obool))),X16477))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16479,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X16479,tc_HOL_Obool),X16478)),X16477), inference(variable_rename,[status(thm)],[fact_Int__Union2])). 6.97/7.24 fof(c_0_9615, plain, ![X10164, X10165, X10166, X10167, X10168]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10167,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10168,tc_fun(X10167,tc_HOL_Obool)),X10166),X10164)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10168,tc_fun(X10167,tc_HOL_Obool)),X10165),X10164))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10168,tc_fun(X10167,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10168,tc_HOL_Obool)),X10166),X10165)),X10164), inference(variable_rename,[status(thm)],[fact_INT__Un])). 6.97/7.24 fof(c_0_9616, plain, ![X10267, X10268, X10269, X10270, X10271]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10270,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10271,tc_fun(X10270,tc_HOL_Obool)),X10269),X10267)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10271,tc_fun(X10270,tc_HOL_Obool)),X10268),X10267))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10271,tc_fun(X10270,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10271,tc_HOL_Obool)),X10269),X10268)),X10267), inference(variable_rename,[status(thm)],[fact_UN__Un])). 6.97/7.24 cnf(c_0_9617, plain, (hAPP(c_List_Orotate(X1,X2),hAPP(c_List_Orotate(X1,X3),X4))=hAPP(c_List_Orotate(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),X4)), inference(split_conjunct,[status(thm)],[c_0_5631])). 6.97/7.24 fof(c_0_9618, plain, ![X8683, X8684, X8685]:hAPP(c_Set_OPow(X8685),hAPP(hAPP(c_Set_Oinsert(X8685),X8684),X8683))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X8685,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X8685),X8683)),hAPP(c_Set_Oimage(tc_fun(X8685,tc_HOL_Obool),tc_fun(X8685,tc_HOL_Obool),hAPP(c_Set_Oinsert(X8685),X8684)),hAPP(c_Set_OPow(X8685),X8683))), inference(variable_rename,[status(thm)],[fact_Pow__insert])). 6.97/7.24 cnf(c_0_9619, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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),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)))))), inference(split_conjunct,[status(thm)],[c_0_5632])). 6.97/7.24 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[c_0_5633, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.24 fof(c_0_9621, plain, ![X814, X815, X816, X817]:c_Random__Sequence_Omap(X817,X816,X815,X814)=c_Random__Sequence_Obind(X817,X816,X814,hAPP(c_Fun_Ocomp(X816,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_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X816)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),X817,c_Random__Sequence_Osingle(X816)),X815)), inference(variable_rename,[status(thm)],[fact_Random__Sequence_Omap__def])). 6.97/7.24 cnf(c_0_9622, 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_5634, c_0_4645]), c_0_4645])). 6.97/7.24 cnf(c_0_9623, plain, (hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))=hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(c_List_Orev(X2),X4))), inference(split_conjunct,[status(thm)],[c_0_5635]), ['final']). 6.97/7.24 fof(c_0_9624, plain, ![X8543, X8544, X8545, X8546]:hAPP(hAPP(c_Nat_Ocompow(tc_prod(X8546,X8546),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X8545),X8544)),X8543)=hAPP(hAPP(c_Relation_Orel__comp(X8546,X8546,X8546),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X8546,X8546),tc_HOL_Obool),X8545),X8543)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X8546,X8546),tc_HOL_Obool),X8544),X8543)), inference(variable_rename,[status(thm)],[fact_rel__pow__add])). 6.97/7.24 fof(c_0_9625, plain, ![X3081, X3082, X3083, X3084]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3083,tc_fun(tc_fun(X3084,tc_HOL_Obool),tc_HOL_Obool)),X3082),hAPP(hAPP(c_COMBB(tc_fun(X3084,tc_HOL_Obool),tc_fun(tc_fun(X3084,tc_HOL_Obool),tc_HOL_Obool),X3083),c_Set_OPow(X3084)),X3081))=hAPP(c_Set_OPow(X3084),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3083,tc_fun(X3084,tc_HOL_Obool)),X3082),X3081)), inference(variable_rename,[status(thm)],[fact_Pow__INT__eq])). 6.97/7.24 cnf(c_0_9626, 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),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),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)],[inference(rw,[status(thm)],[c_0_5636, c_0_5174]), c_0_5174])). 6.97/7.24 cnf(c_0_9627, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),hAPP(hAPP(c_Relation_Orel__comp(X1,X4,X2),X5),X6)),X7)=hAPP(hAPP(c_Relation_Orel__comp(X1,X4,X3),X5),hAPP(hAPP(c_Relation_Orel__comp(X4,X2,X3),X6),X7))), inference(split_conjunct,[status(thm)],[c_0_5637]), ['final']). 6.97/7.24 cnf(c_0_9628, plain, (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),c_Transitive__Closure_Ortrancl(X1,X2)),X2)), inference(split_conjunct,[status(thm)],[c_0_5638]), ['final']). 6.97/7.24 cnf(c_0_9629, plain, (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),esk566_1(X1)),esk567_1(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_5639])). 6.97/7.24 cnf(c_0_9630, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)=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,X3),X2))),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),X3)),X2)))), inference(split_conjunct,[status(thm)],[c_0_5640])). 6.97/7.24 cnf(c_0_9631, 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_5641]), ['final']). 6.97/7.24 cnf(c_0_9632, 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_5642])). 6.97/7.24 fof(c_0_9633, plain, ![X1178, X1179, X1180, X1181, X1182, X1183]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1180,tc_fun(X1182,tc_HOL_Obool)),X1179),hAPP(hAPP(c_COMBB(tc_fun(X1183,tc_HOL_Obool),tc_fun(X1182,tc_HOL_Obool),X1180),c_Set_Oimage(X1183,X1182,X1181)),X1178))=hAPP(c_Set_Oimage(X1183,X1182,X1181),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1180,tc_fun(X1183,tc_HOL_Obool)),X1179),X1178)), inference(variable_rename,[status(thm)],[fact_image__UN])). 6.97/7.24 cnf(c_0_9634, plain, (hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(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(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X4),c_Set_Ovimage(X1,X2,X3)),X6))), inference(split_conjunct,[status(thm)],[c_0_5643])). 6.97/7.24 fof(c_0_9635, plain, ![X11154, X11155, X11156, X11157, X11158, X11159]:hAPP(c_Relation_OImage(X11159,X11158,X11157),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11156,tc_fun(X11159,tc_HOL_Obool)),X11155),X11154))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11156,tc_fun(X11158,tc_HOL_Obool)),X11155),hAPP(hAPP(c_COMBB(tc_fun(X11159,tc_HOL_Obool),tc_fun(X11158,tc_HOL_Obool),X11156),c_Relation_OImage(X11159,X11158,X11157)),X11154)), inference(variable_rename,[status(thm)],[fact_Image__UN])). 6.97/7.24 fof(c_0_9636, plain, ![X12832, X12833, X12834, X12835]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X12835,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12834,tc_fun(X12835,tc_HOL_Obool)),X12833),X12832))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12834,tc_fun(X12835,tc_HOL_Obool)),X12833),hAPP(hAPP(c_COMBB(tc_fun(X12835,tc_HOL_Obool),tc_fun(X12835,tc_HOL_Obool),X12834),c_Groups_Ouminus__class_Ouminus(tc_fun(X12835,tc_HOL_Obool))),X12832)), inference(variable_rename,[status(thm)],[fact_Compl__INT])). 6.97/7.24 fof(c_0_9637, plain, ![X12860, X12861, X12862, X12863]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X12863,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12862,tc_fun(X12863,tc_HOL_Obool)),X12861),X12860))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12862,tc_fun(X12863,tc_HOL_Obool)),X12861),hAPP(hAPP(c_COMBB(tc_fun(X12863,tc_HOL_Obool),tc_fun(X12863,tc_HOL_Obool),X12862),c_Groups_Ouminus__class_Ouminus(tc_fun(X12863,tc_HOL_Obool))),X12860)), inference(variable_rename,[status(thm)],[fact_Compl__UN])). 6.97/7.24 fof(c_0_9638, plain, ![X2137, X2138, X2139, X2140, X2141]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2141,tc_fun(X2140,tc_HOL_Obool)),X2139),hAPP(hAPP(c_COMBB(tc_fun(X2140,tc_HOL_Obool),tc_fun(X2140,tc_HOL_Obool),X2141),hAPP(c_Set_Oinsert(X2140),X2138)),X2137))=hAPP(hAPP(c_Set_Oinsert(X2140),X2138),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2141,tc_fun(X2140,tc_HOL_Obool)),X2139),X2137)), inference(variable_rename,[status(thm)],[fact_INT__simps_I5_J])). 6.97/7.24 fof(c_0_9639, plain, ![X8678, X8679, X8680, X8681]:hAPP(hAPP(c_List_Oappend(X8681),hAPP(hAPP(c_List_Odrop(X8681),X8680),X8679)),hAPP(hAPP(c_List_Odrop(X8681),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X8680),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8681)),X8679))),X8678))=hAPP(hAPP(c_List_Odrop(X8681),X8680),hAPP(hAPP(c_List_Oappend(X8681),X8679),X8678)), inference(variable_rename,[status(thm)],[fact_drop__append])). 6.97/7.24 fof(c_0_9640, plain, ![X11617, X11618, X11619, X11620]:hAPP(hAPP(c_List_Otake(X11620),X11619),hAPP(hAPP(c_List_Oappend(X11620),X11618),X11617))=hAPP(hAPP(c_List_Oappend(X11620),hAPP(hAPP(c_List_Otake(X11620),X11619),X11618)),hAPP(hAPP(c_List_Otake(X11620),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11619),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11620)),X11618))),X11617)), inference(variable_rename,[status(thm)],[fact_take__append])). 6.97/7.24 cnf(c_0_9641, 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_5644])). 6.97/7.24 cnf(c_0_9642, plain, (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))=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))), inference(split_conjunct,[status(thm)],[c_0_5645])). 6.97/7.24 cnf(c_0_9643, 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)],[inference(rw,[status(thm)],[c_0_5646, c_0_4692]), c_0_5647]), c_0_4692]), ['final']). 6.97/7.24 fof(c_0_9644, plain, ![X5094, X5095, X5096, X5097]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5097,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5097,tc_HOL_Obool)),X5096),X5095)),X5094)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5097,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5097,tc_HOL_Obool)),X5096),X5094)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5097,tc_HOL_Obool)),X5095),X5094)), inference(variable_rename,[status(thm)],[fact_Un__Diff])). 6.97/7.24 fof(c_0_9645, plain, ![X6868, X6869, X6870, X6871]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6871,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6871,tc_HOL_Obool)),X6870),X6869)),X6868)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6871,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6871,tc_HOL_Obool)),X6870),X6868)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6871,tc_HOL_Obool)),X6869),X6868)), inference(variable_rename,[status(thm)],[fact_Int__Un__distrib2])). 6.97/7.24 fof(c_0_9646, plain, ![X13832, X13833, X13834, X13835]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13835,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13835,tc_HOL_Obool)),X13834),X13833)),X13832)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13835,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13835,tc_HOL_Obool)),X13834),X13832)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13835,tc_HOL_Obool)),X13833),X13832)), inference(variable_rename,[status(thm)],[fact_Un__Int__distrib2])). 6.97/7.24 fof(c_0_9647, plain, ![X16634, X16635, X16636, X16637]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16637,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16637,tc_HOL_Obool)),X16636),X16635)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16637,tc_HOL_Obool)),X16636),X16634))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16637,tc_HOL_Obool)),X16636),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16637,tc_HOL_Obool)),X16635),X16634)), inference(variable_rename,[status(thm)],[fact_Un__Int__distrib])). 6.97/7.24 fof(c_0_9648, plain, ![X12366, X12367, X12368, X12369]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12369,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12369,tc_HOL_Obool)),X12368),X12367)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12369,tc_HOL_Obool)),X12368),X12366))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12369,tc_HOL_Obool)),X12368),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12369,tc_HOL_Obool)),X12367),X12366)), inference(variable_rename,[status(thm)],[fact_Diff__Int])). 6.97/7.24 fof(c_0_9649, plain, ![X11811, X11812, X11813, X11814]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11814,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11814,tc_HOL_Obool)),X11813),X11812)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11814,tc_HOL_Obool)),X11813),X11811))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11814,tc_HOL_Obool)),X11813),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11814,tc_HOL_Obool)),X11812),X11811)), inference(variable_rename,[status(thm)],[fact_Int__Un__distrib])). 6.97/7.24 cnf(c_0_9650, 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)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_5648])). 6.97/7.24 cnf(c_0_9651, 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_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)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Ominus__class_Ominus(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5649, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.24 fof(c_0_9652, plain, ![X460, X461, X462, X463]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X463,tc_HOL_Obool)),X462),hAPP(hAPP(c_Set_Oinsert(X463),X461),X460))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X463,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X463,tc_HOL_Obool)),X462),X460)),hAPP(hAPP(c_Set_Oinsert(X463),X461),c_Orderings_Obot__class_Obot(tc_fun(X463,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_Diff__insert])). 6.97/7.24 fof(c_0_9653, plain, ![X2421, X2422, X2423, X2424, X2425]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X2425,X2424),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X2425,X2424),X2423),X2421)),hAPP(hAPP(c_Product__Type_OSigma(X2425,X2424),X2422),X2421))=hAPP(hAPP(c_Product__Type_OSigma(X2425,X2424),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2425,tc_HOL_Obool)),X2423),X2422)),X2421), inference(variable_rename,[status(thm)],[fact_Sigma__Int__distrib1])). 6.97/7.24 fof(c_0_9654, plain, ![X7413, X7414, X7415, X7416, X7417]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7417,X7416),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X7417,X7416),X7415),X7413)),hAPP(hAPP(c_Product__Type_OSigma(X7417,X7416),X7414),X7413))=hAPP(hAPP(c_Product__Type_OSigma(X7417,X7416),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7417,tc_HOL_Obool)),X7415),X7414)),X7413), inference(variable_rename,[status(thm)],[fact_Sigma__Un__distrib1])). 6.97/7.24 fof(c_0_9655, plain, ![X10083, X10084, X10085, X10086, X10087]:hAPP(hAPP(c_Product__Type_OSigma(X10087,X10086),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10087,tc_HOL_Obool)),X10085),X10084)),X10083)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X10087,X10086),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X10087,X10086),X10085),X10083)),hAPP(hAPP(c_Product__Type_OSigma(X10087,X10086),X10084),X10083)), inference(variable_rename,[status(thm)],[fact_Sigma__Diff__distrib1])). 6.97/7.24 fof(c_0_9656, plain, ![X14086, X14087]:c_Random_Opick(X14087,X14086)=c_Random_Opick(X14087,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X14087),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X14087,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X14087,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X14087)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X14086)), inference(variable_rename,[status(thm)],[fact_pick__drop__zero])). 6.97/7.24 cnf(c_0_9657, 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_5650])). 6.97/7.24 fof(c_0_9658, plain, ![X4367, X4368]:c_Random_Oselect__weight(X4368,X4367)=c_Random_Oselect__weight(X4368,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X4368),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X4368,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4368,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X4368)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X4367)), inference(variable_rename,[status(thm)],[fact_select__weigth__drop__zero])). 6.97/7.24 fof(c_0_9659, plain, ![X6738, X6739]:c_HOL_OThe(X6739,hAPP(hAPP(c_COMBB(tc_fun(X6739,tc_HOL_Obool),tc_HOL_Obool,X6739),hAPP(c_fequal,X6738)),hAPP(hAPP(c_COMBC(X6739,tc_fun(X6739,tc_HOL_Obool),tc_fun(X6739,tc_HOL_Obool)),c_Set_Oinsert(X6739)),c_Orderings_Obot__class_Obot(tc_fun(X6739,tc_HOL_Obool)))))=c_Set_Othe__elem(X6739,X6738), inference(variable_rename,[status(thm)],[fact_the__elem__def])). 6.97/7.24 cnf(c_0_9660, 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_5651, c_0_4645]), c_0_4645])). 6.97/7.24 fof(c_0_9661, plain, ![X2033, X2034, X2035, X2036, X2037]:hAPP(hAPP(c_List_Oappend(tc_prod(X2037,X2036)),hAPP(hAPP(c_List_Omap(X2036,tc_prod(X2037,X2036)),hAPP(c_Product__Type_OPair(X2037,X2036),X2035)),X2033)),c_Enum_Oproduct(X2037,X2036,X2034,X2033))=c_Enum_Oproduct(X2037,X2036,hAPP(hAPP(c_List_Olist_OCons(X2037),X2035),X2034),X2033), inference(variable_rename,[status(thm)],[fact_product_Osimps_I2_J])). 6.97/7.24 cnf(c_0_9662, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[c_0_5652, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411])). 6.97/7.24 fof(c_0_9663, plain, ![X13183, X13184]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X13184),X13183)=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)),X13184)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X13183))), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J])). 6.97/7.24 cnf(c_0_9664, 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_5653])). 6.97/7.24 cnf(c_0_9665, plain, (c_Product__Type_Oprod_Oprod__size(X1,X2,X3,X4,X5)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X3,hAPP(c_Product__Type_Ofst(X1,X2),X5))),hAPP(X4,hAPP(c_Product__Type_Osnd(X1,X2),X5)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_5654])). 6.97/7.24 cnf(c_0_9666, plain, (hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),X1),X2)=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)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5655, c_0_5656]), c_0_5657]), c_0_5657])). 6.97/7.24 cnf(c_0_9667, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(hAPP(c_List_Oappend(X1),X4),X5))=hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5))), inference(split_conjunct,[status(thm)],[c_0_5658]), ['final']). 6.97/7.24 cnf(c_0_9668, 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),X1),X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5659, c_0_4410]), c_0_4410])). 6.97/7.24 cnf(c_0_9669, plain, (hAPP(c_List_Ofilter(X3,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot),hAPP(c_fequal,X2))),hAPP(hAPP(c_List_Olist_OCons(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))),X4)|X1!=X2), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5660, c_0_4573]), c_0_4573])). 6.97/7.24 cnf(c_0_9670, 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_5661, c_0_4467])). 6.97/7.24 cnf(c_0_9671, 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_5662])). 6.97/7.24 cnf(c_0_9672, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__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_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_5663])). 6.97/7.24 cnf(c_0_9673, plain, (c_Divides_Opdivmod(X1,X2)=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)))), inference(split_conjunct,[status(thm)],[c_0_5664])). 6.97/7.24 cnf(c_0_9674, 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_5665]), ['final']). 6.97/7.24 fof(c_0_9675, plain, ![X3904, X3905, X3906, X3907]:hAPP(c_Product__Type_Oprod_Oprod__case(X3907,X3906,X3905),hAPP(hAPP(c_COMBB(tc_fun(X3906,tc_prod(X3907,X3906)),tc_fun(X3906,X3905),X3907),hAPP(c_COMBB(tc_prod(X3907,X3906),X3905,X3906),X3904)),c_Product__Type_OPair(X3907,X3906)))=X3904, inference(variable_rename,[status(thm)],[fact_split__eta])). 6.97/7.24 fof(c_0_9676, plain, ![X11299, X11300, X11301, X11302, X11303]:c_List_OtakeWhile(tc_prod(X11303,X11302),hAPP(c_Fun_Ocomp(X11303,tc_HOL_Obool,tc_prod(X11303,X11302),X11301),c_Product__Type_Ofst(X11303,X11302)),hAPP(hAPP(c_List_Ozip(X11303,X11302),X11300),X11299))=hAPP(hAPP(c_List_Ozip(X11303,X11302),c_List_OtakeWhile(X11303,X11301,X11300)),X11299), inference(variable_rename,[status(thm)],[fact_zip__takeWhile__fst])). 6.97/7.24 fof(c_0_9677, plain, ![X5319, X5320, X5321, X5322, X5323]:hAPP(hAPP(c_List_Ozip(X5323,X5322),X5321),c_List_OtakeWhile(X5322,X5320,X5319))=c_List_OtakeWhile(tc_prod(X5323,X5322),hAPP(c_Fun_Ocomp(X5322,tc_HOL_Obool,tc_prod(X5323,X5322),X5320),c_Product__Type_Osnd(X5323,X5322)),hAPP(hAPP(c_List_Ozip(X5323,X5322),X5321),X5319)), inference(variable_rename,[status(thm)],[fact_zip__takeWhile__snd])). 6.97/7.24 cnf(c_0_9678, plain, (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))=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))|X1!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5666])). 6.97/7.24 fof(c_0_9679, plain, ![X10789, X10790, X10791, X10792, X10793]:hAPP(hAPP(c_List_Olist__update(X10793,hAPP(hAPP(c_List_Oappend(X10793),X10792),hAPP(hAPP(c_List_Olist_OCons(X10793),X10791),X10790))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10793)),X10792)),X10789)=hAPP(hAPP(c_List_Oappend(X10793),X10792),hAPP(hAPP(c_List_Olist_OCons(X10793),X10789),X10790)), inference(variable_rename,[status(thm)],[fact_list__update__length])). 6.97/7.24 cnf(c_0_9680, 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)),c_List_Olist_ONil(X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X1),tc_HOL_Obool))))=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_5667])). 6.97/7.24 fof(c_0_9681, plain, ![X14607, X14608, X14609, X14610]:hAPP(hAPP(c_List_Odrop(X14610),X14609),hAPP(hAPP(c_List_Olist_OCons(X14610),X14608),X14607))=c_Nat_Onat_Onat__case(tc_List_Olist(X14610),hAPP(hAPP(c_List_Olist_OCons(X14610),X14608),X14607),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X14610),tc_List_Olist(X14610)),c_List_Odrop(X14610)),X14607),X14609), inference(variable_rename,[status(thm)],[fact_drop__Cons])). 6.97/7.24 fof(c_0_9682, plain, ![X14898, X14899, X14900, X14901, X14902]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14901,tc_HOL_Obool)),hAPP(c_Relation_OImage(X14902,X14901,X14900),X14898)),hAPP(c_Relation_OImage(X14902,X14901,X14899),X14898))=hAPP(c_Relation_OImage(X14902,X14901,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X14902,X14901),tc_HOL_Obool)),X14900),X14899)),X14898), inference(variable_rename,[status(thm)],[fact_Un__Image])). 6.97/7.24 cnf(c_0_9683, 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_5668, c_0_5560])). 6.97/7.24 cnf(c_0_9684, plain, (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,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1),X3))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))), inference(split_conjunct,[status(thm)],[c_0_5669])). 6.97/7.24 cnf(c_0_9685, 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_5670, c_0_4632])). 6.97/7.24 cnf(c_0_9686, plain, (hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2))=X2), inference(split_conjunct,[status(thm)],[c_0_5671]), ['final']). 6.97/7.24 cnf(c_0_9687, 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_5672, c_0_5560])). 6.97/7.24 cnf(c_0_9688, 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_5673])). 6.97/7.24 fof(c_0_9689, plain, ![X309, X310, X311, X312]:c_New__Random__Sequence_Oneg__bind(X312,X311,X309,hAPP(c_Fun_Ocomp(X311,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(X311)))))),X312,c_New__Random__Sequence_Oneg__single(X311)),X310))=c_New__Random__Sequence_Oneg__map(X312,X311,X310,X309), inference(variable_rename,[status(thm)],[fact_neg__map__def])). 6.97/7.24 cnf(c_0_9690, 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_5674])). 6.97/7.24 fof(c_0_9691, plain, ![X11252, X11253]: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)),X11253)),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),X11252),X11253)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X11253),X11252), inference(variable_rename,[status(thm)],[fact_image__add__int__atLeastLessThan])). 6.97/7.24 fof(c_0_9692, plain, ![X8752, X8753, X8754, X8755]:hAPP(c_Relation_Oconverse(X8755,X8754),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X8755,X8754),tc_HOL_Obool)),X8753),X8752))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X8754,X8755),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X8755,X8754),X8753)),hAPP(c_Relation_Oconverse(X8755,X8754),X8752)), inference(variable_rename,[status(thm)],[fact_converse__Int])). 6.97/7.24 fof(c_0_9693, plain, ![X16160, X16161, X16162, X16163]:hAPP(c_Relation_Oconverse(X16163,X16162),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X16163,X16162),tc_HOL_Obool)),X16161),X16160))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X16162,X16163),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X16163,X16162),X16161)),hAPP(c_Relation_Oconverse(X16163,X16162),X16160)), inference(variable_rename,[status(thm)],[fact_converse__Un])). 6.97/7.24 cnf(c_0_9694, 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_5675])). 6.97/7.24 fof(c_0_9695, plain, ![X11006, X11007, X11008, X11009]:hAPP(hAPP(c_Nat_Ocompow(X11009,X11009),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11008),X11007)),X11006)=hAPP(c_Fun_Ocomp(X11009,X11009,X11009,hAPP(hAPP(c_Nat_Ocompow(X11009,X11009),X11008),X11006)),hAPP(hAPP(c_Nat_Ocompow(X11009,X11009),X11007),X11006)), inference(variable_rename,[status(thm)],[fact_funpow__add])). 6.97/7.24 cnf(c_0_9696, 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_5676])). 6.97/7.24 fof(c_0_9697, plain, ![X3769, X3770, X3771, X3772, X3773]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3772,tc_HOL_Obool)),hAPP(c_Relation_OImage(X3773,X3772,X3771),X3770)),hAPP(c_Relation_OImage(X3773,X3772,X3771),X3769))=hAPP(c_Relation_OImage(X3773,X3772,X3771),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3773,tc_HOL_Obool)),X3770),X3769)), inference(variable_rename,[status(thm)],[fact_Image__Un])). 6.97/7.24 cnf(c_0_9698, 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_5677])). 6.97/7.24 cnf(c_0_9699, plain, (hAPP(c_Set_Ovimage(X1,X2,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_Ovimage(X1,X2,X3),X4)),hAPP(c_Set_Ovimage(X1,X2,X3),X5))), inference(split_conjunct,[status(thm)],[c_0_5678])). 6.97/7.24 cnf(c_0_9700, 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_5679])). 6.97/7.24 cnf(c_0_9701, plain, (hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X2)),X3)=hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X2),X3)),X3)), inference(split_conjunct,[status(thm)],[c_0_5680]), ['final']). 6.97/7.24 cnf(c_0_9702, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Int_OMin)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(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))), inference(rw,[status(thm)],[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_5681, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), c_0_4411]), c_0_4411])). 6.97/7.24 cnf(c_0_9703, plain, (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))=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))), inference(split_conjunct,[status(thm)],[c_0_5682])). 6.97/7.24 cnf(c_0_9704, plain, (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_Int_OMin),hAPP(hAPP(c_Groups_Ominus__class_Ominus(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)],[inference(rw,[status(thm)],[c_0_5683, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411])). 6.97/7.24 fof(c_0_9705, plain, ![X7215, X7216, X7217, X7218]:hAPP(hAPP(c_Set_Oinsert(X7218),X7217),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7218,tc_HOL_Obool)),X7216),X7215))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7218,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7218),X7217),X7216)),hAPP(hAPP(c_Set_Oinsert(X7218),X7217),X7215)), inference(variable_rename,[status(thm)],[fact_insert__inter__insert])). 6.97/7.24 fof(c_0_9706, plain, ![X3527, X3528, X3529, X3530]:c_New__Random__Sequence_Opos__map(X3530,X3529,X3528,X3527)=c_New__Random__Sequence_Opos__bind(X3530,X3529,X3527,hAPP(c_Fun_Ocomp(X3529,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(X3529))))),X3530,c_New__Random__Sequence_Opos__single(X3529)),X3528)), inference(variable_rename,[status(thm)],[fact_pos__map__def])). 6.97/7.24 cnf(c_0_9707, plain, (X3=hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5)|hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3)!=X4|hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X2),c_Product__Type_Osnd(X1,X2)),X3)!=X5|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_5207])). 6.97/7.24 cnf(c_0_9708, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),hAPP(hAPP(c_List_Omap(X1,X3),X4),X2))), inference(split_conjunct,[status(thm)],[c_0_5684]), ['final']). 6.97/7.24 fof(c_0_9709, plain, ![X956, X957, X958, X959]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X959,tc_HOL_Obool)),hAPP(c_List_Oset(X959),hAPP(hAPP(c_List_Olist__update(X959,X958),X957),X956))),hAPP(hAPP(c_Set_Oinsert(X959),X956),hAPP(c_List_Oset(X959),X958)))), inference(variable_rename,[status(thm)],[fact_set__update__subset__insert])). 6.97/7.24 cnf(c_0_9710, 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_5685])). 6.97/7.24 fof(c_0_9711, plain, ![X15204, X15205, X15206]: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),X15206),X15205))),X15204)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X15206)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X15205)),X15204)), inference(variable_rename,[status(thm)],[fact_zadd__int__left])). 6.97/7.24 fof(c_0_9712, plain, ![X14314, X14315, X14316, X14317, X14318]:hAPP(hAPP(c_List_Ozip(X14318,X14317),hAPP(hAPP(c_List_Odrop(X14318),X14316),X14315)),hAPP(hAPP(c_List_Odrop(X14317),X14316),X14314))=hAPP(hAPP(c_List_Odrop(tc_prod(X14318,X14317)),X14316),hAPP(hAPP(c_List_Ozip(X14318,X14317),X14315),X14314)), inference(variable_rename,[status(thm)],[fact_drop__zip])). 6.97/7.24 fof(c_0_9713, plain, ![X10213, X10214, X10215, X10216]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10216),X10214)),hAPP(c_Finite__Set_Ocard(X10215),X10213))=hAPP(c_Finite__Set_Ocard(tc_prod(X10216,X10215)),hAPP(hAPP(c_Product__Type_OSigma(X10216,X10215),X10214),hAPP(c_COMBK(tc_fun(X10215,tc_HOL_Obool),X10216),X10213))), inference(variable_rename,[status(thm)],[fact_card__cartesian__product])). 6.97/7.24 fof(c_0_9714, plain, ![X15044, X15045, X15046]:c_List_Opartition(X15046,X15045,X15044)=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X15046),tc_List_Olist(X15046)),hAPP(c_List_Ofilter(X15046,X15045),X15044)),hAPP(c_List_Ofilter(X15046,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X15046,c_fNot),X15045)),X15044)), inference(variable_rename,[status(thm)],[fact_partition__filter__conv])). 6.97/7.24 fof(c_0_9715, plain, ![X10796, X10797, X10798, X10799]:hAPP(c_Hilbert__Choice_Oinv__into(X10799,X10798,c_Orderings_Otop__class_Otop(tc_fun(X10799,tc_HOL_Obool)),X10797),X10796)=c_Hilbert__Choice_OEps(X10799,hAPP(hAPP(c_COMBC(X10799,X10798,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X10798,tc_fun(X10798,tc_HOL_Obool),X10799),c_fequal),X10797)),X10796)), inference(variable_rename,[status(thm)],[fact_inv__def])). 6.97/7.24 cnf(c_0_9716, plain, (c_Wellfounded_Opred__nat=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)))), inference(split_conjunct,[status(thm)],[fact_pred__nat__def])). 6.97/7.24 fof(c_0_9717, plain, ![X6949, X6950, X6951, X6952]:hAPP(hAPP(c_Product__Type_OSigma(X6952,X6951),hAPP(c_List_Oset(X6952),X6950)),hAPP(c_COMBK(tc_fun(X6951,tc_HOL_Obool),X6952),hAPP(c_List_Oset(X6951),X6949)))=hAPP(c_List_Oset(tc_prod(X6952,X6951)),c_Enum_Oproduct(X6952,X6951,X6950,X6949)), inference(variable_rename,[status(thm)],[fact_product__list__set])). 6.97/7.24 cnf(c_0_9718, plain, (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(X3)),X4))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(X1,X3))),hAPP(hAPP(c_List_Ozip(X1,X3),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_5686])). 6.97/7.24 fof(c_0_9719, plain, ![X6393, X6394]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6394,X6394),tc_HOL_Obool)),c_Relation_OId__on(X6394,X6393)),hAPP(hAPP(c_Product__Type_OSigma(X6394,X6394),X6393),hAPP(c_COMBK(tc_fun(X6394,tc_HOL_Obool),X6394),X6393)))), inference(variable_rename,[status(thm)],[fact_Id__on__subset__Times])). 6.97/7.24 fof(c_0_9720, plain, ![X9466, X9467, X9468, X9469, X9470]:hAPP(c_List_Omap(X9468,X9469),hAPP(c_Fun_Ocomp(X9470,X9469,X9468,X9467),X9466))=hAPP(c_Fun_Ocomp(tc_List_Olist(X9470),tc_List_Olist(X9469),tc_List_Olist(X9468),hAPP(c_List_Omap(X9470,X9469),X9467)),hAPP(c_List_Omap(X9468,X9470),X9466)), inference(variable_rename,[status(thm)],[fact_map__comp__map])). 6.97/7.24 fof(c_0_9721, plain, ![X5040, X5041, X5042]:c_Fun_Oinj__on(tc_prod(X5042,X5041),tc_prod(X5041,X5042),hAPP(c_Product__Type_Oprod_Oprod__case(X5042,X5041,tc_prod(X5041,X5042)),hAPP(c_COMBC(X5041,X5042,tc_prod(X5041,X5042)),c_Product__Type_OPair(X5041,X5042))),X5040), inference(variable_rename,[status(thm)],[fact_swap__inj__on])). 6.97/7.24 fof(c_0_9722, plain, ![X15538]:c_Fun_Oinj__on(X15538,tc_fun(X15538,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X15538,tc_fun(X15538,tc_HOL_Obool),tc_fun(X15538,tc_HOL_Obool)),c_Set_Oinsert(X15538)),c_Orderings_Obot__class_Obot(tc_fun(X15538,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X15538,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_inj__singleton])). 6.97/7.24 fof(c_0_9723, plain, ![X7987, X7988, X7989, X7990]:hAPP(c_Relation_ODomain(X7990,X7989),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7990,X7989),tc_HOL_Obool)),X7988),X7987))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7990,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X7990,X7989),X7988)),hAPP(c_Relation_ODomain(X7990,X7989),X7987)), inference(variable_rename,[status(thm)],[fact_Domain__Un__eq])). 6.97/7.24 fof(c_0_9724, plain, ![X3460, X3461, X3462, X3463]:hAPP(c_Relation_ORange(X3463,X3462),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3463,X3462),tc_HOL_Obool)),X3461),X3460))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3462,tc_HOL_Obool)),hAPP(c_Relation_ORange(X3463,X3462),X3461)),hAPP(c_Relation_ORange(X3463,X3462),X3460)), inference(variable_rename,[status(thm)],[fact_Range__Un__eq])). 6.97/7.24 cnf(c_0_9725, 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_5687])). 6.97/7.24 cnf(c_0_9726, 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_5688]), ['final']). 6.97/7.24 cnf(c_0_9727, 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_5689])). 6.97/7.24 cnf(c_0_9728, 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_5690]), ['final']). 6.97/7.24 cnf(c_0_9729, 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_5691])). 6.97/7.24 fof(c_0_9730, plain, ![X9689, X9690, X9691]:hAPP(hAPP(c_Set_Oinsert(X9691),X9690),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9691,tc_HOL_Obool)),X9689),hAPP(hAPP(c_Set_Oinsert(X9691),X9690),c_Orderings_Obot__class_Obot(tc_fun(X9691,tc_HOL_Obool)))))=hAPP(hAPP(c_Set_Oinsert(X9691),X9690),X9689), inference(variable_rename,[status(thm)],[fact_insert__Diff__single])). 6.97/7.24 fof(c_0_9731, plain, ![X15051, X15052, X15053, X15054]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15053,tc_fun(X15054,tc_HOL_Obool))),c_Predicate_Oconversep(X15054,X15053,X15052)),c_Predicate_Oconversep(X15054,X15053,X15051))=c_Predicate_Oconversep(X15054,X15053,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15054,tc_fun(X15053,tc_HOL_Obool))),X15052),X15051)), inference(variable_rename,[status(thm)],[fact_converse__meet])). 6.97/7.24 fof(c_0_9732, plain, ![X13225, X13226, X13227, X13228]:c_Predicate_Oconversep(X13228,X13227,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13228,tc_fun(X13227,tc_HOL_Obool))),X13226),X13225))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13227,tc_fun(X13228,tc_HOL_Obool))),c_Predicate_Oconversep(X13228,X13227,X13226)),c_Predicate_Oconversep(X13228,X13227,X13225)), inference(variable_rename,[status(thm)],[fact_converse__join])). 6.97/7.24 fof(c_0_9733, plain, ![X15696, X15697, X15698, X15699, X15700]:hAPP(hAPP(c_Set_Oinsert(X15700),X15698),hAPP(c_Relation_ODomain(X15700,X15699),X15696))=hAPP(c_Relation_ODomain(X15700,X15699),hAPP(hAPP(c_Set_Oinsert(tc_prod(X15700,X15699)),hAPP(hAPP(c_Product__Type_OPair(X15700,X15699),X15698),X15697)),X15696)), inference(variable_rename,[status(thm)],[fact_Domain__insert])). 6.97/7.24 fof(c_0_9734, plain, ![X1459, X1460, X1461, X1462, X1463]:hAPP(hAPP(c_Set_Oinsert(X1462),X1460),hAPP(c_Relation_ORange(X1463,X1462),X1459))=hAPP(c_Relation_ORange(X1463,X1462),hAPP(hAPP(c_Set_Oinsert(tc_prod(X1463,X1462)),hAPP(hAPP(c_Product__Type_OPair(X1463,X1462),X1461),X1460)),X1459)), inference(variable_rename,[status(thm)],[fact_Range__insert])). 6.97/7.24 fof(c_0_9735, plain, ![X16313, X16314]:X16313=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16314,tc_fun(X16314,tc_HOL_Obool)),X16313),hAPP(hAPP(c_COMBC(X16314,tc_fun(X16314,tc_HOL_Obool),tc_fun(X16314,tc_HOL_Obool)),c_Set_Oinsert(X16314)),c_Orderings_Obot__class_Obot(tc_fun(X16314,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_UN__singleton])). 6.97/7.24 fof(c_0_9736, plain, ![X9682, X9683, X9684, X9685, X9686]:hAPP(c_List_Ofilter(X9686,X9685),hAPP(hAPP(c_List_Omap(X9684,X9686),X9683),X9682))=hAPP(hAPP(c_List_Omap(X9684,X9686),X9683),hAPP(c_List_Ofilter(X9684,hAPP(c_Fun_Ocomp(X9686,tc_HOL_Obool,X9684,X9685),X9683)),X9682)), inference(variable_rename,[status(thm)],[fact_filter__map])). 6.97/7.24 fof(c_0_9737, plain, ![X9505, X9506, X9507]:hBOOL(hAPP(hAPP(c_member(tc_prod(X9507,X9507)),hAPP(hAPP(c_Product__Type_OPair(X9507,X9507),X9506),X9506)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X9507,X9507),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X9505))), inference(variable_rename,[status(thm)],[fact_rel__pow__0__I])). 6.97/7.24 cnf(c_0_9738, 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_5692])). 6.97/7.24 cnf(c_0_9739, plain, (c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X1,X2,X3,X4,X5)=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_5693])). 6.97/7.24 cnf(c_0_9740, plain, (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)))=hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_5694])). 6.97/7.24 cnf(c_0_9741, 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(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))))=hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1))), inference(split_conjunct,[status(thm)],[c_0_5695])). 6.97/7.24 cnf(c_0_9742, plain, (hAPP(c_List_Orotate1(X1),hAPP(c_List_Orotate(X1,X2),X3))=hAPP(c_List_Orotate(X1,hAPP(c_Nat_OSuc,X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_5696])). 6.97/7.24 fof(c_0_9743, plain, ![X1999, X2000, X2001]:c_Transitive__Closure_Ortrancl(X2001,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2001,X2001),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X2001,X2000)),c_Transitive__Closure_Ortrancl(X2001,X1999)))=c_Transitive__Closure_Ortrancl(X2001,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2001,X2001),tc_HOL_Obool)),X2000),X1999)), inference(variable_rename,[status(thm)],[fact_rtrancl__Un__rtrancl])). 6.97/7.24 cnf(c_0_9744, 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_5697])). 6.97/7.24 cnf(c_0_9745, 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_5698])). 6.97/7.24 fof(c_0_9746, plain, ![X8941, X8942, X8943]:hAPP(c_List_Orev(X8943),hAPP(hAPP(c_List_Odrop(X8943),X8942),X8941))=hAPP(hAPP(c_List_Otake(X8943),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8943)),X8941)),X8942)),hAPP(c_List_Orev(X8943),X8941)), inference(variable_rename,[status(thm)],[fact_rev__drop])). 6.97/7.24 fof(c_0_9747, plain, ![X13862, X13863, X13864]:hAPP(c_List_Orev(X13864),hAPP(hAPP(c_List_Otake(X13864),X13863),X13862))=hAPP(hAPP(c_List_Odrop(X13864),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13864)),X13862)),X13863)),hAPP(c_List_Orev(X13864),X13862)), inference(variable_rename,[status(thm)],[fact_rev__take])). 6.97/7.24 fof(c_0_9748, plain, ![X15559, X15560, X15561, X15562, X15563]:hAPP(hAPP(c_Relation_Orel__comp(X15562,X15561,X15563),hAPP(c_Relation_Oconverse(X15561,X15562),X15559)),hAPP(c_Relation_Oconverse(X15563,X15561),X15560))=hAPP(c_Relation_Oconverse(X15563,X15562),hAPP(hAPP(c_Relation_Orel__comp(X15563,X15561,X15562),X15560),X15559)), inference(variable_rename,[status(thm)],[fact_converse__rel__comp])). 6.97/7.24 fof(c_0_9749, plain, ![X5764, X5765, X5766, X5767]:hAPP(hAPP(c_List_Onth(X5767),hAPP(hAPP(c_List_Oappend(X5767),X5766),X5765)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5767)),X5766)),X5764))=hAPP(hAPP(c_List_Onth(X5767),X5765),X5764), inference(variable_rename,[status(thm)],[fact_nth__append__length__plus])). 6.97/7.24 cnf(c_0_9750, 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_5699])). 6.97/7.24 cnf(c_0_9751, 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_5700])). 6.97/7.24 fof(c_0_9752, plain, ![X14721, X14722]:hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X14722),tc_List_Olist(X14722))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X14722),tc_List_Olist(X14722)),c_List_Olist_ONil(X14722)),c_List_Olist_ONil(X14722))),c_List_Olistrel(X14722,X14721))), inference(variable_rename,[status(thm)],[fact_listrel_ONil])). 6.97/7.24 cnf(c_0_9753, 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_5701])). 6.97/7.24 fof(c_0_9754, plain, ![X3566, X3567, X3568, X3569]:hAPP(hAPP(c_List_Oappend(X3569),c_List_Oreplicate(X3569,X3568,X3567)),hAPP(hAPP(c_List_Olist_OCons(X3569),X3567),X3566))=hAPP(hAPP(c_List_Olist_OCons(X3569),X3567),hAPP(hAPP(c_List_Oappend(X3569),c_List_Oreplicate(X3569,X3568,X3567)),X3566)), inference(variable_rename,[status(thm)],[fact_replicate__app__Cons__same])). 6.97/7.24 fof(c_0_9755, plain, ![X10737, X10738, X10739]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X10739,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X10739),X10738)),hAPP(c_Set_OPow(X10739),X10737))=hAPP(c_Set_OPow(X10739),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10739,tc_HOL_Obool)),X10738),X10737)), inference(variable_rename,[status(thm)],[fact_Pow__Int__eq])). 6.97/7.24 fof(c_0_9756, plain, ![X4698, X4699, X4700, X4701]:hAPP(hAPP(c_List_Otake(X4701),X4700),hAPP(hAPP(c_List_Odrop(X4701),X4699),X4698))=hAPP(hAPP(c_List_Odrop(X4701),X4699),hAPP(hAPP(c_List_Otake(X4701),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4700),X4699)),X4698)), inference(variable_rename,[status(thm)],[fact_take__drop])). 6.97/7.24 fof(c_0_9757, plain, ![X1030, X1031, X1032, X1033, X1034]:c_List_Osplice(X1034,hAPP(hAPP(c_List_Olist_OCons(X1034),X1033),X1032),hAPP(hAPP(c_List_Olist_OCons(X1034),X1031),X1030))=hAPP(hAPP(c_List_Olist_OCons(X1034),X1033),hAPP(hAPP(c_List_Olist_OCons(X1034),X1031),c_List_Osplice(X1034,X1032,X1030))), inference(variable_rename,[status(thm)],[fact_splice_Osimps_I3_J])). 6.97/7.24 cnf(c_0_9758, 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_5702])). 6.97/7.24 fof(c_0_9759, plain, ![X9818, X9819, X9820]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X9820),X9818)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X9819),X9818))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X9820),X9819)),X9818), inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib])). 6.97/7.24 fof(c_0_9760, plain, ![X11503, X11504, X11505]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11505),X11503)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11504),X11503))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11505),X11504)),X11503), inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib])). 6.97/7.24 fof(c_0_9761, plain, ![X12993, X12994, X12995]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12995),X12994)),X12993)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12995),X12993)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12994),X12993)), inference(variable_rename,[status(thm)],[fact_diff__mult__distrib])). 6.97/7.24 fof(c_0_9762, plain, ![X3487, X3488, X3489]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3489),X3488)),X3487)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3489),X3487)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3488),X3487)), inference(variable_rename,[status(thm)],[fact_add__mult__distrib])). 6.97/7.24 fof(c_0_9763, plain, ![X10901, X10902, X10903, X10904]:hAPP(hAPP(c_List_Odrop(X10904),X10903),hAPP(hAPP(c_List_Otake(X10904),X10902),X10901))=hAPP(hAPP(c_List_Otake(X10904),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X10902),X10903)),hAPP(hAPP(c_List_Odrop(X10904),X10903),X10901)), inference(variable_rename,[status(thm)],[fact_drop__take])). 6.97/7.24 fof(c_0_9764, plain, ![X8768, X8769, X8770]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8770),X8769)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8770),X8768))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8770),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X8769),X8768)), inference(variable_rename,[status(thm)],[fact_diff__mult__distrib2])). 6.97/7.24 fof(c_0_9765, plain, ![X11836, X11837, X11838]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11838),X11837)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11838),X11836))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11838),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11837),X11836)), inference(variable_rename,[status(thm)],[fact_add__mult__distrib2])). 6.97/7.24 fof(c_0_9766, plain, ![X5897, X5898, X5899]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5899),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5898),X5897))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5899),X5898)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5899),X5897)), inference(variable_rename,[status(thm)],[fact_zpower__zadd__distrib])). 6.97/7.24 fof(c_0_9767, plain, ![X17546, X17547, X17548]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17548),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X17547),X17546))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17548),X17547)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17548),X17546)), inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib2])). 6.97/7.24 cnf(c_0_9768, plain, (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))=hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))|X1!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5703])). 6.97/7.24 fof(c_0_9769, plain, ![X10476, X10477]:hAPP(hAPP(c_Product__Type_OSigma(X10477,X10476),c_Orderings_Otop__class_Otop(tc_fun(X10477,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X10476,tc_HOL_Obool),X10477),c_Orderings_Otop__class_Otop(tc_fun(X10476,tc_HOL_Obool))))=c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X10477,X10476),tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_UNIV__Times__UNIV])). 6.97/7.24 cnf(c_0_9770, 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_5704])). 6.97/7.24 cnf(c_0_9771, 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_5267])). 6.97/7.24 cnf(c_0_9772, plain, (hAPP(c_SetInterval_Oord__class_OatLeast(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_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))))), inference(split_conjunct,[status(thm)],[c_0_5705])). 6.97/7.24 cnf(c_0_9773, 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_5706]), ['final']). 6.97/7.24 fof(c_0_9774, plain, ![X15163, X15164, X15165, X15166, X15167]:hAPP(hAPP(c_List_Omap(X15165,X15167),X15164),c_List_OtakeWhile(X15165,hAPP(c_Fun_Ocomp(X15167,tc_HOL_Obool,X15165,X15166),X15164),X15163))=c_List_OtakeWhile(X15167,X15166,hAPP(hAPP(c_List_Omap(X15165,X15167),X15164),X15163)), inference(variable_rename,[status(thm)],[fact_takeWhile__map])). 6.97/7.24 cnf(c_0_9775, 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_5707])). 6.97/7.24 fof(c_0_9776, plain, ![X15095, X15096, X15097]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15097,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15097,tc_HOL_Obool)),X15096),X15095)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15097,tc_HOL_Obool)),X15096),X15095))=X15096, inference(variable_rename,[status(thm)],[fact_Un__Diff__Int])). 6.97/7.24 fof(c_0_9777, plain, ![X6110, X6111, X6112]:hAPP(c_Relation_OField(X6112),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X6112,X6112),tc_HOL_Obool)),X6111),X6110))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6112,tc_HOL_Obool)),hAPP(c_Relation_OField(X6112),X6111)),hAPP(c_Relation_OField(X6112),X6110)), inference(variable_rename,[status(thm)],[fact_Field__Un])). 6.97/7.24 fof(c_0_9778, plain, ![X11379, X11380]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X11380),tc_List_Olist(X11380)),tc_HOL_Obool)),c_List_Olistrel1(X11380,c_Transitive__Closure_Ortrancl(X11380,X11379))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X11380),c_List_Olistrel1(X11380,X11379)))), inference(variable_rename,[status(thm)],[fact_listrel1__rtrancl__subset__rtrancl__listrel1])). 6.97/7.24 fof(c_0_9779, plain, ![X7591, X7592, X7593, X7594]:c_Fun_Ocomp(X7593,X7593,X7594,hAPP(hAPP(c_Nat_Ocompow(X7593,X7593),X7592),X7591))=hAPP(hAPP(c_Nat_Ocompow(tc_fun(X7594,X7593),tc_fun(X7594,X7593)),X7592),c_Fun_Ocomp(X7593,X7593,X7594,X7591)), inference(variable_rename,[status(thm)],[fact_comp__funpow])). 6.97/7.24 cnf(c_0_9780, 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_5708])). 6.97/7.24 cnf(c_0_9781, 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)),hAPP(c_Nat_OSuc,X3))), inference(split_conjunct,[status(thm)],[c_0_5709])). 6.97/7.24 fof(c_0_9782, plain, ![X4300, X4301, X4302, X4303, X4304, X4305, X4306, X4307]:hAPP(hAPP(c_Product__Type_OPair(X4306,X4304),hAPP(X4303,X4301)),hAPP(X4302,X4300))=hAPP(c_Product__Type_Omap__pair(X4307,X4306,X4305,X4304,X4303,X4302),hAPP(hAPP(c_Product__Type_OPair(X4307,X4305),X4301),X4300)), inference(variable_rename,[status(thm)],[fact_map__pair__simp])). 6.97/7.24 fof(c_0_9783, plain, ![X12547, X12548, X12549, X12550, X12551]:hAPP(hAPP(c_List_Olist__update(X12551,hAPP(hAPP(c_List_Olist_OCons(X12551),X12550),X12549)),hAPP(c_Nat_OSuc,X12548)),X12547)=hAPP(hAPP(c_List_Olist_OCons(X12551),X12550),hAPP(hAPP(c_List_Olist__update(X12551,X12549),X12548),X12547)), inference(variable_rename,[status(thm)],[fact_list__update__code_I3_J])). 6.97/7.24 cnf(c_0_9784, plain, (hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),c_List_OdropWhile(X1,X2,X3))=X3), inference(split_conjunct,[status(thm)],[c_0_5710])). 6.97/7.24 fof(c_0_9785, plain, ![X11383, X11384, X11385]:hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11385,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X11385),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X11384)),X11383)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11385,tc_Nat_Onat),X11384),X11383)), inference(variable_rename,[status(thm)],[fact_int__setsum])). 6.97/7.24 fof(c_0_9786, plain, ![X1602, X1603, X1604]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1604,tc_Nat_Onat),X1603),X1602))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1604,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X1604),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1603)),X1602), inference(variable_rename,[status(thm)],[fact_int__setprod])). 6.97/7.24 cnf(c_0_9787, 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_5711])). 6.97/7.24 cnf(c_0_9788, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_5712])). 6.97/7.24 cnf(c_0_9789, 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_5713])). 6.97/7.24 cnf(c_0_9790, 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(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X3,X5)),hAPP(X4,X6))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_5714])). 6.97/7.24 cnf(c_0_9791, 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_Orderings_Oord__class_Omin(tc_Nat_Onat),X1)),X2)=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_5715])). 6.97/7.24 cnf(c_0_9792, 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_5716])). 6.97/7.24 cnf(c_0_9793, 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_Relation_OId(X1))=c_Transitive__Closure_Ortrancl(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5717])). 6.97/7.24 fof(c_0_9794, plain, ![X16446, X16447, X16448, X16449]:hAPP(hAPP(c_Nat_Ocompow(X16449,X16449),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16447),X16448)),X16446)=hAPP(hAPP(c_Nat_Ocompow(X16449,X16449),X16448),hAPP(hAPP(c_Nat_Ocompow(X16449,X16449),X16447),X16446)), inference(variable_rename,[status(thm)],[fact_funpow__mult])). 6.97/7.24 fof(c_0_9795, plain, ![X4341, X4342, X4343]:hAPP(hAPP(c_List_Otake(X4343),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4342),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(X4343),X4341))=hAPP(c_List_Otl(X4343),hAPP(hAPP(c_List_Otake(X4343),X4342),X4341)), inference(variable_rename,[status(thm)],[fact_tl__take])). 6.97/7.24 fof(c_0_9796, plain, ![X15012, X15013, X15014, X15015, X15016]:hAPP(c_New__DSequence_Oneg__bind(X15016,X15015,X15014,X15013),X15012)=c_Lazy__Sequence_Ohb__bind(X15016,X15015,hAPP(X15014,X15012),hAPP(hAPP(c_COMBC(X15016,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X15015))),X15013),X15012)), inference(variable_rename,[status(thm)],[fact_New__DSequence_Oneg__bind__def])). 6.97/7.24 fof(c_0_9797, plain, ![X16772, X16773, X16774, X16775, X16776]:hAPP(c_Lazy__Sequence_Obind(X16776,X16775,hAPP(X16774,X16772)),hAPP(hAPP(c_COMBC(X16776,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X16775)),X16773),X16772))=hAPP(c_New__DSequence_Opos__bind(X16776,X16775,X16774,X16773),X16772), inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__bind__def])). 6.97/7.24 fof(c_0_9798, plain, ![X3736, X3737, X3738, X3739]:hAPP(hAPP(c_List_Onth(X3739),hAPP(hAPP(c_List_Oappend(X3739),X3738),hAPP(hAPP(c_List_Olist_OCons(X3739),X3737),X3736))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3739)),X3738))=X3737, inference(variable_rename,[status(thm)],[fact_nth__append__length])). 6.97/7.24 fof(c_0_9799, plain, ![X10830, X10831, X10832]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10832,tc_fun(X10831,tc_HOL_Obool)),X10830),hAPP(c_COMBK(tc_fun(X10831,tc_HOL_Obool),X10832),c_Orderings_Obot__class_Obot(tc_fun(X10831,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X10831,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_UN__empty2])). 6.97/7.24 cnf(c_0_9800, plain, (c_List_Oreplicate(X1,X2,X3)=hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),hAPP(c_COMBK(X1,tc_Nat_Onat),X3)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))), inference(split_conjunct,[status(thm)],[c_0_5718])). 6.97/7.24 cnf(c_0_9801, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|hAPP(c_Finite__Set_Ocard(X1),X4)=hAPP(c_Nat_OSuc,X5)|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=X2|hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)!=X4|hAPP(c_Finite__Set_Ocard(X1),X2)!=X5), inference(split_conjunct,[status(thm)],[c_0_5303])). 6.97/7.24 cnf(c_0_9802, 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)), inference(er,[status(thm)],[c_0_5719]), ['final']). 6.97/7.24 cnf(c_0_9803, 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_5720]), ['final']). 6.97/7.24 cnf(c_0_9804, 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_5721])). 6.97/7.24 fof(c_0_9805, plain, ![X1232, X1233, X1234, X1235]:hAPP(c_List_Ofilter(X1235,X1234),hAPP(hAPP(c_List_Oappend(X1235),X1233),X1232))=hAPP(hAPP(c_List_Oappend(X1235),hAPP(c_List_Ofilter(X1235,X1234),X1233)),hAPP(c_List_Ofilter(X1235,X1234),X1232)), inference(variable_rename,[status(thm)],[fact_filter__append])). 6.97/7.24 fof(c_0_9806, plain, ![X12464, X12465]:hAPP(c_Set_OPow(X12465),hAPP(c_List_Oset(X12465),X12464))=hAPP(c_Set_Oimage(tc_List_Olist(X12465),tc_fun(X12465,tc_HOL_Obool),c_List_Oset(X12465)),hAPP(c_List_Oset(tc_List_Olist(X12465)),c_Enum_Osublists(X12465,X12464))), inference(variable_rename,[status(thm)],[fact_sublists__powset])). 6.97/7.24 cnf(c_0_9807, 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(c_COMBK(tc_fun(X3,tc_HOL_Obool),X1),X4))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=X2), inference(split_conjunct,[status(thm)],[c_0_5722])). 6.97/7.24 fof(c_0_9808, plain, ![X5746, X5747]:hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X5747,X5746),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X5747),X5746)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5747,X5746)))), inference(variable_rename,[status(thm)],[fact_divmod__nat__rel])). 6.97/7.24 fof(c_0_9809, plain, ![X15017, X15018]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X15018),tc_List_Olist(X15018)),tc_HOL_Obool)),c_List_Olistrel(X15018,X15017)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X15018),c_List_Olistrel1(X15018,X15017)))), inference(variable_rename,[status(thm)],[fact_listrel__subset__rtrancl__listrel1])). 6.97/7.24 fof(c_0_9810, plain, ![X10258, X10259, X10260, X10261, X10262, X10263]:hAPP(c_List_Ofoldl(X10263,X10262,X10261,hAPP(c_List_Ofoldl(X10263,X10262,X10261,X10260),X10259)),X10258)=hAPP(c_List_Ofoldl(X10263,X10262,X10261,X10260),hAPP(hAPP(c_List_Oappend(X10262),X10259),X10258)), inference(variable_rename,[status(thm)],[fact_foldl__append])). 6.97/7.24 fof(c_0_9811, plain, ![X16763, X16764, X16765]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16765,tc_HOL_Obool)),hAPP(c_List_Oset(X16765),hAPP(hAPP(c_List_Odrop(X16765),X16764),X16763))),hAPP(c_List_Oset(X16765),X16763))), inference(variable_rename,[status(thm)],[fact_set__drop__subset])). 6.97/7.24 fof(c_0_9812, plain, ![X1628, X1629, X1630]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1630,tc_HOL_Obool)),hAPP(c_List_Oset(X1630),hAPP(hAPP(c_List_Otake(X1630),X1629),X1628))),hAPP(c_List_Oset(X1630),X1628))), inference(variable_rename,[status(thm)],[fact_set__take__subset])). 6.97/7.24 fof(c_0_9813, plain, ![X4234, X4235, X4236]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4236,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4236,tc_HOL_Obool)),X4235),X4234)),X4234)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4236,tc_HOL_Obool)),X4235),X4234), inference(variable_rename,[status(thm)],[fact_Diff__idemp])). 6.97/7.24 fof(c_0_9814, plain, ![X13616, X13617, X13618]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13618,tc_HOL_Obool)),X13617),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13618,tc_HOL_Obool)),X13617),X13616))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13618,tc_HOL_Obool)),X13617),X13616), inference(variable_rename,[status(thm)],[fact_Un__left__absorb])). 6.97/7.24 fof(c_0_9815, plain, ![X9543, X9544, X9545]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9545,tc_HOL_Obool)),X9544),X9543)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9545,tc_HOL_Obool)),X9544),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9545,tc_HOL_Obool)),X9544),X9543)), inference(variable_rename,[status(thm)],[fact_Int__left__absorb])). 6.97/7.24 fof(c_0_9816, plain, ![X15812, X15813, X15814]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15814,tc_HOL_Obool)),X15813),X15812)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15814,tc_HOL_Obool)),X15813),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15814,tc_HOL_Obool)),X15812),X15813)), inference(variable_rename,[status(thm)],[fact_Un__Diff__cancel])). 6.97/7.24 cnf(c_0_9817, 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_5723, c_0_4471]), c_0_4471])). 6.97/7.24 fof(c_0_9818, plain, ![X11767, X11768, X11769, X11770]:hAPP(hAPP(c_List_Olist_OCons(X11770),X11768),hAPP(hAPP(c_List_Otake(X11770),X11769),X11767))=hAPP(hAPP(c_List_Otake(X11770),hAPP(c_Nat_OSuc,X11769)),hAPP(hAPP(c_List_Olist_OCons(X11770),X11768),X11767)), inference(variable_rename,[status(thm)],[fact_take__Suc__Cons])). 6.97/7.24 fof(c_0_9819, plain, ![X4961, X4962, X4963]:c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X4961),X4962)=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),X4963),X4962)),X4961)),X4962), inference(variable_rename,[status(thm)],[fact_mod__mult__self4])). 6.97/7.24 cnf(c_0_9820, 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_5724])). 6.97/7.24 cnf(c_0_9821, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),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_5725, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4565])). 6.97/7.24 fof(c_0_9822, plain, ![X14816, X14817]:c_List_Olex(X14817,X14816)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(X14817),tc_List_Olist(X14817)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(X14817,X14816)), inference(variable_rename,[status(thm)],[fact_lex__def])). 6.97/7.24 cnf(c_0_9823, 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_5726])). 6.97/7.24 cnf(c_0_9824, plain, (hAPP(c_Set_Ovimage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5727])). 6.97/7.24 cnf(c_0_9825, plain, (hAPP(c_Set_Ovimage(X1,X1,c_COMBI(X1)),X2)=X2), inference(split_conjunct,[status(thm)],[c_0_5728])). 6.97/7.24 cnf(c_0_9826, plain, (hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X2)=X2), inference(split_conjunct,[status(thm)],[c_0_5729])). 6.97/7.24 cnf(c_0_9827, 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_5730])). 6.97/7.24 fof(c_0_9828, plain, ![X17149, X17150, X17151]:c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17151),X17149),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17150),X17149))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X17151,X17150)),X17149), inference(variable_rename,[status(thm)],[fact_mod__mult__distrib])). 6.97/7.24 fof(c_0_9829, plain, ![X935, X936, X937]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X937),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X936,X935))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X937),X936),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X937),X935)), inference(variable_rename,[status(thm)],[fact_mod__mult__distrib2])). 6.97/7.24 fof(c_0_9830, plain, ![X3263, X3264, X3265]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3265),X3264)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3265),X3263))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3264),X3263), inference(variable_rename,[status(thm)],[fact_diff__cancel])). 6.97/7.24 fof(c_0_9831, plain, ![X384, X385, X386]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X386),X384)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X386),X385)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X384),X385)), inference(variable_rename,[status(thm)],[fact_diff__cancel2])). 6.97/7.24 cnf(c_0_9832, 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_5731])). 6.97/7.24 cnf(c_0_9833, plain, (hAPP(hAPP(c_Product__Type_OSigma(X3,X1),X4),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X3),X2))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X1),tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=X2), inference(split_conjunct,[status(thm)],[c_0_5732])). 6.97/7.24 cnf(c_0_9834, plain, (X1=c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X2,X3,X1,X4,c_Lazy__Sequence_Olazy__sequence_OEmpty(X3))), inference(split_conjunct,[status(thm)],[c_0_5733])). 6.97/7.24 fof(c_0_9835, plain, ![X7582, X7583]:hAPP(c_List_Orev(X7583),X7582)=hAPP(c_List_Ofoldl(tc_List_Olist(X7583),X7583,hAPP(c_COMBC(X7583,tc_List_Olist(X7583),tc_List_Olist(X7583)),c_List_Olist_OCons(X7583)),c_List_Olist_ONil(X7583)),X7582), inference(variable_rename,[status(thm)],[fact_rev__foldl__cons])). 6.97/7.24 cnf(c_0_9836, 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_5734])). 6.97/7.24 fof(c_0_9837, plain, ![X8498, X8499, X8500]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X8500),tc_HOL_Obool)),c_List_Olistsp(X8500,X8499)),c_List_Olistsp(X8500,X8498))=c_List_Olistsp(X8500,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8500,tc_HOL_Obool)),X8499),X8498)), inference(variable_rename,[status(thm)],[fact_listsp__inf__eq])). 6.97/7.24 cnf(c_0_9838, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X3,tc_HOL_Obool)),X2),X4)),X5)=X5|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=X2), inference(split_conjunct,[status(thm)],[c_0_5735])). 6.97/7.24 cnf(c_0_9839, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(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_5736])). 6.97/7.24 cnf(c_0_9840, 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_5737])). 6.97/7.24 cnf(c_0_9841, plain, (X3=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X2),X5))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=X2), inference(split_conjunct,[status(thm)],[c_0_5738])). 6.97/7.24 fof(c_0_9842, plain, ![X7822, X7823, X7824]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7824)),hAPP(c_List_Ofilter(X7824,X7823),X7822))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7824)),X7822))), inference(variable_rename,[status(thm)],[fact_length__filter__le])). 6.97/7.24 cnf(c_0_9843, 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_Orotate(X1,X3),X2))), inference(split_conjunct,[status(thm)],[c_0_5739])). 6.97/7.24 cnf(c_0_9844, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)),X1)),X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5740, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.24 cnf(c_0_9845, 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_5741])). 6.97/7.24 cnf(c_0_9846, 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))|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_5742])). 6.97/7.24 cnf(c_0_9847, 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)), inference(split_conjunct,[status(thm)],[c_0_5743]), ['final']). 6.97/7.24 fof(c_0_9848, plain, ![X8865, X8866, X8867]:c_Random_Oselect__weight(X8867,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X8867)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X8867),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X8866)),X8865))=c_Random_Oselect__weight(X8867,X8865), inference(variable_rename,[status(thm)],[fact_select__weight__cons__zero])). 6.97/7.24 fof(c_0_9849, plain, ![X1554, X1555, X1556]:hAPP(hAPP(c_Nat_Ocompow(X1556,X1556),hAPP(c_Nat_OSuc,X1555)),X1554)=hAPP(c_Fun_Ocomp(X1556,X1556,X1556,X1554),hAPP(hAPP(c_Nat_Ocompow(X1556,X1556),X1555),X1554)), inference(variable_rename,[status(thm)],[fact_funpow_Osimps_I2_J])). 6.97/7.24 cnf(c_0_9850, 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_5744])). 6.97/7.24 cnf(c_0_9851, 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_5745, c_0_5746]), ['final']). 6.97/7.24 cnf(c_0_9852, 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_5747])). 6.97/7.24 cnf(c_0_9853, 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_5748]), ['final']). 6.97/7.24 cnf(c_0_9854, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=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))), inference(split_conjunct,[status(thm)],[c_0_5749])). 6.97/7.24 fof(c_0_9855, plain, ![X9983, X9984, X9985]:hAPP(c_List_Ofilter(X9985,hAPP(c_fequal,X9984)),X9983)=c_List_Oreplicate(X9985,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9985)),hAPP(c_List_Ofilter(X9985,hAPP(c_fequal,X9984)),X9983)),X9984), inference(variable_rename,[status(thm)],[fact_replicate__length__filter])). 6.97/7.24 fof(c_0_9856, plain, ![X14369, X14370]:hAPP(c_Relation_OField(X14370),X14369)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14370,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X14370,X14370),X14369)),hAPP(c_Relation_ORange(X14370,X14370),X14369)), inference(variable_rename,[status(thm)],[fact_Field__def])). 6.97/7.24 fof(c_0_9857, plain, ![X13029, X13030, X13031]:hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X13031,X13030,X13030),hAPP(c_COMBK(tc_fun(X13030,X13030),X13031),c_COMBI(X13030))),X13029)=hAPP(c_Product__Type_Osnd(X13031,X13030),X13029), inference(variable_rename,[status(thm)],[fact_snd__def])). 6.97/7.24 fof(c_0_9858, plain, ![X3329, X3330, X3331]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3331,tc_HOL_Obool)),hAPP(c_List_Oset(X3331),c_List_Osublist(X3331,X3330,X3329))),hAPP(c_List_Oset(X3331),X3330))), inference(variable_rename,[status(thm)],[fact_set__sublist__subset])). 6.97/7.24 fof(c_0_9859, plain, ![X9444, X9445, X9446]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9446,tc_HOL_Obool)),X9445),X9444)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9446,tc_HOL_Obool)),X9445),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9446,tc_HOL_Obool)),X9444)), inference(variable_rename,[status(thm)],[fact_Diff__Compl])). 6.97/7.24 fof(c_0_9860, plain, ![X5920, X5921, X5922]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5922,tc_HOL_Obool)),hAPP(c_List_Oset(X5922),c_List_Oremove1(X5922,X5921,X5920))),hAPP(c_List_Oset(X5922),X5920))), inference(variable_rename,[status(thm)],[fact_set__remove1__subset])). 6.97/7.24 fof(c_0_9861, plain, ![X1487, X1488, X1489]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1489)),c_List_OtakeWhile(X1489,X1488,X1487))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1489)),X1487))), inference(variable_rename,[status(thm)],[fact_length__takeWhile__le])). 6.97/7.24 fof(c_0_9862, plain, ![X6322, X6323]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X6323,tc_HOL_Obool),tc_HOL_Obool)),X6322),hAPP(c_Set_OPow(X6323),c_Complete__Lattice_OSup__class_OSup(tc_fun(X6323,tc_HOL_Obool),X6322)))), inference(variable_rename,[status(thm)],[fact_subset__Pow__Union])). 6.97/7.24 fof(c_0_9863, plain, ![X15836, X15837]: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,X15837)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X15836))), inference(variable_rename,[status(thm)],[fact_negative__zless])). 6.97/7.24 fof(c_0_9864, plain, ![X13138, X13139, X13140, X13141]:hAPP(hAPP(c_List_Oappend(X13141),hAPP(hAPP(c_List_Oappend(X13141),X13140),X13139)),X13138)=hAPP(hAPP(c_List_Oappend(X13141),X13140),hAPP(hAPP(c_List_Oappend(X13141),X13139),X13138)), inference(variable_rename,[status(thm)],[fact_append__assoc])). 6.97/7.24 fof(c_0_9865, plain, ![X10103, X10104, X10105, X10106]:hAPP(hAPP(c_List_Odrop(X10106),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10105),X10104)),X10103)=hAPP(hAPP(c_List_Odrop(X10106),X10105),hAPP(hAPP(c_List_Odrop(X10106),X10104),X10103)), inference(variable_rename,[status(thm)],[fact_drop__drop])). 6.97/7.24 cnf(c_0_9866, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X2),X3)),X4)=hAPP(hAPP(c_List_Otake(X1),X2),hAPP(hAPP(c_List_Otake(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_5750])). 6.97/7.24 cnf(c_0_9867, plain, (hAPP(hAPP(c_List_Olist_OCons(X2),X6),X1)=hAPP(hAPP(c_List_Oappend(X2),X5),X4)|X1!=hAPP(hAPP(c_List_Oappend(X2),X3),X4)|X5!=hAPP(hAPP(c_List_Olist_OCons(X2),X6),X3)), inference(split_conjunct,[status(thm)],[c_0_5751])). 6.97/7.24 fof(c_0_9868, plain, ![X11916, X11917, X11918]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X11918),X11917)),X11916)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X11918),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11917),X11916)), inference(variable_rename,[status(thm)],[fact_zpower__zpower])). 6.97/7.24 fof(c_0_9869, plain, ![X16333, X16334, X16335]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X16335),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16334),X16333))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X16335),X16334)),X16333), inference(variable_rename,[status(thm)],[fact_div__mult2__eq])). 6.97/7.24 fof(c_0_9870, plain, ![X14403, X14404, X14405]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14405),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14404),X14403))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14405),X14404)),X14403), inference(variable_rename,[status(thm)],[fact_zmult__assoc])). 6.97/7.24 fof(c_0_9871, plain, ![X12650, X12651, X12652]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12652),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12651),X12650))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12652),X12651)),X12650), inference(variable_rename,[status(thm)],[fact_nat__mult__assoc])). 6.97/7.24 fof(c_0_9872, plain, ![X9432, X9433, X9434, X9435]:hAPP(X9435,hAPP(hAPP(hAPP(c_Nat_Ocompow(X9434,X9434),X9433),X9435),X9432))=hAPP(hAPP(hAPP(c_Nat_Ocompow(X9434,X9434),X9433),X9435),hAPP(X9435,X9432)), inference(variable_rename,[status(thm)],[fact_funpow__swap1])). 6.97/7.24 cnf(c_0_9873, plain, (hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X1)))|X1!=hAPP(hAPP(c_List_Oappend(X2),X3),hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_5752])). 6.97/7.24 fof(c_0_9874, plain, ![X7668, X7669]:c_List_Obutlast(X7669,X7668)=hAPP(hAPP(c_List_Otake(X7669),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7669)),X7668)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X7668), inference(variable_rename,[status(thm)],[fact_butlast__conv__take])). 6.97/7.24 fof(c_0_9875, plain, ![X10385, X10386, X10387]: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,X10387,X10386)),X10385),X10386)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X10387),X10385),X10386), inference(variable_rename,[status(thm)],[fact_zpower__zmod])). 6.97/7.24 fof(c_0_9876, plain, ![X2353, X2354, X2355]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2355),X2353),X2354)=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,X2355,X2354)),X2353),X2354), inference(variable_rename,[status(thm)],[fact_zdiff__zmod__left])). 6.97/7.24 fof(c_0_9877, plain, ![X7346, X7347, X7348, X7349]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7348,tc_fun(X7349,tc_HOL_Obool)),X7346),X7347)=c_Complete__Lattice_OInf__class_OInf(tc_fun(X7349,tc_HOL_Obool),hAPP(c_Set_Oimage(X7348,tc_fun(X7349,tc_HOL_Obool),X7347),X7346)), inference(variable_rename,[status(thm)],[fact_Inter__image__eq])). 6.97/7.24 fof(c_0_9878, plain, ![X11002, X11003, X11004, X11005]:c_List_Oreplicate(X11005,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11004),X11003),X11002)=hAPP(hAPP(c_List_Oappend(X11005),c_List_Oreplicate(X11005,X11004,X11002)),c_List_Oreplicate(X11005,X11003,X11002)), inference(variable_rename,[status(thm)],[fact_replicate__add])). 6.97/7.24 fof(c_0_9879, plain, ![X12839, X12840, X12841]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12841),c_Divides_Odiv__class_Omod(tc_Int_Oint,X12840,X12839)),X12839)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12841),X12840),X12839), inference(variable_rename,[status(thm)],[fact_zmod__zmult1__eq])). 6.97/7.24 fof(c_0_9880, plain, ![X7021, X7022, X7023]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X7023),X7022),X7021)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X7023),c_Divides_Odiv__class_Omod(tc_Int_Oint,X7022,X7021)),X7021), inference(variable_rename,[status(thm)],[fact_zdiff__zmod__right])). 6.97/7.24 cnf(c_0_9881, 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,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_5753])). 6.97/7.24 cnf(c_0_9882, plain, (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))))=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)))), inference(rw,[status(thm)],[c_0_5754, c_0_5435])). 6.97/7.24 fof(c_0_9883, plain, ![X5336, X5337, X5338]:hAPP(c_List_Orev(X5338),hAPP(hAPP(c_List_Oappend(X5338),X5337),X5336))=hAPP(hAPP(c_List_Oappend(X5338),hAPP(c_List_Orev(X5338),X5336)),hAPP(c_List_Orev(X5338),X5337)), inference(variable_rename,[status(thm)],[fact_rev__append])). 6.97/7.24 fof(c_0_9884, plain, ![X11144, X11145]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X11145)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X11144))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X11145),X11144)), inference(variable_rename,[status(thm)],[fact_zdiv__int])). 6.97/7.24 fof(c_0_9885, plain, ![X6914, X6915]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6915),X6914))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6915)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6914)), inference(variable_rename,[status(thm)],[fact_zadd__int])). 6.97/7.24 fof(c_0_9886, plain, ![X3045, X3046]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3046),X3045))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3046)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3045)), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J])). 6.97/7.24 cnf(c_0_9887, 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_5382])). 6.97/7.24 fof(c_0_9888, plain, ![X2094, X2095, X2096, X2097, X2098]:hAPP(hAPP(c_List_Olist__update(X2098,X2097),X2096),X2094)=hAPP(hAPP(c_List_Olist__update(X2098,hAPP(hAPP(c_List_Olist__update(X2098,X2097),X2096),X2095)),X2096),X2094), inference(variable_rename,[status(thm)],[fact_list__update__overwrite])). 6.97/7.24 cnf(c_0_9889, 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_5755])). 6.97/7.24 fof(c_0_9890, plain, ![X1386, X1387, X1388]:c_Orderings_Obot__class_Obot(tc_fun(X1388,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1388,tc_HOL_Obool)),X1387),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1388,tc_HOL_Obool)),X1386),X1387)), inference(variable_rename,[status(thm)],[fact_Diff__disjoint])). 6.97/7.24 fof(c_0_9891, plain, ![X2404, X2405]: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),X2405),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2404)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2405,X2404), inference(variable_rename,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__functions_I2_J])). 6.97/7.24 fof(c_0_9892, plain, ![X4933, X4934, X4935, X4936, X4937, X4938, X4939]:hAPP(c_Product__Type_Osnd(X4939,X4938),hAPP(c_Product__Type_Omap__pair(X4937,X4939,X4936,X4938,X4935,X4934),X4933))=hAPP(X4934,hAPP(c_Product__Type_Osnd(X4937,X4936),X4933)), inference(variable_rename,[status(thm)],[fact_snd__prod__fun])). 6.97/7.24 fof(c_0_9893, plain, ![X4239, X4240, X4241, X4242, X4243, X4244, X4245]:hAPP(c_Product__Type_Ofst(X4245,X4244),hAPP(c_Product__Type_Omap__pair(X4243,X4245,X4242,X4244,X4241,X4240),X4239))=hAPP(X4241,hAPP(c_Product__Type_Ofst(X4243,X4242),X4239)), inference(variable_rename,[status(thm)],[fact_fst__map__pair])). 6.97/7.24 fof(c_0_9894, plain, ![X5593, X5594, X5595]:hAPP(c_List_Ofilter(X5595,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X5595,c_fNot),X5594)),X5593)=hAPP(c_Product__Type_Osnd(tc_List_Olist(X5595),tc_List_Olist(X5595)),c_List_Opartition(X5595,X5594,X5593)), inference(variable_rename,[status(thm)],[fact_partition__filter2])). 6.97/7.24 fof(c_0_9895, plain, ![X14844, X14845, X14846]:hBOOL(hAPP(hAPP(c_member(tc_prod(X14846,X14846)),hAPP(hAPP(c_Product__Type_OPair(X14846,X14846),X14845),X14845)),c_Transitive__Closure_Ortrancl(X14846,X14844))), inference(variable_rename,[status(thm)],[fact_rtrancl_Ortrancl__refl])). 6.97/7.24 fof(c_0_9896, plain, ![X4727, X4728]:c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X4728),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X4728))),c_List_Otranspose(X4728,X4727)))), inference(variable_rename,[status(thm)],[fact_sorted__transpose])). 6.97/7.24 cnf(c_0_9897, plain, (c_List_Oconcat(X1,c_List_Oreplicate(tc_List_Olist(X1),X2,c_List_Olist_ONil(X1)))=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_5756])). 6.97/7.24 fof(c_0_9898, plain, ![X13910, X13911]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X13911),hAPP(c_List_Oset(X13911),X13910))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13911)),X13910))), inference(variable_rename,[status(thm)],[fact_card__length])). 6.97/7.24 cnf(c_0_9899, 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_5757])). 6.97/7.24 cnf(c_0_9900, 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_5758])). 6.97/7.24 fof(c_0_9901, plain, ![X12381, X12382, X12383, X12384, X12385, X12386, X12387]:hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X12387,X12386,X12385,X12384),X12383),X12382),X12381)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X12386,X12385,X12384),X12382),hAPP(X12383,X12381)), inference(variable_rename,[status(thm)],[fact_scomp__apply])). 6.97/7.24 fof(c_0_9902, plain, ![X13849]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13849),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13849),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13849),X13849)))), inference(variable_rename,[status(thm)],[fact_le__cube])). 6.97/7.24 cnf(c_0_9903, plain, (c_List_Olistset(X1,c_List_Olist_ONil(tc_fun(X1,tc_HOL_Obool)))=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_5759])). 6.97/7.24 cnf(c_0_9904, plain, (c_Relation_OId(X1)=hAPP(c_Relation_Oconverse(X1,X1),c_Relation_OId(X1))), inference(split_conjunct,[status(thm)],[c_0_5760])). 6.97/7.24 cnf(c_0_9905, plain, (c_List_Olists(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=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_5761])). 6.97/7.24 cnf(c_0_9906, plain, (hAPP(hAPP(X1,X2),X3)=hAPP(hAPP(c_Product__Type_Ointernal__split(X4,X5,X6),X1),hAPP(hAPP(c_Product__Type_OPair(X4,X5),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5762])). 6.97/7.24 cnf(c_0_9907, plain, (c_Product__Type_Ointernal__split(X1,X2,X3)=c_Product__Type_Oprod_Oprod__case(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_5763])). 6.97/7.24 fof(c_0_9908, plain, ![X3714, X3715]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3715),hAPP(c_Nat_OSuc,X3714))=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),X3715),X3714)), inference(variable_rename,[status(thm)],[fact_diff__Suc])). 6.97/7.24 fof(c_0_9909, plain, ![X1880, X1881]:c_Complete__Lattice_OSup__class_OSup(tc_fun(X1881,tc_HOL_Obool),X1880)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1881,tc_HOL_Obool),tc_fun(X1881,tc_HOL_Obool)),X1880),c_COMBI(tc_fun(X1881,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Union__def])). 6.97/7.24 fof(c_0_9910, plain, ![X3560, X3561]:c_Complete__Lattice_OInf__class_OInf(tc_fun(X3561,tc_HOL_Obool),X3560)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X3561,tc_HOL_Obool),tc_fun(X3561,tc_HOL_Obool)),X3560),c_COMBI(tc_fun(X3561,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Inter__def])). 6.97/7.24 cnf(c_0_9911, 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_5167])). 6.97/7.24 fof(c_0_9912, plain, ![X4000, X4001, X4002, X4003]:hAPP(hAPP(c_Relation_Orel__comp(X4003,X4002,X4001),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4003,X4002),tc_HOL_Obool))),X4000)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4003,X4001),tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_rel__comp__empty1])). 6.97/7.24 cnf(c_0_9913, 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_5764])). 6.97/7.24 cnf(c_0_9914, 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_5765])). 6.97/7.24 fof(c_0_9915, plain, ![X8520, X8521, X8522, X8523, X8524]:c_Predicate_Oconversep(X8524,X8523,c_Predicate_Opred__comp(X8524,X8522,X8523,X8521,X8520))=c_Predicate_Opred__comp(X8523,X8522,X8524,c_Predicate_Oconversep(X8522,X8523,X8520),c_Predicate_Oconversep(X8524,X8522,X8521)), inference(variable_rename,[status(thm)],[fact_converse__pred__comp])). 6.97/7.24 fof(c_0_9916, plain, ![X1336, X1337, X1338, X1339]:hAPP(hAPP(c_List_Olist__update(X1339,hAPP(hAPP(c_List_Olist_OCons(X1339),X1338),X1337)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1336)=hAPP(hAPP(c_List_Olist_OCons(X1339),X1336),X1337), inference(variable_rename,[status(thm)],[fact_list__update__code_I2_J])). 6.97/7.24 fof(c_0_9917, plain, ![X15880, X15881, X15882, X15883]:c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X15883,X15881),tc_HOL_Obool))=hAPP(hAPP(c_Relation_Orel__comp(X15883,X15882,X15881),X15880),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X15882,X15881),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_rel__comp__empty2])). 6.97/7.24 fof(c_0_9918, plain, ![X822, X823, X824, X825]:c_List_Oremdups(X825,hAPP(hAPP(c_List_Omap(X824,X825),X823),X822))=c_List_Oremdups(X825,hAPP(hAPP(c_List_Omap(X824,X825),X823),c_List_Oremdups(X824,X822))), inference(variable_rename,[status(thm)],[fact_remdups__map__remdups])). 6.97/7.24 fof(c_0_9919, plain, ![X12462, X12463]: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),X12463),X12462)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X12463,X12462))=c_Code__Numeral_Odiv__mod__code__numeral(X12463,X12462), inference(variable_rename,[status(thm)],[fact_div__mod__code__numeral__def])). 6.97/7.24 fof(c_0_9920, plain, ![X12711, X12712, X12713, X12714]:hAPP(hAPP(c_List_Onth(X12714),X12712),X12711)=hAPP(hAPP(c_List_Onth(X12714),hAPP(hAPP(c_List_Olist_OCons(X12714),X12713),X12712)),hAPP(c_Nat_OSuc,X12711)), inference(variable_rename,[status(thm)],[fact_nth__Cons__Suc])). 6.97/7.24 cnf(c_0_9921, 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_5766])). 6.97/7.24 fof(c_0_9922, plain, ![X7586, X7587, X7588]:hAPP(hAPP(c_List_Otake(X7588),X7587),hAPP(c_List_Otl(X7588),X7586))=hAPP(c_List_Otl(X7588),hAPP(hAPP(c_List_Otake(X7588),hAPP(c_Nat_OSuc,X7587)),X7586)), inference(variable_rename,[status(thm)],[fact_take__tl])). 6.97/7.24 fof(c_0_9923, plain, ![X10994, X10995, X10996, X10997]:hAPP(hAPP(c_List_Odrop(X10997),hAPP(c_Nat_OSuc,X10996)),hAPP(hAPP(c_List_Olist_OCons(X10997),X10995),X10994))=hAPP(hAPP(c_List_Odrop(X10997),X10996),X10994), inference(variable_rename,[status(thm)],[fact_drop__Suc__Cons])). 6.97/7.24 fof(c_0_9924, plain, ![X1047, X1048, X1049]: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),X1049),X1048)),X1047),X1048)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1047,X1048), inference(variable_rename,[status(thm)],[fact_mod__mult__self3])). 6.97/7.24 fof(c_0_9925, plain, ![X5946, X5947, X5948]:X5946=hAPP(hAPP(c_List_Oappend(X5948),hAPP(hAPP(c_List_Otake(X5948),X5947),X5946)),hAPP(hAPP(c_List_Odrop(X5948),X5947),X5946)), inference(variable_rename,[status(thm)],[fact_append__take__drop__id])). 6.97/7.24 cnf(c_0_9926, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),X3)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_5767])). 6.97/7.24 fof(c_0_9927, plain, ![X8509, X8510, X8511]:hAPP(hAPP(c_List_Otake(X8511),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X8511),X8510),X8509))=hAPP(hAPP(c_List_Olist_OCons(X8511),X8510),c_List_Olist_ONil(X8511)), inference(variable_rename,[status(thm)],[fact_take__1__Cons])). 6.97/7.24 cnf(c_0_9928, 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_5768])). 6.97/7.24 cnf(c_0_9929, 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_5769])). 6.97/7.24 fof(c_0_9930, plain, ![X7802, X7803, X7804]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7804,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7804,tc_HOL_Obool)),X7803),X7802)),X7803)), inference(variable_rename,[status(thm)],[fact_Diff__subset])). 6.97/7.24 fof(c_0_9931, plain, ![X15985, X15986, X15987]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15987,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15987,tc_HOL_Obool)),X15986),X15985)),X15986)), inference(variable_rename,[status(thm)],[fact_Int__lower1])). 6.97/7.24 fof(c_0_9932, plain, ![X2749, X2750, X2751]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2751,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2751,tc_HOL_Obool)),X2750),X2749)),X2749)), inference(variable_rename,[status(thm)],[fact_Int__lower2])). 6.97/7.24 fof(c_0_9933, plain, ![X13448, X13449]:c_Relation_Osym(X13449,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X13449,X13449),tc_HOL_Obool)),X13448),hAPP(c_Relation_Oconverse(X13449,X13449),X13448))), inference(variable_rename,[status(thm)],[fact_sym__Int__converse])). 6.97/7.24 fof(c_0_9934, plain, ![X6688, X6689]:c_Relation_Osym(X6689,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X6689,X6689),tc_HOL_Obool)),X6688),hAPP(c_Relation_Oconverse(X6689,X6689),X6688))), inference(variable_rename,[status(thm)],[fact_sym__Un__converse])). 6.97/7.24 cnf(c_0_9935, plain, (hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X4,hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X1))|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_5770])). 6.97/7.24 fof(c_0_9936, plain, ![X14287, X14288, X14289]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14289,tc_HOL_Obool)),X14288),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14289,tc_HOL_Obool)),X14288),X14287))), inference(variable_rename,[status(thm)],[fact_Un__upper1])). 6.97/7.24 fof(c_0_9937, plain, ![X2005, X2006, X2007]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2007,tc_HOL_Obool)),X2006),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2007,tc_HOL_Obool)),X2005),X2006))), inference(variable_rename,[status(thm)],[fact_Un__upper2])). 6.97/7.24 fof(c_0_9938, plain, ![X669]: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,X669)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(variable_rename,[status(thm)],[fact_negative__zless__0])). 6.97/7.24 cnf(c_0_9939, plain, (hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin),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)],[inference(rw,[status(thm)],[c_0_5771, c_0_5772]), c_0_4741]), c_0_5002])). 6.97/7.24 cnf(c_0_9940, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5773, c_0_4741]), c_0_5002]), ['final']). 6.97/7.24 fof(c_0_9941, plain, ![X447, X448]: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),X448))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X447))), inference(variable_rename,[status(thm)],[fact_negative__zle])). 6.97/7.24 fof(c_0_9942, plain, ![X8778, X8779]: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),X8779)),X8778))), inference(variable_rename,[status(thm)],[fact_zero__le__zpower__abs])). 6.97/7.24 cnf(c_0_9943, plain, (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))=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)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X1), inference(split_conjunct,[status(thm)],[c_0_5342])). 6.97/7.24 cnf(c_0_9944, 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_5774, c_0_4413]), c_0_4413]), ['final']). 6.97/7.24 cnf(c_0_9945, plain, (X1=hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),X4)|X4!=hAPP(hAPP(c_List_Oappend(X2),X3),X1)), inference(split_conjunct,[status(thm)],[c_0_5237])). 6.97/7.24 cnf(c_0_9946, plain, (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)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_5775])). 6.97/7.24 cnf(c_0_9947, plain, (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)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_5776])). 6.97/7.24 cnf(c_0_9948, plain, (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)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_5777])). 6.97/7.24 cnf(c_0_9949, 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_5778])). 6.97/7.24 cnf(c_0_9950, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X2),c_Relation_OId(X1)),X3)=X3), inference(split_conjunct,[status(thm)],[c_0_5779])). 6.97/7.24 fof(c_0_9951, plain, ![X16412, X16413, X16414]:hAPP(hAPP(c_List_Otake(X16414),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16414)),c_List_OtakeWhile(X16414,X16413,X16412))),X16412)=c_List_OtakeWhile(X16414,X16413,X16412), inference(variable_rename,[status(thm)],[fact_takeWhile__eq__take])). 6.97/7.24 cnf(c_0_9952, plain, (X1=hAPP(hAPP(c_Relation_Orel__comp(X2,X3,X3),X1),c_Relation_OId(X3))), inference(split_conjunct,[status(thm)],[c_0_5780])). 6.97/7.24 fof(c_0_9953, plain, ![X3831, X3832, X3833]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X3833))),c_Enum_On__lists(X3833,X3832,X3831))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3833)),X3831)),X3832), inference(variable_rename,[status(thm)],[fact_length__n__lists])). 6.97/7.24 cnf(c_0_9954, plain, (X1=hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),X3)|X3!=hAPP(hAPP(c_List_Oappend(X2),X1),X4)), inference(split_conjunct,[status(thm)],[c_0_5237])). 6.97/7.24 cnf(c_0_9955, plain, (c_Sum__Type_OPlus(X1,X4,X2,X3)=c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X1,X4),tc_HOL_Obool))|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_5781])). 6.97/7.24 fof(c_0_9956, plain, ![X5913, X5914, X5915]:hAPP(hAPP(c_Product__Type_OPair(X5914,X5913),hAPP(c_Product__Type_Ofst(X5914,X5913),X5915)),hAPP(c_Product__Type_Osnd(X5914,X5913),X5915))=X5915, inference(variable_rename,[status(thm)],[fact_surjective__pairing])). 6.97/7.24 cnf(c_0_9957, 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_5782])). 6.97/7.24 fof(c_0_9958, plain, ![X13697, X13698]:c_Orderings_Otop__class_Otop(tc_fun(X13698,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13698,tc_HOL_Obool)),X13697),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X13698,tc_HOL_Obool)),X13697)), inference(variable_rename,[status(thm)],[fact_Compl__partition])). 6.97/7.24 fof(c_0_9959, plain, ![X7841, X7842, X7843, X7844, X7845, X7846]:c_Product__Type_Oprod_Oprod__rec(X7846,X7845,X7844,X7843,hAPP(hAPP(c_Product__Type_OPair(X7846,X7845),X7842),X7841))=hAPP(hAPP(X7843,X7842),X7841), inference(variable_rename,[status(thm)],[fact_prod_Orecs])). 6.97/7.24 fof(c_0_9960, plain, ![X12150, X12151, X12152, X12153, X12154, X12155]:hAPP(c_List_Olist_Olist__case(X12155,X12154,X12153,X12152),hAPP(hAPP(c_List_Olist_OCons(X12154),X12151),X12150))=hAPP(hAPP(X12152,X12151),X12150), inference(variable_rename,[status(thm)],[fact_list_Osimps_I5_J])). 6.97/7.24 cnf(c_0_9961, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5783, c_0_4409]), c_0_4410]), c_0_4411])). 6.97/7.24 cnf(c_0_9962, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X2)=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))))), inference(split_conjunct,[status(thm)],[c_0_5784])). 6.97/7.24 fof(c_0_9963, plain, ![X17344, X17345]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17345)),hAPP(c_List_Otl(X17345),X17344))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17345)),X17344)),c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_length__tl])). 6.97/7.24 fof(c_0_9964, plain, ![X5143, X5144]:hBOOL(hAPP(hAPP(c_member(tc_fun(X5144,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5144,tc_HOL_Obool))),hAPP(c_Set_OPow(X5144),X5143))), inference(variable_rename,[status(thm)],[fact_Pow__bottom])). 6.97/7.24 cnf(c_0_9965, 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_5785])). 6.97/7.24 cnf(c_0_9966, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X1),X2))=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))), inference(split_conjunct,[status(thm)],[c_0_5786])). 6.97/7.24 cnf(c_0_9967, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))|X1!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X3)))), inference(split_conjunct,[status(thm)],[c_0_5787])). 6.97/7.24 cnf(c_0_9968, plain, (hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))=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))), inference(split_conjunct,[status(thm)],[c_0_5788])). 6.97/7.24 cnf(c_0_9969, plain, (hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))=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))), inference(split_conjunct,[status(thm)],[c_0_5789])). 6.97/7.24 cnf(c_0_9970, plain, (hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2))=hAPP(c_List_Orev(X2),X1)|X1!=hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2))), inference(split_conjunct,[status(thm)],[c_0_5790])). 6.97/7.24 fof(c_0_9971, plain, ![X9024, X9025, X9026, X9027, X9028]:hAPP(hAPP(c_Product__Type_Oscomp(X9028,X9027,X9028,X9026),hAPP(c_Product__Type_OPair(X9027,X9028),X9025)),X9024)=hAPP(X9024,X9025), inference(variable_rename,[status(thm)],[fact_Pair__scomp])). 6.97/7.24 fof(c_0_9972, plain, ![X11632, X11633]:c_Sum__Type_OPlus(X11633,X11632,c_Orderings_Otop__class_Otop(tc_fun(X11633,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X11632,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X11633,X11632),tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_UNIV__Plus__UNIV])). 6.97/7.24 fof(c_0_9973, plain, ![X5411, X5412]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5412,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5412,tc_HOL_Obool))),X5411)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5412,tc_HOL_Obool)),X5411), inference(variable_rename,[status(thm)],[fact_Compl__eq__Diff__UNIV])). 6.97/7.24 cnf(c_0_9974, 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_5791])). 6.97/7.24 fof(c_0_9975, plain, ![X11621, X11622, X11623, X11624]:hAPP(hAPP(c_List_Odrop(X11624),X11623),c_List_Oreplicate(X11624,X11622,X11621))=c_List_Oreplicate(X11624,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11622),X11623),X11621), inference(variable_rename,[status(thm)],[fact_drop__replicate])). 6.97/7.24 fof(c_0_9976, plain, ![X16863, X16864, X16865, X16866]:hAPP(hAPP(c_List_Onth(X16866),hAPP(hAPP(c_List_Olist_OCons(X16866),X16865),X16864)),X16863)=c_Nat_Onat_Onat__case(X16866,X16865,hAPP(c_List_Onth(X16866),X16864),X16863), inference(variable_rename,[status(thm)],[fact_nth_Osimps])). 6.97/7.24 fof(c_0_9977, plain, ![X15982, X15983, X15984]:hAPP(hAPP(c_Set_Oinsert(X15984),X15982),c_Orderings_Obot__class_Obot(tc_fun(X15984,tc_HOL_Obool)))=hAPP(c_List_Oset(X15984),c_List_Oreplicate(X15984,hAPP(c_Nat_OSuc,X15983),X15982)), inference(variable_rename,[status(thm)],[fact_set__replicate__Suc])). 6.97/7.24 cnf(c_0_9978, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(X2,X1))), inference(split_conjunct,[status(thm)],[c_0_5792])). 6.97/7.24 cnf(c_0_9979, 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_5793, c_0_5794])). 6.97/7.24 fof(c_0_9980, plain, ![X9178, X9179]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X9179)),X9178)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X9179),X9178)), inference(variable_rename,[status(thm)],[fact_int__power])). 6.97/7.24 fof(c_0_9981, plain, ![X9295, X9296]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X9296),X9295))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X9296)),X9295), inference(variable_rename,[status(thm)],[fact_zmult__zminus])). 6.97/7.24 fof(c_0_9982, plain, ![X17500, X17501, X17502]:hAPP(hAPP(c_Set_Oinsert(X17502),X17501),hAPP(hAPP(c_Set_Oinsert(X17502),X17501),X17500))=hAPP(hAPP(c_Set_Oinsert(X17502),X17501),X17500), inference(variable_rename,[status(thm)],[fact_insert__absorb2])). 6.97/7.24 cnf(c_0_9983, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)=hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5795])). 6.97/7.24 fof(c_0_9984, plain, ![X13691, X13692]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X13692),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X13691))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X13692)),X13691), inference(variable_rename,[status(thm)],[fact_zdiv__zminus2])). 6.97/7.24 fof(c_0_9985, plain, ![X12259, X12260]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12260),X12259))=c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X12260),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X12259)), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J])). 6.97/7.24 cnf(c_0_9986, plain, (hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1))=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X1))), inference(split_conjunct,[status(thm)],[c_0_5796])). 6.97/7.24 fof(c_0_9987, plain, ![X9328, X9329, X9330, X9331, X9332, X9333]:hAPP(hAPP(c_Product__Type_Ocurry(X9333,X9332,X9331,X9330),X9329),X9328)=hAPP(X9330,hAPP(hAPP(c_Product__Type_OPair(X9333,X9332),X9329),X9328)), inference(variable_rename,[status(thm)],[fact_curry__def])). 6.97/7.24 fof(c_0_9988, plain, ![X2587, X2588]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2588),X2587)=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,X2588,X2587)),X2587), inference(variable_rename,[status(thm)],[fact_zminus__zmod])). 6.97/7.24 cnf(c_0_9989, 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),hAPP(c_Nat_OSuc,X2))))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2)), inference(rw,[status(thm)],[c_0_5797, c_0_4471])). 6.97/7.24 fof(c_0_9990, plain, ![X4333, X4334, X4335]:c_Orderings_Otop__class_Otop(tc_fun(X4334,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4335,tc_fun(X4334,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X4335,tc_HOL_Obool))),X4333), inference(variable_rename,[status(thm)],[fact_INT__empty])). 6.97/7.24 fof(c_0_9991, plain, ![X5563, X5564]: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),X5564),X5563))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X5564,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X5563)), inference(variable_rename,[status(thm)],[fact_zmod__zminus2])). 6.97/7.24 fof(c_0_9992, plain, ![X6976, X6977]:hAPP(c_Finite__Set_Ocard(X6977),X6976)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6977,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X6977),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X6976), inference(variable_rename,[status(thm)],[fact_card__eq__setsum])). 6.97/7.24 cnf(c_0_9993, plain, (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))))=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)))), inference(rw,[status(thm)],[c_0_5798, c_0_5435])). 6.97/7.24 fof(c_0_9994, plain, ![X3211, X3212]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3212,X3211))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3212),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3211)), inference(variable_rename,[status(thm)],[fact_zmod__int])). 6.97/7.24 fof(c_0_9995, plain, ![X377, X378]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X378,X377))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X378),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X377)), inference(variable_rename,[status(thm)],[fact_zmod__zminus__zminus])). 6.97/7.24 fof(c_0_9996, plain, ![X8815, X8816, X8817, X8818, X8819, X8820]:c_Fun_Ofun__upd(X8820,X8819,c_Fun_Ofun__upd(X8820,X8819,X8818,X8817,X8816),X8817,X8815)=c_Fun_Ofun__upd(X8820,X8819,X8818,X8817,X8815), inference(variable_rename,[status(thm)],[fact_fun__upd__upd])). 6.97/7.24 cnf(c_0_9997, 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])). 6.97/7.24 fof(c_0_9998, plain, ![X16883, X16884]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16884),X16883)),hAPP(c_Nat_OSuc,X16884))), inference(variable_rename,[status(thm)],[fact_diff__less__Suc])). 6.97/7.24 fof(c_0_9999, plain, ![X6375, X6376]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6376),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6375),X6376)))), inference(variable_rename,[status(thm)],[fact_less__add__Suc2])). 6.97/7.24 fof(c_0_10000, plain, ![X14525, X14526, X14527]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14527,tc_HOL_Obool)),X14526),hAPP(hAPP(c_Set_Oinsert(X14527),X14525),X14526))), inference(variable_rename,[status(thm)],[fact_subset__insertI])). 6.97/7.24 cnf(c_0_10001, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))))|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_5328])). 6.97/7.24 fof(c_0_10002, plain, ![X1673]: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),X1673))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(variable_rename,[status(thm)],[fact_negative__zle__0])). 6.97/7.24 fof(c_0_10003, plain, ![X8668, X8669]:hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X8669,X8668))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X8669),hAPP(c_Nat_OSuc,X8668)), inference(variable_rename,[status(thm)],[fact_image__Suc__atLeastAtMost])). 6.97/7.24 fof(c_0_10004, plain, ![X2831, X2832, X2833, X2834]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2834)),hAPP(hAPP(c_List_Olist__update(X2834,X2833),X2832),X2831))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2834)),X2833), inference(variable_rename,[status(thm)],[fact_length__list__update])). 6.97/7.24 cnf(c_0_10005, 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_5799])). 6.97/7.24 fof(c_0_10006, plain, ![X14937, X14938]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14938)),c_List_Obutlast(X14938,X14937))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14938)),X14937)),c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_length__butlast])). 6.97/7.24 cnf(c_0_10007, 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_5800])). 6.97/7.24 cnf(c_0_10008, 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']). 6.97/7.24 cnf(c_0_10009, plain, (c_Transitive__Closure_Ortrancl(X1,X2)=c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Otrancl(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5801])). 6.97/7.24 fof(c_0_10010, plain, ![X2481, X2482]:hAPP(hAPP(c_Relation_Orel__comp(X2482,X2482,X2482),c_Transitive__Closure_Ortrancl(X2482,X2481)),c_Transitive__Closure_Ortrancl(X2482,X2481))=c_Transitive__Closure_Ortrancl(X2482,X2481), inference(variable_rename,[status(thm)],[fact_rtrancl__idemp__self__comp])). 6.97/7.24 fof(c_0_10011, plain, ![X15910, X15911, X15912, X15913, X15914]:hAPP(hAPP(c_List_Omap(X15914,X15913),X15912),c_List_Oreplicate(X15914,X15911,X15910))=c_List_Oreplicate(X15913,X15911,hAPP(X15912,X15910)), inference(variable_rename,[status(thm)],[fact_map__replicate])). 6.97/7.24 cnf(c_0_10012, plain, (c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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(split_conjunct,[status(thm)],[c_0_5802])). 6.97/7.24 fof(c_0_10013, plain, ![X13702, X13703, X13704]:hAPP(hAPP(c_Product__Type_OSigma(X13704,X13703),c_Orderings_Obot__class_Obot(tc_fun(X13704,tc_HOL_Obool))),X13702)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X13704,X13703),tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Sigma__empty1])). 6.97/7.24 cnf(c_0_10014, 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_5803, c_0_5746])). 6.97/7.24 fof(c_0_10015, plain, ![X15098, X15099, X15100, X15101]:hAPP(hAPP(c_Product__Type_Oscomp(X15101,X15100,X15099,tc_prod(X15100,X15099)),X15098),c_Product__Type_OPair(X15100,X15099))=X15098, inference(variable_rename,[status(thm)],[fact_scomp__Pair])). 6.97/7.24 cnf(c_0_10016, plain, (hAPP(c_Relation_OImage(X1,X1,c_Relation_OId(X1)),X2)=X2), inference(split_conjunct,[status(thm)],[c_0_5804])). 6.97/7.24 fof(c_0_10017, plain, ![X13887, X13888, X13889, X13890, X13891]:X13887=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13891,X13890,X13889),X13888),X13887),c_Orderings_Obot__class_Obot(tc_fun(X13890,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_fold__image__empty])). 6.97/7.24 cnf(c_0_10018, plain, (X1=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))), inference(rw,[status(thm)],[c_0_5805, c_0_5435])). 6.97/7.24 fof(c_0_10019, plain, ![X8332, X8333]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8333,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X8333,tc_HOL_Obool))),X8332)=c_Orderings_Otop__class_Otop(tc_fun(X8333,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Un__UNIV__left])). 6.97/7.24 fof(c_0_10020, plain, ![X1843, X1844]:c_Orderings_Obot__class_Obot(tc_fun(X1844,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1844,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1844,tc_HOL_Obool))),X1843), inference(variable_rename,[status(thm)],[fact_empty__Diff])). 6.97/7.24 fof(c_0_10021, plain, ![X16557, X16558]:c_Orderings_Obot__class_Obot(tc_fun(X16558,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16558,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X16558,tc_HOL_Obool))),X16557), inference(variable_rename,[status(thm)],[fact_Int__empty__left])). 6.97/7.24 fof(c_0_10022, plain, ![X432, X433, X434]:X432=hAPP(c_Finite__Set_Ofold1(X434,X433),hAPP(hAPP(c_Set_Oinsert(X434),X432),c_Orderings_Obot__class_Obot(tc_fun(X434,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_fold1__singleton])). 6.97/7.24 fof(c_0_10023, plain, ![X4702, X4703]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4703,tc_HOL_Obool)),X4702),c_Orderings_Otop__class_Otop(tc_fun(X4703,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X4703,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Diff__UNIV])). 6.97/7.24 fof(c_0_10024, plain, ![X4906, X4907]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4907,tc_HOL_Obool)),X4906),c_Orderings_Obot__class_Obot(tc_fun(X4907,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X4907,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Int__empty__right])). 6.97/7.24 fof(c_0_10025, plain, ![X15442, X15443]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15443,tc_HOL_Obool)),X15442),c_Orderings_Otop__class_Otop(tc_fun(X15443,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X15443,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Un__UNIV__right])). 6.97/7.24 cnf(c_0_10026, 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_5806])). 6.97/7.24 cnf(c_0_10027, 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_5807])). 6.97/7.24 fof(c_0_10028, plain, ![X15988]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X15988))=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),X15988)), inference(variable_rename,[status(thm)],[fact_int__Suc])). 6.97/7.24 cnf(c_0_10029, plain, (c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2)=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)))), inference(split_conjunct,[status(thm)],[c_0_5808])). 6.97/7.24 fof(c_0_10030, plain, ![X4027, X4028]:c_List_Olistrel1(X4028,hAPP(c_Relation_Oconverse(X4028,X4028),X4027))=hAPP(c_Relation_Oconverse(tc_List_Olist(X4028),tc_List_Olist(X4028)),c_List_Olistrel1(X4028,X4027)), inference(variable_rename,[status(thm)],[fact_listrel1__converse])). 6.97/7.24 fof(c_0_10031, plain, ![X5396, X5397]: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)),X5397),X5396), inference(variable_rename,[status(thm)],[fact_inj__on__add__nat])). 6.97/7.24 fof(c_0_10032, plain, ![X10647]:hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X10647)),c_Int_OInteg)), inference(variable_rename,[status(thm)],[fact_Rep__Integ])). 6.97/7.24 fof(c_0_10033, plain, ![X16325, X16326, X16327, X16328, X16329, X16330]:hAPP(hAPP(hAPP(c_COMBC(X16330,X16329,X16328),X16327),X16326),X16325)=hAPP(hAPP(X16327,X16325),X16326), inference(variable_rename,[status(thm)],[help_c__COMBC__1])). 6.97/7.24 fof(c_0_10034, plain, ![X15193, X15194, X15195, X15196, X15197, X15198]:hAPP(hAPP(hAPP(c_COMBB(X15198,X15197,X15196),X15195),X15194),X15193)=hAPP(X15195,hAPP(X15194,X15193)), inference(variable_rename,[status(thm)],[help_c__COMBB__1])). 6.97/7.24 fof(c_0_10035, plain, ![X5393, X5394, X5395]:hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5395,X5394,X5395),c_COMBK(X5395,X5394)),X5393)=hAPP(c_Product__Type_Ofst(X5395,X5394),X5393), inference(variable_rename,[status(thm)],[fact_fst__def])). 6.97/7.24 cnf(c_0_10036, 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_5809])). 6.97/7.24 cnf(c_0_10037, 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_5810, c_0_4467]), ['final']). 6.97/7.24 fof(c_0_10038, plain, ![X16940, X16941, X16942]:hAPP(c_Relation_OImage(X16942,X16942,c_Relation_OId__on(X16942,X16941)),X16940)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16942,tc_HOL_Obool)),X16941),X16940), inference(variable_rename,[status(thm)],[fact_Image__Id__on])). 6.97/7.24 fof(c_0_10039, plain, ![X4912, X4913, X4914, X4915, X4916, X4917]:c_Nitpick_Opair__box_Opair__box__rec(X4917,X4916,X4915,X4914,c_Nitpick_Opair__box_OPairBox(X4917,X4916,X4913,X4912))=hAPP(hAPP(X4914,X4913),X4912), inference(variable_rename,[status(thm)],[fact_pair__box_Orecs])). 6.97/7.24 fof(c_0_10040, plain, ![X10097, X10098, X10099, X10100, X10101, X10102]:hAPP(hAPP(X10099,X10098),X10097)=c_Nitpick_Opair__box_Opair__box__case(X10102,X10101,X10100,X10099,c_Nitpick_Opair__box_OPairBox(X10102,X10101,X10098,X10097)), inference(variable_rename,[status(thm)],[fact_pair__box_Osimps_I2_J])). 6.97/7.24 fof(c_0_10041, plain, ![X13804, X13805, X13806]:hAPP(c_Product__Type_Ofst(tc_List_Olist(X13806),tc_List_Olist(X13806)),c_List_Opartition(X13806,X13805,X13804))=hAPP(c_List_Ofilter(X13806,X13805),X13804), inference(variable_rename,[status(thm)],[fact_partition__filter1])). 6.97/7.24 fof(c_0_10042, plain, ![X5535, X5536, X5537]:c_List_Obutlast(X5537,hAPP(hAPP(c_List_Odrop(X5537),X5536),X5535))=hAPP(hAPP(c_List_Odrop(X5537),X5536),c_List_Obutlast(X5537,X5535)), inference(variable_rename,[status(thm)],[fact_drop__butlast])). 6.97/7.24 cnf(c_0_10043, 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_5811])). 6.97/7.24 cnf(c_0_10044, plain, (c_Divides_Odivmod__nat(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)), inference(split_conjunct,[status(thm)],[c_0_5812])). 6.97/7.24 cnf(c_0_10045, plain, (c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X1,X2,X3,hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X4))))=hAPP(X3,X4)), inference(rw,[status(thm)],[c_0_5813, c_0_5435])). 6.97/7.24 fof(c_0_10046, plain, ![X10244, X10245]:c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X10245),X10244)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X10245,X10244)),X10244), inference(variable_rename,[status(thm)],[fact_mod__Suc__eq__Suc__mod])). 6.97/7.24 fof(c_0_10047, plain, ![X1992, X1993, X1994]:hAPP(hAPP(c_List_Olist_OCons(X1994),X1992),c_List_Oreplicate(X1994,X1993,X1992))=c_List_Oreplicate(X1994,hAPP(c_Nat_OSuc,X1993),X1992), inference(variable_rename,[status(thm)],[fact_replicate__Suc])). 6.97/7.24 fof(c_0_10048, plain, ![X5722, X5723, X5724]:hAPP(c_List_Oset(X5724),c_List_Oinsert(X5724,X5723,X5722))=hAPP(hAPP(c_Set_Oinsert(X5724),X5723),hAPP(c_List_Oset(X5724),X5722)), inference(variable_rename,[status(thm)],[fact_List_Oset__insert])). 6.97/7.24 cnf(c_0_10049, 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_5814, c_0_5815])). 6.97/7.24 cnf(c_0_10050, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),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_5816])). 6.97/7.24 cnf(c_0_10051, 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)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X1), inference(split_conjunct,[status(thm)],[c_0_5817])). 6.97/7.24 fof(c_0_10052, plain, ![X13838, X13839, X13840, X13841, X13842]:hAPP(hAPP(c_Finite__Set_Ofold(X13842,X13841,X13840),X13839),X13838)=c_HOL_OThe(X13841,c_Finite__Set_Ofold__graph(X13842,X13841,X13840,X13839,X13838)), inference(variable_rename,[status(thm)],[fact_fold__def])). 6.97/7.24 fof(c_0_10053, plain, ![X7622]: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)),X7622))=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X7622), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J])). 6.97/7.24 cnf(c_0_10054, 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_5818])). 6.97/7.24 fof(c_0_10055, plain, ![X4091, X4092, X4093]:X4092=hAPP(hAPP(c_List_Onth(X4093),hAPP(hAPP(c_List_Olist_OCons(X4093),X4092),X4091)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_nth__Cons__0])). 6.97/7.24 cnf(c_0_10056, plain, (hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X1),X3)=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool))|X1!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5819])). 6.97/7.24 fof(c_0_10057, plain, ![X12955]:c_Complete__Lattice_OSup__class_OSup(tc_fun(X12955,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X12955,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X12955,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Union__empty])). 6.97/7.24 fof(c_0_10058, plain, ![X1763]:c_Complete__Lattice_OInf__class_OInf(tc_fun(X1763,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1763,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X1763,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Inter__UNIV])). 6.97/7.24 fof(c_0_10059, plain, ![X7837]:c_Orderings_Otop__class_Otop(tc_fun(X7837,tc_HOL_Obool))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X7837,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X7837,tc_HOL_Obool),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Union__UNIV])). 6.97/7.24 fof(c_0_10060, plain, ![X17349]:c_Orderings_Otop__class_Otop(tc_fun(X17349,tc_HOL_Obool))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X17349,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X17349,tc_HOL_Obool),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Inter__empty])). 6.97/7.24 fof(c_0_10061, plain, ![X12347, X12348, X12349]:hAPP(hAPP(c_List_Olist__update(X12349,X12348),X12347),hAPP(hAPP(c_List_Onth(X12349),X12348),X12347))=X12348, inference(variable_rename,[status(thm)],[fact_list__update__id])). 6.97/7.24 fof(c_0_10062, plain, ![X15265, X15266, X15267]:c_List_Oset__Cons(X15267,X15266,c_List_Olistset(X15267,X15265))=c_List_Olistset(X15267,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X15267,tc_HOL_Obool)),X15266),X15265)), inference(variable_rename,[status(thm)],[fact_listset_Osimps_I2_J])). 6.97/7.24 fof(c_0_10063, plain, ![X4506, X4507, X4508]:X4506=hAPP(hAPP(c_List_Odrop(X4508),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X4508),X4507),X4506)), inference(variable_rename,[status(thm)],[fact_drop__1__Cons])). 6.97/7.24 cnf(c_0_10064, 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_5820])). 6.97/7.24 fof(c_0_10065, plain, ![X5476, X5477, X5478, X5479]:hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5479,X5478,X5477,X5476,c_Orderings_Obot__class_Obot(tc_fun(X5479,tc_HOL_Obool))),X5476)), inference(variable_rename,[status(thm)],[fact_fold__graph_Oequations_I1_J])). 6.97/7.24 fof(c_0_10066, plain, ![X738]:(X738=hAPP(c_Int_OAbs__Integ,esk17_1(X738))&hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk17_1(X738)),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])])])])). 6.97/7.24 cnf(c_0_10067, plain, (c_Relation_Otrans(X1,c_Transitive__Closure_Otrancl(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5821])). 6.97/7.24 fof(c_0_10068, plain, ![X13962, X13963]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13963,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X13963,tc_HOL_Obool))),X13962)), inference(variable_rename,[status(thm)],[fact_empty__subsetI])). 6.97/7.24 fof(c_0_10069, plain, ![X16318, X16319]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X16319),X16318)),X16319)), inference(variable_rename,[status(thm)],[fact_div__le__dividend])). 6.97/7.24 fof(c_0_10070, plain, ![X1394, X1395]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1395),X1394)),X1395)), inference(variable_rename,[status(thm)],[fact_diff__le__self])). 6.97/7.24 fof(c_0_10071, plain, ![X13320]: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,X13320))))), inference(variable_rename,[status(thm)],[fact_neg__zminus__int])). 6.97/7.24 fof(c_0_10072, plain, ![X14339, X14340]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14340,tc_HOL_Obool)),X14339),c_Orderings_Otop__class_Otop(tc_fun(X14340,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_subset__UNIV])). 6.97/7.24 fof(c_0_10073, plain, ![X13853, X13854]:hBOOL(hAPP(hAPP(c_member(tc_fun(X13854,tc_HOL_Obool)),X13853),hAPP(c_Set_OPow(X13854),X13853))), inference(variable_rename,[status(thm)],[fact_Pow__top])). 6.97/7.24 cnf(c_0_10074, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),c_Divides_Odivmod__nat(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_5822])). 6.97/7.24 fof(c_0_10075, plain, ![X7529, X7530, X7531]:hBOOL(hAPP(hAPP(c_member(X7531),X7530),hAPP(hAPP(c_Set_Oinsert(X7531),X7530),X7529))), inference(variable_rename,[status(thm)],[fact_insertI1])). 6.97/7.24 fof(c_0_10076, plain, ![X2111, X2112]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2112),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2111),X2112))), inference(variable_rename,[status(thm)],[fact_le__add2])). 6.97/7.24 cnf(c_0_10077, 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_5823, c_0_5824])). 6.97/7.24 cnf(c_0_10078, 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_5825]), ['final']). 6.97/7.24 fof(c_0_10079, plain, ![X7319]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7319),X7319))), inference(variable_rename,[status(thm)],[fact_le__square])). 6.97/7.24 fof(c_0_10080, plain, ![X6990]:c_Relation_Orefl__on(X6990,c_Orderings_Obot__class_Obot(tc_fun(X6990,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X6990,X6990),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_refl__on__empty])). 6.97/7.24 cnf(c_0_10081, plain, (c_List_Obutlast(X1,X2)=X3|hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),c_List_Olist_ONil(X1)))!=X2), inference(split_conjunct,[status(thm)],[c_0_5331])). 6.97/7.24 cnf(c_0_10082, 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_5331])). 6.97/7.24 fof(c_0_10083, plain, ![X14755, X14756, X14757]:hAPP(c_Relation_ORange(X14757,X14756),hAPP(c_Relation_Oconverse(X14756,X14757),X14755))=hAPP(c_Relation_ODomain(X14756,X14757),X14755), inference(variable_rename,[status(thm)],[fact_Range__converse])). 6.97/7.24 fof(c_0_10084, plain, ![X5221, X5222, X5223]:hAPP(c_Relation_ORange(X5223,X5222),X5221)=hAPP(c_Relation_ODomain(X5222,X5223),hAPP(c_Relation_Oconverse(X5223,X5222),X5221)), inference(variable_rename,[status(thm)],[fact_Range__def])). 6.97/7.24 fof(c_0_10085, plain, ![X9561, X9562]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X9562),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9562),X9561))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_diff__add__0])). 6.97/7.24 fof(c_0_10086, plain, ![X3686, X3687, X3688, X3689, X3690]:hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X3690),X3689),X3688),X3687),X3686)=c_New__DSequence_Opos__single(X3690,X3689), inference(variable_rename,[status(thm)],[fact_pos__single__def])). 6.97/7.24 fof(c_0_10087, plain, ![X524, X525, X526, X527, X528]:hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(X528),X527),X526),X525),X524)=c_New__DSequence_Oneg__single(X528,X527), inference(variable_rename,[status(thm)],[fact_neg__single__def])). 6.97/7.24 cnf(c_0_10088, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)!=X3), inference(split_conjunct,[status(thm)],[c_0_5826])). 6.97/7.24 fof(c_0_10089, plain, ![X9074, X9075]:c_List_Otranspose(X9075,X9074)=c_List_Otranspose(X9075,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X9075)),c_List_Olist_ONil(X9075)),X9074)), inference(variable_rename,[status(thm)],[fact_transpose_Osimps_I2_J])). 6.97/7.24 fof(c_0_10090, plain, ![X1184, X1185, X1186, X1187]:c_Lazy__Sequence_Oflat(X1186,c_Lazy__Sequence_Omap(X1187,tc_Lazy__Sequence_Olazy__sequence(X1186),X1184,X1185))=hAPP(c_Lazy__Sequence_Obind(X1187,X1186,X1185),X1184), inference(variable_rename,[status(thm)],[fact__05])). 6.97/7.24 fof(c_0_10091, plain, ![X5694, X5695]:hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5695),X5694))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5694),X5695), inference(variable_rename,[status(thm)],[fact_card__atLeastLessThan])). 6.97/7.24 cnf(c_0_10092, plain, (c_Divides_Opdivmod(X2,X1)=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))|X1!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_5827])). 6.97/7.24 fof(c_0_10093, plain, ![X15280, X15281]:c_Fun_Oid(tc_prod(X15281,X15280))=c_Product__Type_Omap__pair(X15281,X15281,X15280,X15280,c_COMBI(X15281),c_COMBI(X15280)), inference(variable_rename,[status(thm)],[fact_map__pair_Oidentity])). 6.97/7.24 fof(c_0_10094, plain, ![X17606, X17607]:c_Fun_Oid(tc_prod(X17607,X17606))=c_Product__Type_Omap__pair(X17607,X17607,X17606,X17606,c_Fun_Oid(X17607),c_Fun_Oid(X17606)), inference(variable_rename,[status(thm)],[fact_map__pair_Oid])). 6.97/7.24 fof(c_0_10095, plain, ![X12227, X12228]:X12227=c_Predicate_Opred__comp(X12228,X12228,X12228,c_fequal,c_Predicate_Opred__comp(X12228,X12228,X12228,X12227,c_fequal)), inference(variable_rename,[status(thm)],[fact_eq__comp__r])). 6.97/7.24 fof(c_0_10096, plain, ![X12910, X12911, X12912, X12913]:hAPP(hAPP(c_Finite__Set_Ofold(X12913,X12912,X12911),X12910),c_Orderings_Obot__class_Obot(tc_fun(X12913,tc_HOL_Obool)))=X12910, inference(variable_rename,[status(thm)],[fact_fold__empty])). 6.97/7.24 fof(c_0_10097, plain, ![X3431, X3432]:X3431=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3432,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3432,tc_HOL_Obool))),X3431), inference(variable_rename,[status(thm)],[fact_Int__UNIV__left])). 6.97/7.24 fof(c_0_10098, plain, ![X17608, X17609]:X17609=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17609),X17608)),X17608), inference(variable_rename,[status(thm)],[fact_diff__add__inverse2])). 6.97/7.24 fof(c_0_10099, plain, ![X5660, X5661]:X5660=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5661),X5660)),X5661), inference(variable_rename,[status(thm)],[fact_diff__add__inverse])). 6.97/7.24 cnf(c_0_10100, plain, (hAPP(c_Random_Oiterate(X2,X3,X1,X4),X5)=hAPP(c_Product__Type_OPair(X2,X3),X5)|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X1), inference(split_conjunct,[status(thm)],[c_0_5828])). 6.97/7.24 cnf(c_0_10101, 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_5451])). 6.97/7.24 fof(c_0_10102, plain, ![X14656, X14657]:c_Set_Othe__elem(X14657,hAPP(hAPP(c_Set_Oinsert(X14657),X14656),c_Orderings_Obot__class_Obot(tc_fun(X14657,tc_HOL_Obool))))=X14656, inference(variable_rename,[status(thm)],[fact_the__elem__eq])). 6.97/7.24 cnf(c_0_10103, plain, (c_Int_Osucc(c_Int_Opred(X1))=X1), inference(split_conjunct,[status(thm)],[c_0_5829])). 6.97/7.24 fof(c_0_10104, plain, ![X15902]:hAPP(c_Relation_OField(X15902),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X15902,X15902),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X15902,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Field__empty])). 6.97/7.24 fof(c_0_10105, plain, ![X14559, X14560, X14561]:c_Orderings_Obot__class_Obot(tc_fun(X14560,tc_HOL_Obool))=hAPP(c_Relation_OImage(X14561,X14560,X14559),c_Orderings_Obot__class_Obot(tc_fun(X14561,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Image__empty])). 6.97/7.24 fof(c_0_10106, plain, ![X2468, X2469]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2469,tc_HOL_Obool)),X2468),c_Orderings_Otop__class_Otop(tc_fun(X2469,tc_HOL_Obool)))=X2468, inference(variable_rename,[status(thm)],[fact_Int__UNIV__right])). 6.97/7.24 fof(c_0_10107, plain, ![X9778, X9779]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9779,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9779,tc_HOL_Obool)),X9778))=X9778, inference(variable_rename,[status(thm)],[fact_double__complement])). 6.97/7.24 fof(c_0_10108, plain, ![X13199, X13200]:X13199=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13200,tc_HOL_Obool)),X13199),c_Orderings_Obot__class_Obot(tc_fun(X13200,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Diff__empty])). 6.97/7.24 fof(c_0_10109, plain, ![X16188, X16189]:hAPP(c_Relation_Oconverse(X16189,X16189),c_Transitive__Closure_Ortrancl(X16189,X16188))=c_Transitive__Closure_Ortrancl(X16189,hAPP(c_Relation_Oconverse(X16189,X16189),X16188)), inference(variable_rename,[status(thm)],[fact_rtrancl__converse])). 6.97/7.24 fof(c_0_10110, plain, ![X2213, X2214, X2215, X2216]:c_Lazy__Sequence_Olazy__sequence_OInsert(X2216,X2215,c_Lazy__Sequence_Oappend(X2216,X2214,X2213))=c_Lazy__Sequence_Oappend(X2216,c_Lazy__Sequence_Olazy__sequence_OInsert(X2216,X2215,X2214),X2213), inference(variable_rename,[status(thm)],[fact__01])). 6.97/7.24 fof(c_0_10111, plain, ![X3789, X3790, X3791]:hAPP(c_List_Ofilter(X3791,X3790),c_List_Oremdups(X3791,X3789))=c_List_Oremdups(X3791,hAPP(c_List_Ofilter(X3791,X3790),X3789)), inference(variable_rename,[status(thm)],[fact_remdups__filter])). 6.97/7.24 fof(c_0_10112, plain, ![X11732]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11732,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X11732,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X11732,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Compl__UNIV__eq])). 6.97/7.24 fof(c_0_10113, plain, ![X9091]:c_Orderings_Otop__class_Otop(tc_fun(X9091,tc_HOL_Obool))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9091,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X9091,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Compl__empty__eq])). 6.97/7.24 cnf(c_0_10114, plain, (c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))=hAPP(c_Set_Oimage(X1,X3,X4),X2)|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=X2), inference(split_conjunct,[status(thm)],[c_0_5830])). 6.97/7.24 cnf(c_0_10115, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)), inference(split_conjunct,[status(thm)],[c_0_5831])). 6.97/7.24 cnf(c_0_10116, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(c_Relation_ODomain(X1,X2),X3)|c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))!=X3), inference(split_conjunct,[status(thm)],[c_0_5832])). 6.97/7.24 cnf(c_0_10117, plain, (c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))=hAPP(c_Relation_ORange(X2,X3),X1)|X1!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5833])). 6.97/7.24 cnf(c_0_10118, 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))|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=X1), inference(split_conjunct,[status(thm)],[c_0_5428])). 6.97/7.24 fof(c_0_10119, plain, ![X3414, X3415, X3416, X3417]:hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X3417,X3416)),c_Nitpick_Opair__box_OPairBox(X3417,X3416,X3415,X3414))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_pair__box_Osize_I2_J])). 6.97/7.24 cnf(c_0_10120, plain, (c_Relation_Osingle__valued(X1,X1,c_Relation_OId(X1))), inference(split_conjunct,[status(thm)],[c_0_5834])). 6.97/7.24 cnf(c_0_10121, plain, (hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_5835])). 6.97/7.24 cnf(c_0_10122, 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_5836])). 6.97/7.24 fof(c_0_10123, plain, ![X7525, X7526]:hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X7526)),c_List_Olist_ONil(X7526)),c_List_Olists(X7526,X7525))), inference(variable_rename,[status(thm)],[fact_lists_ONil])). 6.97/7.24 fof(c_0_10124, plain, ![X4102]: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),X4102))), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J])). 6.97/7.24 cnf(c_0_10125, plain, (c_List_Obutlast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))=c_List_Olist_ONil(X1)|c_List_Olist_ONil(X1)!=X2), inference(split_conjunct,[status(thm)],[c_0_5837])). 6.97/7.24 fof(c_0_10126, plain, ![X610, X611]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X611)),hAPP(c_List_Orotate1(X611),X610))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X611)),X610), inference(variable_rename,[status(thm)],[fact_length__rotate1])). 6.97/7.24 fof(c_0_10127, plain, ![X13157, X13158]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13158)),X13157)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13158)),hAPP(c_List_Orev(X13158),X13157)), inference(variable_rename,[status(thm)],[fact_length__rev])). 6.97/7.24 fof(c_0_10128, plain, ![X5316, X5317, X5318]:c_Lazy__Sequence_Oappend(X5318,X5317,c_Lazy__Sequence_Oflat(X5318,X5316))=c_Lazy__Sequence_Oflat(X5318,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(X5318),X5317,X5316)), inference(variable_rename,[status(thm)],[fact__03])). 6.97/7.24 fof(c_0_10129, plain, ![X13513]:c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X13513,tc_HOL_Obool),tc_HOL_Obool))=hAPP(c_Set_OPow(X13513),c_Orderings_Otop__class_Otop(tc_fun(X13513,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Pow__UNIV])). 6.97/7.24 cnf(c_0_10130, 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_5838])). 6.97/7.24 cnf(c_0_10131, plain, (c_List_Osublist(X1,X2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X3))=hAPP(hAPP(c_List_Otake(X1),X3),X2)), inference(split_conjunct,[status(thm)],[c_0_5839])). 6.97/7.24 fof(c_0_10132, plain, ![X14272, X14273]:hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X14273,X14272))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14273),X14272), inference(variable_rename,[status(thm)],[fact_div__int__def])). 6.97/7.24 fof(c_0_10133, plain, ![X5276, X5277, X5278, X5279]:X5276=hAPP(c_Product__Type_Oprod_Oprod__case(X5279,X5278,X5277),c_Product__Type_Ocurry(X5279,X5278,X5277,X5276)), inference(variable_rename,[status(thm)],[fact_split__curry])). 6.97/7.24 cnf(c_0_10134, 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_4449])). 6.97/7.24 fof(c_0_10135, plain, ![X12727, X12728, X12729, X12730]:c_Product__Type_Ocurry(X12730,X12729,X12728,hAPP(c_Product__Type_Oprod_Oprod__case(X12730,X12729,X12728),X12727))=X12727, inference(variable_rename,[status(thm)],[fact_curry__split])). 6.97/7.24 cnf(c_0_10136, plain, (c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)=c_Wellfounded_Oless__than), inference(split_conjunct,[status(thm)],[fact_less__than__def])). 6.97/7.24 fof(c_0_10137, plain, ![X6071, X6072]:hAPP(hAPP(c_Nat_Ocompow(tc_prod(X6072,X6072),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X6071)=X6071, inference(variable_rename,[status(thm)],[fact_rel__pow__1])). 6.97/7.24 fof(c_0_10138, plain, ![X15481, X15482]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15482,tc_HOL_Obool)),X15481),X15481)=c_Orderings_Obot__class_Obot(tc_fun(X15482,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Diff__cancel])). 6.97/7.24 fof(c_0_10139, plain, ![X11847, X11848, X11849]:hAPP(hAPP(c_List_Ozip(X11849,X11848),c_List_Olist_ONil(X11849)),X11847)=c_List_Olist_ONil(tc_prod(X11849,X11848)), inference(variable_rename,[status(thm)],[fact_zip__Nil])). 6.97/7.24 fof(c_0_10140, plain, ![X14217, X14218, X14219]:hAPP(hAPP(c_List_Ozip(X14219,X14218),X14217),c_List_Olist_ONil(X14218))=c_List_Olist_ONil(tc_prod(X14219,X14218)), inference(variable_rename,[status(thm)],[fact_zip_Osimps_I1_J])). 6.97/7.24 fof(c_0_10141, plain, ![X3651, X3652]:hAPP(c_Relation_OField(X3652),hAPP(c_Relation_Oconverse(X3652,X3652),X3651))=hAPP(c_Relation_OField(X3652),X3651), inference(variable_rename,[status(thm)],[fact_Field__converse])). 6.97/7.24 cnf(c_0_10142, 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])). 6.97/7.24 cnf(c_0_10143, 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_5840, c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10144, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X1!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_5841])). 6.97/7.24 cnf(c_0_10145, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)|X1!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_5842])). 6.97/7.24 cnf(c_0_10146, plain, (X3=c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))|c_List_Olist_ONil(X1)!=X2), inference(split_conjunct,[status(thm)],[c_0_5843])). 6.97/7.24 cnf(c_0_10147, plain, (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_5844, c_0_5184])). 6.97/7.24 fof(c_0_10148, plain, ![X7536, X7537, X7538, X7539]:c_Nitpick_Ofold__graph_H(X7539,X7538,X7537,X7536,c_Orderings_Obot__class_Obot(tc_fun(X7539,tc_HOL_Obool)),X7536), inference(variable_rename,[status(thm)],[fact_fold__graph_H_Ointros_I1_J])). 6.97/7.24 fof(c_0_10149, plain, ![X9274, X9275]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X9275,X9274)),X9275)), inference(variable_rename,[status(thm)],[fact_mod__less__eq__dividend])). 6.97/7.24 cnf(c_0_10150, plain, (c_Relation_Oantisym(X1,c_Relation_OId(X1))), inference(split_conjunct,[status(thm)],[c_0_5845])). 6.97/7.24 cnf(c_0_10151, plain, (c_Relation_Osym(X1,c_Relation_OId(X1))), inference(split_conjunct,[status(thm)],[c_0_5846])). 6.97/7.24 cnf(c_0_10152, plain, (hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X4),X1))|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_5847])). 6.97/7.24 cnf(c_0_10153, plain, (hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_fequal,X1)))|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_5848])). 6.97/7.24 fof(c_0_10154, plain, ![X14838]:c_Fun_Oid(X14838)=c_Hilbert__Choice_Oinv__into(X14838,X14838,c_Orderings_Otop__class_Otop(tc_fun(X14838,tc_HOL_Obool)),c_Fun_Oid(X14838)), inference(variable_rename,[status(thm)],[fact_inv__id])). 6.97/7.24 fof(c_0_10155, plain, ![X10455, X10456]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X10456,X10455)),X10455)=c_Groups_Ozero__class_Ozero(tc_Int_Oint), inference(variable_rename,[status(thm)],[fact_zmod__zdiv__trivial])). 6.97/7.24 cnf(c_0_10156, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))), inference(split_conjunct,[status(thm)],[c_0_5849])). 6.97/7.24 cnf(c_0_10157, plain, (X1=hAPP(c_Code__Numeral_Onat__of,esk433_1(X1))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_5850])). 6.97/7.24 fof(c_0_10158, plain, ![X9664]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X9664))), inference(variable_rename,[status(thm)],[fact_zero__less__Suc])). 6.97/7.24 cnf(c_0_10159, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=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)))), inference(split_conjunct,[status(thm)],[c_0_5851])). 6.97/7.24 cnf(c_0_10160, plain, (hAPP(c_New__DSequence_Opos__decr__bind(X2,X3,X4,X5),X1)=c_Lazy__Sequence_Oempty(X3)|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X1), inference(split_conjunct,[status(thm)],[c_0_5852])). 6.97/7.24 cnf(c_0_10161, plain, (c_Lazy__Sequence_Ohit__bound(X2)=hAPP(c_New__DSequence_Oneg__decr__bind(X3,X2,X4,X5),X1)|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X1), inference(split_conjunct,[status(thm)],[c_0_5853])). 6.97/7.24 fof(c_0_10162, plain, ![X6183, X6184, X6185]:c_List_Oremdups(X6185,c_List_Oinsert(X6185,X6184,X6183))=c_List_Oinsert(X6185,X6184,c_List_Oremdups(X6185,X6183)), inference(variable_rename,[status(thm)],[fact_insert__remdups])). 6.97/7.24 fof(c_0_10163, plain, ![X884]:c_Relation_OId__on(X884,c_Orderings_Obot__class_Obot(tc_fun(X884,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X884,X884),tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Id__on__empty])). 6.97/7.24 fof(c_0_10164, plain, ![X3221]:c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3221)=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)],[fact_posDivAlg__0])). 6.97/7.24 cnf(c_0_10165, plain, (c_Divides_OnegateSnd=c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[fact_negateSnd__def])). 6.97/7.24 fof(c_0_10166, plain, ![X12223, X12224, X12225, X12226]:c_Fun_Ooverride__on(X12226,X12225,X12224,X12223,c_Orderings_Obot__class_Obot(tc_fun(X12226,tc_HOL_Obool)))=X12224, inference(variable_rename,[status(thm)],[fact_override__on__emptyset])). 6.97/7.24 fof(c_0_10167, plain, ![X5123, X5124, X5125, X5126]:hAPP(hAPP(c_Power_Opower_Opower(X5126,X5125,X5124),X5123),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X5125, inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__0])). 6.97/7.24 fof(c_0_10168, plain, ![X12578, X12579, X12580]:hAPP(c_List_Orev(X12580),c_List_Oreplicate(X12580,X12579,X12578))=c_List_Oreplicate(X12580,X12579,X12578), inference(variable_rename,[status(thm)],[fact_rev__replicate])). 6.97/7.24 fof(c_0_10169, plain, ![X9546, X9547, X9548]:hAPP(c_List_Ohd(X9548),hAPP(hAPP(c_List_Olist_OCons(X9548),X9547),X9546))=X9547, inference(variable_rename,[status(thm)],[fact_hd_Osimps])). 6.97/7.24 fof(c_0_10170, plain, ![X13021, X13022, X13023]:X13021=hAPP(c_List_Otl(X13023),hAPP(hAPP(c_List_Olist_OCons(X13023),X13022),X13021)), inference(variable_rename,[status(thm)],[fact_tl_Osimps_I2_J])). 6.97/7.24 fof(c_0_10171, plain, ![X12472, X12473]:hAPP(hAPP(c_List_Olist_OCons(X12473),X12472),c_List_Olist_ONil(X12473))=c_List_Oinsert(X12473,X12472,c_List_Olist_ONil(X12473)), inference(variable_rename,[status(thm)],[fact_insert__Nil])). 6.97/7.24 fof(c_0_10172, plain, ![X10370, X10371, X10372]:hAPP(c_Relation_Oconverse(X10372,X10371),hAPP(c_Relation_Oconverse(X10371,X10372),X10370))=X10370, inference(variable_rename,[status(thm)],[fact_converse__converse])). 6.97/7.24 fof(c_0_10173, plain, ![X4377, X4378]:c_Divides_Odiv__class_Omod(tc_Int_Oint,X4378,X4377)=hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X4378,X4377)), inference(variable_rename,[status(thm)],[fact_mod__int__def])). 6.97/7.24 fof(c_0_10174, plain, ![X14869]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X14869)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X14869, inference(variable_rename,[status(thm)],[fact_diff__Suc__1])). 6.97/7.24 fof(c_0_10175, plain, ![X4229, X4230]:hAPP(c_Relation_ODomain(X4230,X4230),c_Transitive__Closure_Ortrancl(X4230,X4229))=c_Orderings_Otop__class_Otop(tc_fun(X4230,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Domain__rtrancl])). 6.97/7.24 fof(c_0_10176, plain, ![X17566, X17567]:hAPP(c_Relation_ORange(X17567,X17567),c_Transitive__Closure_Ortrancl(X17567,X17566))=c_Orderings_Otop__class_Otop(tc_fun(X17567,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Range__rtrancl])). 6.97/7.24 fof(c_0_10177, plain, ![X16485, X16486]:hAPP(c_List_Oset(X16486),hAPP(c_List_Orotate1(X16486),X16485))=hAPP(c_List_Oset(X16486),X16485), inference(variable_rename,[status(thm)],[fact_set__rotate1])). 6.97/7.24 fof(c_0_10178, plain, ![X5445, X5446]:hAPP(c_List_Oset(X5446),hAPP(c_List_Orev(X5446),X5445))=hAPP(c_List_Oset(X5446),X5445), inference(variable_rename,[status(thm)],[fact_set__rev])). 6.97/7.24 cnf(c_0_10179, plain, (X1=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_5854])). 6.97/7.24 fof(c_0_10180, plain, ![X4026]:hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4026))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4026), inference(variable_rename,[status(thm)],[fact_abs__int__eq])). 6.97/7.24 cnf(c_0_10181, 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])). 6.97/7.24 fof(c_0_10182, plain, ![X11036, X11037]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11037,tc_HOL_Obool)),X11036),X11036)), inference(variable_rename,[status(thm)],[fact_subset__refl])). 6.97/7.24 fof(c_0_10183, plain, ![X12388, X12389]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X12389),X12388))), inference(variable_rename,[status(thm)],[fact_finite__atLeastLessThan__int])). 6.97/7.24 fof(c_0_10184, plain, ![X662, X663]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X663),X662))), inference(variable_rename,[status(thm)],[fact_finite__atLeastLessThan])). 6.97/7.24 cnf(c_0_10185, plain, (c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5855])). 6.97/7.24 fof(c_0_10186, plain, ![X11364, X11365, X11366]:hAPP(c_Finite__Set_Ofold1(X11366,X11365),X11364)=c_HOL_OThe(X11366,c_Finite__Set_Ofold1Set(X11366,X11365,X11364)), inference(variable_rename,[status(thm)],[fact_fold1__def])). 6.97/7.24 cnf(c_0_10187, plain, (c_Wellfounded_Owf(X1,hAPP(c_Wellfounded_Omeasure(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5856])). 6.97/7.24 fof(c_0_10188, plain, ![X16630]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16630),hAPP(c_Nat_OSuc,X16630))), inference(variable_rename,[status(thm)],[fact_lessI])). 6.97/7.24 fof(c_0_10189, plain, ![X4331, X4332]:c_Relation_Orefl__on(X4332,c_Orderings_Otop__class_Otop(tc_fun(X4332,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X4332,X4331)), inference(variable_rename,[status(thm)],[fact_refl__rtrancl])). 6.97/7.24 fof(c_0_10190, plain, ![X12880, X12881, X12882]:hAPP(hAPP(c_List_Olist__update(X12882,c_List_Olist_ONil(X12882)),X12881),X12880)=c_List_Olist_ONil(X12882), inference(variable_rename,[status(thm)],[fact_list__update__code_I1_J])). 6.97/7.24 fof(c_0_10191, plain, ![X4425]:c_List_Olists(X4425,c_Orderings_Otop__class_Otop(tc_fun(X4425,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X4425),tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_lists__UNIV])). 6.97/7.24 fof(c_0_10192, plain, ![X13793, X13794]:hAPP(hAPP(c_Nat_Ocompow(X13794,X13794),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13793)=c_Fun_Oid(X13794), inference(variable_rename,[status(thm)],[fact_funpow_Osimps_I1_J])). 6.97/7.24 fof(c_0_10193, plain, ![X2247, X2248, X2249, X2250]:c_Nat_Onat_Onat__case(X2250,X2249,X2248,hAPP(c_Nat_OSuc,X2247))=hAPP(X2248,X2247), inference(variable_rename,[status(thm)],[fact_nat__case__Suc])). 6.97/7.24 fof(c_0_10194, plain, ![X15564, X15565, X15566]:c_Nitpick_OAbs__Frac(X15566,c_Nitpick_Onorm__frac(X15565,X15564))=hAPP(hAPP(c_Nitpick_Ofrac(X15566),X15565),X15564), inference(variable_rename,[status(thm)],[fact_Nitpick_Ofrac__def])). 6.97/7.24 fof(c_0_10195, plain, ![X7921, X7922]:c_List_Olistrel(X7922,c_Transitive__Closure_Ortrancl(X7922,X7921))=c_Transitive__Closure_Ortrancl(tc_List_Olist(X7922),c_List_Olistrel1(X7922,X7921)), inference(variable_rename,[status(thm)],[fact_listrel__rtrancl__eq__rtrancl__listrel1])). 6.97/7.24 fof(c_0_10196, plain, ![X16493, X16494]:hAPP(c_Relation_Oconverse(X16494,X16494),c_Relation_OId__on(X16494,X16493))=c_Relation_OId__on(X16494,X16493), inference(variable_rename,[status(thm)],[fact_converse__Id__on])). 6.97/7.24 fof(c_0_10197, plain, ![X4212, X4213, X4214, X4215, X4216]:hAPP(c_Fun_Ofun__upd(X4216,X4215,X4214,X4213,X4212),X4213)=X4212, inference(variable_rename,[status(thm)],[fact_fun__upd__same])). 6.97/7.24 fof(c_0_10198, plain, ![X6695, X6696, X6697]:X6695=hAPP(c_Fun_Ocomp(X6697,X6697,X6696,c_Fun_Oid(X6697)),X6695), inference(variable_rename,[status(thm)],[fact_id__o])). 6.97/7.24 fof(c_0_10199, plain, ![X9537, X9538, X9539]:hAPP(c_Fun_Ocomp(X9539,X9538,X9539,X9537),c_Fun_Oid(X9539))=X9537, inference(variable_rename,[status(thm)],[fact_o__id])). 6.97/7.24 fof(c_0_10200, plain, ![X3935, X3936, X3937, X3938]:X3936=hAPP(c_List_Olist_Olist__case(X3938,X3937,X3936,X3935),c_List_Olist_ONil(X3937)), inference(variable_rename,[status(thm)],[fact_list_Osimps_I4_J])). 6.97/7.24 fof(c_0_10201, plain, ![X17622, X17623, X17624, X17625]:X17622=hAPP(c_List_Ofoldl(X17625,X17624,X17623,X17622),c_List_Olist_ONil(X17624)), inference(variable_rename,[status(thm)],[fact_foldl__Nil])). 6.97/7.24 fof(c_0_10202, plain, ![X5652, X5653, X5654]:c_Enum_Oproduct(X5654,X5653,c_List_Olist_ONil(X5654),X5652)=c_List_Olist_ONil(tc_prod(X5654,X5653)), inference(variable_rename,[status(thm)],[fact_product_Osimps_I1_J])). 6.97/7.24 fof(c_0_10203, plain, ![X11115, X11116]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11116,tc_HOL_Obool)),X11115),X11115)=X11115, inference(variable_rename,[status(thm)],[fact_Int__absorb])). 6.97/7.24 fof(c_0_10204, plain, ![X3117, X3118]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3118,tc_HOL_Obool)),X3117),X3117)=X3117, inference(variable_rename,[status(thm)],[fact_Un__absorb])). 6.97/7.24 fof(c_0_10205, plain, ![X11901, X11902, X11903]:X11902=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11903)),c_List_Oreplicate(X11903,X11902,X11901)), inference(variable_rename,[status(thm)],[fact_length__replicate])). 6.97/7.24 fof(c_0_10206, plain, ![X14761, X14762]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X14762)),X14761)=c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X14762,X14761), inference(variable_rename,[status(thm)],[fact_atLeastSucLessThan__greaterThanLessThan])). 6.97/7.24 fof(c_0_10207, plain, ![X15191, X15192]:c_Complete__Lattice_OSup__class_OSup(tc_fun(X15192,tc_HOL_Obool),hAPP(c_Set_OPow(X15192),X15191))=X15191, inference(variable_rename,[status(thm)],[fact_Union__Pow__eq])). 6.97/7.24 fof(c_0_10208, plain, ![X17109, X17110]:hAPP(c_List_Oset(X17110),X17109)=hAPP(c_List_Oset(X17110),c_List_Oremdups(X17110,X17109)), inference(variable_rename,[status(thm)],[fact_set__remdups])). 6.97/7.24 cnf(c_0_10209, plain, (X2=c_Fun_Ofun__upd(X4,X5,X2,X3,X1)|X1!=hAPP(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_5857])). 6.97/7.24 cnf(c_0_10210, 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_5858])). 6.97/7.24 fof(c_0_10211, plain, ![X15866]:hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15866)=hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X15866)), inference(variable_rename,[status(thm)],[fact_nat__of__number])). 6.97/7.24 cnf(c_0_10212, plain, (c_List_Olist__all2(X1,X3,X4,X2,c_List_Olist_ONil(X3))|c_List_Olist_ONil(X1)!=X2), inference(split_conjunct,[status(thm)],[c_0_5859])). 6.97/7.24 cnf(c_0_10213, 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])). 6.97/7.24 cnf(c_0_10214, 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_5860])). 6.97/7.24 fof(c_0_10215, plain, ![X12169, X12170, X12171]:c_Fun_Oinj__on(X12171,X12170,X12169,c_Orderings_Obot__class_Obot(tc_fun(X12171,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_inj__on__empty])). 6.97/7.24 fof(c_0_10216, plain, ![X8562, X8563]:c_Fun_Oinj__on(tc_List_Olist(X8563),tc_List_Olist(X8563),c_List_Orev(X8563),X8562), inference(variable_rename,[status(thm)],[fact_inj__on__rev])). 6.97/7.24 fof(c_0_10217, plain, ![X10136]: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)),X10136)), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J])). 6.97/7.24 fof(c_0_10218, plain, ![X10442, X10443]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X10443,X10442))), inference(variable_rename,[status(thm)],[fact_finite__atLeastAtMost__int])). 6.97/7.24 fof(c_0_10219, plain, ![X10945, X10946]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X10946,X10945))), inference(variable_rename,[status(thm)],[fact_finite__atLeastAtMost])). 6.97/7.24 fof(c_0_10220, plain, ![X2464, X2465]:c_List_Olist_ONil(X2465)=c_List_Osublist(X2465,X2464,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_sublist__empty])). 6.97/7.24 cnf(c_0_10221, 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_5861])). 6.97/7.24 fof(c_0_10222, plain, ![X1631]:c_Relation_Oantisym(X1631,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1631,X1631),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_antisym__empty])). 6.97/7.24 fof(c_0_10223, plain, ![X540]:c_Wellfounded_Owf(X540,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X540,X540),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_wf__empty])). 6.97/7.24 fof(c_0_10224, plain, ![X4780]:hBOOL(hAPP(c_Finite__Set_Ofinite(X4780),c_Orderings_Obot__class_Obot(tc_fun(X4780,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_finite_Oequations_I1_J])). 6.97/7.24 cnf(c_0_10225, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_5862])). 6.97/7.24 fof(c_0_10226, plain, ![X590, X591]:c_List_Olist_ONil(X591)=hAPP(hAPP(c_List_Otake(X591),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X590), inference(variable_rename,[status(thm)],[fact_take__0])). 6.97/7.24 fof(c_0_10227, plain, ![X2844, X2845]:c_List_Olist_ONil(X2845)=hAPP(hAPP(c_List_Odrop(X2845),X2844),c_List_Olist_ONil(X2845)), inference(variable_rename,[status(thm)],[fact_drop__Nil])). 6.97/7.24 fof(c_0_10228, plain, ![X15738, X15739]:c_List_Olist_ONil(X15739)=hAPP(hAPP(c_List_Otake(X15739),X15738),c_List_Olist_ONil(X15739)), inference(variable_rename,[status(thm)],[fact_take__Nil])). 6.97/7.24 cnf(c_0_10229, 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_5863])). 6.97/7.24 fof(c_0_10230, plain, ![X7778]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7778)=c_Groups_Ozero__class_Ozero(tc_Int_Oint), inference(variable_rename,[status(thm)],[fact_zdiv__zero])). 6.97/7.24 fof(c_0_10231, plain, ![X16925]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X16925)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_diff__0__eq__0])). 6.97/7.24 fof(c_0_10232, plain, ![X9294]:(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X9294),c_Groups_Ozero__class_Ozero(tc_Int_Oint))&X9294=c_Divides_Odiv__class_Omod(tc_Int_Oint,X9294,c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(variable_rename,[status(thm)],[fact_DIVISION__BY__ZERO])). 6.97/7.24 cnf(c_0_10233, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_5864])). 6.97/7.24 fof(c_0_10234, plain, ![X3799]:c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,X3799)=c_Lazy__Sequence_Osmall__lazy_H(X3799,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3799)), inference(variable_rename,[status(thm)],[fact_small__lazy__int__def])). 6.97/7.24 fof(c_0_10235, plain, ![X7552]:hAPP(c_List_Omap(X7552,X7552),c_Fun_Oid(X7552))=c_Fun_Oid(tc_List_Olist(X7552)), inference(variable_rename,[status(thm)],[fact_List_Omap_Oid])). 6.97/7.24 fof(c_0_10236, plain, ![X5365]:c_Fun_Oid(tc_List_Olist(X5365))=hAPP(c_List_Omap(X5365,X5365),c_COMBI(X5365)), inference(variable_rename,[status(thm)],[fact_List_Omap_Oidentity])). 6.97/7.24 fof(c_0_10237, plain, ![X9460, X9461, X9462, X9463]:X9461=c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X9463,X9462,X9461,X9460,c_Lazy__Sequence_Olazy__sequence_OEmpty(X9462)), inference(variable_rename,[status(thm)],[fact_lazy__sequence_Orecs_I1_J])). 6.97/7.24 fof(c_0_10238, plain, ![X3510, X3511, X3512]:c_Predicate_Oconversep(X3512,X3511,c_Predicate_Oconversep(X3511,X3512,X3510))=X3510, inference(variable_rename,[status(thm)],[fact_conversep__conversep])). 6.97/7.24 fof(c_0_10239, plain, ![X8218, X8219]:hAPP(c_Set_Oimage(X8219,X8219,c_Fun_Oid(X8219)),X8218)=X8218, inference(variable_rename,[status(thm)],[fact_image__id])). 6.97/7.24 fof(c_0_10240, plain, ![X11317, X11318]:X11317=hAPP(c_Set_Oimage(X11318,X11318,c_COMBI(X11318)),X11317), inference(variable_rename,[status(thm)],[fact_image__ident])). 6.97/7.24 fof(c_0_10241, plain, ![X12695, X12696, X12697]:hAPP(c_Nat_Onat_Onat__rec(X12697,X12696,X12695),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X12696, inference(variable_rename,[status(thm)],[fact_nat__rec__0])). 6.97/7.24 fof(c_0_10242, plain, ![X3823, X3824, X3825, X3826]:X3824=hAPP(hAPP(c_COMBK(X3826,X3825),X3824),X3823), inference(variable_rename,[status(thm)],[help_c__COMBK__1])). 6.97/7.24 fof(c_0_10243, plain, ![X14997, X14998]:hAPP(c_Relation_ODomain(X14998,X14998),c_Relation_OId__on(X14998,X14997))=X14997, inference(variable_rename,[status(thm)],[fact_Domain__Id__on])). 6.97/7.24 fof(c_0_10244, plain, ![X3015, X3016]:X3015=hAPP(c_Relation_ORange(X3016,X3016),c_Relation_OId__on(X3016,X3015)), inference(variable_rename,[status(thm)],[fact_Range__Id__on])). 6.97/7.24 fof(c_0_10245, plain, ![X7186, X7187]:hAPP(hAPP(c_List_Oappend(X7187),c_List_Olist_ONil(X7187)),X7186)=X7186, inference(variable_rename,[status(thm)],[fact_append__Nil])). 6.97/7.24 fof(c_0_10246, plain, ![X6413, X6414, X6415]:hAPP(c_New__DSequence_Opos__single(X6415,X6414),X6413)=hAPP(c_Lazy__Sequence_Osingle(X6415),X6414), inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__single__def])). 6.97/7.24 fof(c_0_10247, plain, ![X1878, X1879]:X1878=hAPP(hAPP(c_List_Odrop(X1879),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1878), inference(variable_rename,[status(thm)],[fact_drop__0])). 6.97/7.24 fof(c_0_10248, plain, ![X13380, X13381]:hAPP(hAPP(c_List_Oappend(X13381),X13380),c_List_Olist_ONil(X13381))=X13380, inference(variable_rename,[status(thm)],[fact_append__Nil2])). 6.97/7.24 fof(c_0_10249, plain, ![X2846]:c_Orderings_Obot__class_Obot(tc_fun(X2846,tc_HOL_Obool))=hAPP(c_List_Oset(X2846),c_List_Olist_ONil(X2846)), inference(variable_rename,[status(thm)],[fact_List_Oset_Osimps_I1_J])). 6.97/7.24 cnf(c_0_10250, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=X1), inference(split_conjunct,[status(thm)],[c_0_5865])). 6.97/7.24 fof(c_0_10251, plain, ![X16889]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X16889)=X16889, inference(variable_rename,[status(thm)],[fact_zmult__1])). 6.97/7.24 fof(c_0_10252, plain, ![X5472]:X5472=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5472), inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0])). 6.97/7.24 fof(c_0_10253, plain, ![X9370]:X9370=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X9370), inference(variable_rename,[status(thm)],[fact_nat__mult__1])). 6.97/7.24 fof(c_0_10254, plain, ![X11528]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11528),c_Groups_Oone__class_Oone(tc_Int_Oint))=X11528, inference(variable_rename,[status(thm)],[fact_zmult__1__right])). 6.97/7.24 fof(c_0_10255, plain, ![X8600]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8600),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X8600, inference(variable_rename,[status(thm)],[fact_nat__mult__1__right])). 6.97/7.24 cnf(c_0_10256, 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_5866])). 6.97/7.24 fof(c_0_10257, plain, ![X16702]:X16702=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16702),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_minus__nat_Odiff__0])). 6.97/7.24 fof(c_0_10258, plain, ![X6994]:X6994=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6994)), inference(variable_rename,[status(thm)],[fact_zminus__zminus])). 6.97/7.24 fof(c_0_10259, plain, ![X1925, X1926]:c_Hoare__Mirabelle_Ohoare__derivs(X1926,X1925,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1926),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_empty])). 6.97/7.24 fof(c_0_10260, plain, ![X12350, X12351]:c_List_Olistrelp(X12351,X12350,c_List_Olist_ONil(X12351),c_List_Olist_ONil(X12351)), inference(variable_rename,[status(thm)],[fact_listrelp_Oequations_I1_J])). 6.97/7.24 fof(c_0_10261, plain, ![X16271, X16272, X16273]:c_Lazy__Sequence_Olazy__sequence_OEmpty(X16272)=c_Lazy__Sequence_Omap(X16273,X16272,X16271,c_Lazy__Sequence_Olazy__sequence_OEmpty(X16273)), inference(variable_rename,[status(thm)],[fact__07])). 6.97/7.24 fof(c_0_10262, plain, ![X3958, X3959, X3960]:c_List_Olist_ONil(X3959)=c_List_Omaps(X3960,X3959,X3958,c_List_Olist_ONil(X3960)), inference(variable_rename,[status(thm)],[fact_maps__simps_I2_J])). 6.97/7.24 fof(c_0_10263, plain, ![X4237, X4238]:hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X4238,tc_HOL_Obool)),X4237)), inference(variable_rename,[status(thm)],[fact_top1I])). 6.97/7.24 fof(c_0_10264, plain, ![X6008, X6009]:c_Relation_Ototal__on(X6009,c_Orderings_Obot__class_Obot(tc_fun(X6009,tc_HOL_Obool)),X6008), inference(variable_rename,[status(thm)],[fact_total__on__empty])). 6.97/7.24 fof(c_0_10265, plain, ![X11766]:hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X11766),X11766)), inference(variable_rename,[status(thm)],[fact_dvd_Oorder__refl])). 6.97/7.24 fof(c_0_10266, plain, ![X6489]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6489),X6489)), inference(variable_rename,[status(thm)],[fact_zle__refl])). 6.97/7.24 fof(c_0_10267, plain, ![X3095]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3095),X3095)), inference(variable_rename,[status(thm)],[fact_le__refl])). 6.97/7.24 fof(c_0_10268, plain, ![X15935, X15936]:c_Fun_Obij__betw(X15936,X15936,c_Fun_Oid(X15936),X15935,X15935), inference(variable_rename,[status(thm)],[fact_bij__betw__id])). 6.97/7.24 fof(c_0_10269, plain, ![X1325, X1326]:hBOOL(hAPP(c_List_Olistsp(X1326,X1325),c_List_Olist_ONil(X1326))), inference(variable_rename,[status(thm)],[fact_listsp_Oequations_I1_J])). 6.97/7.24 fof(c_0_10270, plain, ![X7779, X7780]:hBOOL(hAPP(c_List_Odistinct(X7780),c_List_Oremdups(X7780,X7779))), inference(variable_rename,[status(thm)],[fact_distinct__remdups])). 6.97/7.24 fof(c_0_10271, plain, ![X9914, X9915]:hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X9915,X9914))), inference(variable_rename,[status(thm)],[fact_distinct__upto])). 6.97/7.24 cnf(c_0_10272, 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])). 6.97/7.24 cnf(c_0_10273, 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])). 6.97/7.24 cnf(c_0_10274, 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])). 6.97/7.24 fof(c_0_10275, plain, ![X5420]:c_Finite__Set_Ofun__left__comm__idem(X5420,tc_fun(X5420,tc_HOL_Obool),c_Set_Oinsert(X5420)), inference(variable_rename,[status(thm)],[fact_fun__left__comm__idem__insert])). 6.97/7.24 cnf(c_0_10276, plain, (c_List_Olist__all2(X3,X3,c_fequal,X1,X2)|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_5867])). 6.97/7.24 cnf(c_0_10277, plain, (hBOOL(hAPP(hAPP(c_fequal,X1),X2))|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_5868])). 6.97/7.24 fof(c_0_10278, plain, ![X6262, X6263]:hAPP(c_List_Ofilter(X6263,X6262),c_List_Olist_ONil(X6263))=c_List_Olist_ONil(X6263), inference(variable_rename,[status(thm)],[fact_filter_Osimps_I1_J])). 6.97/7.24 fof(c_0_10279, plain, ![X3029]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3029),X3029)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_diff__self__eq__0])). 6.97/7.24 fof(c_0_10280, plain, ![X6379, X6380]:hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X6380,X6379),c_Lazy__Sequence_Olazy__sequence_OEmpty(X6380))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osize_I1_J])). 6.97/7.24 fof(c_0_10281, plain, ![X4952]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4952)),c_List_Olist_ONil(X4952))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_list_Osize_I3_J])). 6.97/7.24 fof(c_0_10282, plain, ![X13387]:hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X13387)),c_Lazy__Sequence_Olazy__sequence_OEmpty(X13387))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osize_I3_J])). 6.97/7.24 fof(c_0_10283, plain, ![X9356, X9357, X9358]:hAPP(c_New__DSequence_Oneg__single(X9358,X9357),X9356)=c_Lazy__Sequence_Ohb__single(X9358,X9357), inference(variable_rename,[status(thm)],[fact_New__DSequence_Oneg__single__def])). 6.97/7.24 fof(c_0_10284, plain, ![X4550, X4551]:c_Transitive__Closure_Ortrancl(X4551,c_Transitive__Closure_Ortrancl(X4551,X4550))=c_Transitive__Closure_Ortrancl(X4551,X4550), inference(variable_rename,[status(thm)],[fact_rtrancl__idemp])). 6.97/7.24 fof(c_0_10285, plain, ![X14325, X14326]:c_List_Oremdups(X14326,c_List_Oremdups(X14326,X14325))=c_List_Oremdups(X14326,X14325), inference(variable_rename,[status(thm)],[fact_remdups__remdups])). 6.97/7.24 fof(c_0_10286, plain, ![X11977]:c_List_Otranspose(X11977,c_List_Olist_ONil(tc_List_Olist(X11977)))=c_List_Olist_ONil(tc_List_Olist(X11977)), inference(variable_rename,[status(thm)],[fact_transpose_Osimps_I1_J])). 6.97/7.24 fof(c_0_10287, plain, ![X4753, X4754, X4755]:c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X4755,X4754,X4753,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=X4754, inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I4_J])). 6.97/7.24 fof(c_0_10288, plain, ![X17669, X17670, X17671]:c_Nat_Onat_Onat__case(X17671,X17670,X17669,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X17670, inference(variable_rename,[status(thm)],[fact_nat__case__0])). 6.97/7.24 fof(c_0_10289, plain, ![X2002, X2003, X2004]:X2003=c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X2004,X2003,X2002,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), inference(variable_rename,[status(thm)],[fact_code__numeral_Orecs_I1_J])). 6.97/7.24 cnf(c_0_10290, plain, (X1=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OPls)), inference(split_conjunct,[status(thm)],[c_0_5869])). 6.97/7.24 cnf(c_0_10291, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X1)=c_Int_OPls), inference(split_conjunct,[status(thm)],[c_0_5870])). 6.97/7.24 fof(c_0_10292, plain, ![X1126, X1127]:c_List_OtakeWhile(X1127,X1126,c_List_Olist_ONil(X1127))=c_List_Olist_ONil(X1127), inference(variable_rename,[status(thm)],[fact_takeWhile_Osimps_I1_J])). 6.97/7.24 fof(c_0_10293, plain, ![X3226, X3227]:c_List_Olist_ONil(X3227)=c_List_Osublist(X3227,c_List_Olist_ONil(X3227),X3226), inference(variable_rename,[status(thm)],[fact_sublist__nil])). 6.97/7.24 fof(c_0_10294, plain, ![X14731, X14732]:c_List_Olist_ONil(X14732)=c_List_Oremove1(X14732,X14731,c_List_Olist_ONil(X14732)), inference(variable_rename,[status(thm)],[fact_remove1_Osimps_I1_J])). 6.97/7.24 fof(c_0_10295, plain, ![X15821, X15822]:c_List_Olist_Olist__size(X15822,X15821,c_List_Olist_ONil(X15822))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_list_Osize_I1_J])). 6.97/7.24 fof(c_0_10296, plain, ![X5830, X5831]:c_Fun_Oinj__on(X5831,X5831,c_COMBI(X5831),X5830), inference(variable_rename,[status(thm)],[fact_inj__on__id2])). 6.97/7.24 fof(c_0_10297, plain, ![X5195, X5196]:c_Fun_Oinj__on(X5196,X5196,c_Fun_Oid(X5196),X5195), inference(variable_rename,[status(thm)],[fact_inj__on__id])). 6.97/7.24 fof(c_0_10298, plain, ![X10977, X10978]:c_Relation_Osingle__valued(X10978,X10978,c_Relation_OId__on(X10978,X10977)), inference(variable_rename,[status(thm)],[fact_single__valued__Id__on])). 6.97/7.24 fof(c_0_10299, plain, ![X10924, X10925]:c_List_Oreplicate(X10925,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X10924)=c_List_Olist_ONil(X10925), inference(variable_rename,[status(thm)],[fact_replicate__0])). 6.97/7.24 fof(c_0_10300, plain, ![X7467]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X7467), inference(variable_rename,[status(thm)],[fact_zmod__zero])). 6.97/7.24 fof(c_0_10301, plain, ![X17007, X17008]:c_Relation_Orefl__on(X17008,X17007,c_Relation_OId__on(X17008,X17007)), inference(variable_rename,[status(thm)],[fact_refl__on__Id__on])). 6.97/7.24 fof(c_0_10302, plain, ![X9099]:hBOOL(hAPP(c_List_Odistinct(X9099),c_List_Olist_ONil(X9099))), inference(variable_rename,[status(thm)],[fact_distinct_Osimps_I1_J])). 6.97/7.24 fof(c_0_10303, plain, ![X10666]:c_Relation_Otrans(tc_fun(X10666,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X10666)), inference(variable_rename,[status(thm)],[fact_trans__finite__psubset])). 6.97/7.24 fof(c_0_10304, plain, ![X11342]:c_Wellfounded_Owf(tc_fun(X11342,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X11342)), inference(variable_rename,[status(thm)],[fact_wf__finite__psubset])). 6.97/7.24 fof(c_0_10305, plain, ![X17067]:c_Lazy__Sequence_Olazy__sequence_OEmpty(X17067)=c_Lazy__Sequence_Oflat(X17067,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(X17067))), inference(variable_rename,[status(thm)],[fact__04])). 6.97/7.24 fof(c_0_10306, plain, ![X13750]:hAPP(c_List_Otl(X13750),c_List_Olist_ONil(X13750))=c_List_Olist_ONil(X13750), inference(variable_rename,[status(thm)],[fact_tl_Osimps_I1_J])). 6.97/7.24 fof(c_0_10307, plain, ![X10457]:c_List_Olist_ONil(X10457)=hAPP(c_List_Orev(X10457),c_List_Olist_ONil(X10457)), inference(variable_rename,[status(thm)],[fact_rev_Osimps_I1_J])). 6.97/7.24 fof(c_0_10308, plain, ![X17376, X17377]:c_Lazy__Sequence_Oappend(X17377,c_Lazy__Sequence_Olazy__sequence_OEmpty(X17377),X17376)=X17376, inference(variable_rename,[status(thm)],[fact__02])). 6.97/7.24 fof(c_0_10309, plain, ![X11349, X11350]:c_List_Osplice(X11350,X11349,c_List_Olist_ONil(X11350))=X11349, inference(variable_rename,[status(thm)],[fact_splice__Nil2])). 6.97/7.24 fof(c_0_10310, plain, ![X6622, X6623]:X6622=c_List_Osplice(X6623,c_List_Olist_ONil(X6623),X6622), inference(variable_rename,[status(thm)],[fact_splice_Osimps_I1_J])). 6.97/7.24 fof(c_0_10311, plain, ![X16238, X16239]:c_HOL_OThe(X16239,hAPP(c_fequal,X16238))=X16238, inference(variable_rename,[status(thm)],[fact_the__sym__eq__trivial])). 6.97/7.24 fof(c_0_10312, plain, ![X15888, X15889]:X15888=c_Hilbert__Choice_OEps(X15889,hAPP(c_fequal,X15888)), inference(variable_rename,[status(thm)],[fact_some__sym__eq__trivial])). 6.97/7.24 cnf(c_0_10313, plain, (hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X1))=X1), inference(split_conjunct,[status(thm)],[c_0_5871])). 6.97/7.24 cnf(c_0_10314, plain, (X1=hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X1))), inference(split_conjunct,[status(thm)],[c_0_5872])). 6.97/7.24 fof(c_0_10315, plain, ![X16228]:X16228=hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X16228)), inference(variable_rename,[status(thm)],[fact_Rep__Integ__inverse])). 6.97/7.24 cnf(c_0_10316, plain, (c_Groups_Ozero__class_Ozero(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_5399])). 6.97/7.24 fof(c_0_10317, plain, ![X9510]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X9510,X9510), inference(variable_rename,[status(thm)],[fact_zmod__self])). 6.97/7.24 fof(c_0_10318, plain, ![X12432]:c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X12432), inference(variable_rename,[status(thm)],[fact_inj__Suc])). 6.97/7.24 fof(c_0_10319, plain, ![X16019, X16020]:c_List_Olist__all(X16020,X16019,c_List_Olist_ONil(X16020)), inference(variable_rename,[status(thm)],[fact_list__all__simps_I2_J])). 6.97/7.24 fof(c_0_10320, plain, ![X5111, X5112]:c_Relation_Oantisym(X5112,c_Relation_OId__on(X5112,X5111)), inference(variable_rename,[status(thm)],[fact_antisym__Id__on])). 6.97/7.24 fof(c_0_10321, plain, ![X9687, X9688]:c_Relation_Otrans(X9688,c_Transitive__Closure_Ortrancl(X9688,X9687)), inference(variable_rename,[status(thm)],[fact_trans__rtrancl])). 6.97/7.24 cnf(c_0_10322, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(c_Code__Numeral_Oint__of,X1)|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X1), inference(split_conjunct,[status(thm)],[c_0_4462])). 6.97/7.24 fof(c_0_10323, plain, ![X2801, X2802]:c_Relation_Otrans(X2802,c_Relation_OId__on(X2802,X2801)), inference(variable_rename,[status(thm)],[fact_trans__Id__on])). 6.97/7.24 fof(c_0_10324, plain, ![X14562, X14563]:c_Relation_Osym(X14563,c_Relation_OId__on(X14563,X14562)), inference(variable_rename,[status(thm)],[fact_sym__Id__on])). 6.97/7.24 fof(c_0_10325, plain, ![X6120, X6121]:c_Wellfounded_Owf(X6121,c_List_Omeasures(X6121,X6120)), inference(variable_rename,[status(thm)],[fact_wf__measures])). 6.97/7.24 fof(c_0_10326, plain, ![X2013, X2014]:c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X2014,X2013)), inference(variable_rename,[status(thm)],[fact_sorted__upto])). 6.97/7.24 fof(c_0_10327, plain, ![X15286]:c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X15286)), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J])). 6.97/7.24 cnf(c_0_10328, plain, (X2=c_Nitpick_Onat__gcd(X2,X1)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1), inference(split_conjunct,[status(thm)],[c_0_5873])). 6.97/7.24 fof(c_0_10329, plain, ![X6978]:c_List_Obutlast(X6978,c_List_Olist_ONil(X6978))=c_List_Olist_ONil(X6978), inference(variable_rename,[status(thm)],[fact_butlast_Osimps_I1_J])). 6.97/7.24 fof(c_0_10330, plain, ![X3464]:c_List_Oremdups(X3464,c_List_Olist_ONil(X3464))=c_List_Olist_ONil(X3464), inference(variable_rename,[status(thm)],[fact_remdups_Osimps_I1_J])). 6.97/7.24 fof(c_0_10331, plain, ![X8089, X8090]:c_Lazy__Sequence_Oempty(X8090)=hAPP(c_New__DSequence_Opos__empty(X8090),X8089), inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__empty__def])). 6.97/7.24 cnf(c_0_10332, plain, (c_Random_Oinc__shift(X2,X1)=c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_5874])). 6.97/7.24 fof(c_0_10333, plain, ![X17071]:c_Quickcheck_Obeyond(X17071,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), inference(variable_rename,[status(thm)],[fact_beyond__zero])). 6.97/7.24 cnf(c_0_10334, 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])). 6.97/7.24 cnf(c_0_10335, plain, (c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)=hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[fact_one__code__numeral__def])). 6.97/7.24 fof(c_0_10336, plain, ![X3286]:c_Predicate_Oconversep(X3286,X3286,c_fequal)=c_fequal, inference(variable_rename,[status(thm)],[fact_conversep__eq])). 6.97/7.24 fof(c_0_10337, plain, ![X16832, X16833]:X16832=hAPP(c_COMBI(X16833),X16832), inference(variable_rename,[status(thm)],[help_c__COMBI__1])). 6.97/7.24 fof(c_0_10338, plain, ![X12298, X12299]:X12298=hAPP(c_Fun_Oid(X12299),X12298), inference(variable_rename,[status(thm)],[fact_id__apply])). 6.97/7.24 cnf(c_0_10339, plain, (X1=hAPP(c_Code__Numeral_Oof__nat,esk571_1(X1))), inference(split_conjunct,[status(thm)],[c_0_5875])). 6.97/7.24 fof(c_0_10340, plain, ![X1690]:hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X1690)=X1690, inference(variable_rename,[status(thm)],[fact_nat__size])). 6.97/7.24 fof(c_0_10341, plain, ![X9156, X9157]:class_Nat_Osize(tc_Nitpick_Opair__box(X9157,X9156)), inference(variable_rename,[status(thm)],[arity_Nitpick__Opair____box__Nat_Osize])). 6.97/7.24 fof(c_0_10342, plain, ![X12842, X12843]:class_Nat_Osize(tc_sum(X12843,X12842)), inference(variable_rename,[status(thm)],[arity_sum__Nat_Osize])). 6.97/7.24 fof(c_0_10343, plain, ![X6743, X6744]:class_Nat_Osize(tc_prod(X6744,X6743)), inference(variable_rename,[status(thm)],[arity_prod__Nat_Osize])). 6.97/7.24 fof(c_0_10344, plain, ![X11708]:c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X11708)), inference(variable_rename,[status(thm)],[fact_wf__int__ge__less__than2])). 6.97/7.24 fof(c_0_10345, plain, ![X6864]:c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X6864)), inference(variable_rename,[status(thm)],[fact_wf__int__ge__less__than])). 6.97/7.24 fof(c_0_10346, plain, ![X858]:c_Equiv__Relations_Oequivp(X858,c_fequal), inference(variable_rename,[status(thm)],[fact_identity__equivp])). 6.97/7.24 fof(c_0_10347, plain, ![X12047]:class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X12047)), inference(variable_rename,[status(thm)],[arity_Hoare____Mirabelle__Otriple__Nat_Osize])). 6.97/7.24 fof(c_0_10348, plain, ![X11035]:class_Nat_Osize(tc_List_Olist(X11035)), inference(variable_rename,[status(thm)],[arity_List__Olist__Nat_Osize])). 6.97/7.24 fof(c_0_10349, plain, ![X2688]:class_Nat_Osize(tc_Option_Ooption(X2688)), inference(variable_rename,[status(thm)],[arity_Option__Ooption__Nat_Osize])). 6.97/7.24 fof(c_0_10350, plain, ![X307]:class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X307)), inference(variable_rename,[status(thm)],[arity_Lazy____Sequence__Olazy____sequence__Nat_Osize])). 6.97/7.24 cnf(c_0_10351, 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_5876, c_0_4798]), c_0_4798]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10352, 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|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))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5877, c_0_4798]), c_0_4798]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10353, 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|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))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5878, c_0_4798]), c_0_4798]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10354, 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))|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_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_5879, c_0_4798]), c_0_4798]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10355, 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_5880, c_0_4798]), c_0_4798]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10356, 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(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)|X1=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_5881, c_0_5538]), c_0_5539]), ['final']). 6.97/7.24 cnf(c_0_10357, 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(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)=X1|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5882, c_0_5538]), c_0_5539]), ['final']). 6.97/7.24 cnf(c_0_10358, 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(c_fequal,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))=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)],[c_0_5883, c_0_5538]), c_0_5539]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), ['final']). 6.97/7.24 cnf(c_0_10359, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),X3)),X2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X3)))),hAPP(X3,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),X3)),X2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X3))))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(X3,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),X3)),X2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X3))))))|~c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3)), inference(split_conjunct,[status(thm)],[c_0_5884]), ['final']). 6.97/7.24 cnf(c_0_10360, 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_5885]), ['final']). 6.97/7.24 cnf(c_0_10361, 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_5886]), ['final']). 6.97/7.24 cnf(c_0_10362, 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_5887]), ['final']). 6.97/7.24 cnf(c_0_10363, 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_5888]), ['final']). 6.97/7.24 cnf(c_0_10364, 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)),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))),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)),hAPP(c_COMBC(X1,X3,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))),hAPP(c_COMBC(X1,X3,tc_HOL_Obool),X6))))),X5)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X7))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5889, c_0_4798]), c_0_4798]), ['final']). 6.97/7.24 cnf(c_0_10365, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|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_5521]), ['final']). 6.97/7.24 cnf(c_0_10366, 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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),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_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)],[c_0_5890, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10367, 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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))),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)],[c_0_5892, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10368, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))|c_Random__Sequence_ORandom(X2,X3,X1,X4)=hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X2,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(X3,X4)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(X2,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(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))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(X2,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2))))),tc_prod(X2,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(X2)),hAPP(hAPP(c_COMBB(X2,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(X2,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(X2)),c_Product__Type_Ofst(X2,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)))))))), inference(split_conjunct,[status(thm)],[c_0_5893]), ['final']). 6.97/7.24 cnf(c_0_10369, plain, (c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_fun(X2,X1))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_HOL_Obool),X1),hAPP(c_COMBS(tc_fun(X2,X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X2,X1)),c_fconj),X3))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_fun(X2,X1),X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X2,X1),X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_fun(X2,X1))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X2,X1),X2,X1),c_COMBI(tc_fun(X2,X1))),X4)))))=hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,X1),X3),X4)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5894, c_0_4798]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10370, plain, (c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_fun(X2,X1))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_HOL_Obool),X1),hAPP(c_COMBS(tc_fun(X2,X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X2,X1)),c_fconj),X3))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_fun(X2,X1),X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X2,X1),X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_fun(X2,X1))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X2,X1),X2,X1),c_COMBI(tc_fun(X2,X1))),X4)))))=hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,X1),X3),X4)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5895, c_0_4798]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10371, 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))|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_5896, c_0_4798]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10372, 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))|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_5897, c_0_4798]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10373, 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_5898, c_0_4798]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10374, 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_5899]), ['final']). 6.97/7.24 cnf(c_0_10375, 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_5900]), ['final']). 6.97/7.24 cnf(c_0_10376, 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_5901, c_0_4798]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10377, 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_5902, c_0_4798]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10378, 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))|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))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5903, c_0_4798]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10379, 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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin),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)],[c_0_5904, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), c_0_4741]), c_0_5038]), c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_10380, 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_5905]), ['final']). 6.97/7.24 cnf(c_0_10381, 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_5906, c_0_5560]), ['final']). 6.97/7.24 cnf(c_0_10382, 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),esk25_6(X6,X4,X3,X2,X5,X1))))!=hAPP(X6,esk25_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_5907, c_0_4798]), c_0_4798]), c_0_4817]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10383, 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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),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)],[c_0_5908, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), ['final']). 6.97/7.24 cnf(c_0_10384, 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_5909, c_0_4467]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10385, 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_5885]), ['final']). 6.97/7.24 cnf(c_0_10386, 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_5886]), ['final']). 6.97/7.24 cnf(c_0_10387, 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),esk47_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_5910, c_0_4798]), c_0_4798]), c_0_4817]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10388, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))),c_Int_OMin)=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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|X1=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)],[c_0_5911, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4741]), ['final']). 6.97/7.24 cnf(c_0_10389, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk508_2(X2,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),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_COMBS(X1,X1,tc_HOL_Obool),X2),c_COMBI(X1))))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),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_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1)),c_fequal)),X2)))))|~c_Equiv__Relations_Opart__equivp(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5912]), ['final']). 6.97/7.24 cnf(c_0_10390, 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_5913, c_0_5038]), c_0_5038]), ['final']). 6.97/7.24 cnf(c_0_10391, 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_5887]), ['final']). 6.97/7.24 cnf(c_0_10392, 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_5914]), ['final']). 6.97/7.24 cnf(c_0_10393, 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_5888]), ['final']). 6.97/7.24 cnf(c_0_10394, 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_5915]), ['final']). 6.97/7.24 cnf(c_0_10395, 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_5916, c_0_4798]), ['final']). 6.97/7.24 cnf(c_0_10396, 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_5917, c_0_5539]), ['final']). 6.97/7.24 cnf(c_0_10397, 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_5918, c_0_5539]), ['final']). 6.97/7.24 cnf(c_0_10398, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))=hAPP(c_Code__Numeral_Oint__of,X1)|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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))!=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)],[c_0_5919, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), ['final']). 6.97/7.24 cnf(c_0_10399, 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_5920]), ['final']). 6.97/7.24 cnf(c_0_10400, 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),esk47_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_5921, c_0_4798]), ['final']). 6.97/7.24 cnf(c_0_10401, 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_5922]), ['final']). 6.97/7.24 cnf(c_0_10402, 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_5923]), ['final']). 6.97/7.24 cnf(c_0_10403, 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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin)),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)],[c_0_5924, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), c_0_4741]), ['final']). 6.97/7.24 cnf(c_0_10404, plain, (c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2,X1)=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5925]), ['final']). 6.97/7.24 cnf(c_0_10405, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2,X1)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5926]), ['final']). 6.97/7.24 cnf(c_0_10406, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin),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)],[c_0_5927, c_0_4415]), c_0_4415]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), c_0_4415]), c_0_4741]), c_0_4415]), c_0_5038]), c_0_5815]), c_0_4415]), ['final']). 6.97/7.24 cnf(c_0_10407, 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_5928, c_0_5929]), c_0_4817]), c_0_4467]), c_0_4798]), c_0_4817]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10408, 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_5930]), ['final']). 6.97/7.24 cnf(c_0_10409, 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_5931, c_0_5929]), c_0_4817]), c_0_4467]), c_0_4798]), c_0_4817]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10410, 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),esk25_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_5932, c_0_4798]), ['final']). 6.97/7.24 cnf(c_0_10411, plain, (c_List_Olist_ONil(tc_List_Olist(X2))=X3|c_List_Otranspose(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)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk171_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_5933, c_0_4471]), c_0_4471]), ['final']). 6.97/7.24 cnf(c_0_10412, 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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),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)],[c_0_5934, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), ['final']). 6.97/7.24 cnf(c_0_10413, 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),esk171_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_5935]), c_0_4773]), c_0_5936]), c_0_5937]), ['final']). 6.97/7.24 cnf(c_0_10414, 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)],[c_0_5938, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891])])]), ['final']). 6.97/7.24 cnf(c_0_10415, plain, (c_List_Olist_ONil(tc_List_Olist(X1))=X2|c_List_Otranspose(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)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),esk171_3(X3,X1,X2)))!=X3), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5939, c_0_4471]), c_0_4471]), ['final']). 6.97/7.24 cnf(c_0_10416, 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_5940, c_0_5941]), ['final']). 6.97/7.24 cnf(c_0_10417, 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_5942]), ['final']). 6.97/7.24 cnf(c_0_10418, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))|c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2)=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5943]), ['final']). 6.97/7.24 cnf(c_0_10419, 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),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)],[c_0_5944, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10420, 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_5945, c_0_4415]), c_0_5065]), c_0_5065]), c_0_5946]), c_0_4817]), c_0_5947]), ['final']). 6.97/7.24 cnf(c_0_10421, 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),esk171_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_5948]), c_0_4773]), c_0_5936]), c_0_5937]), ['final']). 6.97/7.24 cnf(c_0_10422, 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)],[c_0_5949, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10423, 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_5950]), ['final']). 6.97/7.24 cnf(c_0_10424, plain, (X3=X4|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_5951]), ['final']). 6.97/7.24 cnf(c_0_10425, 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)],[c_0_5952, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10426, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))|c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5926]), ['final']). 6.97/7.24 cnf(c_0_10427, 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_5953, c_0_5954]), c_0_4817]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10428, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))),c_Int_OMin)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin),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)],[c_0_5955, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), c_0_4415]), c_0_4415]), c_0_4741]), c_0_4415]), c_0_4415]), c_0_4415]), ['final']). 6.97/7.24 cnf(c_0_10429, 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_5956, c_0_5954]), c_0_4817]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10430, 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__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),X5)))=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)),X5)),X3)),X6)),X4)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5957, c_0_4467]), c_0_4467]), c_0_5947]), ['final']). 6.97/7.24 cnf(c_0_10431, 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,esk565_4(X1,X3,X4,X2)))),hAPP(X4,esk565_4(X1,X3,X4,X2))))), inference(rw,[status(thm)],[c_0_5958, c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10432, 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),esk173_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk174_8(X3,X4,X5,X6,X7,X8,X2,X1))),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk175_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk176_8(X3,X4,X5,X6,X7,X8,X2,X1)))),X4))|hBOOL(hAPP(hAPP(X3,X6),X5))|~hBOOL(hAPP(hAPP(X3,X8),X7))|~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),X8),X7)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X5))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X4)))), inference(split_conjunct,[status(thm)],[c_0_5959]), ['final']). 6.97/7.24 cnf(c_0_10433, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2,X1)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5960]), ['final']). 6.97/7.24 cnf(c_0_10434, 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_5961, c_0_4415]), c_0_5065]), c_0_5065]), c_0_5946]), c_0_4817]), c_0_5947]), ['final']). 6.97/7.24 cnf(c_0_10435, 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_5962, c_0_4415]), c_0_5065]), c_0_5065]), c_0_5946]), c_0_4817]), c_0_5947]), c_0_5963]), ['final']). 6.97/7.24 cnf(c_0_10436, plain, (hBOOL(hAPP(hAPP(X1,esk438_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),esk439_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),esk439_3(X1,X2,X3)),esk438_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk439_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)],[c_0_5964, c_0_5815]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), ['final']). 6.97/7.24 cnf(c_0_10437, 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)],[c_0_5965, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891])])]), ['final']). 6.97/7.24 cnf(c_0_10438, 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),esk579_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk580_8(X3,X4,X5,X6,X7,X8,X2,X1))),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk581_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk582_8(X3,X4,X5,X6,X7,X8,X2,X1)))),X4))|hBOOL(hAPP(hAPP(X3,X8),X7))|~hBOOL(hAPP(hAPP(X3,X6),X5))|~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),X8),X7)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X5))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X4)))), inference(split_conjunct,[status(thm)],[c_0_5966]), ['final']). 6.97/7.24 cnf(c_0_10439, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk9_6(X2,X3,X4,X5,X1,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))=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)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~class_Groups_Ocomm__monoid__mult(X6)), inference(split_conjunct,[status(thm)],[c_0_5967]), ['final']). 6.97/7.24 cnf(c_0_10440, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(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(X5,X1),X6),X7))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X5,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_fun(X5,X1),tc_fun(tc_fun(X5,tc_HOL_Obool),X1),X2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1)),hAPP(hAPP(c_COMBC(X2,tc_fun(X5,X1),tc_fun(X5,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,X1),tc_fun(tc_fun(X5,X1),tc_fun(X5,X1)),X2),c_COMBB(X1,X1,X5)),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X3))),X6))),X7)),X4)|~class_Rings_Osemiring__0(X1)), inference(split_conjunct,[status(thm)],[c_0_5968]), ['final']). 6.97/7.24 cnf(c_0_10441, 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_5969, c_0_4798]), c_0_4798]), c_0_4806]), ['final']). 6.97/7.24 cnf(c_0_10442, 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,esk565_4(X1,X3,X4,X2)))), inference(rw,[status(thm)],[c_0_5970, c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10443, 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_5971, c_0_5972]), ['final']). 6.97/7.24 cnf(c_0_10444, 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_5973, c_0_5972]), ['final']). 6.97/7.24 cnf(c_0_10445, 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_5899]), ['final']). 6.97/7.24 cnf(c_0_10446, 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_5900]), ['final']). 6.97/7.24 cnf(c_0_10447, plain, (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)=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))|~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_5974]), ['final']). 6.97/7.24 cnf(c_0_10448, 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_5975]), ['final']). 6.97/7.24 cnf(c_0_10449, 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_5976]), ['final']). 6.97/7.24 cnf(c_0_10450, 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_5977]), ['final']). 6.97/7.24 cnf(c_0_10451, 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_5978, c_0_5539]), c_0_5539]), ['final']). 6.97/7.24 cnf(c_0_10452, 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_5979]), ['final']). 6.97/7.24 cnf(c_0_10453, plain, (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))=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)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,esk9_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_5967]), ['final']). 6.97/7.24 cnf(c_0_10454, 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),esk387_7(X3,X4,X5,X6,X7,X2,X1)),esk388_7(X3,X4,X5,X6,X7,X2,X1))),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X4))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X3)))|hAPP(hAPP(c_Product__Type_OPair(X1,X2),X7),X6)=hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X4)|~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),X7),X6)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X4))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_5980]), ['final']). 6.97/7.24 cnf(c_0_10455, plain, (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))=hAPP(hAPP(X8,X9),X10)|~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_5981]), ['final']). 6.97/7.24 cnf(c_0_10456, 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_5982, c_0_5539]), c_0_5539]), ['final']). 6.97/7.24 cnf(c_0_10457, plain, (hBOOL(hAPP(hAPP(X1,esk290_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),esk291_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk290_3(X1,X2,X3)),esk291_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk291_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)],[c_0_5983, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), ['final']). 6.97/7.24 cnf(c_0_10458, 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_5984, c_0_5985]), ['final']). 6.97/7.24 cnf(c_0_10459, 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)],[c_0_5986, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10460, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk191_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_5987]), ['final']). 6.97/7.24 cnf(c_0_10461, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk190_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_5987]), ['final']). 6.97/7.24 cnf(c_0_10462, 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),esk581_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk582_8(X3,X4,X5,X6,X7,X8,X2,X1))),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X5))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X4)))|hBOOL(hAPP(hAPP(X3,X8),X7))|~hBOOL(hAPP(hAPP(X3,X6),X5))|~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),X8),X7)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X5))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X4)))), inference(split_conjunct,[status(thm)],[c_0_5966]), ['final']). 6.97/7.24 cnf(c_0_10463, 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),esk173_8(X5,X6,X7,X8,X4,X3,X2,X1)),esk174_8(X5,X6,X7,X8,X4,X3,X2,X1)))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X6)))|hBOOL(hAPP(hAPP(X5,X8),X7))|~hBOOL(hAPP(hAPP(X5,X3),X4))|~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),X8),X7))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X6)))), inference(split_conjunct,[status(thm)],[c_0_5959]), ['final']). 6.97/7.24 cnf(c_0_10464, 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)],[c_0_5988, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10465, 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_5989, c_0_5560]), ['final']). 6.97/7.24 cnf(c_0_10466, 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),esk387_7(X5,X6,X7,X4,X3,X2,X1)),esk388_7(X5,X6,X7,X4,X3,X2,X1)))),X5))|hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)=hAPP(hAPP(c_Product__Type_OPair(X1,X2),X7),X6)|~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),X7),X6))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X5)))), inference(split_conjunct,[status(thm)],[c_0_5980]), ['final']). 6.97/7.24 cnf(c_0_10467, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk336_6(X3,X4,X5,X6,X2,X1)),esk337_6(X3,X4,X5,X6,X2,X1))),hAPP(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3)))))|hBOOL(hAPP(hAPP(X3,X6),X5))|~c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X5)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X4)))), inference(rw,[status(thm)],[c_0_5990, c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10468, 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,esk190_11(X3,X4,X5,X2,X1,X6,X7,X8,X9,X10,X11)),esk191_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_5987]), ['final']). 6.97/7.24 cnf(c_0_10469, plain, (c_Orderings_Oorder__class_Omono(X1,tc_fun(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(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))),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))),X5))|~class_Orderings_Oorder(X1)|~c_Orderings_Oorder__class_Omono(X1,tc_fun(X2,tc_HOL_Obool),X3)), inference(split_conjunct,[status(thm)],[c_0_5991]), ['final']). 6.97/7.24 cnf(c_0_10470, 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),esk62_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_5992, c_0_4798]), c_0_4467]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10471, 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)),esk575_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_5905]), ['final']). 6.97/7.24 cnf(c_0_10472, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk65_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_5993]), ['final']). 6.97/7.24 cnf(c_0_10473, 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(hAPP(c_member(X2),esk62_4(X4,X1,X3,X2)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5994, c_0_4798]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10474, 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)],[c_0_5995, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10475, 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_5996, c_0_5538]), c_0_5065]), c_0_5538]), c_0_5065]), ['final']). 6.97/7.24 cnf(c_0_10476, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),X3),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X4),X2))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X5,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),X6,X5),hAPP(hAPP(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)|hBOOL(hAPP(hAPP(c_member(X5),esk197_6(X3,X2,X1,X4,X5,X6)),X4))|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(X2,esk198_6(X3,X2,X1,X4,X5,X6))),hAPP(X2,esk199_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_5997]), ['final']). 6.97/7.24 cnf(c_0_10477, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk199_6(X2,X3,X4,X5,X1,X6)),X5))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X4,c_Groups_Otimes__class_Otimes(X6)),X2),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X5),X3))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),X6,X1),hAPP(hAPP(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)|hBOOL(hAPP(hAPP(c_member(X1),esk197_6(X2,X3,X4,X5,X1,X6)),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~class_Groups_Ocomm__monoid__mult(X6)), inference(split_conjunct,[status(thm)],[c_0_5997]), ['final']). 6.97/7.24 cnf(c_0_10478, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk198_6(X2,X3,X4,X5,X1,X6)),X5))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X4,c_Groups_Otimes__class_Otimes(X6)),X2),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X5),X3))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),X6,X1),hAPP(hAPP(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)|hBOOL(hAPP(hAPP(c_member(X1),esk197_6(X2,X3,X4,X5,X1,X6)),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~class_Groups_Ocomm__monoid__mult(X6)), inference(split_conjunct,[status(thm)],[c_0_5997]), ['final']). 6.97/7.24 cnf(c_0_10479, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(c_Hilbert__Choice_Oinv__into(tc_List_Olist(X2),tc_fun(X2,tc_HOL_Obool),c_List_Odistinct(X2),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)],[inference(rw,[status(thm)],[c_0_5998, c_0_4817]), c_0_5999]), c_0_6000]), ['final']). 6.97/7.24 cnf(c_0_10480, 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_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)))=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)))|~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)],[c_0_6001, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10481, 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_Ominus__class_Ominus(tc_Int_Oint),X4),c_Int_OMin)))),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)],[inference(rw,[status(thm)],[c_0_6002, c_0_6003]), c_0_4741]), ['final']). 6.97/7.24 cnf(c_0_10482, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk199_6(X2,X3,X4,X5,X1,X6)),X5))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X4,c_Groups_Otimes__class_Otimes(X6)),X2),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X5),X3))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),X6,X1),hAPP(hAPP(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)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(X3,esk197_6(X2,X3,X4,X5,X1,X6))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~class_Groups_Ocomm__monoid__mult(X6)), inference(split_conjunct,[status(thm)],[c_0_5997]), ['final']). 6.97/7.24 cnf(c_0_10483, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk198_6(X2,X3,X4,X5,X1,X6)),X5))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X4,c_Groups_Otimes__class_Otimes(X6)),X2),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X5),X3))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),X6,X1),hAPP(hAPP(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)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(X3,esk197_6(X2,X3,X4,X5,X1,X6))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~class_Groups_Ocomm__monoid__mult(X6)), inference(split_conjunct,[status(thm)],[c_0_5997]), ['final']). 6.97/7.24 cnf(c_0_10484, 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)),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)))=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))), inference(split_conjunct,[status(thm)],[c_0_6004]), ['final']). 6.97/7.24 cnf(c_0_10485, 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_6005, c_0_6006]), ['final']). 6.97/7.24 cnf(c_0_10486, 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_6007, c_0_4415]), c_0_5065]), c_0_5946]), ['final']). 6.97/7.24 cnf(c_0_10487, 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_6008, c_0_4415]), c_0_5065]), c_0_5946]), ['final']). 6.97/7.24 cnf(c_0_10488, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk147_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_6009]), ['final']). 6.97/7.24 cnf(c_0_10489, 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_5915]), ['final']). 6.97/7.24 cnf(c_0_10490, 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),esk217_3(X3,X2,X1)),esk217_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)),esk216_3(X3,X2,X1)))), inference(rw,[status(thm)],[c_0_6010, c_0_4806]), ['final']). 6.97/7.24 cnf(c_0_10491, plain, (c_Relation_Orefl__on(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk217_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)),esk216_3(X3,X2,X1)))), inference(rw,[status(thm)],[c_0_6011, c_0_4806]), ['final']). 6.97/7.24 cnf(c_0_10492, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk266_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_6012]), ['final']). 6.97/7.24 cnf(c_0_10493, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),X3),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X4),X2))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X5,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),X6,X5),hAPP(hAPP(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)|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(X2,esk198_6(X3,X2,X1,X4,X5,X6))),hAPP(X2,esk199_6(X3,X2,X1,X4,X5,X6)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,esk197_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_5997]), ['final']). 6.97/7.24 cnf(c_0_10494, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X3)))|~c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(X3,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),X3)),X4))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X3))))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4))), inference(er,[status(thm)],[c_0_6013]), ['final']). 6.97/7.24 cnf(c_0_10495, 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)],[c_0_6014, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10496, 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)],[c_0_6015, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10497, 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)],[c_0_6016, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10498, plain, (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)=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))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6017]), ['final']). 6.97/7.24 cnf(c_0_10499, 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,esk65_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_5993]), ['final']). 6.97/7.24 cnf(c_0_10500, 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_6018]), ['final']). 6.97/7.24 cnf(c_0_10501, plain, (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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),X2)))=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)))|~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)],[c_0_6019, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), c_0_5002]), c_0_5002]), c_0_5002]), ['final']). 6.97/7.24 cnf(c_0_10502, 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_6020, c_0_6021]), ['final']). 6.97/7.24 cnf(c_0_10503, 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_6022, c_0_4821]), c_0_4415]), c_0_4413]), ['final']). 6.97/7.24 cnf(c_0_10504, 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_6023, c_0_5538]), ['final']). 6.97/7.24 cnf(c_0_10505, 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_5914]), ['final']). 6.97/7.24 cnf(c_0_10506, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X3,c_Groups_Otimes__class_Otimes(X6)),X1),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X3,tc_HOL_Obool)),X4),X2))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X5,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),X6,X5),hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X3,c_Groups_Otimes__class_Otimes(X6)),X1),c_Groups_Oone__class_Oone(X6))),X2)),c_Groups_Oone__class_Oone(X6)),X4)|hBOOL(hAPP(hAPP(c_member(X5),esk197_6(X1,X2,X3,X4,X5,X6)),X4))|esk198_6(X1,X2,X3,X4,X5,X6)!=esk199_6(X1,X2,X3,X4,X5,X6)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~class_Groups_Ocomm__monoid__mult(X6)), inference(split_conjunct,[status(thm)],[c_0_5997]), ['final']). 6.97/7.24 cnf(c_0_10507, 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),esk110_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_6024, c_0_4467]), c_0_4467]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10508, 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,esk311_2(X2,X1)))|hBOOL(hAPP(X2,esk311_2(X2,X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6025, c_0_4467]), c_0_4817]), c_0_4817]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10509, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|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_6026, c_0_5606]), ['final']). 6.97/7.24 cnf(c_0_10510, 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_5920]), ['final']). 6.97/7.24 cnf(c_0_10511, plain, (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)),X5)),X6)=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),X6),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X5)))|~class_Groups_Ocomm__monoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_6027]), ['final']). 6.97/7.24 cnf(c_0_10512, 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)),esk311_2(X1,X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6028, c_0_4467]), c_0_4817]), c_0_4817]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10513, 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_6029, c_0_6030]), ['final']). 6.97/7.24 cnf(c_0_10514, 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_6031]), ['final']). 6.97/7.24 cnf(c_0_10515, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))|c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2)!=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5943]), ['final']). 6.97/7.24 cnf(c_0_10516, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))|c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))!=c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5926]), ['final']). 6.97/7.24 cnf(c_0_10517, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_Hilbert__Choice_Oinv__into(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),c_List_Odistinct(X1),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)],[inference(rw,[status(thm)],[c_0_6032, c_0_4817]), c_0_5999]), c_0_6000]), ['final']). 6.97/7.24 cnf(c_0_10518, 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,esk311_2(X2,X1)))|~hBOOL(hAPP(X1,esk311_2(X2,X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6033, c_0_4467]), c_0_4817]), c_0_4817]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10519, 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)],[c_0_6034, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10520, 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_6035]), ['final']). 6.97/7.24 cnf(c_0_10521, 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_6036, c_0_4798]), ['final']). 6.97/7.24 cnf(c_0_10522, 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_6037, c_0_4798]), c_0_4768]), ['final']). 6.97/7.24 cnf(c_0_10523, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk272_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_6038]), ['final']). 6.97/7.24 cnf(c_0_10524, 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_6039]), ['final']). 6.97/7.24 cnf(c_0_10525, plain, (hAPP(c_Divides_Oadjust(X1),c_Divides_OnegDivAlg(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),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)],[c_0_6040, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), ['final']). 6.97/7.24 cnf(c_0_10526, 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,esk110_4(X4,X1,X3,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6041, c_0_4467]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10527, 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_6042, c_0_4798]), c_0_4768]), ['final']). 6.97/7.24 cnf(c_0_10528, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk226_5(X5,X4,X3,X2,X1)),esk226_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_6043]), ['final']). 6.97/7.24 cnf(c_0_10529, 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_6044, c_0_5538]), ['final']). 6.97/7.24 cnf(c_0_10530, 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_6045]), ['final']). 6.97/7.24 cnf(c_0_10531, plain, (hAPP(X1,esk266_5(X1,X2,X3,X4,X5))=c_Groups_Ozero__class_Ozero(X5)|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_Rings_Oinverse__class_Odivide(X5),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(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))|~class_Fields_Ofield(X5)), inference(split_conjunct,[status(thm)],[c_0_6012]), ['final']). 6.97/7.24 cnf(c_0_10532, 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_6046]), ['final']). 6.97/7.24 cnf(c_0_10533, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X3,c_Groups_Otimes__class_Otimes(X6)),X1),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X3,tc_HOL_Obool)),X4),X2))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X5,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),X6,X5),hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X3,c_Groups_Otimes__class_Otimes(X6)),X1),c_Groups_Oone__class_Oone(X6))),X2)),c_Groups_Oone__class_Oone(X6)),X4)|esk198_6(X1,X2,X3,X4,X5,X6)!=esk199_6(X1,X2,X3,X4,X5,X6)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(X2,esk197_6(X1,X2,X3,X4,X5,X6))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~class_Groups_Ocomm__monoid__mult(X6)), inference(split_conjunct,[status(thm)],[c_0_5997]), ['final']). 6.97/7.24 cnf(c_0_10534, 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_5923]), ['final']). 6.97/7.24 cnf(c_0_10535, 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_5922]), ['final']). 6.97/7.24 cnf(c_0_10536, 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_6047]), ['final']). 6.97/7.24 cnf(c_0_10537, 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_6048, c_0_5539]), c_0_5539]), ['final']). 6.97/7.24 cnf(c_0_10538, 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)],[c_0_6049, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10539, 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_6050, c_0_5538]), c_0_5065]), c_0_6051]), c_0_5538]), c_0_5065]), ['final']). 6.97/7.24 cnf(c_0_10540, 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_6052]), ['final']). 6.97/7.24 cnf(c_0_10541, 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,esk124_3(X2,X1,X3))),hAPP(X1,esk124_3(X2,X1,X3))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6053, c_0_5941]), c_0_5941]), c_0_5941]), ['final']). 6.97/7.24 cnf(c_0_10542, 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_6054, c_0_4415]), c_0_5065]), c_0_5065]), c_0_5946]), c_0_4817]), c_0_5947]), ['final']). 6.97/7.24 cnf(c_0_10543, 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_6055, c_0_4415]), c_0_5065]), c_0_5065]), c_0_5946]), c_0_4817]), c_0_5947]), ['final']). 6.97/7.24 cnf(c_0_10544, plain, (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)))|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)))|~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_6056]), ['final']). 6.97/7.24 cnf(c_0_10545, plain, (hAPP(c_Divides_Oadjust(X1),c_Divides_OnegDivAlg(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),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)],[c_0_6057, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), ['final']). 6.97/7.24 cnf(c_0_10546, 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_6058, c_0_5963]), c_0_4415]), c_0_5065]), c_0_5065]), c_0_5946]), c_0_4817]), c_0_5947]), ['final']). 6.97/7.24 cnf(c_0_10547, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),X4)),X3)=hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),c_List_Otranspose(X1,X2)),X3)),X4)|~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_6059]), ['final']). 6.97/7.24 cnf(c_0_10548, 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_5930]), ['final']). 6.97/7.24 cnf(c_0_10549, 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_6060, c_0_4798]), c_0_4768]), ['final']). 6.97/7.24 cnf(c_0_10550, 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)],[c_0_6061, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10551, 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_6062, c_0_4798]), c_0_4768]), ['final']). 6.97/7.24 cnf(c_0_10552, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|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_6063]), ['final']). 6.97/7.24 cnf(c_0_10553, 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),esk202_4(X4,X3,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X3),esk202_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_4889]), ['final']). 6.97/7.24 cnf(c_0_10554, 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_6064, c_0_5539]), c_0_5539]), ['final']). 6.97/7.24 cnf(c_0_10555, 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_5342]), ['final']). 6.97/7.24 cnf(c_0_10556, plain, (hAPP(c_Set_Oimage(X1,X3,X4),X2)=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)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_6065]), ['final']). 6.97/7.24 cnf(c_0_10557, 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_6066, c_0_5538]), c_0_6067]), ['final']). 6.97/7.24 cnf(c_0_10558, 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_6068, c_0_5538]), c_0_6069]), ['final']). 6.97/7.24 cnf(c_0_10559, 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_6070, c_0_5539]), c_0_5539]), ['final']). 6.97/7.24 cnf(c_0_10560, 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_6071]), ['final']). 6.97/7.24 cnf(c_0_10561, 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,esk272_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_6038]), ['final']). 6.97/7.24 cnf(c_0_10562, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X3)),c_Int_OMin)))|~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)],[c_0_6072, c_0_4415]), ['final']). 6.97/7.24 cnf(c_0_10563, 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_Ominus__class_Ominus(X1)),X3)),X4)),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(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_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6073]), ['final']). 6.97/7.24 cnf(c_0_10564, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Oplus__class_Oplus(X1)),X3)),X5)),X4))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6074]), ['final']). 6.97/7.24 cnf(c_0_10565, plain, (c_Orderings_Oord__class_OLeast(X1,hAPP(c_Set_Oimage(X2,X1,X3),X4))=hAPP(X3,c_Orderings_Oord__class_OLeast(X2,X4))|hBOOL(hAPP(hAPP(c_member(X2),esk554_5(X4,X3,X2,X1,X5)),X4))|~c_Orderings_Oorder__class_Omono(X2,X1,X3)|~class_Orderings_Oorder(X1)|~class_Orderings_Oorder(X2)|~hBOOL(hAPP(hAPP(c_member(X2),X5),X4))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6075, c_0_4798]), c_0_4798]), ['final']). 6.97/7.24 cnf(c_0_10566, 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(hAPP(c_member(X2),X4),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6076, c_0_4467]), c_0_4798]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10567, 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_6077]), ['final']). 6.97/7.24 cnf(c_0_10568, 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)),esk539_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),esk539_4(X3,X4,X2,X1)))),X3)))), inference(rw,[status(thm)],[c_0_6078, c_0_4977]), ['final']). 6.97/7.24 cnf(c_0_10569, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk547_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_6079]), ['final']). 6.97/7.24 cnf(c_0_10570, 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_6080]), ['final']). 6.97/7.24 cnf(c_0_10571, 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_6081, c_0_5539]), c_0_5539]), ['final']). 6.97/7.24 cnf(c_0_10572, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk166_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_6082]), ['final']). 6.97/7.24 cnf(c_0_10573, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk161_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_6083]), ['final']). 6.97/7.24 cnf(c_0_10574, 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_6084, c_0_4768]), ['final']). 6.97/7.24 cnf(c_0_10575, 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_6085, c_0_6086]), ['final']). 6.97/7.24 cnf(c_0_10576, 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_5601]), ['final']). 6.97/7.24 cnf(c_0_10577, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk85_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_6087]), ['final']). 6.97/7.24 cnf(c_0_10578, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk158_8(X2,X3,X4,X1,X5,X6,X7,X8)),X4))|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))=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))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|~c_Fun_Oinj__on(X8,X7,X6,X5)), inference(split_conjunct,[status(thm)],[c_0_6088]), ['final']). 6.97/7.24 cnf(c_0_10579, 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)))),esk599_3(X2,X3,X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6089, c_0_4645]), c_0_4645]), ['final']). 6.97/7.24 cnf(c_0_10580, 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)))),esk598_3(X2,X3,X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6090, c_0_4645]), c_0_4645]), ['final']). 6.97/7.24 cnf(c_0_10581, 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_6091]), ['final']). 6.97/7.24 cnf(c_0_10582, plain, (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)))=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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)))|~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_6092, c_0_4415]), ['final']). 6.97/7.24 cnf(c_0_10583, 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_6093, c_0_5538]), ['final']). 6.97/7.24 cnf(c_0_10584, 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_6094, c_0_5538]), ['final']). 6.97/7.24 cnf(c_0_10585, plain, (hAPP(c_Divides_Oadjust(X1),c_Divides_OposDivAlg(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),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)],[c_0_6095, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), ['final']). 6.97/7.24 cnf(c_0_10586, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),X2)=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))))|~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_6096, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_6097]), ['final']). 6.97/7.24 cnf(c_0_10587, 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)],[c_0_6098, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10588, 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)],[c_0_6099, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10589, 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)],[c_0_6100, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891])])]), ['final']). 6.97/7.24 cnf(c_0_10590, 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)],[c_0_6101, c_0_6030]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10591, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk509_5(X2,X3,X4,X5,X1)),esk510_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_6102]), ['final']). 6.97/7.24 cnf(c_0_10592, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk97_5(X2,X3,X4,X5,X1)),esk96_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_6103]), ['final']). 6.97/7.24 cnf(c_0_10593, 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_5942]), ['final']). 6.97/7.24 cnf(c_0_10594, 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_6104, c_0_5002]), c_0_5002]), ['final']). 6.97/7.24 cnf(c_0_10595, 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(X1)),X2)),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(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(X3)),X4)))|hBOOL(hAPP(X5,hAPP(hAPP(c_List_Ozip(X1,X3),X2),X4)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6105, c_0_4881]), c_0_6106]), c_0_4881]), c_0_6106]), ['final']). 6.97/7.24 cnf(c_0_10596, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|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))=c_Groups_Ozero__class_Ozero(X3)|~class_Groups_Oab__group__add(X3)), inference(split_conjunct,[status(thm)],[c_0_4840]), ['final']). 6.97/7.24 cnf(c_0_10597, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk466_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)),esk464_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_6107]), ['final']). 6.97/7.24 cnf(c_0_10598, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk465_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)),esk464_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_6107]), ['final']). 6.97/7.24 cnf(c_0_10599, 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_6108, c_0_5174]), c_0_5174]), c_0_5174]), ['final']). 6.97/7.24 cnf(c_0_10600, 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_6109]), ['final']). 6.97/7.24 cnf(c_0_10601, 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_6110]), ['final']). 6.97/7.24 cnf(c_0_10602, plain, (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))=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)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6111]), ['final']). 6.97/7.24 cnf(c_0_10603, 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),esk202_4(X4,X3,X1,X2))),hAPP(hAPP(c_List_Onth(X2),X3),esk202_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_4889]), ['final']). 6.97/7.24 cnf(c_0_10604, plain, (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)))=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))), inference(split_conjunct,[status(thm)],[c_0_6112]), ['final']). 6.97/7.24 cnf(c_0_10605, plain, (hAPP(c_Divides_Oadjust(X1),c_Divides_OposDivAlg(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),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)],[c_0_6113, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), ['final']). 6.97/7.24 cnf(c_0_10606, 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_6114]), ['final']). 6.97/7.24 cnf(c_0_10607, 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)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),X3))|~c_Equiv__Relations_Oequiv(X1,X5,X3)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_6115, c_0_6116]), c_0_6117]), ['final']). 6.97/7.24 cnf(c_0_10608, 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_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_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)))|~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_6118]), ['final']). 6.97/7.24 cnf(c_0_10609, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk541_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(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2))=hAPP(hAPP(X7,hAPP(X4,X3)),hAPP(X4,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_6119]), ['final']). 6.97/7.24 cnf(c_0_10610, 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)],[c_0_6120, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10611, 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)],[c_0_6121, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10612, 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(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))|~class_Groups_Ocomm__monoid__mult(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_6122]), ['final']). 6.97/7.24 cnf(c_0_10613, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk96_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_6103]), ['final']). 6.97/7.24 cnf(c_0_10614, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk509_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_6102]), ['final']). 6.97/7.24 cnf(c_0_10615, 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),X2)),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))=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)))|~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_6123]), ['final']). 6.97/7.24 cnf(c_0_10616, 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)],[c_0_6124, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10617, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk202_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_6125, c_0_4881]), ['final']). 6.97/7.24 cnf(c_0_10618, 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_6126, c_0_4881]), ['final']). 6.97/7.24 cnf(c_0_10619, 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)],[c_0_6127, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10620, 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)],[c_0_6128, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10621, 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)),X4),X3)),c_Wellfounded_Omax__ext(X1,X2)))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk321_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_6129]), ['final']). 6.97/7.24 cnf(c_0_10622, 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_6130, c_0_6030]), c_0_6030]), ['final']). 6.97/7.24 cnf(c_0_10623, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,X4))),X5))=hAPP(c_List_Ofilter(X2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_fequal,hAPP(X3,X4)))),hAPP(hAPP(c_List_Omap(X1,X2),X3),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_6131, c_0_5065]), c_0_5065]), ['final']). 6.97/7.24 cnf(c_0_10624, 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_6132]), ['final']). 6.97/7.24 cnf(c_0_10625, 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_6133]), ['final']). 6.97/7.24 cnf(c_0_10626, plain, (hAPP(hAPP(c_List_Onth(tc_List_Olist(X2)),c_List_Otranspose(X2,X3)),X1)=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))|~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_6134]), ['final']). 6.97/7.24 cnf(c_0_10627, 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),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X3))),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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),X3)))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6135]), ['final']). 6.97/7.24 cnf(c_0_10628, 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),esk78_4(X2,X3,X4,X1)),X5)),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_5466]), ['final']). 6.97/7.24 cnf(c_0_10629, 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_6136]), ['final']). 6.97/7.24 cnf(c_0_10630, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X4,c_Groups_Otimes__class_Otimes(X5)),X1),c_Groups_Oone__class_Oone(X5)),X3)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X4,c_Groups_Otimes__class_Otimes(X5)),X1),c_Groups_Oone__class_Oone(X5)),X2))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X4,c_Groups_Otimes__class_Otimes(X5)),X1),c_Groups_Oone__class_Oone(X5)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2))|hAPP(X1,esk147_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_6009]), ['final']). 6.97/7.24 cnf(c_0_10631, 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_6137]), ['final']). 6.97/7.24 cnf(c_0_10632, 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)],[c_0_6138, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10633, 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_6139, c_0_6067]), ['final']). 6.97/7.24 cnf(c_0_10634, 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_6140, c_0_6069]), ['final']). 6.97/7.24 cnf(c_0_10635, 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)))|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)))|X1=X2|esk347_4(X1,X2,X3,X4)!=esk348_4(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_6141]), ['final']). 6.97/7.24 cnf(c_0_10636, 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)],[c_0_6142, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10637, 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_6143]), ['final']). 6.97/7.24 cnf(c_0_10638, plain, (c_Orderings_Oord__class_OLeast(X1,hAPP(c_Set_Oimage(X2,X1,X3),X4))=hAPP(X3,c_Orderings_Oord__class_OLeast(X2,X4))|~c_Orderings_Oorder__class_Omono(X2,X1,X3)|~class_Orderings_Oorder(X1)|~class_Orderings_Oorder(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X5),esk554_5(X4,X3,X2,X1,X5)))|~hBOOL(hAPP(hAPP(c_member(X2),X5),X4))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6144, c_0_4798]), c_0_4798]), ['final']). 6.97/7.24 cnf(c_0_10639, 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_5950]), ['final']). 6.97/7.24 cnf(c_0_10640, plain, (hBOOL(hAPP(hAPP(X1,esk173_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk174_8(X1,X2,X3,X4,X5,X6,X7,X8)))|hBOOL(hAPP(hAPP(X1,X4),X3))|~hBOOL(hAPP(hAPP(X1,X6),X5))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X8,X7),tc_prod(X8,X7))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X8,X7),tc_prod(X8,X7)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X6),X5)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X4),X3))),c_Transitive__Closure_Ortrancl(tc_prod(X8,X7),X2)))), inference(split_conjunct,[status(thm)],[c_0_5959]), ['final']). 6.97/7.24 cnf(c_0_10641, 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_6145]), ['final']). 6.97/7.24 cnf(c_0_10642, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X4,tc_HOL_Obool),X1),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1),X2)),X3)|hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),esk464_4(X2,X3,X4,X1)),X3))|c_Groups_Ozero__class_Ozero(X1)!=hAPP(X2,esk467_4(X2,X3,X4,X1))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X4,tc_HOL_Obool)),X3))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6107]), ['final']). 6.97/7.24 cnf(c_0_10643, 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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),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)],[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_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), ['final']). 6.97/7.24 cnf(c_0_10644, plain, (hBOOL(hAPP(hAPP(X1,esk581_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk582_8(X1,X2,X3,X4,X5,X6,X7,X8)))|hBOOL(hAPP(hAPP(X1,X6),X5))|~hBOOL(hAPP(hAPP(X1,X4),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X8,X7),tc_prod(X8,X7))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X8,X7),tc_prod(X8,X7)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X6),X5)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X4),X3))),c_Transitive__Closure_Ortrancl(tc_prod(X8,X7),X2)))), inference(split_conjunct,[status(thm)],[c_0_5966]), ['final']). 6.97/7.24 cnf(c_0_10645, 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(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_4895]), ['final']). 6.97/7.24 cnf(c_0_10646, 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),X5)),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)))|~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_Olexord(X1,X4)))|~c_Relation_Otrans(X1,X4)), inference(split_conjunct,[status(thm)],[c_0_6147]), ['final']). 6.97/7.24 cnf(c_0_10647, 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_6148]), ['final']). 6.97/7.24 cnf(c_0_10648, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),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_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin)),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)],[c_0_6149, c_0_4415]), c_0_4415]), c_0_4415]), c_0_4741]), c_0_4415]), c_0_4415]), ['final']). 6.97/7.24 cnf(c_0_10649, 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_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_6150]), ['final']). 6.97/7.24 cnf(c_0_10650, 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(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_4896]), ['final']). 6.97/7.24 cnf(c_0_10651, 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_6151]), ['final']). 6.97/7.24 cnf(c_0_10652, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk258_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_6152]), ['final']). 6.97/7.24 cnf(c_0_10653, 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_6153]), ['final']). 6.97/7.24 cnf(c_0_10654, 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_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),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_6154]), ['final']). 6.97/7.24 cnf(c_0_10655, plain, (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)))))=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))|~class_Rings_Oring__1(X1)), inference(rw,[status(thm)],[c_0_6155, c_0_5539]), ['final']). 6.97/7.24 cnf(c_0_10656, 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),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X3))),c_SetInterval_Oord__class_OatLeastAtMost(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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),X3)))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6156]), ['final']). 6.97/7.24 cnf(c_0_10657, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,X4))),X5))=hAPP(c_List_Ofilter(X2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_fequal,hAPP(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(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6157, c_0_5065]), c_0_5065]), ['final']). 6.97/7.24 cnf(c_0_10658, 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),X3)),c_Nat_Osize__class_Osize(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),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))),X2)))), inference(split_conjunct,[status(thm)],[c_0_6158]), ['final']). 6.97/7.24 cnf(c_0_10659, 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_6159, c_0_5174]), c_0_5174]), ['final']). 6.97/7.24 cnf(c_0_10660, 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_6160, c_0_5174]), c_0_5174]), ['final']). 6.97/7.24 cnf(c_0_10661, plain, (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))=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))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,esk158_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_6088]), ['final']). 6.97/7.24 cnf(c_0_10662, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk221_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_6161]), ['final']). 6.97/7.24 cnf(c_0_10663, 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)],[c_0_6162, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10664, plain, (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(X2,X1))=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),X2),X1),X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6163, c_0_6164]), c_0_6164]), ['final']). 6.97/7.24 cnf(c_0_10665, 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),esk202_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_6165, c_0_4881]), ['final']). 6.97/7.24 cnf(c_0_10666, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk411_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_6166]), ['final']). 6.97/7.24 cnf(c_0_10667, plain, (X2=X3|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk599_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_6167, c_0_4645]), c_0_4645]), ['final']). 6.97/7.24 cnf(c_0_10668, plain, (X2=X3|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk598_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_6168, c_0_4645]), c_0_4645]), ['final']). 6.97/7.24 cnf(c_0_10669, 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_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),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_6169]), ['final']). 6.97/7.24 cnf(c_0_10670, plain, (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))=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)|~class_Fields_Ofield__inverse__zero(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6170]), ['final']). 6.97/7.24 cnf(c_0_10671, 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),esk108_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_6171, c_0_4467]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10672, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk466_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),esk464_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_6107]), ['final']). 6.97/7.24 cnf(c_0_10673, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk465_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),esk464_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_6107]), ['final']). 6.97/7.24 cnf(c_0_10674, 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_4900]), ['final']). 6.97/7.24 cnf(c_0_10675, 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_6172, c_0_4467]), c_0_4467]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10676, 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)),esk464_4(X1,X2,X3,X4)),X2))|esk466_4(X1,X2,X3,X4)!=esk465_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_6107]), ['final']). 6.97/7.24 cnf(c_0_10677, 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_6173, c_0_5174]), c_0_5174]), ['final']). 6.97/7.24 cnf(c_0_10678, 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_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),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_6174]), ['final']). 6.97/7.24 cnf(c_0_10679, 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_6175]), ['final']). 6.97/7.24 cnf(c_0_10680, 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)],[c_0_6176, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10681, 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_6177]), ['final']). 6.97/7.24 cnf(c_0_10682, 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_6178]), ['final']). 6.97/7.24 cnf(c_0_10683, 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)],[c_0_6179, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10684, 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_6180, c_0_5174]), c_0_5174]), ['final']). 6.97/7.24 cnf(c_0_10685, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk185_5(X2,X3,X4,X5,X1)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk186_5(X2,X3,X4,X5,X1)),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_6181]), ['final']). 6.97/7.24 cnf(c_0_10686, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk28_5(X3,X4,X5,X2,X1))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk29_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_6182]), ['final']). 6.97/7.24 cnf(c_0_10687, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[c_0_6183, c_0_4415]), ['final']). 6.97/7.24 cnf(c_0_10688, 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)],[c_0_6184, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10689, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk321_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_6129]), ['final']). 6.97/7.24 cnf(c_0_10690, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk78_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),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_5466]), ['final']). 6.97/7.24 cnf(c_0_10691, 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_6185]), ['final']). 6.97/7.24 cnf(c_0_10692, 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_6186]), ['final']). 6.97/7.24 cnf(c_0_10693, 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_6187, c_0_4813]), c_0_4813]), ['final']). 6.97/7.24 cnf(c_0_10694, 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_6188]), ['final']). 6.97/7.24 cnf(c_0_10695, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5),X2))|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),X1),X2)),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6))|~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_6189]), ['final']). 6.97/7.24 cnf(c_0_10696, 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_6190]), ['final']). 6.97/7.24 cnf(c_0_10697, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk467_4(X2,X3,X1,X4)),esk466_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)),esk464_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_6107]), ['final']). 6.97/7.24 cnf(c_0_10698, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk467_4(X2,X3,X1,X4)),esk465_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)),esk464_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_6107]), ['final']). 6.97/7.24 cnf(c_0_10699, 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_6191]), ['final']). 6.97/7.24 cnf(c_0_10700, 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_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))))))=c_Big__Operators_Olinorder__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_6192]), ['final']). 6.97/7.24 cnf(c_0_10701, 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,esk221_8(X5,X4,X3,X6,X1,X2,X7,X8)))!=hAPP(c_Fun_Ocomp(X2,X2,X1,hAPP(X6,esk221_8(X5,X4,X3,X6,X1,X2,X7,X8))),X3)), inference(split_conjunct,[status(thm)],[c_0_6161]), ['final']). 6.97/7.24 cnf(c_0_10702, 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_6193, c_0_4415]), c_0_5065]), c_0_5946]), ['final']). 6.97/7.24 cnf(c_0_10703, 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_6194, c_0_4415]), c_0_5065]), c_0_5946]), ['final']). 6.97/7.24 cnf(c_0_10704, 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_6195]), ['final']). 6.97/7.24 cnf(c_0_10705, 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_6196])]), ['final']). 6.97/7.24 cnf(c_0_10706, 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_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_6197]), ['final']). 6.97/7.24 cnf(c_0_10707, 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(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_6198]), ['final']). 6.97/7.24 cnf(c_0_10708, 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,X2)),c_Big__Operators_Olattice__class_OSup__fin(X1,X3))=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)))|~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_6199]), ['final']). 6.97/7.24 cnf(c_0_10709, 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,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))|~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_6200]), ['final']). 6.97/7.24 cnf(c_0_10710, 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)))|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)))|X2=X3|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk348_4(X2,X3,X4,X1)),esk347_4(X2,X3,X4,X1))),X4))), inference(split_conjunct,[status(thm)],[c_0_6141]), ['final']). 6.97/7.24 cnf(c_0_10711, 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)))|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)))|X2=X3|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk347_4(X2,X3,X4,X1)),esk348_4(X2,X3,X4,X1))),X4))), inference(split_conjunct,[status(thm)],[c_0_6141]), ['final']). 6.97/7.24 cnf(c_0_10712, 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),esk212_7(X4,X3,X7,X1,X2,X6,X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),esk213_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_6201]), ['final']). 6.97/7.24 cnf(c_0_10713, 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_6202]), ['final']). 6.97/7.24 cnf(c_0_10714, 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_6203]), ['final']). 6.97/7.24 cnf(c_0_10715, plain, (hBOOL(hAPP(hAPP(c_member(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))=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)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_6204]), ['final']). 6.97/7.24 cnf(c_0_10716, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk185_5(X2,X3,X4,X5,X1)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk186_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_6181]), ['final']). 6.97/7.24 cnf(c_0_10717, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk28_5(X3,X4,X5,X2,X1))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk29_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_6182]), ['final']). 6.97/7.24 cnf(c_0_10718, 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),esk202_4(X4,X3,X2,X1)),X2)=hAPP(hAPP(c_List_Otake(X1),esk202_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_4889]), ['final']). 6.97/7.24 cnf(c_0_10719, plain, (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))|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_6205]), ['final']). 6.97/7.24 cnf(c_0_10720, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk385_5(X2,X3,X4,X1,c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),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)),X4)))),X2))|hBOOL(hAPP(hAPP(c_member(X1),X3),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),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)),X4))))|~c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),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)),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(er,[status(thm)],[c_0_6206]), ['final']). 6.97/7.24 cnf(c_0_10721, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk575_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_5905]), ['final']). 6.97/7.24 cnf(c_0_10722, 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_6207, c_0_6208]), c_0_6208]), ['final']). 6.97/7.24 cnf(c_0_10723, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|c_Nitpick_Ofold__graph_H(X2,X3,X4,X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(hAPP(c_Set_Oinsert(X2),esk212_7(X6,X7,X1,X5,X4,X3,X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),esk213_7(X6,X7,X1,X5,X4,X3,X2))|~c_Nitpick_Ofold__graph_H(X2,X3,X4,X5,X1,hAPP(hAPP(X4,X7),X6))), inference(split_conjunct,[status(thm)],[c_0_6201]), ['final']). 6.97/7.24 cnf(c_0_10724, 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_6209]), ['final']). 6.97/7.24 cnf(c_0_10725, 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_6210]), ['final']). 6.97/7.24 cnf(c_0_10726, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk484_6(X2,X3,X4,X5,X6,X1)),X6))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X6),X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),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_6211]), ['final']). 6.97/7.24 cnf(c_0_10727, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk371_6(X2,X3,X4,X5,X6,X1)),X5))|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)),X5),X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),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_6212]), ['final']). 6.97/7.24 cnf(c_0_10728, 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,esk108_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_6213, c_0_4467]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10729, 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_6214]), ['final']). 6.97/7.24 cnf(c_0_10730, 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),X5),X4))=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)),X5)),X4)|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6215]), ['final']). 6.97/7.24 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),X6)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X5))),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_4932]), ['final']). 6.97/7.24 cnf(c_0_10732, 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_4932]), ['final']). 6.97/7.24 cnf(c_0_10733, 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_6216]), ['final']). 6.97/7.24 cnf(c_0_10734, 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_4930]), ['final']). 6.97/7.24 cnf(c_0_10735, 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),X5),X4))=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)),X5)),X4)|~class_Groups_Ocomm__monoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_6217]), ['final']). 6.97/7.24 cnf(c_0_10736, 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,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(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_6218]), ['final']). 6.97/7.24 cnf(c_0_10737, 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_6219]), ['final']). 6.97/7.24 cnf(c_0_10738, 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_6220]), ['final']). 6.97/7.24 cnf(c_0_10739, 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_6221]), ['final']). 6.97/7.24 cnf(c_0_10740, 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_6222, c_0_4798]), c_0_4798]), ['final']). 6.97/7.24 cnf(c_0_10741, plain, (X5=X4|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_6223]), ['final']). 6.97/7.24 cnf(c_0_10742, 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)),esk478_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),esk478_4(X2,X4,X3,X1)))),X2)), inference(rw,[status(thm)],[c_0_6224, c_0_4977]), ['final']). 6.97/7.24 cnf(c_0_10743, 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)],[c_0_6225, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10744, 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,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(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_6226]), ['final']). 6.97/7.24 cnf(c_0_10745, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk576_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_6227]), ['final']). 6.97/7.24 cnf(c_0_10746, plain, (hBOOL(hAPP(hAPP(c_member(X2),X4),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))=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))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6228]), ['final']). 6.97/7.24 cnf(c_0_10747, 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_6229]), ['final']). 6.97/7.24 cnf(c_0_10748, 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_6230]), ['final']). 6.97/7.24 cnf(c_0_10749, 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_6231, c_0_4798]), ['final']). 6.97/7.24 cnf(c_0_10750, 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_6232, c_0_5174]), ['final']). 6.97/7.24 cnf(c_0_10751, 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_6233]), ['final']). 6.97/7.24 cnf(c_0_10752, 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_6234]), ['final']). 6.97/7.24 cnf(c_0_10753, 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_6235]), ['final']). 6.97/7.24 cnf(c_0_10754, 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_6236]), ['final']). 6.97/7.24 cnf(c_0_10755, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk470_8(X3,X4,X5,X2,X1,X6,X7,X8)),esk471_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_6237]), ['final']). 6.97/7.24 cnf(c_0_10756, 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_6238]), ['final']). 6.97/7.24 cnf(c_0_10757, 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_6239]), ['final']). 6.97/7.24 cnf(c_0_10758, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk287_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk289_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_6240, c_0_4645]), ['final']). 6.97/7.24 cnf(c_0_10759, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk287_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk288_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_6241, c_0_4645]), ['final']). 6.97/7.24 cnf(c_0_10760, 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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6242, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), ['final']). 6.97/7.24 cnf(c_0_10761, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),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)),c_Int_OMin)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),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)],[c_0_6243, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), ['final']). 6.97/7.24 cnf(c_0_10762, 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_6244, c_0_5174]), ['final']). 6.97/7.24 cnf(c_0_10763, 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_6245]), ['final']). 6.97/7.24 cnf(c_0_10764, plain, (hAPP(X1,esk551_7(X2,X3,X1,X4,X5,X6,X7))=hAPP(X1,esk550_7(X2,X3,X1,X4,X5,X6,X7))|X2=X3|~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)),X3),X1)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X2),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_6246]), ['final']). 6.97/7.24 cnf(c_0_10765, 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_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_6247]), ['final']). 6.97/7.24 cnf(c_0_10766, 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)],[c_0_6248, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10767, 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)],[c_0_6249, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10768, 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_6250, c_0_6164]), ['final']). 6.97/7.24 cnf(c_0_10769, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk421_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)),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3)), inference(split_conjunct,[status(thm)],[c_0_6233]), ['final']). 6.97/7.24 cnf(c_0_10770, 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_6251, c_0_6252]), c_0_6253]), ['final']). 6.97/7.24 cnf(c_0_10771, 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_4900]), ['final']). 6.97/7.24 cnf(c_0_10772, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk572_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_6254]), ['final']). 6.97/7.24 cnf(c_0_10773, plain, (hAPP(X1,esk214_6(X2,X3,X1,X4,X5,X6))=hAPP(X1,esk215_6(X2,X3,X1,X4,X5,X6))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X6),hAPP(c_Fun_Ocomp(X2,X6,X5,X3),X1)),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X6),X3),hAPP(c_Set_Oimage(X5,X2,X1),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~class_Groups_Ocomm__monoid__add(X6)), inference(split_conjunct,[status(thm)],[c_0_6255]), ['final']). 6.97/7.24 cnf(c_0_10774, 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),esk230_4(X2,X3,X4,X1)),hAPP(c_List_Oset(X1),X4)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6256, c_0_4813]), c_0_4813]), ['final']). 6.97/7.24 cnf(c_0_10775, 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_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_6257]), ['final']). 6.97/7.24 cnf(c_0_10776, 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_6258]), ['final']). 6.97/7.24 cnf(c_0_10777, 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_6259]), ['final']). 6.97/7.24 cnf(c_0_10778, 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),X4)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2))),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_6260]), ['final']). 6.97/7.24 cnf(c_0_10779, 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_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X6),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X5))|~c_Equiv__Relations_Oequiv(X1,X6,X4)), inference(er,[status(thm)],[c_0_6261]), ['final']). 6.97/7.24 cnf(c_0_10780, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk215_6(X2,X3,X4,X5,X1,X6)),X5))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X6),hAPP(c_Fun_Ocomp(X2,X6,X1,X3),X4)),X5)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X6),X3),hAPP(c_Set_Oimage(X1,X2,X4),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~class_Groups_Ocomm__monoid__add(X6)), inference(split_conjunct,[status(thm)],[c_0_6255]), ['final']). 6.97/7.24 cnf(c_0_10781, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk214_6(X2,X3,X4,X5,X1,X6)),X5))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X6),hAPP(c_Fun_Ocomp(X2,X6,X1,X3),X4)),X5)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X6),X3),hAPP(c_Set_Oimage(X1,X2,X4),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~class_Groups_Ocomm__monoid__add(X6)), inference(split_conjunct,[status(thm)],[c_0_6255]), ['final']). 6.97/7.24 cnf(c_0_10782, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),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),X4),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X5))|~c_Equiv__Relations_Oequiv(X1,X5,X3)), inference(split_conjunct,[status(thm)],[c_0_4884]), ['final']). 6.97/7.24 cnf(c_0_10783, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),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)),X3))))|~c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),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)),X3))|~hBOOL(hAPP(hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),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)),X3)))),esk385_5(X4,X2,X3,X1,c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),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)),X3)))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4))), inference(er,[status(thm)],[c_0_6262]), ['final']). 6.97/7.24 cnf(c_0_10784, 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)],[c_0_6263, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891])]), ['final']). 6.97/7.24 cnf(c_0_10785, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk15_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_6264]), ['final']). 6.97/7.24 cnf(c_0_10786, plain, (hAPP(c_Set_Oimage(X1,X4,c_Fun_Ofun__upd(X1,X4,X5,X2,X6)),X3)=hAPP(hAPP(c_Set_Oinsert(X4),X6),hAPP(c_Set_Oimage(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_6265]), ['final']). 6.97/7.24 cnf(c_0_10787, 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)),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_6266]), ['final']). 6.97/7.24 cnf(c_0_10788, 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_6267, c_0_5174]), ['final']). 6.97/7.24 cnf(c_0_10789, 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_6268]), ['final']). 6.97/7.24 cnf(c_0_10790, 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_6269]), ['final']). 6.97/7.24 cnf(c_0_10791, 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_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_6270]), ['final']). 6.97/7.24 cnf(c_0_10792, 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_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_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_6271]), ['final']). 6.97/7.24 cnf(c_0_10793, 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_6272]), ['final']). 6.97/7.24 cnf(c_0_10794, 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_6273]), ['final']). 6.97/7.24 cnf(c_0_10795, 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_6274]), ['final']). 6.97/7.24 cnf(c_0_10796, plain, (X4=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))|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))=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))|~c_Relation_Osingle__valued(X1,X2,hAPP(c_Relation_Oconverse(X2,X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6275]), ['final']). 6.97/7.24 cnf(c_0_10797, 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,esk15_6(X3,X2,X1,X4,X5,X6))),hAPP(X3,esk15_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_6264]), ['final']). 6.97/7.24 cnf(c_0_10798, 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_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_6276]), ['final']). 6.97/7.24 cnf(c_0_10799, 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_6277]), ['final']). 6.97/7.24 cnf(c_0_10800, 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_6278]), ['final']). 6.97/7.24 cnf(c_0_10801, plain, (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),X4),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_6279]), ['final']). 6.97/7.24 cnf(c_0_10802, 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)))|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)),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_6109]), ['final']). 6.97/7.24 cnf(c_0_10803, 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)),esk23_3(X3,X2,X1)),X2))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk21_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_6280, c_0_6281]), ['final']). 6.97/7.24 cnf(c_0_10804, 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)),esk22_3(X3,X2,X1)),X2))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk21_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_6282, c_0_6281]), ['final']). 6.97/7.24 cnf(c_0_10805, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),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)],[c_0_6283, c_0_4415]), c_0_4415]), c_0_4415]), c_0_4415]), c_0_4415]), ['final']). 6.97/7.24 cnf(c_0_10806, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk118_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk119_2(X1,X2)))))|hBOOL(hAPP(X1,esk121_2(X1,X2)))|hBOOL(hAPP(X1,esk118_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_6284, c_0_6285]), ['final']). 6.97/7.24 cnf(c_0_10807, 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),esk202_4(X4,X3,X1,X2)),X1)=hAPP(hAPP(c_List_Otake(X2),esk202_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_4889]), ['final']). 6.97/7.24 cnf(c_0_10808, 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_6286]), ['final']). 6.97/7.24 cnf(c_0_10809, 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),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2))),c_List_Olex(X1,X6)))), inference(csr,[status(thm)],[c_0_6287, c_0_6288]), ['final']). 6.97/7.24 cnf(c_0_10810, 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_6289]), ['final']). 6.97/7.24 cnf(c_0_10811, 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_6290, c_0_4977]), c_0_6291])])]), ['final']). 6.97/7.24 cnf(c_0_10812, 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~c_Finite__Set_Ofun__left__comm(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_6292]), ['final']). 6.97/7.24 cnf(c_0_10813, 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_6293]), ['final']). 6.97/7.24 cnf(c_0_10814, 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_6294]), ['final']). 6.97/7.24 cnf(c_0_10815, 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_6295]), ['final']). 6.97/7.24 cnf(c_0_10816, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X1,tc_HOL_Obool)),X5),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(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))|~c_Fun_Obij__betw(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_6296]), ['final']). 6.97/7.24 cnf(c_0_10817, 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))|X3=X2), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6297, c_0_5065]), c_0_5065]), ['final']). 6.97/7.24 cnf(c_0_10818, 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_6298]), ['final']). 6.97/7.24 cnf(c_0_10819, 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_6299]), ['final']). 6.97/7.24 cnf(c_0_10820, 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,esk108_5(X5,X3,X4,X2,X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6300, c_0_4467]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10821, 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_6301]), ['final']). 6.97/7.24 cnf(c_0_10822, 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))))),esk463_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_6302]), ['final']). 6.97/7.24 cnf(c_0_10823, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk467_4(X2,X3,X1,X4)),esk466_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),esk464_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_6107]), ['final']). 6.97/7.24 cnf(c_0_10824, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk467_4(X2,X3,X1,X4)),esk465_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),esk464_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_6107]), ['final']). 6.97/7.24 cnf(c_0_10825, 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_6303]), ['final']). 6.97/7.24 cnf(c_0_10826, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(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_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(X1,tc_fun(X3,tc_HOL_Obool)),X2),X5))), inference(split_conjunct,[status(thm)],[c_0_5738]), ['final']). 6.97/7.24 cnf(c_0_10827, 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_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)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5))), inference(split_conjunct,[status(thm)],[c_0_6304]), ['final']). 6.97/7.24 cnf(c_0_10828, 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_5736]), ['final']). 6.97/7.24 cnf(c_0_10829, 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_6305]), ['final']). 6.97/7.24 cnf(c_0_10830, 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_6306, c_0_6208]), ['final']). 6.97/7.24 cnf(c_0_10831, plain, (hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),hAPP(c_Hilbert__Choice_Oinv__into(X2,X5,hAPP(c_Set_Oimage(X1,X2,X4),X3),X6),X7))=hAPP(c_Hilbert__Choice_Oinv__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_6307, c_0_6208]), ['final']). 6.97/7.24 cnf(c_0_10832, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk111_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)))|X4=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Groups_Ocomm__monoid__add(X5)|~class_Groups_Oordered__cancel__ab__semigroup__add(X5)), inference(split_conjunct,[status(thm)],[c_0_6308]), ['final']). 6.97/7.24 cnf(c_0_10833, 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),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6309]), ['final']). 6.97/7.24 cnf(c_0_10834, 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_6310]), ['final']). 6.97/7.24 cnf(c_0_10835, 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_6311]), ['final']). 6.97/7.24 cnf(c_0_10836, 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_6312]), ['final']). 6.97/7.24 cnf(c_0_10837, plain, (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))=hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),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_6313]), ['final']). 6.97/7.24 cnf(c_0_10838, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Groups_Ozero__class_Ozero(X1)=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))=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))|~class_Fields_Ofield(X1)), inference(split_conjunct,[status(thm)],[c_0_6314]), ['final']). 6.97/7.24 cnf(c_0_10839, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk525_4(X2,X3,X4,X1)),X4))|hAPP(c_Finite__Set_Ocard(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OSigma(X1,X3),X4),X2))=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)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_6315]), ['final']). 6.97/7.24 cnf(c_0_10840, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk494_4(X2,X3,X4,X1)),hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),X3)),X2))))|hBOOL(hAPP(X2,X4))|~c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3)|~hBOOL(hAPP(hAPP(c_member(X1),X4),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),X3)))), inference(rw,[status(thm)],[c_0_6316, c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10841, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk52_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_6317]), ['final']). 6.97/7.24 cnf(c_0_10842, 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_6318]), ['final']). 6.97/7.24 cnf(c_0_10843, plain, (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))=hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),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_6319]), ['final']). 6.97/7.24 cnf(c_0_10844, 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,esk576_5(X3,X2,X4,X5,X1))),hAPP(X3,esk576_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_6227]), ['final']). 6.97/7.24 cnf(c_0_10845, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk413_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_6320]), ['final']). 6.97/7.24 cnf(c_0_10846, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk308_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_6321]), ['final']). 6.97/7.24 cnf(c_0_10847, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|X3=c_Groups_Ozero__class_Ozero(X1)|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_6322]), ['final']). 6.97/7.24 cnf(c_0_10848, 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_6323]), ['final']). 6.97/7.24 cnf(c_0_10849, 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_4569]), ['final']). 6.97/7.24 cnf(c_0_10850, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk225_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_6324]), ['final']). 6.97/7.24 cnf(c_0_10851, 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,esk187_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_6325, c_0_4798]), c_0_4817]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10852, 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_6326]), ['final']). 6.97/7.24 cnf(c_0_10853, 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_6327]), ['final']). 6.97/7.24 cnf(c_0_10854, 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_6328]), ['final']). 6.97/7.24 cnf(c_0_10855, plain, (hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X5)),hAPP(c_Set_Oimage(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)))))))|c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4))|~c_Fun_Oinj__on(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_6329]), ['final']). 6.97/7.24 cnf(c_0_10856, 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_6330]), ['final']). 6.97/7.24 cnf(c_0_10857, 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_6331]), ['final']). 6.97/7.24 cnf(c_0_10858, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X4,tc_HOL_Obool),X1),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1),X2)),X3)|c_Groups_Ozero__class_Ozero(X1)!=hAPP(X2,esk467_4(X2,X3,X4,X1))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),esk464_4(X2,X3,X4,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X4,tc_HOL_Obool)),X3))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6107]), ['final']). 6.97/7.24 cnf(c_0_10859, plain, (hAPP(c_Fun_Ocomp(X1,X4,X2,c_Hilbert__Choice_Oinv__into(X4,X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),X5)),c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3))=c_Hilbert__Choice_Oinv__into(X4,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5))|~c_Fun_Obij__betw(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)))|~c_Fun_Obij__betw(X4,X1,X5,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_6332]), ['final']). 6.97/7.24 cnf(c_0_10860, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),hAPP(hAPP(c_Set_Oinsert(X2),X5),X3))=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))))))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6333]), ['final']). 6.97/7.24 cnf(c_0_10861, 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)),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6334, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), ['final']). 6.97/7.24 cnf(c_0_10862, 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_6335]), ['final']). 6.97/7.24 cnf(c_0_10863, 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_4930]), ['final']). 6.97/7.24 cnf(c_0_10864, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk274_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk273_3(X1,X2,X3)))=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk276_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk275_3(X1,X2,X3)))=X2|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6336, c_0_5815]), c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_10865, plain, (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)=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))|~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_6337]), ['final']). 6.97/7.24 cnf(c_0_10866, 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)),esk21_3(X3,X2,X1)),X2))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),esk22_3(X3,X2,X1)),esk23_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_6338, c_0_6281]), ['final']). 6.97/7.24 cnf(c_0_10867, 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_6339]), ['final']). 6.97/7.24 cnf(c_0_10868, 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_6340, c_0_5174]), c_0_5174]), ['final']). 6.97/7.24 cnf(c_0_10869, 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)],[c_0_6341, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891])]), ['final']). 6.97/7.24 cnf(c_0_10870, 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)],[c_0_6342, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891])]), ['final']). 6.97/7.24 cnf(c_0_10871, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))),X5)=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)),X5)),X4))|~class_Rings_Osemiring__0(X1)), inference(split_conjunct,[status(thm)],[c_0_6343]), ['final']). 6.97/7.24 cnf(c_0_10872, 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)),esk31_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_6344]), ['final']). 6.97/7.24 cnf(c_0_10873, plain, (c_FunDef_Oreduction__pair(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(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_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))), inference(split_conjunct,[status(thm)],[c_0_6035]), ['final']). 6.97/7.24 cnf(c_0_10874, 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_6345]), ['final']). 6.97/7.24 cnf(c_0_10875, 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_6346]), ['final']). 6.97/7.24 cnf(c_0_10876, 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),esk113_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_6347]), ['final']). 6.97/7.24 cnf(c_0_10877, 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_6348]), ['final']). 6.97/7.24 cnf(c_0_10878, 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_6349]), ['final']). 6.97/7.24 cnf(c_0_10879, 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_6350]), ['final']). 6.97/7.24 cnf(c_0_10880, 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)],[c_0_6351, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10881, 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)],[c_0_6352, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10882, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk118_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk119_2(X1,X2)))))|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk120_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|hBOOL(hAPP(X1,esk118_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_6353, c_0_6285]), ['final']). 6.97/7.24 cnf(c_0_10883, plain, (hBOOL(hAPP(hAPP(X1,esk497_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk498_3(X1,X2,X3)),c_Int_OMin)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk497_3(X1,X2,X3)),esk498_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_6354, c_0_4741]), ['final']). 6.97/7.24 cnf(c_0_10884, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk274_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk273_3(X1,X2,X3)))=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk276_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk275_3(X1,X2,X3)))=X2|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6355, c_0_5815]), c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_10885, 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_6356]), ['final']). 6.97/7.24 cnf(c_0_10886, plain, (hBOOL(hAPP(hAPP(X1,X4),X3))|~hBOOL(hAPP(hAPP(X1,esk175_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk176_8(X1,X2,X3,X4,X5,X6,X7,X8)))|~hBOOL(hAPP(hAPP(X1,X6),X5))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X8,X7),tc_prod(X8,X7))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X8,X7),tc_prod(X8,X7)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X6),X5)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X4),X3))),c_Transitive__Closure_Ortrancl(tc_prod(X8,X7),X2)))), inference(split_conjunct,[status(thm)],[c_0_5959]), ['final']). 6.97/7.24 cnf(c_0_10887, plain, (hBOOL(hAPP(hAPP(X1,X6),X5))|~hBOOL(hAPP(hAPP(X1,esk579_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk580_8(X1,X2,X3,X4,X5,X6,X7,X8)))|~hBOOL(hAPP(hAPP(X1,X4),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X8,X7),tc_prod(X8,X7))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X8,X7),tc_prod(X8,X7)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X6),X5)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X4),X3))),c_Transitive__Closure_Ortrancl(tc_prod(X8,X7),X2)))), inference(split_conjunct,[status(thm)],[c_0_5966]), ['final']). 6.97/7.24 cnf(c_0_10888, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk79_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_5466]), ['final']). 6.97/7.24 cnf(c_0_10889, 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)),X5)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),X6)),X5)|hAPP(X4,esk517_6(X3,X2,X6,X4,X5,X1))!=hAPP(X6,esk517_6(X3,X2,X6,X4,X5,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6357, c_0_4768]), c_0_4768]), ['final']). 6.97/7.24 cnf(c_0_10890, 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_6358]), ['final']). 6.97/7.24 cnf(c_0_10891, 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)|esk466_4(X1,X2,X3,X4)!=esk465_4(X1,X2,X3,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),esk464_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_6107]), ['final']). 6.97/7.24 cnf(c_0_10892, 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_6359, c_0_4977])]), ['final']). 6.97/7.24 cnf(c_0_10893, 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),esk400_4(X3,X4,X2,X1))),esk399_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_4931]), ['final']). 6.97/7.24 cnf(c_0_10894, 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,esk209_8(X6,X3,X5,X5,X4,X4,X1,X2))!=hAPP(X6,esk209_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_6360])]), ['final']). 6.97/7.24 cnf(c_0_10895, 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_6361]), ['final']). 6.97/7.24 cnf(c_0_10896, 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_6362]), ['final']). 6.97/7.24 cnf(c_0_10897, 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)),esk23_3(X3,X2,X1)),X2))|hAPP(c_Finite__Set_Ocard(X1),esk21_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_6363, c_0_6281]), ['final']). 6.97/7.24 cnf(c_0_10898, 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)),esk22_3(X3,X2,X1)),X2))|hAPP(c_Finite__Set_Ocard(X1),esk21_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_6364, c_0_6281]), ['final']). 6.97/7.24 cnf(c_0_10899, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk265_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,esk264_4(X1,X2,X3,X4)))),hAPP(X2,esk264_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_6365, c_0_6030]), ['final']). 6.97/7.24 cnf(c_0_10900, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk265_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,esk264_4(X2,X3,X4,X1)))),hAPP(X3,esk264_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_6366, c_0_6030]), ['final']). 6.97/7.24 cnf(c_0_10901, 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_6367]), ['final']). 6.97/7.24 cnf(c_0_10902, plain, (X2=X3|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk550_7(X2,X3,X4,X5,X6,X7,X1)),esk551_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)),X3),X4)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X2),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_6246]), ['final']). 6.97/7.24 cnf(c_0_10903, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk476_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_6368]), ['final']). 6.97/7.24 cnf(c_0_10904, 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_6369, c_0_6370]), c_0_6030]), ['final']). 6.97/7.24 cnf(c_0_10905, 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),esk421_4(X3,X4,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X4),esk421_4(X3,X4,X2,X1)))),X3))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_6233]), ['final']). 6.97/7.24 cnf(c_0_10906, 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,esk230_4(X2,X1,X3,X4)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6371, c_0_4813]), c_0_4813]), ['final']). 6.97/7.24 cnf(c_0_10907, 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_6372]), ['final']). 6.97/7.24 cnf(c_0_10908, plain, (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_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),X5),X3)),hAPP(X5,X2))|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_6373]), ['final']). 6.97/7.24 cnf(c_0_10909, 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_6374]), c_0_6375]), c_0_6376]), ['final']). 6.97/7.24 cnf(c_0_10910, 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_Olist__update(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X4)),X1),X5)=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))), inference(split_conjunct,[status(thm)],[c_0_6377]), ['final']). 6.97/7.24 cnf(c_0_10911, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk551_7(X2,X3,X4,X5,X6,X7,X1)),X7))|X2=X3|~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)),X3),X4)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X2),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_6246]), ['final']). 6.97/7.24 cnf(c_0_10912, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk550_7(X2,X3,X4,X5,X6,X7,X1)),X7))|X2=X3|~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)),X3),X4)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X2),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_6246]), ['final']). 6.97/7.24 cnf(c_0_10913, 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,esk547_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_6079]), ['final']). 6.97/7.24 cnf(c_0_10914, plain, (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_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))|c_Groups_Oone__class_Oone(X1)!=hAPP(X2,esk166_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_6082]), ['final']). 6.97/7.24 cnf(c_0_10915, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk53_5(X2,X3,X4,X1,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),X4))),hAPP(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),X4)),X2))))|hBOOL(hAPP(X2,X3))|~c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X4)|~hBOOL(hAPP(hAPP(c_member(X1),X3),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),X4)))), inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_6378, c_0_4467])]), ['final']). 6.97/7.24 cnf(c_0_10916, 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_6379]), ['final']). 6.97/7.24 cnf(c_0_10917, 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,X3),X2))=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))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5019]), ['final']). 6.97/7.24 cnf(c_0_10918, 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_6380]), ['final']). 6.97/7.24 cnf(c_0_10919, plain, (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_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))|c_Groups_Oone__class_Oone(X1)!=hAPP(X2,esk161_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_6083]), ['final']). 6.97/7.24 cnf(c_0_10920, plain, (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))=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))|c_Groups_Ozero__class_Ozero(X1)!=hAPP(X2,esk85_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_6087]), ['final']). 6.97/7.24 cnf(c_0_10921, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X2),X1)),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),X2),c_List_Olist_ONil(X3)))),hAPP(hAPP(c_List_Oappend(X3),X6),hAPP(hAPP(c_List_Olist_OCons(X3),X1),c_List_Olist_ONil(X3))))),c_List_Olistrel1(X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_6109]), ['final']). 6.97/7.24 cnf(c_0_10922, 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,esk329_5(X3,X4,X5,X2,X1)))),hAPP(X2,esk329_5(X3,X4,X5,X2,X1)))),c_Transitive__Closure_Ortrancl(X1,X5)))), inference(split_conjunct,[status(thm)],[c_0_6381]), ['final']). 6.97/7.24 cnf(c_0_10923, 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_6382]), ['final']). 6.97/7.24 cnf(c_0_10924, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk257_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3)))=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk255_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk254_3(X1,X2,X3)))=X2|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6383, c_0_5815]), c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_10925, 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)],[c_0_6384, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_10926, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk28_5(X2,X3,X4,X5,X1)),X4)),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_6182]), ['final']). 6.97/7.24 cnf(c_0_10927, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk185_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_6181]), ['final']). 6.97/7.24 cnf(c_0_10928, 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_6385]), ['final']). 6.97/7.24 cnf(c_0_10929, 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),hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))))=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))|~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_6386]), ['final']). 6.97/7.24 cnf(c_0_10930, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk257_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3)))=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk255_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk254_3(X1,X2,X3)))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6387, c_0_5815]), c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_10931, plain, (X2=c_Groups_Oone__class_Oone(X1)|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_6388]), ['final']). 6.97/7.24 cnf(c_0_10932, 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_6389]), ['final']). 6.97/7.24 cnf(c_0_10933, 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_6272]), ['final']). 6.97/7.24 cnf(c_0_10934, 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_6273]), ['final']). 6.97/7.24 cnf(c_0_10935, 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_6274]), ['final']). 6.97/7.24 cnf(c_0_10936, 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_6277]), ['final']). 6.97/7.24 cnf(c_0_10937, plain, (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)))=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_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_6390]), ['final']). 6.97/7.24 cnf(c_0_10938, plain, (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))=hAPP(X4,X5)|~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_6391]), ['final']). 6.97/7.24 cnf(c_0_10939, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk344_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_Ominus__class_Ominus(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),X4),X2))), inference(rw,[status(thm)],[c_0_6392, c_0_4741]), ['final']). 6.97/7.24 cnf(c_0_10940, plain, (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)))=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))|~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_6393]), ['final']). 6.97/7.24 cnf(c_0_10941, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk135_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_6394, c_0_5038]), ['final']). 6.97/7.24 cnf(c_0_10942, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk524_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_6395]), ['final']). 6.97/7.24 cnf(c_0_10943, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk367_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_6396]), ['final']). 6.97/7.24 cnf(c_0_10944, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk316_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),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(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__add(X5)), inference(split_conjunct,[status(thm)],[c_0_6397]), ['final']). 6.97/7.24 cnf(c_0_10945, 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_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_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_6398]), ['final']). 6.97/7.24 cnf(c_0_10946, 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_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))|~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_6399]), ['final']). 6.97/7.24 cnf(c_0_10947, 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_6400]), ['final']). 6.97/7.24 cnf(c_0_10948, 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_6401]), ['final']). 6.97/7.24 cnf(c_0_10949, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk183_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),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(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__add(X5)), inference(split_conjunct,[status(thm)],[c_0_6402]), ['final']). 6.97/7.24 cnf(c_0_10950, 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_6403]), ['final']). 6.97/7.24 cnf(c_0_10951, 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_6404]), ['final']). 6.97/7.24 cnf(c_0_10952, 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_6405]), ['final']). 6.97/7.24 cnf(c_0_10953, 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_6406]), ['final']). 6.97/7.24 cnf(c_0_10954, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk30_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_6344]), ['final']). 6.97/7.24 cnf(c_0_10955, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk112_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_6347]), ['final']). 6.97/7.24 cnf(c_0_10956, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk287_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)))|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_List_Oset(X1),esk288_2(X2,X1))),hAPP(c_List_Oset(X1),esk289_2(X2,X1)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2))), inference(rw,[status(thm)],[c_0_6407, c_0_4645]), ['final']). 6.97/7.24 cnf(c_0_10957, plain, (hAPP(hAPP(c_List_Ozip(X3,X1),hAPP(hAPP(c_List_Oappend(X3),X4),X6)),hAPP(hAPP(c_List_Oappend(X1),X2),X5))=hAPP(hAPP(c_List_Oappend(tc_prod(X3,X1)),hAPP(hAPP(c_List_Ozip(X3,X1),X4),X2)),hAPP(hAPP(c_List_Ozip(X3,X1),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(X1)),X5)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X6)), inference(split_conjunct,[status(thm)],[c_0_6408]), ['final']). 6.97/7.24 cnf(c_0_10958, 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(c_List_Ohd(X2),hAPP(hAPP(c_List_Odrop(X2),X1),X3))),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_6409]), ['final']). 6.97/7.24 cnf(c_0_10959, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk345_4(X1,X2,X3,X4)),esk344_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_Ominus__class_Ominus(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),X4),X2))), inference(rw,[status(thm)],[c_0_6410, c_0_4741]), ['final']). 6.97/7.24 cnf(c_0_10960, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk136_4(X1,X2,X3,X4)),esk135_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_6411, c_0_5038]), ['final']). 6.97/7.24 cnf(c_0_10961, plain, (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(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,esk303_3(X3,X2,X1))),hAPP(X2,esk304_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),esk303_3(X3,X2,X1)),esk304_3(X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6412]), ['final']). 6.97/7.24 cnf(c_0_10962, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),hAPP(X3,esk470_8(X4,X5,X3,X6,X7,X8,X2,X1))),hAPP(X5,esk471_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_6237]), ['final']). 6.97/7.24 cnf(c_0_10963, plain, (hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk370_3(X3,X2,X1)),X4))=hAPP(X2,esk370_3(X3,X2,X1))|~c_Wellfounded_Owf(X1,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)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(X2,hAPP(c_Nat_OSuc,esk369_3(X3,X2,X1)))),hAPP(X2,esk369_3(X3,X2,X1)))),c_Transitive__Closure_Ortrancl(X1,X3)))), inference(rw,[status(thm)],[c_0_6413, c_0_5174]), ['final']). 6.97/7.24 cnf(c_0_10964, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk535_4(X2,X3,X4,X1)),X4))|hBOOL(hAPP(hAPP(c_member(X1),esk534_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_6414]), ['final']). 6.97/7.24 cnf(c_0_10965, 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),X3)))=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)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_6415, c_0_4410]), ['final']). 6.97/7.24 cnf(c_0_10966, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk289_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),esk287_2(X2,X1)))), inference(rw,[status(thm)],[c_0_6416, c_0_4645]), ['final']). 6.97/7.24 cnf(c_0_10967, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk288_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),esk287_2(X2,X1)))), inference(rw,[status(thm)],[c_0_6417, c_0_4645]), ['final']). 6.97/7.24 cnf(c_0_10968, 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),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X6))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X4)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X6),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X4)))|~c_Equiv__Relations_Oequiv(X1,X7,X4)), inference(split_conjunct,[status(thm)],[c_0_4944]), ['final']). 6.97/7.24 cnf(c_0_10969, 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,esk577_5(X3,X2,X4,X5,X1))),X3))|~class_Groups_Oordered__ab__semigroup__add(X1)|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_6418]), ['final']). 6.97/7.24 cnf(c_0_10970, 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_6419]), ['final']). 6.97/7.24 cnf(c_0_10971, 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_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Set_Oinsert(X3),X4)),X5))=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))), inference(split_conjunct,[status(thm)],[c_0_5666]), ['final']). 6.97/7.24 cnf(c_0_10972, 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_6420]), ['final']). 6.97/7.24 cnf(c_0_10973, 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_6421]), ['final']). 6.97/7.24 cnf(c_0_10974, 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_6422, c_0_5065]), c_0_6423]), c_0_4781]), ['final']). 6.97/7.24 cnf(c_0_10975, 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)),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_4952]), ['final']). 6.97/7.24 cnf(c_0_10976, 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_6424]), ['final']). 6.97/7.24 cnf(c_0_10977, 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,esk52_6(X2,X1,X3,X4,X5,X6))!=hAPP(X3,esk52_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_6317]), ['final']). 6.97/7.24 cnf(c_0_10978, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk28_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_6182]), ['final']). 6.97/7.24 cnf(c_0_10979, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk185_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_6181]), ['final']). 6.97/7.24 cnf(c_0_10980, 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)),esk21_3(X3,X2,X1)),X2))|esk23_3(X3,X2,X1)!=esk22_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_6425, c_0_6281]), ['final']). 6.97/7.24 cnf(c_0_10981, 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_6426, c_0_5538]), c_0_4817]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_10982, 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_4974]), ['final']). 6.97/7.24 cnf(c_0_10983, 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,esk258_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_6152]), ['final']). 6.97/7.24 cnf(c_0_10984, 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(X6,tc_fun(X1,tc_HOL_Obool)),X4),X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6,tc_fun(X1,tc_HOL_Obool)),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,esk371_6(X3,X2,X1,X4,X5,X6))),hAPP(X3,esk371_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_6212]), ['final']). 6.97/7.24 cnf(c_0_10985, 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(X6,tc_fun(X1,tc_HOL_Obool)),X5),X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,tc_fun(X1,tc_HOL_Obool)),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,esk484_6(X3,X2,X1,X4,X5,X6))),hAPP(X3,esk484_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_6211]), ['final']). 6.97/7.24 cnf(c_0_10986, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,X1),hAPP(c_Fun_Ocomp(X4,X1,X6,X2),X3)),X5)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1),X2),hAPP(c_Set_Oimage(X6,X4,X3),X5))|c_Groups_Ozero__class_Ozero(X1)!=hAPP(X2,hAPP(X3,esk214_6(X4,X2,X3,X5,X6,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6),X5))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6255]), ['final']). 6.97/7.24 cnf(c_0_10987, 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_6427]), ['final']). 6.97/7.24 cnf(c_0_10988, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))),c_Int_OMin)),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_6428, c_0_4741]), ['final']). 6.97/7.24 cnf(c_0_10989, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk302_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_6429, c_0_5174]), ['final']). 6.97/7.24 cnf(c_0_10990, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk330_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_6430, c_0_5174]), ['final']). 6.97/7.24 cnf(c_0_10991, 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_6431, c_0_5174]), c_0_5174]), ['final']). 6.97/7.24 cnf(c_0_10992, 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,esk163_4(X4,X3,X2,X1)),esk164_4(X4,X3,X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk163_4(X4,X3,X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk164_4(X4,X3,X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))), inference(split_conjunct,[status(thm)],[c_0_6432]), ['final']). 6.97/7.24 cnf(c_0_10993, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1))),c_Int_OMin)),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_6433, c_0_4741]), ['final']). 6.97/7.24 cnf(c_0_10994, 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))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),X6)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_6434]), ['final']). 6.97/7.24 cnf(c_0_10995, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk225_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_6324]), ['final']). 6.97/7.24 cnf(c_0_10996, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk413_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_6320]), ['final']). 6.97/7.24 cnf(c_0_10997, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk308_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_6321]), ['final']). 6.97/7.24 cnf(c_0_10998, 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_6435]), ['final']). 6.97/7.24 cnf(c_0_10999, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk207_3(X2,X3,X1)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X3),X2)))|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))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_6436]), ['final']). 6.97/7.24 cnf(c_0_11000, 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_6437]), ['final']). 6.97/7.24 cnf(c_0_11001, 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_6216]), ['final']). 6.97/7.24 cnf(c_0_11002, plain, (hAPP(X1,esk265_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,esk264_4(X2,X1,X3,X4)))),hAPP(X1,esk264_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_6438, c_0_6030]), ['final']). 6.97/7.24 cnf(c_0_11003, plain, (c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X2,X4),tc_HOL_Obool))=hAPP(c_Set_Oimage(tc_prod(X1,X5),tc_prod(X2,X4),c_Product__Type_Omap__pair(X1,X2,X5,X4,X3,X6)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1,X5),tc_HOL_Obool)))|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))|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_6439]), ['final']). 6.97/7.24 cnf(c_0_11004, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk206_3(X2,X3,X1)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X3),X2)))|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))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_6436]), ['final']). 6.97/7.24 cnf(c_0_11005, 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_6440]), ['final']). 6.97/7.24 cnf(c_0_11006, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk148_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_6441]), ['final']). 6.97/7.24 cnf(c_0_11007, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(X3,X4)),hAPP(X3,X5))))|~c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X3)), inference(split_conjunct,[status(thm)],[c_0_6442]), ['final']). 6.97/7.24 cnf(c_0_11008, 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,esk411_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_6166]), ['final']). 6.97/7.24 cnf(c_0_11009, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk140_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_6443]), ['final']). 6.97/7.24 cnf(c_0_11010, 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_6444, c_0_4977]), c_0_6291])])]), ['final']). 6.97/7.24 cnf(c_0_11011, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),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_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X3)), inference(split_conjunct,[status(thm)],[c_0_6445]), ['final']). 6.97/7.24 cnf(c_0_11012, 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_6446]), ['final']). 6.97/7.24 cnf(c_0_11013, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X3),X2)),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),X3),X2)),c_List_Omeasures(X4,X5)))), inference(split_conjunct,[status(thm)],[c_0_6349]), ['final']). 6.97/7.24 cnf(c_0_11014, 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_6447, c_0_4977]), c_0_6291])]), c_0_6448])]), ['final']). 6.97/7.24 cnf(c_0_11015, plain, (hAPP(hAPP(X3,hAPP(X6,X7)),hAPP(X6,X8))=hAPP(X6,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X7),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))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X7),X8)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_6449]), ['final']). 6.97/7.24 cnf(c_0_11016, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X6),hAPP(c_Fun_Ocomp(X1,X6,X5,X2),X3)),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X6),X2),hAPP(c_Set_Oimage(X5,X1,X3),X4))|esk214_6(X1,X2,X3,X4,X5,X6)!=esk215_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_6255]), ['final']). 6.97/7.24 cnf(c_0_11017, 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),esk129_7(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,X5)),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X2,X4))), inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_6450])]), ['final']). 6.97/7.24 cnf(c_0_11018, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk376_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_6451]), ['final']). 6.97/7.24 cnf(c_0_11019, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk354_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_6452]), ['final']). 6.97/7.24 cnf(c_0_11020, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk424_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_6453]), ['final']). 6.97/7.24 cnf(c_0_11021, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk328_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_6454]), ['final']). 6.97/7.24 cnf(c_0_11022, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X2))|~c_Relation_Otrans(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),X5)),X2))), inference(split_conjunct,[status(thm)],[c_0_6455]), ['final']). 6.97/7.24 cnf(c_0_11023, plain, (hAPP(c_Finite__Set_Ocard(tc_prod(X4,X1)),hAPP(hAPP(c_Product__Type_OSigma(X4,X1),X3),X2))=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)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,esk525_4(X2,X1,X3,X4))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), inference(split_conjunct,[status(thm)],[c_0_6315]), ['final']). 6.97/7.24 cnf(c_0_11024, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|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),esk179_2(X2,X1)),esk180_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk179_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk180_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))), inference(split_conjunct,[status(thm)],[c_0_6456]), ['final']). 6.97/7.24 cnf(c_0_11025, 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),esk86_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_6457])]), ['final']). 6.97/7.24 cnf(c_0_11026, 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_6458]), ['final']). 6.97/7.24 cnf(c_0_11027, plain, (hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk250_3(X1,X2,X3)),c_Int_OMin)),esk251_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),esk250_3(X1,X2,X3)),esk251_3(X1,X2,X3)))), inference(rw,[status(thm)],[c_0_6459, c_0_4741]), ['final']). 6.97/7.24 cnf(c_0_11028, 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))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6460, c_0_4471]), c_0_4471]), c_0_4471]), ['final']). 6.97/7.24 cnf(c_0_11029, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),esk287_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)))|esk289_2(X1,X2)!=esk288_2(X1,X2)|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),X1))), inference(rw,[status(thm)],[c_0_6461, c_0_4645]), ['final']). 6.97/7.24 cnf(c_0_11030, plain, (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))=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))|~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_6462]), ['final']). 6.97/7.24 cnf(c_0_11031, 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,esk572_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_6254]), ['final']). 6.97/7.24 cnf(c_0_11032, 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_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))|~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_6463]), ['final']). 6.97/7.24 cnf(c_0_11033, 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)),X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))|hAPP(hAPP(c_List_Oappend(X2),X3),X1)!=hAPP(hAPP(c_List_Oappend(X2),X4),X5)), inference(split_conjunct,[status(thm)],[c_0_4956]), ['final']). 6.97/7.24 cnf(c_0_11034, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk577_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_Groups_Oordered__ab__semigroup__add(X5)|~class_Rings_Osemiring__1(X5)), inference(split_conjunct,[status(thm)],[c_0_6418]), ['final']). 6.97/7.24 cnf(c_0_11035, 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_Enum_Oenum(X1)|~class_Orderings_Oorder(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))), inference(rw,[status(thm)],[c_0_6464, c_0_5065]), ['final']). 6.97/7.24 cnf(c_0_11036, 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_6465]), ['final']). 6.97/7.24 cnf(c_0_11037, 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_6466]), ['final']). 6.97/7.24 cnf(c_0_11038, 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_6467, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_6468]), c_0_4413]), c_0_6469]), ['final']). 6.97/7.24 cnf(c_0_11039, 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_6470]), ['final']). 6.97/7.24 cnf(c_0_11040, plain, (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)))=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_6471]), ['final']). 6.97/7.24 cnf(c_0_11041, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),esk514_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(X1)),X5)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)), inference(split_conjunct,[status(thm)],[c_0_6472]), ['final']). 6.97/7.24 cnf(c_0_11042, plain, (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)))=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)))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_6473]), ['final']). 6.97/7.24 cnf(c_0_11043, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),esk240_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(X2)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)), inference(split_conjunct,[status(thm)],[c_0_6474]), ['final']). 6.97/7.24 cnf(c_0_11044, 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_6475]), ['final']). 6.97/7.24 cnf(c_0_11045, 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_6476]), ['final']). 6.97/7.24 cnf(c_0_11046, 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_6477]), ['final']). 6.97/7.24 cnf(c_0_11047, plain, (hAPP(hAPP(c_List_Odrop(X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),c_List_OtakeWhile(X3,X1,X4))),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)],[inference(rw,[status(thm)],[c_0_6478, c_0_4813]), c_0_4813]), ['final']). 6.97/7.24 cnf(c_0_11048, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk128_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,esk127_3(X1,X2,X3)))),hAPP(X2,esk127_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_6479, c_0_6030]), ['final']). 6.97/7.24 cnf(c_0_11049, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk58_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,esk57_3(X1,X2,X3)))),hAPP(X2,esk57_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_6480, c_0_6030]), ['final']). 6.97/7.24 cnf(c_0_11050, plain, (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(c_Set_Oimage(X1,X1,X2),X3))=hAPP(X2,c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3))|~class_Orderings_Olinorder(X1)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(X2,esk281_3(X3,X2,X1))),hAPP(X2,esk282_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omax(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_6481]), ['final']). 6.97/7.24 cnf(c_0_11051, plain, (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(c_Set_Oimage(X1,X1,X2),X3))=hAPP(X2,c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))|~class_Orderings_Olinorder(X1)|hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),esk441_3(X3,X2,X1)),esk442_3(X3,X2,X1)))!=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(X2,esk441_3(X3,X2,X1))),hAPP(X2,esk442_3(X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6482]), ['final']). 6.97/7.24 cnf(c_0_11052, 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),esk209_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_6483])]), ['final']). 6.97/7.24 cnf(c_0_11053, 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),esk209_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_6484])]), ['final']). 6.97/7.24 cnf(c_0_11054, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk274_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk273_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_6485, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11055, 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_6486, c_0_4881]), c_0_4881]), c_0_6487]), ['final']). 6.97/7.24 cnf(c_0_11056, 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_6488]), ['final']). 6.97/7.24 cnf(c_0_11057, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk276_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk275_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk274_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_6489, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11058, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk265_4(X2,X3,X4,X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk264_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_4971]), ['final']). 6.97/7.24 cnf(c_0_11059, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk265_4(X1,X2,X3,X4)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),esk264_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_4971]), ['final']). 6.97/7.24 cnf(c_0_11060, plain, (hBOOL(hAPP(hAPP(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk48_3(X1,X2,X3))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk49_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk49_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_6490]), ['final']). 6.97/7.24 cnf(c_0_11061, 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_6491]), ['final']). 6.97/7.24 cnf(c_0_11062, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk274_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk273_3(X1,X2,X3)))=X2|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))), inference(rw,[status(thm)],[c_0_6492, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11063, plain, (hAPP(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X3),X2))=hAPP(hAPP(X6,hAPP(X4,X3)),hAPP(X4,X2))|hAPP(X1,esk541_7(X2,X3,X4,X1,X5,X6,X7))!=X5|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X3))|~c_Finite__Set_Ofolding__image__simple(X8,X7,X6,X5,X1,X4)), inference(split_conjunct,[status(thm)],[c_0_6119]), ['final']). 6.97/7.24 cnf(c_0_11064, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk276_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk275_3(X1,X2,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)),esk274_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))), inference(rw,[status(thm)],[c_0_6493, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11065, 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_6494, c_0_5538]), c_0_5539]), c_0_5065]), ['final']). 6.97/7.24 cnf(c_0_11066, 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_6495, c_0_5174]), ['final']). 6.97/7.24 cnf(c_0_11067, 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_6496]), ['final']). 6.97/7.24 cnf(c_0_11068, 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_6497, c_0_6498]), ['final']). 6.97/7.24 cnf(c_0_11069, 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_6499]), ['final']). 6.97/7.24 cnf(c_0_11070, 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_6500]), ['final']). 6.97/7.24 cnf(c_0_11071, 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_6501]), ['final']). 6.97/7.24 cnf(c_0_11072, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk555_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_6502]), ['final']). 6.97/7.24 cnf(c_0_11073, 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_6214]), ['final']). 6.97/7.24 cnf(c_0_11074, 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_6219]), ['final']). 6.97/7.24 cnf(c_0_11075, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X2),X1)),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),X2),X6)),hAPP(hAPP(c_Product__Type_OPair(X3,X5),X1),X7))),c_Wellfounded_Olex__prod(X3,X5,X4,X8)))), inference(split_conjunct,[status(thm)],[c_0_4900]), ['final']). 6.97/7.24 cnf(c_0_11076, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),X5),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(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_6373]), ['final']). 6.97/7.24 cnf(c_0_11077, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk542_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_6503]), ['final']). 6.97/7.24 cnf(c_0_11078, 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_6504]), ['final']). 6.97/7.24 cnf(c_0_11079, 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_6505, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_6506]), ['final']). 6.97/7.24 cnf(c_0_11080, 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_6507, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4821]), ['final']). 6.97/7.24 cnf(c_0_11081, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk559_4(X2,X3,X4,X1)),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk558_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)))), inference(split_conjunct,[status(thm)],[c_0_6508]), ['final']). 6.97/7.24 cnf(c_0_11082, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk219_6(X3,X4,X1,X5,X2,X6)),esk220_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_6509]), ['final']). 6.97/7.24 cnf(c_0_11083, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk218_6(X3,X4,X2,X5,X6,X1)),esk219_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_6509]), ['final']). 6.97/7.24 cnf(c_0_11084, 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),esk192_2(X2,X1)),esk193_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk192_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk193_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))), inference(split_conjunct,[status(thm)],[c_0_6510]), ['final']). 6.97/7.24 cnf(c_0_11085, 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_6382]), ['final']). 6.97/7.24 cnf(c_0_11086, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X6))),X4)))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X6))|~class_Rings_Ocomm__ring(X1)|~class_Rings_Odvd(X1)), inference(split_conjunct,[status(thm)],[c_0_6511]), ['final']). 6.97/7.24 cnf(c_0_11087, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))=X2|X2=c_Groups_Oone__class_Oone(X1)|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),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(rw,[status(thm)],[c_0_6512, c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_11088, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|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_6513, c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_11089, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|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),esk75_2(X2,X1)),esk76_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk75_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk76_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))), inference(split_conjunct,[status(thm)],[c_0_6514]), ['final']). 6.97/7.24 cnf(c_0_11090, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X3))),hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X3)))))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X3)))))|~c_Orderings_Oorder__class_Omono(X1,X1,X3)), inference(split_conjunct,[status(thm)],[c_0_6515]), ['final']). 6.97/7.24 cnf(c_0_11091, 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_6516, c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_11092, 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_6517, c_0_5891]), ['final']). 6.97/7.24 cnf(c_0_11093, plain, (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))=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))|~class_Rings_Oring(X1)|~class_Int_Onumber(X1)), inference(split_conjunct,[status(thm)],[c_0_6518]), ['final']). 6.97/7.24 cnf(c_0_11094, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk276_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk275_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_6519, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11095, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk274_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk273_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk276_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_6520, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11096, 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_6521]), ['final']). 6.97/7.24 cnf(c_0_11097, 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_6522]), ['final']). 6.97/7.24 cnf(c_0_11098, 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_6523]), ['final']). 6.97/7.24 cnf(c_0_11099, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk330_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_6524, c_0_5174]), ['final']). 6.97/7.24 cnf(c_0_11100, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk302_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_6525, c_0_5174]), ['final']). 6.97/7.24 cnf(c_0_11101, plain, (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))=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))|~class_Int_Onumber(X1)|~class_Rings_Osemiring(X1)), inference(split_conjunct,[status(thm)],[c_0_6526]), ['final']). 6.97/7.24 cnf(c_0_11102, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk556_4(X1,X2,X3,X4)),esk555_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_6502]), ['final']). 6.97/7.24 cnf(c_0_11103, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk543_4(X2,X3,X4,X1)),esk542_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_6503]), ['final']). 6.97/7.24 cnf(c_0_11104, 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_6527]), ['final']). 6.97/7.24 cnf(c_0_11105, 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)),esk22_3(X3,X2,X1)),esk23_3(X3,X2,X1))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(c_Finite__Set_Ocard(X1),esk21_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_6528, c_0_6281]), ['final']). 6.97/7.24 cnf(c_0_11106, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X5),X4))|~class_Divides_Osemiring__div(X1)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_6529]), ['final']). 6.97/7.24 cnf(c_0_11107, 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,esk375_5(X3,X2,X1,X4,X5)),hAPP(X3,esk375_5(X3,X2,X1,X4,X5)))), inference(split_conjunct,[status(thm)],[c_0_6530]), ['final']). 6.97/7.24 cnf(c_0_11108, 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_6531, c_0_4821]), ['final']). 6.97/7.24 cnf(c_0_11109, 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_6532, c_0_5539]), ['final']). 6.97/7.24 cnf(c_0_11110, 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_4889]), ['final']). 6.97/7.24 cnf(c_0_11111, plain, (c_Relation_Orefl__on(X1,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X4),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),X3))|~c_Relation_Orefl__on(X1,hAPP(X2,esk195_5(X3,X2,X1,X4,X5)),hAPP(X3,esk195_5(X3,X2,X1,X4,X5)))), inference(split_conjunct,[status(thm)],[c_0_6533]), ['final']). 6.97/7.24 cnf(c_0_11112, 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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),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_6534, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), ['final']). 6.97/7.24 cnf(c_0_11113, plain, (hBOOL(hAPP(hAPP(c_member(X1),X5),X4))|hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),hAPP(hAPP(X3,X5),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_6535]), ['final']). 6.97/7.24 cnf(c_0_11114, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk118_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk119_2(X1,X2)))))|hBOOL(hAPP(X1,esk120_2(X1,X2)))|hBOOL(hAPP(X1,esk118_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_6536, c_0_6285]), ['final']). 6.97/7.24 cnf(c_0_11115, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk276_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk275_3(X1,X2,X3)))=X2|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))), inference(rw,[status(thm)],[c_0_6537, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11116, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk274_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk273_3(X1,X2,X3)))=X2|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk276_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))), inference(rw,[status(thm)],[c_0_6538, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11117, 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_6539, c_0_5538]), c_0_4817]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_11118, 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_6540, c_0_5560]), ['final']). 6.97/7.24 cnf(c_0_11119, plain, (X1=X2|hAPP(c_List_Oset(X3),X1)!=hAPP(c_List_Oset(X3),X2)|~c_Fun_Oinj__on(X3,X4,X5,hAPP(c_List_Oset(X3),hAPP(hAPP(c_List_Oappend(X3),X1),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))|~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_6541, c_0_6542]), ['final']). 6.97/7.24 cnf(c_0_11120, 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_6543]), ['final']). 6.97/7.24 cnf(c_0_11121, plain, (hAPP(hAPP(c_List_Oappend(X1),esk151_4(X2,X3,X4,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),esk149_4(X2,X3,X4,X1)),esk152_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)))), inference(split_conjunct,[status(thm)],[c_0_6544]), ['final']). 6.97/7.24 cnf(c_0_11122, 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_6545, c_0_5746]), ['final']). 6.97/7.24 cnf(c_0_11123, plain, (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)))=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_6546]), ['final']). 6.97/7.24 cnf(c_0_11124, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),esk151_4(X3,X1,X4,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),esk150_4(X3,X1,X4,X2)),esk152_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_6544]), ['final']). 6.97/7.24 cnf(c_0_11125, plain, (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)=X4|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_4988]), ['final']). 6.97/7.24 cnf(c_0_11126, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X5),X3),c_List_Oremove1(X2,X3,X4))=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))|X3!=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))), inference(split_conjunct,[status(thm)],[c_0_6547]), ['final']). 6.97/7.24 cnf(c_0_11127, 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_6548, c_0_4415]), c_0_4415]), ['final']). 6.97/7.24 cnf(c_0_11128, 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_6326]), ['final']). 6.97/7.24 cnf(c_0_11129, 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_6327]), ['final']). 6.97/7.24 cnf(c_0_11130, 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_6330]), ['final']). 6.97/7.24 cnf(c_0_11131, 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_6331]), ['final']). 6.97/7.24 cnf(c_0_11132, plain, (X4=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|X5=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|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))|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)), inference(split_conjunct,[status(thm)],[c_0_6549]), ['final']). 6.97/7.24 cnf(c_0_11133, 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_6550]), ['final']). 6.97/7.24 cnf(c_0_11134, 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_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_6551]), ['final']). 6.97/7.24 cnf(c_0_11135, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=esk123_3(X1,X2,X3)|hBOOL(hAPP(hAPP(X1,esk123_3(X1,X2,X3)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,esk122_3(X1,X2,X3),esk123_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_6552]), ['final']). 6.97/7.24 cnf(c_0_11136, 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_6553]), ['final']). 6.97/7.24 cnf(c_0_11137, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk255_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk254_3(X1,X2,X3)))=X2|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))), inference(rw,[status(thm)],[c_0_6554, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11138, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk257_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3)))=X2|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)),esk255_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))), inference(rw,[status(thm)],[c_0_6555, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11139, plain, (hAPP(c_List_Ofilter(X2,X5),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X6),X4))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X6),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))|~hBOOL(hAPP(X5,X6))), inference(split_conjunct,[status(thm)],[c_0_6556]), ['final']). 6.97/7.24 cnf(c_0_11140, 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_6557]), ['final']). 6.97/7.24 cnf(c_0_11141, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk398_3(X2,X3,X1)),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))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Int_Oint),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_6558]), ['final']). 6.97/7.24 cnf(c_0_11142, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk546_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_6559]), ['final']). 6.97/7.24 cnf(c_0_11143, 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_6560]), ['final']). 6.97/7.24 cnf(c_0_11144, 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),esk345_4(X4,X3,X2,X1)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),c_Int_OMin)),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))), inference(rw,[status(thm)],[c_0_6561, c_0_4741]), ['final']). 6.97/7.24 cnf(c_0_11145, 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),esk136_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_6562, c_0_5038]), ['final']). 6.97/7.24 cnf(c_0_11146, 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_6563, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11147, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk255_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk254_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(rw,[status(thm)],[c_0_6564, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11148, plain, (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)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),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)),X4),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_4569]), ['final']). 6.97/7.24 cnf(c_0_11149, plain, (hBOOL(hAPP(hAPP(X1,esk390_7(X2,X3,X4,X5,X6,X7,X1)),esk389_7(X2,X3,X4,X5,X6,X7,X1)))|hBOOL(hAPP(X4,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X7,X6,X2),X3),X5)))|~hBOOL(hAPP(hAPP(X1,hAPP(c_Product__Type_Osnd(X7,X6),X5)),hAPP(c_Product__Type_Ofst(X7,X6),X5)))), inference(split_conjunct,[status(thm)],[c_0_6565]), ['final']). 6.97/7.24 cnf(c_0_11150, 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_6566, c_0_5174]), ['final']). 6.97/7.24 cnf(c_0_11151, 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_6567]), ['final']). 6.97/7.24 cnf(c_0_11152, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk257_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk255_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(rw,[status(thm)],[c_0_6568, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11153, 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_6569, c_0_4813]), ['final']). 6.97/7.24 cnf(c_0_11154, 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_6570]), ['final']). 6.97/7.24 cnf(c_0_11155, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk142_5(X2,X3,X4,X5,X1)),hAPP(X3,esk141_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_6443]), ['final']). 6.97/7.24 cnf(c_0_11156, 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_6527]), ['final']). 6.97/7.24 cnf(c_0_11157, 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)))|X4=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,esk111_5(X3,X2,X4,X5,X1))),hAPP(X3,esk111_5(X3,X2,X4,X5,X1))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~class_Groups_Ocomm__monoid__add(X1)|~class_Groups_Oordered__cancel__ab__semigroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6308]), ['final']). 6.97/7.24 cnf(c_0_11158, 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_6571]), ['final']). 6.97/7.24 cnf(c_0_11159, 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_6572]), ['final']). 6.97/7.24 cnf(c_0_11160, 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_6573]), ['final']). 6.97/7.24 cnf(c_0_11161, 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_6574]), ['final']). 6.97/7.24 cnf(c_0_11162, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk149_4(X2,X3,X4,X1)),esk150_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_6544]), ['final']). 6.97/7.24 cnf(c_0_11163, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X5),X4))=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))))|~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_6575]), ['final']). 6.97/7.24 cnf(c_0_11164, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk381_6(X2,X3,X4,X5,X6,X1)),esk382_6(X2,X3,X4,X5,X6,X1))),X6))|c_Equiv__Relations_Ocongruent2(X1,X5,X2,X6,X4,X3)), inference(split_conjunct,[status(thm)],[c_0_6576]), ['final']). 6.97/7.24 cnf(c_0_11165, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk383_6(X2,X3,X4,X1,X5,X6)),esk384_6(X2,X3,X4,X1,X5,X6))),X4))|c_Equiv__Relations_Ocongruent2(X6,X1,X2,X5,X4,X3)), inference(split_conjunct,[status(thm)],[c_0_6576]), ['final']). 6.97/7.24 cnf(c_0_11166, 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_Rings_Oring(X1)|~class_Int_Onumber(X1)), inference(split_conjunct,[status(thm)],[c_0_6577]), ['final']). 6.97/7.24 cnf(c_0_11167, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk276_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk275_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_6578, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11168, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk274_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk273_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_6579, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11169, 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(X1)|~c_Nat__Transfer_Onat__set(X2)), inference(split_conjunct,[status(thm)],[c_0_6580]), ['final']). 6.97/7.24 cnf(c_0_11170, 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),esk34_2(X2,X1)),esk35_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk34_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk35_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))), inference(split_conjunct,[status(thm)],[c_0_6581]), ['final']). 6.97/7.24 cnf(c_0_11171, 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_6582]), ['final']). 6.97/7.24 cnf(c_0_11172, 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_6583, c_0_6584]), c_0_6585]), ['final']). 6.97/7.24 cnf(c_0_11173, 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_6586]), ['final']). 6.97/7.24 cnf(c_0_11174, 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_6587]), ['final']). 6.97/7.24 cnf(c_0_11175, 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_6588]), ['final']). 6.97/7.24 cnf(c_0_11176, 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_6401]), ['final']). 6.97/7.24 cnf(c_0_11177, plain, (X1=hAPP(hAPP(c_List_Olist_OCons(X2),esk112_5(X3,X1,X4,X5,X2)),esk113_5(X3,X1,X4,X5,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)),hAPP(hAPP(c_List_Olist_OCons(X2),X5),X4)),X1)),c_List_Olistrel(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_6347]), ['final']). 6.97/7.24 cnf(c_0_11178, plain, (X1=hAPP(hAPP(c_List_Olist_OCons(X2),esk30_5(X3,X4,X5,X1,X2)),esk31_5(X3,X4,X5,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),hAPP(hAPP(c_List_Olist_OCons(X2),X5),X4))),c_List_Olistrel(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_6344]), ['final']). 6.97/7.24 cnf(c_0_11179, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk451_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_6589, c_0_5174]), ['final']). 6.97/7.24 cnf(c_0_11180, 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_6590, c_0_4798]), c_0_4817]), c_0_4467]), ['final']). 6.97/7.24 cnf(c_0_11181, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk257_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3)))=X2|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))), inference(rw,[status(thm)],[c_0_6591, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11182, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk255_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk254_3(X1,X2,X3)))=X2|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk257_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))), inference(rw,[status(thm)],[c_0_6592, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11183, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk276_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk275_3(X1,X2,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)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))), inference(rw,[status(thm)],[c_0_6593, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11184, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk274_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk273_3(X1,X2,X3)))=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)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))), inference(rw,[status(thm)],[c_0_6594, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11185, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X5))|X3=X2|~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_6595]), ['final']). 6.97/7.24 cnf(c_0_11186, 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)),esk368_4(X3,X4,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_6039]), ['final']). 6.97/7.24 cnf(c_0_11187, plain, (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_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_6260]), ['final']). 6.97/7.24 cnf(c_0_11188, plain, (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))=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)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_6596]), ['final']). 6.97/7.24 cnf(c_0_11189, 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_6597]), ['final']). 6.97/7.24 cnf(c_0_11190, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk257_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(rw,[status(thm)],[c_0_6598, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11191, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk255_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk254_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk257_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(rw,[status(thm)],[c_0_6599, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11192, 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)))|esk509_5(X1,X2,X3,X4,X5)!=esk510_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_6102]), ['final']). 6.97/7.24 cnf(c_0_11193, 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)))|esk97_5(X1,X2,X3,X4,X5)!=esk96_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_6103]), ['final']). 6.97/7.24 cnf(c_0_11194, plain, (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))|~c_Relation_Osingle__valued(X1,X2,hAPP(c_Relation_Oconverse(X2,X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6600]), ['final']). 6.97/7.24 cnf(c_0_11195, 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_6601]), ['final']). 6.97/7.24 cnf(c_0_11196, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk268_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk267_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_6602, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11197, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk496_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk495_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_6603, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11198, 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_6604]), ['final']). 6.97/7.24 cnf(c_0_11199, 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_6605]), ['final']). 6.97/7.24 cnf(c_0_11200, 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_6606]), ['final']). 6.97/7.24 cnf(c_0_11201, 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_6607]), ['final']). 6.97/7.24 cnf(c_0_11202, 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_6608, c_0_6506]), c_0_4415]), c_0_6609]), c_0_5815]), c_0_4821]), c_0_6610]), c_0_6611]), c_0_4415]), c_0_4415]), ['final']). 6.97/7.24 cnf(c_0_11203, 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_6612]), ['final']). 6.97/7.24 cnf(c_0_11204, plain, (hBOOL(hAPP(X1,hAPP(c_Nat_OSuc,esk95_4(X2,X3,X4,X1))))|hBOOL(hAPP(X3,esk95_4(X2,X3,X4,X1)))|hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,X3))=c_Orderings_Oord__class_OLeast(tc_Nat_Onat,X1)|hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X3,X2))|~hBOOL(hAPP(X1,X4))), inference(split_conjunct,[status(thm)],[c_0_6613]), ['final']). 6.97/7.24 cnf(c_0_11205, 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),esk438_3(X1,X2,X3)),esk439_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_4482]), ['final']). 6.97/7.24 cnf(c_0_11206, 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_6614]), ['final']). 6.97/7.24 cnf(c_0_11207, 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_6615]), ['final']). 6.97/7.24 cnf(c_0_11208, 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_6616]), ['final']). 6.97/7.24 cnf(c_0_11209, 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_6617]), ['final']). 6.97/7.24 cnf(c_0_11210, 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_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_6618]), ['final']). 6.97/7.24 cnf(c_0_11211, 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),esk290_3(X1,X2,X3)),esk291_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_4488]), ['final']). 6.97/7.24 cnf(c_0_11212, 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),esk497_3(X1,X2,X3)),esk498_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_4968]), ['final']). 6.97/7.24 cnf(c_0_11213, 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),esk48_3(X1,X2,X3)),esk49_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_6490]), ['final']). 6.97/7.24 cnf(c_0_11214, 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),esk250_3(X1,X2,X3)),esk251_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_4997]), ['final']). 6.97/7.24 cnf(c_0_11215, plain, (hAPP(X1,esk128_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,esk127_3(X2,X1,X3)))),hAPP(X1,esk127_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_6619, c_0_6030]), ['final']). 6.97/7.24 cnf(c_0_11216, plain, (hAPP(X1,esk58_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,esk57_3(X2,X1,X3)))),hAPP(X1,esk57_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_6620, c_0_6030]), ['final']). 6.97/7.24 cnf(c_0_11217, 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_6621]), ['final']). 6.97/7.24 cnf(c_0_11218, 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)|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)),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_Fun_Oinj__on(X1,X2,X3,X5)), inference(split_conjunct,[status(thm)],[c_0_6271]), ['final']). 6.97/7.24 cnf(c_0_11219, 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_6622]), ['final']). 6.97/7.24 cnf(c_0_11220, 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),esk122_3(X1,X2,X3)),esk123_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_6552]), ['final']). 6.97/7.24 cnf(c_0_11221, 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))), inference(split_conjunct,[status(thm)],[c_0_6623]), ['final']). 6.97/7.24 cnf(c_0_11222, 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_6624]), ['final']). 6.97/7.24 cnf(c_0_11223, 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_6625]), ['final']). 6.97/7.24 cnf(c_0_11224, 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)), inference(split_conjunct,[status(thm)],[c_0_6626]), ['final']). 6.97/7.24 cnf(c_0_11225, 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_6627]), ['final']). 6.97/7.24 cnf(c_0_11226, plain, (c_List_OtakeWhile(X2,hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),hAPP(c_Orderings_Oord__class_Oless(X1),X5)),X3),X4)=hAPP(c_List_Ofilter(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_6628]), ['final']). 6.97/7.24 cnf(c_0_11227, 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),esk415_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_6629]), ['final']). 6.97/7.24 cnf(c_0_11228, 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)),X5)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),X6)),X5)|hBOOL(hAPP(hAPP(c_member(X1),esk517_6(X3,X2,X4,X6,X5,X1)),X5))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6630, c_0_4768]), c_0_4768]), ['final']). 6.97/7.24 cnf(c_0_11229, 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_6631]), ['final']). 6.97/7.24 cnf(c_0_11230, 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_6632]), ['final']). 6.97/7.24 cnf(c_0_11231, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_6633, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), ['final']). 6.97/7.24 cnf(c_0_11232, 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),esk100_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_6634, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11233, plain, (hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X4,X6))=hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X6)),hAPP(X4,X5))|~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_6635]), ['final']). 6.97/7.24 cnf(c_0_11234, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk319_6(X3,X4,X5,X2,X1,X6)),esk320_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_6636]), ['final']). 6.97/7.24 cnf(c_0_11235, 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_6637, c_0_4413]), ['final']). 6.97/7.24 cnf(c_0_11236, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_6638, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), ['final']). 6.97/7.24 cnf(c_0_11237, 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_6639]), ['final']). 6.97/7.24 cnf(c_0_11238, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk375_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_6530]), ['final']). 6.97/7.24 cnf(c_0_11239, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk195_5(X2,X3,X4,X5,X1)),X5))|c_Relation_Orefl__on(X4,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X5),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X5),X2))), inference(split_conjunct,[status(thm)],[c_0_6533]), ['final']). 6.97/7.24 cnf(c_0_11240, plain, (c_Wellfounded_Oacyclic(X1,X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk346_2(X2,X1)),esk346_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_6640, c_0_5174]), ['final']). 6.97/7.24 cnf(c_0_11241, 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_4956]), ['final']). 6.97/7.24 cnf(c_0_11242, plain, (c_Nitpick_Ofold__graph_H(X1,X4,X5,X6,X3,hAPP(hAPP(X5,X8),X9))|~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)|hAPP(hAPP(X5,X8),X9)!=hAPP(hAPP(X5,X2),X7)), inference(split_conjunct,[status(thm)],[c_0_6201]), ['final']). 6.97/7.24 cnf(c_0_11243, 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_6641]), ['final']). 6.97/7.24 cnf(c_0_11244, 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)), inference(split_conjunct,[status(thm)],[c_0_6642]), ['final']). 6.97/7.24 cnf(c_0_11245, plain, (c_Wellfounded_Oacyclic(X1,X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk51_2(X2,X1)),esk51_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_6643, c_0_5174]), ['final']). 6.97/7.24 cnf(c_0_11246, plain, (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_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)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_6644]), ['final']). 6.97/7.24 cnf(c_0_11247, plain, (hBOOL(hAPP(X1,esk415_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_6629]), ['final']). 6.97/7.24 cnf(c_0_11248, plain, (hBOOL(hAPP(X1,esk100_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_5042]), ['final']). 6.97/7.24 cnf(c_0_11249, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|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)),X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_5019]), ['final']). 6.97/7.24 cnf(c_0_11250, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk233_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_6645]), ['final']). 6.97/7.24 cnf(c_0_11251, 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)), inference(split_conjunct,[status(thm)],[c_0_6646]), ['final']). 6.97/7.24 cnf(c_0_11252, 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)|X5=X4|~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_6647]), ['final']). 6.97/7.24 cnf(c_0_11253, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))=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)|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_6648]), ['final']). 6.97/7.24 cnf(c_0_11254, 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),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)!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_6649]), ['final']). 6.97/7.24 cnf(c_0_11255, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4))=hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X4))|~c_Fun_Obij__betw(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_6650]), ['final']). 6.97/7.24 cnf(c_0_11256, 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_6651]), ['final']). 6.97/7.24 cnf(c_0_11257, 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_6652, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), ['final']). 6.97/7.24 cnf(c_0_11258, 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),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_6653, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), ['final']). 6.97/7.24 cnf(c_0_11259, 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)),esk63_3(X2,X3,X1))),X3)),X2))), inference(split_conjunct,[status(thm)],[c_0_6654]), ['final']). 6.97/7.24 cnf(c_0_11260, 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),X6),hAPP(hAPP(c_Set_Oinsert(X1),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_6655]), ['final']). 6.97/7.24 cnf(c_0_11261, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),hAPP(hAPP(X3,X5),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__idem(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_6656]), ['final']). 6.97/7.24 cnf(c_0_11262, 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_6657, c_0_6658]), ['final']). 6.97/7.24 cnf(c_0_11263, plain, (hAPP(c_List_Ofilter(X1,X3),X2)=c_List_OtakeWhile(X1,X3,X2)|hBOOL(hAPP(hAPP(c_member(X1),esk36_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_6659, c_0_4813]), ['final']). 6.97/7.24 cnf(c_0_11264, 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_6660]), ['final']). 6.97/7.24 cnf(c_0_11265, 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_6661]), ['final']). 6.97/7.24 cnf(c_0_11266, 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_6662]), ['final']). 6.97/7.24 cnf(c_0_11267, 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_6663]), ['final']). 6.97/7.24 cnf(c_0_11268, 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_6664]), ['final']). 6.97/7.24 cnf(c_0_11269, 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_6665]), ['final']). 6.97/7.24 cnf(c_0_11270, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk362_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_6666]), ['final']). 6.97/7.24 cnf(c_0_11271, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk317_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_6667]), ['final']). 6.97/7.24 cnf(c_0_11272, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk342_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_6668]), ['final']). 6.97/7.24 cnf(c_0_11273, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk324_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_6669]), ['final']). 6.97/7.24 cnf(c_0_11274, 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_6670]), ['final']). 6.97/7.24 cnf(c_0_11275, 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_6191]), ['final']). 6.97/7.24 cnf(c_0_11276, 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),esk354_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_6452]), ['final']). 6.97/7.24 cnf(c_0_11277, 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_Nat_Onat),c_Groups_Ozero__class_Ozero(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)],[c_0_6671, c_0_4742]), ['final']). 6.97/7.24 cnf(c_0_11278, 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)],[inference(rw,[status(thm)],[c_0_6672, c_0_4467]), c_0_4817]), ['final']). 6.97/7.24 cnf(c_0_11279, 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_6673]), ['final']). 6.97/7.24 cnf(c_0_11280, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk257_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3)))=X2|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))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))), inference(rw,[status(thm)],[c_0_6674, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11281, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk255_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk254_3(X1,X2,X3)))=X2|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)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))), inference(rw,[status(thm)],[c_0_6675, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11282, 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),esk376_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_6451]), ['final']). 6.97/7.24 cnf(c_0_11283, 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_6676]), ['final']). 6.97/7.24 cnf(c_0_11284, 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_6677]), ['final']). 6.97/7.24 cnf(c_0_11285, 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),esk328_4(X3,X2,X4,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6454]), ['final']). 6.97/7.24 cnf(c_0_11286, 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_6678]), ['final']). 6.97/7.24 cnf(c_0_11287, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk257_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(rw,[status(thm)],[c_0_6679, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11288, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk255_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk254_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(rw,[status(thm)],[c_0_6680, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11289, 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),esk424_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_6453]), ['final']). 6.97/7.24 cnf(c_0_11290, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk378_3(X2,X3,X1)),esk378_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_6681]), ['final']). 6.97/7.24 cnf(c_0_11291, plain, (hAPP(X1,X2)=hAPP(X1,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X3)),hAPP(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X3),X2)),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_6349]), ['final']). 6.97/7.24 cnf(c_0_11292, 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),esk568_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_6682]), ['final']). 6.97/7.24 cnf(c_0_11293, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk482_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))|X6=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_6683]), ['final']). 6.97/7.24 cnf(c_0_11294, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk363_4(X1,X2,X3,X4)),esk362_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),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_6666]), ['final']). 6.97/7.24 cnf(c_0_11295, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk318_4(X1,X2,X3,X4)),esk317_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_6667]), ['final']). 6.97/7.24 cnf(c_0_11296, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk343_4(X1,X2,X3,X4)),esk342_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_6668]), ['final']). 6.97/7.24 cnf(c_0_11297, plain, (X1=c_List_Olist_ONil(X2)|hAPP(hAPP(c_List_Onth(X2),X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)))=hAPP(c_List_Ohd(X2),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X2),tc_List_Olist(X2)),X3),c_List_Orotate1(X2)),X1))), inference(rw,[status(thm)],[c_0_6684, c_0_5794]), ['final']). 6.97/7.24 cnf(c_0_11298, 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_6685]), ['final']). 6.97/7.24 cnf(c_0_11299, 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),esk106_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_6686]), ['final']). 6.97/7.24 cnf(c_0_11300, plain, (X1=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk325_4(X2,X3,X4,X1)),esk324_4(X2,X3,X4,X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X4)))|~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)),X4))), inference(split_conjunct,[status(thm)],[c_0_6669]), ['final']). 6.97/7.24 cnf(c_0_11301, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_3(X2,X3,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X2,X3,X1)),X2))|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)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.24 cnf(c_0_11302, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),esk276_3(X2,X3,X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk274_3(X2,X3,X1)))|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)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.24 cnf(c_0_11303, 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_6687, c_0_4471]), c_0_4471]), ['final']). 6.97/7.24 cnf(c_0_11304, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X3)))|~c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X3)))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4))), inference(er,[status(thm)],[c_0_6688]), ['final']). 6.97/7.24 cnf(c_0_11305, 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_6689]), ['final']). 6.97/7.24 cnf(c_0_11306, 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_6690, c_0_6506]), c_0_4415]), c_0_6609]), c_0_5815]), c_0_4821]), c_0_6610]), c_0_6691]), c_0_4415]), c_0_4415]), ['final']). 6.97/7.24 cnf(c_0_11307, 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_6692]), ['final']). 6.97/7.24 cnf(c_0_11308, 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_Olist_OCons(X3),X2),X4)|hBOOL(hAPP(X1,X2))), inference(rw,[status(thm)],[c_0_6693, c_0_4813]), ['final']). 6.97/7.24 cnf(c_0_11309, 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_6694]), ['final']). 6.97/7.24 cnf(c_0_11310, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.24 cnf(c_0_11311, 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_6695]), ['final']). 6.97/7.24 cnf(c_0_11312, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk274_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk273_3(X1,X2,X3)))=X2|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk275_3(X1,X2,X3)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_6696, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11313, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk276_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk275_3(X1,X2,X3)))=X2|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk273_3(X1,X2,X3)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_6697, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11314, 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_6698]), ['final']). 6.97/7.24 cnf(c_0_11315, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk276_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk274_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.24 cnf(c_0_11316, plain, (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))=hAPP(c_Set_Oimage(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,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_6699]), ['final']). 6.97/7.24 cnf(c_0_11317, 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_6700]), ['final']). 6.97/7.24 cnf(c_0_11318, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X2),X1)),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),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X6))),c_List_Olexord(X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_4930]), ['final']). 6.97/7.24 cnf(c_0_11319, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk327_5(X2,X3,X4,X5,X1)),X5))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X5),X3)),X2))), inference(split_conjunct,[status(thm)],[c_0_6701]), ['final']). 6.97/7.24 cnf(c_0_11320, 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),hAPP(hAPP(c_List_Oappend(X2),X3),X4)),X1)=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)))), inference(split_conjunct,[status(thm)],[c_0_6702]), ['final']). 6.97/7.24 cnf(c_0_11321, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk556_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_6502]), ['final']). 6.97/7.24 cnf(c_0_11322, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk543_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_6503]), ['final']). 6.97/7.24 cnf(c_0_11323, 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_6703, c_0_5202]), ['final']). 6.97/7.24 cnf(c_0_11324, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk252_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_6704]), ['final']). 6.97/7.24 cnf(c_0_11325, 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_4932]), ['final']). 6.97/7.24 cnf(c_0_11326, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),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)),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_6216]), ['final']). 6.97/7.24 cnf(c_0_11327, 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)))|~c_Fun_Obij__betw(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_6705, c_0_4768]), ['final']). 6.97/7.24 cnf(c_0_11328, 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_Obij__betw(X1,X2,X4,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),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)),X3),hAPP(c_Set_Oimage(X1,X2,X4),X5)))), inference(rw,[status(thm)],[c_0_6706, c_0_4768]), ['final']). 6.97/7.24 cnf(c_0_11329, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk155_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_6707]), ['final']). 6.97/7.24 cnf(c_0_11330, 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_6708]), ['final']). 6.97/7.24 cnf(c_0_11331, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk274_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk273_3(X1,X2,X3)))=X2|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk275_3(X1,X2,X3)))), inference(rw,[status(thm)],[c_0_6709, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11332, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk276_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk275_3(X1,X2,X3)))=X2|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk273_3(X1,X2,X3)))), inference(rw,[status(thm)],[c_0_6710, c_0_5815]), ['final']). 6.97/7.24 cnf(c_0_11333, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk107_5(X2,X3,X4,X5,X1)),X5))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X5),X2)))), inference(split_conjunct,[status(thm)],[c_0_6711]), ['final']). 6.97/7.24 cnf(c_0_11334, plain, (hBOOL(hAPP(X1,esk559_4(X1,X2,X3,X4)))|hBOOL(hAPP(hAPP(c_member(X4),esk558_4(X1,X2,X3,X4)),X3))|~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_6508]), ['final']). 6.97/7.24 cnf(c_0_11335, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk559_4(X2,X3,X4,X1)),X3))|hBOOL(hAPP(X2,esk558_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_6508]), ['final']). 6.97/7.24 cnf(c_0_11336, plain, (hBOOL(hAPP(hAPP(c_member(X4),hAPP(X5,X2)),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X4,tc_HOL_Obool),X6)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X4,X5),X3)),hAPP(X6,hAPP(c_Set_Oimage(X1,X4,X5),X3))))), inference(split_conjunct,[status(thm)],[c_0_6712]), ['final']). 6.97/7.24 cnf(c_0_11337, plain, (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))=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)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6713]), ['final']). 6.97/7.24 cnf(c_0_11338, plain, (c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X1|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_5828]), ['final']). 6.97/7.24 cnf(c_0_11339, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk157_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_5291]), ['final']). 6.97/7.24 cnf(c_0_11340, plain, (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)))|c_Wellfounded_Oacyclic(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2))|~c_Wellfounded_Oacyclic(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_6714]), ['final']). 6.97/7.24 cnf(c_0_11341, 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_6715]), ['final']). 6.97/7.24 cnf(c_0_11342, 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_6716]), ['final']). 6.97/7.24 cnf(c_0_11343, 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_6717]), ['final']). 6.97/7.24 cnf(c_0_11344, plain, (hBOOL(hAPP(hAPP(c_member(X1),X6),X5))|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(X1,X2,X3,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))), inference(split_conjunct,[status(thm)],[c_0_6718]), ['final']). 6.97/7.24 cnf(c_0_11345, 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_6719]), ['final']). 6.97/7.24 cnf(c_0_11346, 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_6720]), ['final']). 6.97/7.24 cnf(c_0_11347, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk496_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_5035]), ['final']). 6.97/7.24 cnf(c_0_11348, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk268_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_5034]), ['final']). 6.97/7.24 cnf(c_0_11349, 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)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)))|hAPP(hAPP(c_List_Oappend(X2),X1),X4)!=hAPP(hAPP(c_List_Oappend(X2),X3),X5)), inference(split_conjunct,[status(thm)],[c_0_4956]), ['final']). 6.97/7.25 cnf(c_0_11350, 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_6721]), ['final']). 6.97/7.25 cnf(c_0_11351, plain, (c_Fun_Obij__betw(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X5),X7))|~c_Fun_Obij__betw(X1,X2,X3,X4,X5)|~c_Fun_Obij__betw(X1,X2,X3,X6,X7)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X5),X7)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_6722]), ['final']). 6.97/7.25 cnf(c_0_11352, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk265_4(X1,X2,X3,X4)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk264_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_4971]), ['final']). 6.97/7.25 cnf(c_0_11353, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk70_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_6723]), ['final']). 6.97/7.25 cnf(c_0_11354, plain, (c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Set_Oimage(X1,X4,hAPP(c_Fun_Ocomp(X2,X4,X1,X5),X3)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|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))|hAPP(c_Set_Oimage(X2,X4,X5),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_6724]), ['final']). 6.97/7.25 cnf(c_0_11355, 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),esk32_4(X4,X3,X2,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_6725]), ['final']). 6.97/7.25 cnf(c_0_11356, 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,esk129_7(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,X5)))|~hBOOL(hAPP(X2,X4))), inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_6726])]), ['final']). 6.97/7.25 cnf(c_0_11357, 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)],[c_0_6727, c_0_6728]), c_0_5947]), ['final']). 6.97/7.25 cnf(c_0_11358, 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_6729, c_0_5746]), ['final']). 6.97/7.25 cnf(c_0_11359, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk265_4(X2,X3,X4,X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk264_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_4971]), ['final']). 6.97/7.25 cnf(c_0_11360, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X4))=hAPP(c_Set_Oimage(X1,X2,X4),X3)|~c_Fun_Obij__betw(X1,X2,X4,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)],[inference(rw,[status(thm)],[c_0_6730, c_0_4467]), c_0_4467]), ['final']). 6.97/7.25 cnf(c_0_11361, plain, (X1=hAPP(X2,esk265_4(X1,X2,X3,X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk264_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_4971]), ['final']). 6.97/7.25 cnf(c_0_11362, plain, (X1=hAPP(X2,esk265_4(X1,X2,X3,X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),esk264_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_4971]), ['final']). 6.97/7.25 cnf(c_0_11363, 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_6731, c_0_4817]), ['final']). 6.97/7.25 cnf(c_0_11364, 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,esk86_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_6732])]), ['final']). 6.97/7.25 cnf(c_0_11365, 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_6733, c_0_4817]), ['final']). 6.97/7.25 cnf(c_0_11366, 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_6734, c_0_4817]), ['final']). 6.97/7.25 cnf(c_0_11367, 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,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X2)),X3),X4)),X1)=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)))), inference(split_conjunct,[status(thm)],[c_0_6735]), ['final']). 6.97/7.25 cnf(c_0_11368, plain, (c_List_Olist_ONil(X1)=X2|hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_List_Onth(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3)=hAPP(c_List_Ofoldl(X1,X1,hAPP(c_COMBC(X1,X1,X1),c_Orderings_Oord__class_Omax(X1)),X3),hAPP(c_List_Orev(X1),X2))|~class_Orderings_Olinorder(X1)|~c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Orev(X1),X2))), inference(rw,[status(thm)],[c_0_6736, c_0_4632]), ['final']). 6.97/7.25 cnf(c_0_11369, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),hAPP(c_List_Oset(X4),X5))))|c_List_Olinorder__class_Oinsort__insert__key(X4,X1,X2,X3,X5)=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X1,X2),X3),X5)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6737]), ['final']). 6.97/7.25 cnf(c_0_11370, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk79_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_5466]), ['final']). 6.97/7.25 cnf(c_0_11371, 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_6738]), ['final']). 6.97/7.25 cnf(c_0_11372, 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)],[c_0_6739, c_0_6423]), c_0_4781]), ['final']). 6.97/7.25 cnf(c_0_11373, 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)],[c_0_6740, c_0_6423]), c_0_4781]), ['final']). 6.97/7.25 cnf(c_0_11374, 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_6741]), ['final']). 6.97/7.25 cnf(c_0_11375, plain, (X1=hAPP(hAPP(X2,X3),X4)|hAPP(hAPP(X2,X3),X4)=hAPP(hAPP(X2,esk212_7(X4,X3,X5,X1,X2,X6,X7)),esk213_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_6201]), ['final']). 6.97/7.25 cnf(c_0_11376, plain, (hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X4),X5),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X2)))),X1)=hAPP(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),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_6742, c_0_4471]), ['final']). 6.97/7.25 cnf(c_0_11377, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk503_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_6743]), ['final']). 6.97/7.25 cnf(c_0_11378, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk326_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)))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6744]), ['final']). 6.97/7.25 cnf(c_0_11379, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk20_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)))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Lattices_Osemilattice__inf(X1)), inference(split_conjunct,[status(thm)],[c_0_6745]), ['final']). 6.97/7.25 cnf(c_0_11380, 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_6746]), ['final']). 6.97/7.25 cnf(c_0_11381, 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_6747]), ['final']). 6.97/7.25 cnf(c_0_11382, plain, (hBOOL(hAPP(hAPP(X1,X4),X3))|~hBOOL(hAPP(hAPP(X1,esk336_6(X1,X2,X3,X4,X5,X6)),esk337_6(X1,X2,X3,X4,X5,X6)))|~c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(X6,X5),tc_HOL_Obool),tc_fun(tc_prod(X6,X5),tc_HOL_Obool),X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X5)),hAPP(hAPP(c_Product__Type_OPair(X6,X5),X4),X3)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(X6,X5),tc_HOL_Obool),X2)))), inference(split_conjunct,[status(thm)],[c_0_4809]), ['final']). 6.97/7.25 cnf(c_0_11383, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(X3,esk511_6(X4,X3,X5,X6,X2,X1)),esk512_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_6748]), ['final']). 6.97/7.25 cnf(c_0_11384, 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_6749]), ['final']). 6.97/7.25 cnf(c_0_11385, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X3)),c_Int_OMin)))=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)],[c_0_6750, c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_11386, 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_6751]), ['final']). 6.97/7.25 cnf(c_0_11387, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X2)))))|~c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X2)))), inference(split_conjunct,[status(thm)],[c_0_6752]), ['final']). 6.97/7.25 cnf(c_0_11388, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(X3,X4)),hAPP(X3,X5))),hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X4),X5))))|~class_Lattices_Osemilattice__sup(X1)|~class_Lattices_Osemilattice__sup(X2)|~c_Orderings_Oorder__class_Omono(X2,X1,X3)), inference(split_conjunct,[status(thm)],[c_0_6753]), ['final']). 6.97/7.25 cnf(c_0_11389, 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_6754]), ['final']). 6.97/7.25 cnf(c_0_11390, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hAPP(hAPP(X3,X4),X5)=hAPP(hAPP(X3,esk212_7(X5,X4,X1,X6,X3,X7,X2)),esk213_7(X5,X4,X1,X6,X3,X7,X2))|~c_Nitpick_Ofold__graph_H(X2,X7,X3,X6,X1,hAPP(hAPP(X3,X4),X5))), inference(split_conjunct,[status(thm)],[c_0_6201]), ['final']). 6.97/7.25 cnf(c_0_11391, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),esk236_5(X3,X4,X1,X5,X2)),X3)|hAPP(hAPP(c_List_Oappend(X2),esk235_5(X3,X4,X1,X5,X2)),X1)=X3|hAPP(hAPP(c_List_Oappend(X2),X4),X3)!=hAPP(hAPP(c_List_Oappend(X2),X5),X1)), inference(split_conjunct,[status(thm)],[c_0_6755]), ['final']). 6.97/7.25 cnf(c_0_11392, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),X3),esk236_5(X4,X1,X5,X3,X2))|hAPP(hAPP(c_List_Oappend(X2),esk235_5(X4,X1,X5,X3,X2)),X5)=X4|hAPP(hAPP(c_List_Oappend(X2),X1),X4)!=hAPP(hAPP(c_List_Oappend(X2),X3),X5)), inference(split_conjunct,[status(thm)],[c_0_6755]), ['final']). 6.97/7.25 cnf(c_0_11393, 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_6756]), ['final']). 6.97/7.25 cnf(c_0_11394, 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_6757, c_0_6758]), ['final']). 6.97/7.25 cnf(c_0_11395, 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_6759, c_0_4467]), ['final']). 6.97/7.25 cnf(c_0_11396, 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)), inference(rw,[status(thm)],[c_0_6760, c_0_4632]), ['final']). 6.97/7.25 cnf(c_0_11397, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),esk236_5(X3,X4,X1,X5,X2)),X3)|X5=hAPP(hAPP(c_List_Oappend(X2),X4),esk235_5(X3,X4,X1,X5,X2))|hAPP(hAPP(c_List_Oappend(X2),X4),X3)!=hAPP(hAPP(c_List_Oappend(X2),X5),X1)), inference(split_conjunct,[status(thm)],[c_0_6755]), ['final']). 6.97/7.25 cnf(c_0_11398, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),X3),esk236_5(X4,X1,X5,X3,X2))|X3=hAPP(hAPP(c_List_Oappend(X2),X1),esk235_5(X4,X1,X5,X3,X2))|hAPP(hAPP(c_List_Oappend(X2),X1),X4)!=hAPP(hAPP(c_List_Oappend(X2),X3),X5)), inference(split_conjunct,[status(thm)],[c_0_6755]), ['final']). 6.97/7.25 cnf(c_0_11399, plain, (hBOOL(hAPP(hAPP(c_member(X2),X8),X7))|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(X1,X2,X3,X4,X5,X6)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7))), inference(split_conjunct,[status(thm)],[c_0_6761]), ['final']). 6.97/7.25 cnf(c_0_11400, 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,esk446_3(X3,X2,X1)))),c_Predicate_ORangeP(X1,X1,hAPP(X2,esk447_3(X3,X2,X1))))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~c_Wellfounded_OwfP(X1,hAPP(X2,esk445_3(X3,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_6762]), ['final']). 6.97/7.25 cnf(c_0_11401, 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_6763, c_0_5941]), c_0_5746]), c_0_5941]), ['final']). 6.97/7.25 cnf(c_0_11402, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_6764, c_0_4409]), c_0_4410]), c_0_4411]), ['final']). 6.97/7.25 cnf(c_0_11403, 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_6765]), ['final']). 6.97/7.25 cnf(c_0_11404, 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_6766]), ['final']). 6.97/7.25 cnf(c_0_11405, 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_6767]), ['final']). 6.97/7.25 cnf(c_0_11406, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X5|hAPP(X3,hAPP(c_Set_Oimage(X1,X1,X4),X5))=hAPP(X4,hAPP(X3,X5))|~c_Finite__Set_Ofolding__one__idem(X1,X2,X3)|hAPP(hAPP(X2,hAPP(X4,esk594_5(X5,X4,X3,X2,X1))),hAPP(X4,esk595_5(X5,X4,X3,X2,X1)))!=hAPP(X4,hAPP(hAPP(X2,esk594_5(X5,X4,X3,X2,X1)),esk595_5(X5,X4,X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))), inference(split_conjunct,[status(thm)],[c_0_6768]), ['final']). 6.97/7.25 cnf(c_0_11407, plain, (hBOOL(hAPP(X1,esk121_2(X1,X2)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk118_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk119_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,esk118_2(X1,X2)))|~hBOOL(hAPP(X1,X3))), inference(rw,[status(thm)],[c_0_6769, c_0_6285]), ['final']). 6.97/7.25 cnf(c_0_11408, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk260_4(X3,X4,X1,X2)),esk261_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_6770]), ['final']). 6.97/7.25 cnf(c_0_11409, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|hAPP(c_New__DSequence_Oneg__decr__bind(X2,X3,X4,X5),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))), inference(split_conjunct,[status(thm)],[c_0_5853]), ['final']). 6.97/7.25 cnf(c_0_11410, 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_6771]), ['final']). 6.97/7.25 cnf(c_0_11411, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),hAPP(X3,X4)),hAPP(X3,X5))),hAPP(X3,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X5))))|~class_Orderings_Olinorder(X1)|~class_Lattices_Osemilattice__sup(X2)|~c_Orderings_Oorder__class_Omono(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_6772]), ['final']). 6.97/7.25 cnf(c_0_11412, 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_6773]), ['final']). 6.97/7.25 cnf(c_0_11413, 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_5852]), ['final']). 6.97/7.25 cnf(c_0_11414, 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_6774]), ['final']). 6.97/7.25 cnf(c_0_11415, 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_6775]), ['final']). 6.97/7.25 cnf(c_0_11416, 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(X3,hAPP(X5,esk568_8(X3,X7,hAPP(c_Set_Oimage(X4,X1,X5),X6),X6,X5,X1,X4,X2)))!=hAPP(X7,esk568_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_6776, c_0_6208])]), ['final']). 6.97/7.25 cnf(c_0_11417, 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_6777]), ['final']). 6.97/7.25 cnf(c_0_11418, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk314_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_6778, c_0_5038]), ['final']). 6.97/7.25 cnf(c_0_11419, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk248_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_Ominus__class_Ominus(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_6779, c_0_4741]), ['final']). 6.97/7.25 cnf(c_0_11420, 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,X1))), inference(rw,[status(thm)],[c_0_6780, c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_11421, plain, (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)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,X4)))|~hBOOL(hAPP(hAPP(c_member(X5),X4),X6))), inference(split_conjunct,[status(thm)],[c_0_6781]), ['final']). 6.97/7.25 cnf(c_0_11422, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk400_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_4931]), ['final']). 6.97/7.25 cnf(c_0_11423, 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_6782, c_0_6783]), c_0_6783]), ['final']). 6.97/7.25 cnf(c_0_11424, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X4|X5=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|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__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_6784]), ['final']). 6.97/7.25 cnf(c_0_11425, 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_6785, c_0_6208]), ['final']). 6.97/7.25 cnf(c_0_11426, 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_6786, c_0_6208]), ['final']). 6.97/7.25 cnf(c_0_11427, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X1,X2,X3)),X1))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_11428, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk257_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk255_3(X1,X2,X3)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_11429, 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_6787, c_0_6006]), ['final']). 6.97/7.25 cnf(c_0_11430, 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_6788, c_0_6006]), ['final']). 6.97/7.25 cnf(c_0_11431, plain, (hAPP(c_Finite__Set_Ocard(X2),X5)=hAPP(c_Finite__Set_Ocard(X1),X4)|~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_6789]), ['final']). 6.97/7.25 cnf(c_0_11432, 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_6790]), ['final']). 6.97/7.25 cnf(c_0_11433, 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_6791, c_0_5824]), ['final']). 6.97/7.25 cnf(c_0_11434, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk268_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_5034]), ['final']). 6.97/7.25 cnf(c_0_11435, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk496_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_5035]), ['final']). 6.97/7.25 cnf(c_0_11436, 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)), inference(split_conjunct,[status(thm)],[c_0_6792]), ['final']). 6.97/7.25 cnf(c_0_11437, plain, (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),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),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_6793]), ['final']). 6.97/7.25 cnf(c_0_11438, 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_6794]), ['final']). 6.97/7.25 cnf(c_0_11439, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)),X4)|~class_Divides_Osemiring__div(X1)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6795]), ['final']). 6.97/7.25 cnf(c_0_11440, 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)))|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_6796, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4821]), ['final']). 6.97/7.25 cnf(c_0_11441, 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_6797, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_6506]), ['final']). 6.97/7.25 cnf(c_0_11442, 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),esk32_4(X1,X3,X2,X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_6725]), ['final']). 6.97/7.25 cnf(c_0_11443, 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_6798]), ['final']). 6.97/7.25 cnf(c_0_11444, 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_6799]), ['final']). 6.97/7.25 cnf(c_0_11445, 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_6800]), ['final']). 6.97/7.25 cnf(c_0_11446, 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_6801]), ['final']). 6.97/7.25 cnf(c_0_11447, 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_6802, c_0_4415]), c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_11448, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_11449, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk257_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk255_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_11450, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(X3,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X5))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),hAPP(X3,X4)),hAPP(X3,X5))))|~class_Orderings_Olinorder(X1)|~class_Lattices_Osemilattice__inf(X2)|~c_Orderings_Oorder__class_Omono(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_6803]), ['final']). 6.97/7.25 cnf(c_0_11451, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X5))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),hAPP(X3,X4)),hAPP(X3,X5))))|~class_Lattices_Osemilattice__inf(X1)|~class_Lattices_Osemilattice__inf(X2)|~c_Orderings_Oorder__class_Omono(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_6804]), ['final']). 6.97/7.25 cnf(c_0_11452, 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))|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_6805]), ['final']). 6.97/7.25 cnf(c_0_11453, plain, (hAPP(hAPP(c_List_Otake(X1),X4),X2)=hAPP(hAPP(c_List_Otake(X1),X4),X3)|hAPP(hAPP(c_List_Onth(X1),X2),esk70_4(X3,X2,X1,X4))!=hAPP(hAPP(c_List_Onth(X1),X3),esk70_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(X1)),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))), inference(split_conjunct,[status(thm)],[c_0_6723]), ['final']). 6.97/7.25 cnf(c_0_11454, 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_6806]), ['final']). 6.97/7.25 cnf(c_0_11455, 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_6807]), ['final']). 6.97/7.25 cnf(c_0_11456, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X6),X3)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),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_6808]), ['final']). 6.97/7.25 cnf(c_0_11457, 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)),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_6809]), ['final']). 6.97/7.25 cnf(c_0_11458, 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_6810, c_0_6811]), ['final']). 6.97/7.25 cnf(c_0_11459, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk93_4(X2,X3,X1,X4)),X3))|c_Groups_Oone__class_Oone(X4)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X4,X1,c_Groups_Otimes__class_Otimes(X4)),X2),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_6812]), ['final']). 6.97/7.25 cnf(c_0_11460, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk120_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),esk118_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk119_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,esk118_2(X1,X2)))|~hBOOL(hAPP(X1,X3))), inference(rw,[status(thm)],[c_0_6813, c_0_6285]), ['final']). 6.97/7.25 cnf(c_0_11461, plain, (hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X3,X6)),hAPP(X4,X5))=hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),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_6814]), ['final']). 6.97/7.25 cnf(c_0_11462, 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_6815]), ['final']). 6.97/7.25 cnf(c_0_11463, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk165_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_6816]), ['final']). 6.97/7.25 cnf(c_0_11464, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk257_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3)))=X2|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk255_3(X1,X2,X3)))), inference(rw,[status(thm)],[c_0_6817, c_0_5815]), ['final']). 6.97/7.25 cnf(c_0_11465, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk255_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk254_3(X1,X2,X3)))=X2|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk257_3(X1,X2,X3)))), inference(rw,[status(thm)],[c_0_6818, c_0_5815]), ['final']). 6.97/7.25 cnf(c_0_11466, 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_6819, c_0_6820]), ['final']). 6.97/7.25 cnf(c_0_11467, 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_6821]), ['final']). 6.97/7.25 cnf(c_0_11468, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,esk440_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_6822]), ['final']). 6.97/7.25 cnf(c_0_11469, 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_6823, c_0_4734]), c_0_4734]), ['final']). 6.97/7.25 cnf(c_0_11470, 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_6824]), ['final']). 6.97/7.25 cnf(c_0_11471, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X1),X3),X2)=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))|~class_Groups_Ocomm__monoid__mult(X1)|~class_Groups_Ocomm__monoid__add(X1)|~c_Nat__Transfer_Onat__set(X2)), inference(split_conjunct,[status(thm)],[c_0_6825]), ['final']). 6.97/7.25 cnf(c_0_11472, 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_6826]), ['final']). 6.97/7.25 cnf(c_0_11473, 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_6827]), ['final']). 6.97/7.25 cnf(c_0_11474, 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_6828, c_0_6829]), c_0_6829]), ['final']). 6.97/7.25 cnf(c_0_11475, 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_6830, c_0_6252]), c_0_6253]), ['final']). 6.97/7.25 cnf(c_0_11476, 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|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__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_6831]), ['final']). 6.97/7.25 cnf(c_0_11477, 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_6832]), ['final']). 6.97/7.25 cnf(c_0_11478, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk257_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3)))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk255_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X2))), inference(rw,[status(thm)],[c_0_6833, c_0_5815]), ['final']). 6.97/7.25 cnf(c_0_11479, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk255_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk254_3(X1,X2,X3)))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk257_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X2))), inference(rw,[status(thm)],[c_0_6834, c_0_5815]), ['final']). 6.97/7.25 cnf(c_0_11480, 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),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_6835]), ['final']). 6.97/7.25 cnf(c_0_11481, plain, (hBOOL(hAPP(hAPP(c_member(X4),esk534_4(X1,X2,X3,X4)),X2))|hBOOL(hAPP(X1,X5))|~hBOOL(hAPP(X1,esk535_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_6414]), ['final']). 6.97/7.25 cnf(c_0_11482, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk535_4(X2,X3,X4,X1)),X4))|hBOOL(hAPP(X2,X5))|~hBOOL(hAPP(X2,esk534_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_6414]), ['final']). 6.97/7.25 cnf(c_0_11483, plain, (X1=hAPP(hAPP(c_List_Olist__update(X2,X3),esk400_4(X4,X1,X3,X2)),esk399_4(X4,X1,X3,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)),X3),X1)),c_List_Olistrel1(X2,X4)))), inference(split_conjunct,[status(thm)],[c_0_4931]), ['final']). 6.97/7.25 cnf(c_0_11484, 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_6836])]), ['final']). 6.97/7.25 cnf(c_0_11485, 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__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6837]), ['final']). 6.97/7.25 cnf(c_0_11486, 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),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))|~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_6838]), ['final']). 6.97/7.25 cnf(c_0_11487, 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_6839]), ['final']). 6.97/7.25 cnf(c_0_11488, 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)), inference(split_conjunct,[status(thm)],[c_0_6840]), ['final']). 6.97/7.25 cnf(c_0_11489, 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|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))|~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_6841]), ['final']). 6.97/7.25 cnf(c_0_11490, plain, (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)))))=c_List_Oremove1(X1,X3,c_List_Olinorder__class_Osorted__list__of__set(X1,X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_6842]), ['final']). 6.97/7.25 cnf(c_0_11491, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5)=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))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6843]), ['final']). 6.97/7.25 cnf(c_0_11492, 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_6844]), ['final']). 6.97/7.25 cnf(c_0_11493, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)))=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)],[c_0_6845, c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_11494, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X4)),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X4|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6846]), ['final']). 6.97/7.25 cnf(c_0_11495, 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))|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__eq(X1),X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6847]), ['final']). 6.97/7.25 cnf(c_0_11496, plain, (X5=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(X3,X4)=hAPP(hAPP(X2,hAPP(X3,X5)),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_6848]), ['final']). 6.97/7.25 cnf(c_0_11497, 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)), inference(split_conjunct,[status(thm)],[c_0_6849]), ['final']). 6.97/7.25 cnf(c_0_11498, 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_6850]), ['final']). 6.97/7.25 cnf(c_0_11499, 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_6851, c_0_5746]), ['final']). 6.97/7.25 cnf(c_0_11500, 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_6852]), ['final']). 6.97/7.25 cnf(c_0_11501, 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)))|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_List_Oset(X1),esk288_2(X2,X1))),hAPP(c_List_Oset(X1),esk289_2(X2,X1)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),esk287_2(X2,X1)))), inference(rw,[status(thm)],[c_0_6853, c_0_4645]), ['final']). 6.97/7.25 cnf(c_0_11502, 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_6854]), ['final']). 6.97/7.25 cnf(c_0_11503, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk322_5(X2,X3,X4,X5,X1)),X5))|hBOOL(hAPP(hAPP(c_member(X4),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X5),X2)))), inference(split_conjunct,[status(thm)],[c_0_6855]), ['final']). 6.97/7.25 cnf(c_0_11504, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X5),X3)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),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_6856]), ['final']). 6.97/7.25 cnf(c_0_11505, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk169_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_6857]), ['final']). 6.97/7.25 cnf(c_0_11506, 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_6858]), ['final']). 6.97/7.25 cnf(c_0_11507, 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_6859]), ['final']). 6.97/7.25 cnf(c_0_11508, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk102_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_6860]), ['final']). 6.97/7.25 cnf(c_0_11509, 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_4952]), ['final']). 6.97/7.25 cnf(c_0_11510, 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),esk21_3(X3,X2,X1))!=X3|esk23_3(X3,X2,X1)!=esk22_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_6861, c_0_6281]), ['final']). 6.97/7.25 cnf(c_0_11511, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk366_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_6862]), ['final']). 6.97/7.25 cnf(c_0_11512, 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_6863]), ['final']). 6.97/7.25 cnf(c_0_11513, 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_6864]), ['final']). 6.97/7.25 cnf(c_0_11514, 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_6865]), ['final']). 6.97/7.25 cnf(c_0_11515, 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_6866]), ['final']). 6.97/7.25 cnf(c_0_11516, 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_6867, c_0_4768]), ['final']). 6.97/7.25 cnf(c_0_11517, plain, (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),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),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6835]), ['final']). 6.97/7.25 cnf(c_0_11518, plain, (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),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),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),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_6837]), ['final']). 6.97/7.25 cnf(c_0_11519, 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_6837]), ['final']). 6.97/7.25 cnf(c_0_11520, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4),X3))=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))|~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_6868]), ['final']). 6.97/7.25 cnf(c_0_11521, plain, (hBOOL(hAPP(X4,X2))|hBOOL(hAPP(hAPP(c_member(X1),esk533_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_6414]), ['final']). 6.97/7.25 cnf(c_0_11522, plain, (hBOOL(hAPP(X4,X2))|hBOOL(hAPP(hAPP(c_member(X1),esk533_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_6414]), ['final']). 6.97/7.25 cnf(c_0_11523, plain, (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),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__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6835]), ['final']). 6.97/7.25 cnf(c_0_11524, 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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),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_6838]), ['final']). 6.97/7.25 cnf(c_0_11525, 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_6839]), ['final']). 6.97/7.25 cnf(c_0_11526, 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_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))|~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),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_6835]), ['final']). 6.97/7.25 cnf(c_0_11527, 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_6869]), ['final']). 6.97/7.25 cnf(c_0_11528, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))|~class_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(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_6870, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), ['final']). 6.97/7.25 cnf(c_0_11529, 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),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),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),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_6837]), ['final']). 6.97/7.25 cnf(c_0_11530, 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),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))|~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_6838]), ['final']). 6.97/7.25 cnf(c_0_11531, 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),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)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6838]), ['final']). 6.97/7.25 cnf(c_0_11532, 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_6839]), ['final']). 6.97/7.25 cnf(c_0_11533, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(esk592_2(X2,X1),hAPP(c_Nat_OSuc,X3))),hAPP(esk592_2(X2,X1),X3))),X2))|c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_6871]), ['final']). 6.97/7.25 cnf(c_0_11534, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))|~class_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(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_6872, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), ['final']). 6.97/7.25 cnf(c_0_11535, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~class_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(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_6873, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), ['final']). 6.97/7.25 cnf(c_0_11536, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~class_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(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_6874, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), ['final']). 6.97/7.25 cnf(c_0_11537, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_3(X2,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)),esk274_3(X2,X3,X1)))|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)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.25 cnf(c_0_11538, 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_6839]), ['final']). 6.97/7.25 cnf(c_0_11539, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))|~class_Enum_Oenum(X1)|~class_Orderings_Oorder(X2)|~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_6875, c_0_5065]), ['final']). 6.97/7.25 cnf(c_0_11540, 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),X3),hAPP(hAPP(c_List_Olist_OCons(X5),X2),c_List_Olist_ONil(X5)))),hAPP(hAPP(c_List_Oappend(X5),X4),hAPP(hAPP(c_List_Olist_OCons(X5),X1),c_List_Olist_ONil(X5))))),c_List_Olistrel1(X5,X6)))), inference(split_conjunct,[status(thm)],[c_0_6109]), ['final']). 6.97/7.25 cnf(c_0_11541, 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_6876, c_0_6877]), ['final']). 6.97/7.25 cnf(c_0_11542, 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_6878]), ['final']). 6.97/7.25 cnf(c_0_11543, 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_6879, c_0_6880]), c_0_6881]), ['final']). 6.97/7.25 cnf(c_0_11544, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2))=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)|~class_Fields_Ofield(X1)), inference(split_conjunct,[status(thm)],[c_0_6882]), ['final']). 6.97/7.25 cnf(c_0_11545, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2))=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)|~class_Fields_Ofield(X1)), inference(split_conjunct,[status(thm)],[c_0_6883]), ['final']). 6.97/7.25 cnf(c_0_11546, 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_6884, c_0_6877]), ['final']). 6.97/7.25 cnf(c_0_11547, 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_6220]), ['final']). 6.97/7.25 cnf(c_0_11548, 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_6221]), ['final']). 6.97/7.25 cnf(c_0_11549, plain, (hBOOL(hAPP(hAPP(c_member(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))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6885]), ['final']). 6.97/7.25 cnf(c_0_11550, 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_6886]), ['final']). 6.97/7.25 cnf(c_0_11551, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|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)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4)|~class_Fields_Ofield(X1)), inference(split_conjunct,[status(thm)],[c_0_6887]), ['final']). 6.97/7.25 cnf(c_0_11552, 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),X2),X4))),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4)|~class_Fields_Ofield(X1)), inference(split_conjunct,[status(thm)],[c_0_6888]), ['final']). 6.97/7.25 cnf(c_0_11553, 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),X4),X2))),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_6889]), ['final']). 6.97/7.25 cnf(c_0_11554, 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_6476]), ['final']). 6.97/7.25 cnf(c_0_11555, 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_6435]), ['final']). 6.97/7.25 cnf(c_0_11556, 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_6890]), ['final']). 6.97/7.25 cnf(c_0_11557, 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_6891, c_0_6006]), ['final']). 6.97/7.25 cnf(c_0_11558, 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_6892]), ['final']). 6.97/7.25 cnf(c_0_11559, 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_6893]), ['final']). 6.97/7.25 cnf(c_0_11560, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|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_6894]), ['final']). 6.97/7.25 cnf(c_0_11561, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|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_6895]), ['final']). 6.97/7.25 cnf(c_0_11562, 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_6896]), ['final']). 6.97/7.25 cnf(c_0_11563, 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_6897]), ['final']). 6.97/7.25 cnf(c_0_11564, 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_6898, c_0_6006]), ['final']). 6.97/7.25 cnf(c_0_11565, plain, (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))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),X2))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),esk206_3(X2,X3,X1)),esk207_3(X2,X3,X1))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_6436]), ['final']). 6.97/7.25 cnf(c_0_11566, 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_6269]), ['final']). 6.97/7.25 cnf(c_0_11567, 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__mult(X1)|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6899]), ['final']). 6.97/7.25 cnf(c_0_11568, 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__mult(X1)|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6900]), ['final']). 6.97/7.25 cnf(c_0_11569, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk315_3(X1,X2,X3)),esk314_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_6901, c_0_5038]), ['final']). 6.97/7.25 cnf(c_0_11570, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk249_3(X1,X2,X3)),esk248_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_Ominus__class_Ominus(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_6902, c_0_4741]), ['final']). 6.97/7.25 cnf(c_0_11571, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),esk574_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_6903]), ['final']). 6.97/7.25 cnf(c_0_11572, 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_6904]), ['final']). 6.97/7.25 cnf(c_0_11573, 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__class_OSup__fin(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(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_6905]), ['final']). 6.97/7.25 cnf(c_0_11574, 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),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_5327]), ['final']). 6.97/7.25 cnf(c_0_11575, 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),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_5327]), ['final']). 6.97/7.25 cnf(c_0_11576, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_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)),esk274_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.25 cnf(c_0_11577, 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_6906]), ['final']). 6.97/7.25 cnf(c_0_11578, 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(X7,esk106_8(X3,X7,hAPP(c_Set_Oimage(X4,X1,X5),X6),X6,X5,X1,X4,X2))!=hAPP(X3,hAPP(X5,esk106_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_6907]), ['final']). 6.97/7.25 cnf(c_0_11579, 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_6908, c_0_6909]), c_0_6910]), ['final']). 6.97/7.25 cnf(c_0_11580, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk430_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']). 6.97/7.25 cnf(c_0_11581, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk1_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_6912]), ['final']). 6.97/7.25 cnf(c_0_11582, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk50_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_6913]), ['final']). 6.97/7.25 cnf(c_0_11583, 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_6914, c_0_4813]), ['final']). 6.97/7.25 cnf(c_0_11584, 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_6915]), ['final']). 6.97/7.25 cnf(c_0_11585, 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_6916])]), ['final']). 6.97/7.25 cnf(c_0_11586, 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_6917]), ['final']). 6.97/7.25 cnf(c_0_11587, 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_6918]), ['final']). 6.97/7.25 cnf(c_0_11588, plain, (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))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,tc_Int_Oint),X1),X2)|~c_Nat__Transfer_Ois__nat(hAPP(X1,esk398_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_6558]), ['final']). 6.97/7.25 cnf(c_0_11589, 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,esk546_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_6559]), ['final']). 6.97/7.25 cnf(c_0_11590, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk285_4(X2,X3,X4,X1)),esk286_4(X2,X3,X4,X1))),X4))|c_Equiv__Relations_Ocongruent(X1,X2,X4,X3)), inference(split_conjunct,[status(thm)],[c_0_6919]), ['final']). 6.97/7.25 cnf(c_0_11591, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|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,esk45_3(X3,X2,X1))),hAPP(X2,esk46_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),esk45_3(X3,X2,X1)),esk46_3(X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6920]), ['final']). 6.97/7.25 cnf(c_0_11592, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|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),esk418_3(X3,X2,X1)),esk419_3(X3,X2,X1)))!=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(X2,esk418_3(X3,X2,X1))),hAPP(X2,esk419_3(X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6921]), ['final']). 6.97/7.25 cnf(c_0_11593, plain, (X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|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))|~class_Lattices_Olattice(X1)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(X2,esk11_3(X3,X2,X1))),hAPP(X2,esk12_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),esk11_3(X3,X2,X1)),esk12_3(X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6922]), ['final']). 6.97/7.25 cnf(c_0_11594, plain, (X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|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))|~class_Orderings_Olinorder(X1)|hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),esk394_3(X3,X2,X1)),esk395_3(X3,X2,X1)))!=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(X2,esk394_3(X3,X2,X1))),hAPP(X2,esk395_3(X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6923]), ['final']). 6.97/7.25 cnf(c_0_11595, 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_5467]), ['final']). 6.97/7.25 cnf(c_0_11596, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk338_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_6924]), ['final']). 6.97/7.25 cnf(c_0_11597, 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_6925]), ['final']). 6.97/7.25 cnf(c_0_11598, 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_6926]), ['final']). 6.97/7.25 cnf(c_0_11599, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk69_5(X2,X3,X4,X1,X5)),hAPP(c_Set_Oimage(X5,X1,X4),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))|hBOOL(hAPP(X3,X2))|~c_Fun_Oinj__on(X5,X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_6927]), ['final']). 6.97/7.25 cnf(c_0_11600, 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_6928, c_0_6370]), c_0_6376]), ['final']). 6.97/7.25 cnf(c_0_11601, plain, (hAPP(hAPP(c_List_Oappend(X1),esk130_5(X2,X3,X4,X5,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),esk131_5(X2,X3,X4,X5,X1)))=X2|hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4)!=hAPP(c_List_Ofilter(X1,X3),X2)), inference(split_conjunct,[status(thm)],[c_0_4995]), ['final']). 6.97/7.25 cnf(c_0_11602, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),esk87_5(X3,X4,X1,X5,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),X4),esk88_5(X3,X4,X1,X5,X2)))|hAPP(hAPP(c_List_Olist_OCons(X2),X4),X3)!=hAPP(c_List_Ofilter(X2,X5),X1)), inference(split_conjunct,[status(thm)],[c_0_4996]), ['final']). 6.97/7.25 cnf(c_0_11603, 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_6929, c_0_6930]), ['final']). 6.97/7.25 cnf(c_0_11604, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk125_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_6931]), ['final']). 6.97/7.25 cnf(c_0_11605, 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)|c_List_Olist_ONil(X1)=X2|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6932, c_0_5538]), c_0_5065]), ['final']). 6.97/7.25 cnf(c_0_11606, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|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_6933]), ['final']). 6.97/7.25 cnf(c_0_11607, 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,esk476_5(X1,X2,X3,X4,X5))!=c_Groups_Ozero__class_Ozero(X5)|~class_Groups_Omonoid__add(X5)), inference(split_conjunct,[status(thm)],[c_0_6368]), ['final']). 6.97/7.25 cnf(c_0_11608, 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,X4),X5))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(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)), inference(split_conjunct,[status(thm)],[c_0_6934]), ['final']). 6.97/7.25 cnf(c_0_11609, plain, (hAPP(hAPP(X1,X2),esk574_7(X3,X4,X2,X5,X1,X6,X7))=X3|hBOOL(hAPP(hAPP(c_member(X7),X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X6,X1,X5,hAPP(hAPP(c_Set_Oinsert(X7),X2),X4)),X3))|~c_Finite__Set_Ofun__left__comm(X7,X6,X1)), inference(split_conjunct,[status(thm)],[c_0_6903]), ['final']). 6.97/7.25 cnf(c_0_11610, 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_6935]), ['final']). 6.97/7.25 cnf(c_0_11611, 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,esk502_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_6936]), ['final']). 6.97/7.25 cnf(c_0_11612, 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_6937]), ['final']). 6.97/7.25 cnf(c_0_11613, 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_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_6938]), ['final']). 6.97/7.25 cnf(c_0_11614, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk309_5(X2,X3,X4,X5,X1)),X5))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X4,X3),X5)),X2))), inference(split_conjunct,[status(thm)],[c_0_6939]), ['final']). 6.97/7.25 cnf(c_0_11615, 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,esk476_5(X2,X1,X3,X4,X5)))|~class_Groups_Omonoid__add(X5)), inference(split_conjunct,[status(thm)],[c_0_6368]), ['final']). 6.97/7.25 cnf(c_0_11616, 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_6446]), ['final']). 6.97/7.25 cnf(c_0_11617, 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_6940]), ['final']). 6.97/7.25 cnf(c_0_11618, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk422_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_6941]), ['final']). 6.97/7.25 cnf(c_0_11619, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk83_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_6942]), ['final']). 6.97/7.25 cnf(c_0_11620, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk71_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_6943]), ['final']). 6.97/7.25 cnf(c_0_11621, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk33_5(X2,X3,X4,X1,X5)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X5),X4),X2)))|~class_Complete__Lattice_Ocomplete__lattice(X5)), inference(split_conjunct,[status(thm)],[c_0_6944]), ['final']). 6.97/7.25 cnf(c_0_11622, 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)),esk590_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))), inference(rw,[status(thm)],[c_0_6945, c_0_4645]), ['final']). 6.97/7.25 cnf(c_0_11623, 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_6946]), ['final']). 6.97/7.25 cnf(c_0_11624, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1),X4),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(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_6947]), ['final']). 6.97/7.25 cnf(c_0_11625, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk300_7(X2,X3,X4,X5,X6,X7,X1)),X4))|hAPP(hAPP(X5,X2),X4)=hAPP(hAPP(X5,X3),X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~c_Finite__Set_Ofolding__image(X8,X1,X7,X6,X5)), inference(split_conjunct,[status(thm)],[c_0_6948]), ['final']). 6.97/7.25 cnf(c_0_11626, 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_6949]), ['final']). 6.97/7.25 cnf(c_0_11627, 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)),esk462_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))), inference(rw,[status(thm)],[c_0_6950, c_0_4645]), ['final']). 6.97/7.25 cnf(c_0_11628, 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_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_6951]), ['final']). 6.97/7.25 cnf(c_0_11629, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk536_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_6952]), ['final']). 6.97/7.25 cnf(c_0_11630, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk156_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_6953]), ['final']). 6.97/7.25 cnf(c_0_11631, 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)),esk529_5(X2,X4,X3,X3,X1)))|~class_Groups_Ocomm__monoid__mult(X1)|~class_Groups_Ocomm__monoid__add(X1)|~c_Nat__Transfer_Onat__set(X3)), inference(er,[status(thm)],[c_0_6954]), ['final']). 6.97/7.25 cnf(c_0_11632, 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_6955, c_0_4768]), ['final']). 6.97/7.25 cnf(c_0_11633, 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_6704]), ['final']). 6.97/7.25 cnf(c_0_11634, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),esk588_3(X3,X2,X1)),esk589_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_5673]), ['final']). 6.97/7.25 cnf(c_0_11635, 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)),esk561_5(X2,X4,X3,X3,X1)))|~class_Groups_Ocomm__monoid__mult(X1)|~class_Groups_Ocomm__monoid__add(X1)|~c_Nat__Transfer_Onat__set(X3)), inference(er,[status(thm)],[c_0_6956]), ['final']). 6.97/7.25 cnf(c_0_11636, 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),esk232_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))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6957, c_0_4742]), c_0_4742]), ['final']). 6.97/7.25 cnf(c_0_11637, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk270_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk269_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_6958, c_0_4977]), ['final']). 6.97/7.25 cnf(c_0_11638, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2))|~c_Relation_Osym(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))), inference(split_conjunct,[status(thm)],[c_0_6959]), ['final']). 6.97/7.25 cnf(c_0_11639, 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_6707]), ['final']). 6.97/7.25 cnf(c_0_11640, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_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__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_6960]), ['final']). 6.97/7.25 cnf(c_0_11641, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_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),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Rings_Oordered__ring__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_6960]), ['final']). 6.97/7.25 cnf(c_0_11642, 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_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_6961]), ['final']). 6.97/7.25 cnf(c_0_11643, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)|hBOOL(hAPP(hAPP(c_member(X1),esk570_6(X2,X4,X5,X1,X3,X3)),X3))), inference(er,[status(thm)],[c_0_6962]), ['final']). 6.97/7.25 cnf(c_0_11644, 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_6963, c_0_4798]), ['final']). 6.97/7.25 cnf(c_0_11645, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk363_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_6666]), ['final']). 6.97/7.25 cnf(c_0_11646, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_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),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Oordered__ring__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_6960]), ['final']). 6.97/7.25 cnf(c_0_11647, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_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__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_6960]), ['final']). 6.97/7.25 cnf(c_0_11648, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(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),X3),X2)),X4)),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),X3))), inference(er,[status(thm)],[c_0_6964]), ['final']). 6.97/7.25 cnf(c_0_11649, 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_6965]), ['final']). 6.97/7.25 cnf(c_0_11650, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk126_4(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3),X3,X2)),esk125_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_6966]), ['final']). 6.97/7.25 cnf(c_0_11651, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk318_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_6667]), ['final']). 6.97/7.25 cnf(c_0_11652, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk343_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_6668]), ['final']). 6.97/7.25 cnf(c_0_11653, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk325_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_6669]), ['final']). 6.97/7.25 cnf(c_0_11654, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(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),X3),X2)),X4)),X3)))|~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_6967]), ['final']). 6.97/7.25 cnf(c_0_11655, 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)), inference(split_conjunct,[status(thm)],[c_0_6968]), ['final']). 6.97/7.25 cnf(c_0_11656, 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),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(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_6835]), ['final']). 6.97/7.25 cnf(c_0_11657, 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),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),X2),X3)),X4))|~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_6837]), ['final']). 6.97/7.25 cnf(c_0_11658, 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)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(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_6835]), ['final']). 6.97/7.25 cnf(c_0_11659, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|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))))), inference(split_conjunct,[status(thm)],[c_0_6969]), ['final']). 6.97/7.25 cnf(c_0_11660, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk339_4(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3),X3,X2)),esk338_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_6970]), ['final']). 6.97/7.25 cnf(c_0_11661, 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_6971]), ['final']). 6.97/7.25 cnf(c_0_11662, plain, (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))|~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_6837]), ['final']). 6.97/7.25 cnf(c_0_11663, plain, (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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),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_6838]), ['final']). 6.97/7.25 cnf(c_0_11664, plain, (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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~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_6838]), ['final']). 6.97/7.25 cnf(c_0_11665, 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_6839]), ['final']). 6.97/7.25 cnf(c_0_11666, 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_6972, c_0_6909]), c_0_6910]), ['final']). 6.97/7.25 cnf(c_0_11667, 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_6973, c_0_6880]), c_0_6881]), ['final']). 6.97/7.25 cnf(c_0_11668, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),hAPP(c_List_Oset(X1),X5))=hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),X3),X4),X5)|~c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_6974]), ['final']). 6.97/7.25 cnf(c_0_11669, 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_6975]), ['final']). 6.97/7.25 cnf(c_0_11670, 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_6839]), ['final']). 6.97/7.25 cnf(c_0_11671, plain, (hAPP(c_Finite__Set_Ocard(X1),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(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)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6976]), ['final']). 6.97/7.25 cnf(c_0_11672, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X5),X3)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X4)|X3=c_Groups_Ozero__class_Ozero(X1)|X4=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)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X4),X2))|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_6977]), ['final']). 6.97/7.25 cnf(c_0_11673, 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_6978, c_0_4742]), c_0_4742]), ['final']). 6.97/7.25 cnf(c_0_11674, 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_6979, c_0_4742]), c_0_4742]), ['final']). 6.97/7.25 cnf(c_0_11675, 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),esk493_2(X2,X1)),hAPP(X1,esk493_2(X2,X1))))), inference(rw,[status(thm)],[c_0_6980, c_0_4467]), ['final']). 6.97/7.25 cnf(c_0_11676, 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_6981]), ['final']). 6.97/7.25 cnf(c_0_11677, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk560_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_6508]), ['final']). 6.97/7.25 cnf(c_0_11678, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk560_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))), inference(split_conjunct,[status(thm)],[c_0_6508]), ['final']). 6.97/7.25 cnf(c_0_11679, 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_6982]), ['final']). 6.97/7.25 cnf(c_0_11680, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2)|X3=c_Groups_Ozero__class_Ozero(X1)|X5=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3)!=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X4),X5)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X2))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X5),X4))|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_6977]), ['final']). 6.97/7.25 cnf(c_0_11681, 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_6983]), ['final']). 6.97/7.25 cnf(c_0_11682, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk128_3(X1,X2,X3)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk127_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_5005]), ['final']). 6.97/7.25 cnf(c_0_11683, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk58_3(X1,X2,X3)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk57_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_5006]), ['final']). 6.97/7.25 cnf(c_0_11684, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),X2))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),X2))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_6984]), ['final']). 6.97/7.25 cnf(c_0_11685, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),X2))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X3),X2))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_6985]), ['final']). 6.97/7.25 cnf(c_0_11686, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X4),X2))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X4),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_6986]), ['final']). 6.97/7.25 cnf(c_0_11687, plain, (X1=hAPP(X2,esk128_3(X1,X2,X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk127_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_5005]), ['final']). 6.97/7.25 cnf(c_0_11688, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(hAPP(c_List_Otake(X2),X1),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4))=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))), inference(split_conjunct,[status(thm)],[c_0_6987]), ['final']). 6.97/7.25 cnf(c_0_11689, plain, (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))))=hAPP(c_List_Oset(X1),c_List_Oremove1(X1,X3,X2))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_6988]), ['final']). 6.97/7.25 cnf(c_0_11690, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),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)],[c_0_6989, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), ['final']). 6.97/7.25 cnf(c_0_11691, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),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)],[c_0_6990, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), ['final']). 6.97/7.25 cnf(c_0_11692, plain, (X1=hAPP(X2,esk58_3(X1,X2,X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk57_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_5006]), ['final']). 6.97/7.25 cnf(c_0_11693, 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_6991]), ['final']). 6.97/7.25 cnf(c_0_11694, 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_6992]), ['final']). 6.97/7.25 cnf(c_0_11695, plain, (hBOOL(hAPP(X4,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)))|~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(X4,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))), inference(split_conjunct,[status(thm)],[c_0_6993]), ['final']). 6.97/7.25 cnf(c_0_11696, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[c_0_6994, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), ['final']). 6.97/7.25 cnf(c_0_11697, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)],[c_0_6995, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), ['final']). 6.97/7.25 cnf(c_0_11698, 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_6996]), ['final']). 6.97/7.25 cnf(c_0_11699, 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),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)|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),X2))), inference(split_conjunct,[status(thm)],[c_0_5288]), ['final']). 6.97/7.25 cnf(c_0_11700, 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)))|~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_6997]), ['final']). 6.97/7.25 cnf(c_0_11701, 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_6998]), ['final']). 6.97/7.25 cnf(c_0_11702, 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_6999]), ['final']). 6.97/7.25 cnf(c_0_11703, 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_7000]), ['final']). 6.97/7.25 cnf(c_0_11704, 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_7001]), ['final']). 6.97/7.25 cnf(c_0_11705, 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_7002]), ['final']). 6.97/7.25 cnf(c_0_11706, 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_7003]), ['final']). 6.97/7.25 cnf(c_0_11707, 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_7004]), ['final']). 6.97/7.25 cnf(c_0_11708, 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_7005, c_0_7006]), ['final']). 6.97/7.25 cnf(c_0_11709, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Int_OMin))=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_7007, c_0_6003]), c_0_4741]), ['final']). 6.97/7.25 cnf(c_0_11710, 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_7008]), ['final']). 6.97/7.25 cnf(c_0_11711, 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_7009]), ['final']). 6.97/7.25 cnf(c_0_11712, 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_7010, c_0_7011]), ['final']). 6.97/7.25 cnf(c_0_11713, 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_6997]), ['final']). 6.97/7.25 cnf(c_0_11714, 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_7012]), ['final']). 6.97/7.25 cnf(c_0_11715, 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_7013]), ['final']). 6.97/7.25 cnf(c_0_11716, 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_6441]), ['final']). 6.97/7.25 cnf(c_0_11717, plain, (c_Divides_OposDivAlg(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))|~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_7014]), ['final']). 6.97/7.25 cnf(c_0_11718, 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_7015]), ['final']). 6.97/7.25 cnf(c_0_11719, plain, (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))=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X2),X1))|esk206_3(X1,X2,X3)!=esk207_3(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_6436]), ['final']). 6.97/7.25 cnf(c_0_11720, 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_7016]), ['final']). 6.97/7.25 cnf(c_0_11721, 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_7017]), ['final']). 6.97/7.25 cnf(c_0_11722, 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_7018]), ['final']). 6.97/7.25 cnf(c_0_11723, plain, (hAPP(c_List_Oset(X1),X2)=hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Oappend(X1),X3),X4))|c_List_Opartition(X1,X5,X2)!=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)), inference(rw,[status(thm)],[c_0_7019, c_0_6542]), ['final']). 6.97/7.25 cnf(c_0_11724, 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_7020]), ['final']). 6.97/7.25 cnf(c_0_11725, 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_7021]), ['final']). 6.97/7.25 cnf(c_0_11726, 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_7022]), ['final']). 6.97/7.25 cnf(c_0_11727, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk437_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_7023]), ['final']). 6.97/7.25 cnf(c_0_11728, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X6)))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6)))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X5))|~class_Rings_Ocomm__ring(X1)|~class_Rings_Odvd(X1)), inference(split_conjunct,[status(thm)],[c_0_6511]), ['final']). 6.97/7.25 cnf(c_0_11729, plain, (X1=hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk511_6(X1,X4,X3,X2,X5,X6)),esk512_6(X1,X4,X3,X2,X5,X6))|~hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,tc_fun(X6,tc_HOL_Obool)),X4),X1)))), inference(split_conjunct,[status(thm)],[c_0_6748]), ['final']). 6.97/7.25 cnf(c_0_11730, 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),esk503_3(X2,X3,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6743]), ['final']). 6.97/7.25 cnf(c_0_11731, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk270_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk269_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_7024, c_0_4977]), ['final']). 6.97/7.25 cnf(c_0_11732, 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_6835]), ['final']). 6.97/7.25 cnf(c_0_11733, 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_6837]), ['final']). 6.97/7.25 cnf(c_0_11734, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),esk276_3(X2,X3,X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X2,X3,X1)),X2))|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)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.25 cnf(c_0_11735, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk434_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_7025]), ['final']). 6.97/7.25 cnf(c_0_11736, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_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)),esk255_3(X1,X2,X3)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_11737, 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)))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk326_3(X2,X3,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6744]), ['final']). 6.97/7.25 cnf(c_0_11738, 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)))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk20_3(X2,X3,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Lattices_Osemilattice__inf(X1)), inference(split_conjunct,[status(thm)],[c_0_6745]), ['final']). 6.97/7.25 cnf(c_0_11739, 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_6838]), ['final']). 6.97/7.25 cnf(c_0_11740, 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_6839]), ['final']). 6.97/7.25 cnf(c_0_11741, 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_7026, c_0_6880]), c_0_6881]), ['final']). 6.97/7.25 cnf(c_0_11742, 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_7027]), ['final']). 6.97/7.25 cnf(c_0_11743, 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_7027]), ['final']). 6.97/7.25 cnf(c_0_11744, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk479_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_7028]), ['final']). 6.97/7.25 cnf(c_0_11745, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk444_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_7029]), ['final']). 6.97/7.25 cnf(c_0_11746, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk323_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_7030]), ['final']). 6.97/7.25 cnf(c_0_11747, 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_7031]), ['final']). 6.97/7.25 cnf(c_0_11748, 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,esk447_3(X2,X1,X3))!=hAPP(X1,esk446_3(X2,X1,X3))|~c_Wellfounded_OwfP(X3,hAPP(X1,esk445_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_6762]), ['final']). 6.97/7.25 cnf(c_0_11749, 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_7032, c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_11750, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_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)),esk255_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_11751, 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_7033]), ['final']). 6.97/7.25 cnf(c_0_11752, plain, (hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),esk224_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)))), inference(split_conjunct,[status(thm)],[c_0_7034]), ['final']). 6.97/7.25 cnf(c_0_11753, 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_7035]), ['final']). 6.97/7.25 cnf(c_0_11754, plain, (X1=hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk218_6(X4,X5,X6,X1,X3,X2)),esk220_6(X4,X5,X6,X1,X3,X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X3)),X1),hAPP(hAPP(c_Relation_Orel__comp(X2,X6,X3),X5),X4)))), inference(split_conjunct,[status(thm)],[c_0_6509]), ['final']). 6.97/7.25 cnf(c_0_11755, 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_6835]), ['final']). 6.97/7.25 cnf(c_0_11756, 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_6837]), ['final']). 6.97/7.25 cnf(c_0_11757, 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_7036, c_0_5002]), c_0_5002]), c_0_5002]), ['final']). 6.97/7.25 cnf(c_0_11758, 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_7037]), ['final']). 6.97/7.25 cnf(c_0_11759, 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_7038]), ['final']). 6.97/7.25 cnf(c_0_11760, 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),esk32_4(X4,X3,X2,X1)),X1))), inference(split_conjunct,[status(thm)],[c_0_6725]), ['final']). 6.97/7.25 cnf(c_0_11761, 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_6838]), ['final']). 6.97/7.25 cnf(c_0_11762, 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_6839]), ['final']). 6.97/7.25 cnf(c_0_11763, 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_7039]), ['final']). 6.97/7.25 cnf(c_0_11764, 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_7040]), ['final']). 6.97/7.25 cnf(c_0_11765, 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)), inference(split_conjunct,[status(thm)],[c_0_7041]), ['final']). 6.97/7.25 cnf(c_0_11766, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk168_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_6857]), ['final']). 6.97/7.25 cnf(c_0_11767, 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),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_7042]), ['final']). 6.97/7.25 cnf(c_0_11768, 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(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_7043]), ['final']). 6.97/7.25 cnf(c_0_11769, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk217_3(X2,X3,X1)),X3))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk216_3(X2,X3,X1)),X2))|c_Relation_Orefl__on(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_4503]), ['final']). 6.97/7.25 cnf(c_0_11770, 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_7044, c_0_5174]), ['final']). 6.97/7.25 cnf(c_0_11771, plain, (hAPP(hAPP(c_List_Onth(X3),hAPP(hAPP(c_List_Odrop(X3),X1),X4)),X2)=hAPP(hAPP(c_List_Onth(X3),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)))), inference(split_conjunct,[status(thm)],[c_0_7045]), ['final']). 6.97/7.25 cnf(c_0_11772, plain, (hAPP(hAPP(c_List_Ozip(X1,X3),hAPP(c_List_Orev(X1),X2)),hAPP(c_List_Orev(X3),X4))=hAPP(c_List_Orev(tc_prod(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)), inference(split_conjunct,[status(thm)],[c_0_7046]), ['final']). 6.97/7.25 cnf(c_0_11773, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk141_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_6443]), ['final']). 6.97/7.25 cnf(c_0_11774, 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)],[c_0_7047, c_0_4410]), ['final']). 6.97/7.25 cnf(c_0_11775, 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_7048, c_0_4415]), c_0_4415]), c_0_5002]), c_0_4415]), c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_11776, 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_7049]), ['final']). 6.97/7.25 cnf(c_0_11777, 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_7050]), ['final']). 6.97/7.25 cnf(c_0_11778, 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_Relation_Oconverse(X1,X1),X2)),X2)),X2))|~c_Relation_Osym(X1,X2)|~c_Relation_Otrans(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7051]), ['final']). 6.97/7.25 cnf(c_0_11779, 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_7052]), ['final']). 6.97/7.25 cnf(c_0_11780, plain, (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)=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)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_7053]), ['final']). 6.97/7.25 cnf(c_0_11781, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk276_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.25 cnf(c_0_11782, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_3(X2,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)),X2))|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)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.25 cnf(c_0_11783, 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__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk274_3(X2,X3,X1)))|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)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.25 cnf(c_0_11784, 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_4569]), ['final']). 6.97/7.25 cnf(c_0_11785, 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_7054]), ['final']). 6.97/7.25 cnf(c_0_11786, 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_7055]), ['final']). 6.97/7.25 cnf(c_0_11787, 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_7056]), ['final']). 6.97/7.25 cnf(c_0_11788, 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_7057]), ['final']). 6.97/7.25 cnf(c_0_11789, 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_7058]), ['final']). 6.97/7.25 cnf(c_0_11790, 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_7059]), ['final']). 6.97/7.25 cnf(c_0_11791, 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_7060]), ['final']). 6.97/7.25 cnf(c_0_11792, 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_7061]), ['final']). 6.97/7.25 cnf(c_0_11793, 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_7062]), ['final']). 6.97/7.25 cnf(c_0_11794, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|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_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7063]), ['final']). 6.97/7.25 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|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)),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_7064]), ['final']). 6.97/7.25 cnf(c_0_11796, 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_7065]), ['final']). 6.97/7.25 cnf(c_0_11797, 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_7066]), ['final']). 6.97/7.25 cnf(c_0_11798, 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_7067]), ['final']). 6.97/7.25 cnf(c_0_11799, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk99_4(X2,X3,X4,X1)),c_Quotient_ORespects(X1,X4)))|hBOOL(hAPP(X3,esk98_4(X2,X3,X4,X1)))|~hBOOL(hAPP(X3,X5))|~c_Equiv__Relations_Oequivp(X1,X4)), inference(split_conjunct,[status(thm)],[c_0_7068]), ['final']). 6.97/7.25 cnf(c_0_11800, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3)),X5))=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)))), inference(er,[status(thm)],[c_0_7069]), ['final']). 6.97/7.25 cnf(c_0_11801, 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(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)|~class_Int_Onumber(X1)|~class_Orderings_Oord(X1)), inference(split_conjunct,[status(thm)],[c_0_7070]), ['final']). 6.97/7.25 cnf(c_0_11802, 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_7071]), ['final']). 6.97/7.25 cnf(c_0_11803, 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_7072]), ['final']). 6.97/7.25 cnf(c_0_11804, 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_7073]), ['final']). 6.97/7.25 cnf(c_0_11805, 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_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(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_7074, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), ['final']). 6.97/7.25 cnf(c_0_11806, 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_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(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_7075, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), ['final']). 6.97/7.25 cnf(c_0_11807, 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_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(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_7076, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), ['final']). 6.97/7.25 cnf(c_0_11808, 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_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(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_7077, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), ['final']). 6.97/7.25 cnf(c_0_11809, 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_7078]), ['final']). 6.97/7.25 cnf(c_0_11810, 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_7079]), ['final']). 6.97/7.25 cnf(c_0_11811, 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_7080]), ['final']). 6.97/7.25 cnf(c_0_11812, 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_7081]), ['final']). 6.97/7.25 cnf(c_0_11813, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4)=hAPP(hAPP(c_Orderings_Oord__class_Omin(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__imp__le(X1)), inference(split_conjunct,[status(thm)],[c_0_7082]), ['final']). 6.97/7.25 cnf(c_0_11814, 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_6743]), ['final']). 6.97/7.25 cnf(c_0_11815, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~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_6745]), ['final']). 6.97/7.25 cnf(c_0_11816, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~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_6744]), ['final']). 6.97/7.25 cnf(c_0_11817, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|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_7083]), ['final']). 6.97/7.25 cnf(c_0_11818, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),X4)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))|~class_Lattices_Odistrib__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7084]), ['final']). 6.97/7.25 cnf(c_0_11819, 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(X1)), inference(split_conjunct,[status(thm)],[c_0_7085]), ['final']). 6.97/7.25 cnf(c_0_11820, 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_7086]), ['final']). 6.97/7.25 cnf(c_0_11821, 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_7087]), ['final']). 6.97/7.25 cnf(c_0_11822, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk526_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_7088]), ['final']). 6.97/7.25 cnf(c_0_11823, 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_7089]), ['final']). 6.97/7.25 cnf(c_0_11824, 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_7090]), ['final']). 6.97/7.25 cnf(c_0_11825, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk409_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_7091]), ['final']). 6.97/7.25 cnf(c_0_11826, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2)),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_7092]), ['final']). 6.97/7.25 cnf(c_0_11827, 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_7093]), ['final']). 6.97/7.25 cnf(c_0_11828, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk436_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(X3)),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X4)), inference(split_conjunct,[status(thm)],[c_0_7094]), ['final']). 6.97/7.25 cnf(c_0_11829, 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_7095]), ['final']). 6.97/7.25 cnf(c_0_11830, 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_7096]), ['final']). 6.97/7.25 cnf(c_0_11831, 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_4956]), ['final']). 6.97/7.25 cnf(c_0_11832, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk296_5(X2,X3,X4,X1,X5)),hAPP(X2,esk295_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_7097]), ['final']). 6.97/7.25 cnf(c_0_11833, 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_7098, c_0_4415]), c_0_4415]), c_0_5002]), c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_11834, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk89_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(X4)),X1)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X2)), inference(split_conjunct,[status(thm)],[c_0_7099]), ['final']). 6.97/7.25 cnf(c_0_11835, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_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)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.25 cnf(c_0_11836, plain, (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)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk274_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.25 cnf(c_0_11837, 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,esk516_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)))), inference(split_conjunct,[status(thm)],[c_0_6993]), ['final']). 6.97/7.25 cnf(c_0_11838, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4),X3),X5)),X6))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(X5,X2)),X6))|~class_Orderings_Olinorder(X4)|~class_Complete__Lattice_Ocomplete__lattice(X4)), inference(split_conjunct,[status(thm)],[c_0_7100]), ['final']). 6.97/7.25 cnf(c_0_11839, 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_7101]), ['final']). 6.97/7.25 cnf(c_0_11840, 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(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7102]), ['final']). 6.97/7.25 cnf(c_0_11841, 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_7103]), ['final']). 6.97/7.25 cnf(c_0_11842, 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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X3)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7104]), ['final']). 6.97/7.25 cnf(c_0_11843, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_7105]), ['final']). 6.97/7.25 cnf(c_0_11844, 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),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7106]), ['final']). 6.97/7.25 cnf(c_0_11845, 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_7107]), ['final']). 6.97/7.25 cnf(c_0_11846, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,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),X3),X4)),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(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_7108]), ['final']). 6.97/7.25 cnf(c_0_11847, 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_7109]), ['final']). 6.97/7.25 cnf(c_0_11848, 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_7110]), ['final']). 6.97/7.25 cnf(c_0_11849, 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_7111]), ['final']). 6.97/7.25 cnf(c_0_11850, 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)), inference(split_conjunct,[status(thm)],[c_0_7112]), ['final']). 6.97/7.25 cnf(c_0_11851, 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_7113]), ['final']). 6.97/7.25 cnf(c_0_11852, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,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),X3),X4)),X2),X3)))|~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_7114]), ['final']). 6.97/7.25 cnf(c_0_11853, plain, (c_Fun_Obij__betw(X1,X2,esk372_6(X6,X5,X4,X3,X2,X1),X4,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))), inference(split_conjunct,[status(thm)],[c_0_7115]), ['final']). 6.97/7.25 cnf(c_0_11854, plain, (hAPP(c_Nat_OSuc,esk29_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_6182]), ['final']). 6.97/7.25 cnf(c_0_11855, 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_7116]), ['final']). 6.97/7.25 cnf(c_0_11856, 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_7117]), ['final']). 6.97/7.25 cnf(c_0_11857, 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_7118]), ['final']). 6.97/7.25 cnf(c_0_11858, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk361_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk360_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_7119, c_0_4977]), ['final']). 6.97/7.25 cnf(c_0_11859, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk117_5(X2,X3,X4,X5,X1)),hAPP(c_List_Oset(X1),X3)))|hAPP(hAPP(c_List_Omap(X1,X5),X2),X3)=hAPP(hAPP(c_List_Omap(X1,X5),X4),X3)), inference(split_conjunct,[status(thm)],[c_0_7120]), ['final']). 6.97/7.25 cnf(c_0_11860, plain, (X1=hAPP(c_Nat_OSuc,esk186_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_6181]), ['final']). 6.97/7.25 cnf(c_0_11861, 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_7121]), ['final']). 6.97/7.25 cnf(c_0_11862, 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_7122]), ['final']). 6.97/7.25 cnf(c_0_11863, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk475_3(X2,X1,X3)),X3)),X2))|c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),esk473_2(X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_7123]), ['final']). 6.97/7.25 cnf(c_0_11864, 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_7124]), ['final']). 6.97/7.25 cnf(c_0_11865, 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_7125]), ['final']). 6.97/7.25 cnf(c_0_11866, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_3(X2,X3,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|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)))|~hBOOL(hAPP(X1,esk273_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.25 cnf(c_0_11867, plain, (X4=hAPP(c_Fun_Ocomp(X2,X5,X1,hAPP(c_Fun_Ocomp(X1,X5,X2,X4),c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3))),X3)|~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_7126]), ['final']). 6.97/7.25 cnf(c_0_11868, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk263_4(X2,X3,X1,X4)),X3))|c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),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(split_conjunct,[status(thm)],[c_0_7127]), ['final']). 6.97/7.25 cnf(c_0_11869, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk194_5(X2,X3,X4,X1,X5)),X4))|c_Groups_Ozero__class_Ozero(X5)=hAPP(X3,X2)|c_Groups_Ozero__class_Ozero(X5)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X3),X4)|~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_7128]), ['final']). 6.97/7.25 cnf(c_0_11870, 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_7129]), ['final']). 6.97/7.25 cnf(c_0_11871, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk274_3(X2,X3,X1)))|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)))|~hBOOL(hAPP(X1,esk275_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.25 cnf(c_0_11872, plain, (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))=X3|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X2),X1))), inference(rw,[status(thm)],[c_0_7130, c_0_4977]), ['final']). 6.97/7.25 cnf(c_0_11873, 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_7131]), ['final']). 6.97/7.25 cnf(c_0_11874, plain, (hAPP(c_Set_Oimage(X2,X1,esk501_4(X5,X2,X1,X4)),X5)=X4|X4=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~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))), inference(split_conjunct,[status(thm)],[c_0_5128]), ['final']). 6.97/7.25 cnf(c_0_11875, 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_7132]), ['final']). 6.97/7.25 cnf(c_0_11876, 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_7133]), ['final']). 6.97/7.25 cnf(c_0_11877, 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_7134, c_0_4742]), c_0_4742]), c_0_4742]), ['final']). 6.97/7.25 cnf(c_0_11878, 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)),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)],[inference(rw,[status(thm)],[c_0_7135, c_0_4742]), c_0_4742]), c_0_4742]), ['final']). 6.97/7.25 cnf(c_0_11879, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk408_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_7136]), ['final']). 6.97/7.25 cnf(c_0_11880, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk515_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_7137]), ['final']). 6.97/7.25 cnf(c_0_11881, 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_7138, c_0_6758]), ['final']). 6.97/7.25 cnf(c_0_11882, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),esk283_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_7139]), ['final']). 6.97/7.25 cnf(c_0_11883, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk203_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_7140]), ['final']). 6.97/7.25 cnf(c_0_11884, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))=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))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7141]), ['final']). 6.97/7.25 cnf(c_0_11885, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),esk61_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_7142]), ['final']). 6.97/7.25 cnf(c_0_11886, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X2),esk507_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_7143]), ['final']). 6.97/7.25 cnf(c_0_11887, 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_7144]), ['final']). 6.97/7.25 cnf(c_0_11888, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,X1,esk293_2(X2,X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),esk292_2(X2,X1)))=X2|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(rw,[status(thm)],[c_0_7145, c_0_4467]), ['final']). 6.97/7.25 cnf(c_0_11889, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk43_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_7146]), ['final']). 6.97/7.25 cnf(c_0_11890, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X2),esk154_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']). 6.97/7.25 cnf(c_0_11891, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X4)),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_7148]), ['final']). 6.97/7.25 cnf(c_0_11892, plain, (X3=hAPP(X4,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))|~c_Finite__Set_Ofolding__one(X1,X5,X4)), inference(split_conjunct,[status(thm)],[c_0_6190]), ['final']). 6.97/7.25 cnf(c_0_11893, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk361_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk360_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_7149, c_0_4977]), ['final']). 6.97/7.25 cnf(c_0_11894, plain, (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_Odistrib__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7150]), ['final']). 6.97/7.25 cnf(c_0_11895, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk315_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_7151, c_0_5038]), ['final']). 6.97/7.25 cnf(c_0_11896, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk249_3(X3,X1,X2)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(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_7152, c_0_4741]), ['final']). 6.97/7.25 cnf(c_0_11897, plain, (hAPP(c_Set_Oimage(X2,X1,X3),hAPP(c_Set_Oimage(X1,X2,c_Hilbert__Choice_Oinv__into(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X3)),X4))=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_7153]), ['final']). 6.97/7.25 cnf(c_0_11898, 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_5111]), ['final']). 6.97/7.25 cnf(c_0_11899, 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)), inference(split_conjunct,[status(thm)],[c_0_7154]), ['final']). 6.97/7.25 cnf(c_0_11900, 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_7155]), ['final']). 6.97/7.25 cnf(c_0_11901, 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_7156, c_0_4632]), ['final']). 6.97/7.25 cnf(c_0_11902, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk188_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(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_6846]), ['final']). 6.97/7.25 cnf(c_0_11903, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk188_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(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_6846]), ['final']). 6.97/7.25 cnf(c_0_11904, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|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_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X2))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7157]), ['final']). 6.97/7.25 cnf(c_0_11905, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk273_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.25 cnf(c_0_11906, plain, (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)),esk274_3(X1,X3,X2)))|hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X1)))|~hBOOL(hAPP(X2,esk275_3(X1,X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.25 cnf(c_0_11907, 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_7158]), ['final']). 6.97/7.25 cnf(c_0_11908, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk153_4(X2,X3,X4,X1)),hAPP(c_List_Oset(X1),X4)))|c_List_OtakeWhile(X1,X3,hAPP(hAPP(c_List_Oappend(X1),X4),X2))=hAPP(hAPP(c_List_Oappend(X1),X4),c_List_OtakeWhile(X1,X3,X2))), inference(split_conjunct,[status(thm)],[c_0_7159]), ['final']). 6.97/7.25 cnf(c_0_11909, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk553_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__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_6847]), ['final']). 6.97/7.25 cnf(c_0_11910, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk553_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__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_6847]), ['final']). 6.97/7.25 cnf(c_0_11911, 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_7160]), ['final']). 6.97/7.25 cnf(c_0_11912, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)=hAPP(hAPP(c_Set_Oinsert(X1),esk403_5(X4,X3,X2,X5,X1)),esk404_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_6741]), ['final']). 6.97/7.25 cnf(c_0_11913, 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_7161, c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_11914, plain, (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)))|~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_7162]), ['final']). 6.97/7.25 cnf(c_0_11915, 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_7163]), ['final']). 6.97/7.25 cnf(c_0_11916, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)=hAPP(hAPP(c_Set_Oinsert(X1),esk38_5(X4,X3,X2,X5,X1)),esk39_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_7164]), ['final']). 6.97/7.25 cnf(c_0_11917, 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_7165]), ['final']). 6.97/7.25 cnf(c_0_11918, 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_7166]), ['final']). 6.97/7.25 cnf(c_0_11919, 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_7167]), ['final']). 6.97/7.25 cnf(c_0_11920, 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_7168]), ['final']). 6.97/7.25 cnf(c_0_11921, plain, (X4=X3|hAPP(hAPP(c_List_Onth(X1),X2),X3)!=hAPP(hAPP(c_List_Onth(X1),X2),X4)|~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)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7169]), ['final']). 6.97/7.25 cnf(c_0_11922, plain, (X1=hAPP(hAPP(X2,X3),X4)|hBOOL(hAPP(hAPP(c_member(X5),esk212_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_6201]), ['final']). 6.97/7.25 cnf(c_0_11923, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk519_3(X3,X2,X1)),esk521_3(X3,X2,X1))),X3))|c_Relation_Osingle__valued(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_7170]), ['final']). 6.97/7.25 cnf(c_0_11924, 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_7171]), ['final']). 6.97/7.25 cnf(c_0_11925, 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(tc_Int_Oint),esk274_3(X2,X3,X1)),X2))|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)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.25 cnf(c_0_11926, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),esk276_3(X2,X3,X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|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)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.25 cnf(c_0_11927, plain, (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))=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_7172]), ['final']). 6.97/7.25 cnf(c_0_11928, 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_7173]), ['final']). 6.97/7.25 cnf(c_0_11929, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk519_3(X3,X2,X1)),esk520_3(X3,X2,X1))),X3))|c_Relation_Osingle__valued(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_7170]), ['final']). 6.97/7.25 cnf(c_0_11930, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),esk73_3(X2,X3,X1)),c_Groups_Ozero__class_Ozero(X1))))|~hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~class_Rings_Osemiring__0(X1)|~class_Rings_Odvd(X1)), inference(split_conjunct,[status(thm)],[c_0_7174]), ['final']). 6.97/7.25 cnf(c_0_11931, 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_7175]), ['final']). 6.97/7.25 cnf(c_0_11932, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk8_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_7176]), ['final']). 6.97/7.25 cnf(c_0_11933, 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_7177]), ['final']). 6.97/7.25 cnf(c_0_11934, 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_7178]), ['final']). 6.97/7.25 cnf(c_0_11935, 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_7179]), ['final']). 6.97/7.25 cnf(c_0_11936, 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_7180]), ['final']). 6.97/7.25 cnf(c_0_11937, 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_7181]), ['final']). 6.97/7.25 cnf(c_0_11938, 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),esk32_4(X1,X3,X2,X4)),X4))), inference(split_conjunct,[status(thm)],[c_0_6725]), ['final']). 6.97/7.25 cnf(c_0_11939, 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_7182]), ['final']). 6.97/7.25 cnf(c_0_11940, 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_7183]), ['final']). 6.97/7.25 cnf(c_0_11941, 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)), inference(split_conjunct,[status(thm)],[c_0_7184]), ['final']). 6.97/7.25 cnf(c_0_11942, 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_OatLeastAtMost(X1,X4,X5))=c_SetInterval_Oord__class_OatLeastAtMost(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)), inference(split_conjunct,[status(thm)],[c_0_7185]), ['final']). 6.97/7.25 cnf(c_0_11943, 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)],[c_0_7186, c_0_4410]), ['final']). 6.97/7.25 cnf(c_0_11944, 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_7187]), ['final']). 6.97/7.25 cnf(c_0_11945, 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_Groups_Ocomm__monoid__mult(X1)|~class_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7188]), ['final']). 6.97/7.25 cnf(c_0_11946, 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_Rings_Osemiring__1(X1)|~class_Groups_Ocomm__monoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_7189]), ['final']). 6.97/7.25 cnf(c_0_11947, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk257_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X1,X2,X3)),X1))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_11948, plain, (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)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.25 cnf(c_0_11949, plain, (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__idem(X1,X2,X3,X4,X5,X6)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7))), inference(split_conjunct,[status(thm)],[c_0_7190]), ['final']). 6.97/7.25 cnf(c_0_11950, 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))|hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ocomm__monoid__add(X1)), inference(rw,[status(thm)],[c_0_7191, c_0_4742]), ['final']). 6.97/7.25 cnf(c_0_11951, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk276_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.25 cnf(c_0_11952, 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_7192, c_0_6585]), ['final']). 6.97/7.25 cnf(c_0_11953, 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_7193]), ['final']). 6.97/7.25 cnf(c_0_11954, 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_7099]), ['final']). 6.97/7.25 cnf(c_0_11955, plain, (hBOOL(hAPP(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),esk74_3(X2,X4,X1))))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),c_Groups_Ozero__class_Ozero(X1))))|~hBOOL(hAPP(X4,X3))|~class_Rings_Osemiring__0(X1)|~class_Rings_Odvd(X1)), inference(split_conjunct,[status(thm)],[c_0_7174]), ['final']). 6.97/7.25 cnf(c_0_11956, 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_7194, c_0_5999]), ['final']). 6.97/7.25 cnf(c_0_11957, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4)=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))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7195]), ['final']). 6.97/7.25 cnf(c_0_11958, 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_7196]), ['final']). 6.97/7.25 cnf(c_0_11959, 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_7197]), ['final']). 6.97/7.25 cnf(c_0_11960, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X2),esk212_7(X3,X4,X1,X5,X6,X7,X2)),X1))|~c_Nitpick_Ofold__graph_H(X2,X7,X6,X5,X1,hAPP(hAPP(X6,X4),X3))), inference(split_conjunct,[status(thm)],[c_0_6201]), ['final']). 6.97/7.25 cnf(c_0_11961, plain, (hBOOL(hAPP(X1,esk559_4(X1,X2,X3,X4)))|hBOOL(hAPP(X1,esk558_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_6508]), ['final']). 6.97/7.25 cnf(c_0_11962, 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_7198]), ['final']). 6.97/7.25 cnf(c_0_11963, plain, (hBOOL(hAPP(hAPP(c_member(X1),X5),X4))|X4=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|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_7199]), ['final']). 6.97/7.25 cnf(c_0_11964, 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_7200]), ['final']). 6.97/7.25 cnf(c_0_11965, 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_7201]), ['final']). 6.97/7.25 cnf(c_0_11966, 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_7202]), ['final']). 6.97/7.25 cnf(c_0_11967, 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_7203]), ['final']). 6.97/7.25 cnf(c_0_11968, 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_6474]), ['final']). 6.97/7.25 cnf(c_0_11969, 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_7204]), ['final']). 6.97/7.25 cnf(c_0_11970, 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_7205]), ['final']). 6.97/7.25 cnf(c_0_11971, 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_7206]), ['final']). 6.97/7.25 cnf(c_0_11972, 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_7207]), ['final']). 6.97/7.25 cnf(c_0_11973, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk257_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_11974, 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_7208]), ['final']). 6.97/7.25 cnf(c_0_11975, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2)|~class_Divides_Osemiring__div(X1)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7209]), ['final']). 6.97/7.25 cnf(c_0_11976, 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_7210]), ['final']). 6.97/7.25 cnf(c_0_11977, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6,X5,X3),X2),X4)))|~hBOOL(hAPP(X1,hAPP(hAPP(X2,esk389_7(X3,X2,X1,X4,X5,X6,X7)),esk390_7(X3,X2,X1,X4,X5,X6,X7))))|~hBOOL(hAPP(hAPP(X7,hAPP(c_Product__Type_Osnd(X6,X5),X4)),hAPP(c_Product__Type_Ofst(X6,X5),X4)))), inference(split_conjunct,[status(thm)],[c_0_6565]), ['final']). 6.97/7.25 cnf(c_0_11978, plain, (hAPP(c_Nat_OSuc,esk29_5(X1,X2,X3,X4,X5))=X2|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),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_6182]), ['final']). 6.97/7.25 cnf(c_0_11979, plain, (X1=c_Groups_Ozero__class_Ozero(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_Odivmod__int(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(split_conjunct,[status(thm)],[c_0_7211]), ['final']). 6.97/7.25 cnf(c_0_11980, plain, (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)))|~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_7212]), ['final']). 6.97/7.25 cnf(c_0_11981, 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_7213]), ['final']). 6.97/7.25 cnf(c_0_11982, 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_7214, c_0_4768]), c_0_4768]), ['final']). 6.97/7.25 cnf(c_0_11983, 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_7215]), ['final']). 6.97/7.25 cnf(c_0_11984, plain, (X1=hAPP(c_Nat_OSuc,esk186_5(X2,X1,X3,X4,X5))|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),X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_6181]), ['final']). 6.97/7.25 cnf(c_0_11985, plain, (X1=c_List_Olist_ONil(tc_List_Olist(X2))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),c_List_Otranspose(X2,X1))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X2)),X1),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(X2),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X2))),X1)))), inference(split_conjunct,[status(thm)],[c_0_7216]), ['final']). 6.97/7.25 cnf(c_0_11986, 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_7217]), ['final']). 6.97/7.25 cnf(c_0_11987, 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))), inference(split_conjunct,[status(thm)],[c_0_7218]), ['final']). 6.97/7.25 cnf(c_0_11988, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),c_Groups_Oone__class_Oone(X1))),X2)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7219]), ['final']). 6.97/7.25 cnf(c_0_11989, 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,esk516_3(X2,X1,X3)))))|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_6993]), ['final']). 6.97/7.25 cnf(c_0_11990, 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_7220]), ['final']). 6.97/7.25 cnf(c_0_11991, 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_7221]), ['final']). 6.97/7.25 cnf(c_0_11992, 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_7222]), ['final']). 6.97/7.25 cnf(c_0_11993, plain, (c_SetInterval_Oord__class_OgreaterThanAtMost(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_OgreaterThanAtMost(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_7223]), ['final']). 6.97/7.25 cnf(c_0_11994, 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,esk319_6(X3,X2,X1,X4,X5,X6)),esk320_6(X3,X2,X1,X4,X5,X6))))), inference(split_conjunct,[status(thm)],[c_0_6636]), ['final']). 6.97/7.25 cnf(c_0_11995, 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)))|esk289_2(X1,X2)!=esk288_2(X1,X2)|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),X1))|~hBOOL(hAPP(c_List_Odistinct(X2),esk287_2(X1,X2)))), inference(rw,[status(thm)],[c_0_7224, c_0_4645]), ['final']). 6.97/7.25 cnf(c_0_11996, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_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)),X1))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_11997, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)|hAPP(X5,esk570_6(X2,X4,X5,X1,X3,X3))!=hAPP(X4,esk570_6(X2,X4,X5,X1,X3,X3))), inference(er,[status(thm)],[c_0_7225]), ['final']). 6.97/7.25 cnf(c_0_11998, 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_7226, c_0_4742]), ['final']). 6.97/7.25 cnf(c_0_11999, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X2,X3,X1)),X2))|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)))|~hBOOL(hAPP(X1,esk275_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.25 cnf(c_0_12000, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),esk276_3(X2,X3,X1)))|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)))|~hBOOL(hAPP(X1,esk273_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.25 cnf(c_0_12001, plain, (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))=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)|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7227]), ['final']). 6.97/7.25 cnf(c_0_12002, 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)),esk255_3(X1,X2,X3)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_12003, plain, (X1=hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk295_5(X4,X5,X1,X3,X2)),esk296_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_7097]), ['final']). 6.97/7.25 cnf(c_0_12004, plain, (hAPP(hAPP(X5,hAPP(c_Fun_Ocomp(X2,X1,X2,X8),X7)),X6)=hAPP(hAPP(X5,X8),hAPP(c_Set_Oimage(X2,X2,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_7228]), ['final']). 6.97/7.25 cnf(c_0_12005, 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,esk165_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']). 6.97/7.25 cnf(c_0_12006, 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_7230]), ['final']). 6.97/7.25 cnf(c_0_12007, 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_7231]), ['final']). 6.97/7.25 cnf(c_0_12008, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_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)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_12009, 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)),esk255_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_12010, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|hAPP(hAPP(c_List_Omap(X1,X4),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_7232]), ['final']). 6.97/7.25 cnf(c_0_12011, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),hAPP(hAPP(X3,X5),X6)),X4)=hAPP(hAPP(X3,X5),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))), inference(split_conjunct,[status(thm)],[c_0_7233]), ['final']). 6.97/7.25 cnf(c_0_12012, plain, (hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,X3))=c_Orderings_Oord__class_OLeast(tc_Nat_Onat,X1)|hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,hAPP(c_Nat_OSuc,esk95_4(X2,X3,X4,X1))))|~hBOOL(hAPP(X3,esk95_4(X2,X3,X4,X1)))|~hBOOL(hAPP(X3,X2))|~hBOOL(hAPP(X1,X4))), inference(split_conjunct,[status(thm)],[c_0_6613]), ['final']). 6.97/7.25 cnf(c_0_12013, plain, (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),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_7234]), ['final']). 6.97/7.25 cnf(c_0_12014, plain, (c_List_Olist_ONil(X1)=X2|hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(c_List_Oset(X1),X2))=hAPP(c_List_Ofoldl(X1,X1,c_Groups_Otimes__class_Otimes(X1),hAPP(c_List_Ohd(X1),X2)),hAPP(c_List_Otl(X1),X2))|~class_Lattices_Oab__semigroup__idem__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_7235]), ['final']). 6.97/7.25 cnf(c_0_12015, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk14_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_7236]), ['final']). 6.97/7.25 cnf(c_0_12016, 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_7237]), ['final']). 6.97/7.25 cnf(c_0_12017, plain, (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)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4))|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7238]), ['final']). 6.97/7.25 cnf(c_0_12018, plain, (c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),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(c_Finite__Set_Ofinite(X1),X2))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_6257]), ['final']). 6.97/7.25 cnf(c_0_12019, 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_6270]), ['final']). 6.97/7.25 cnf(c_0_12020, plain, (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),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_7239]), ['final']). 6.97/7.25 cnf(c_0_12021, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X1,X3,X2)),X1))|hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X1)))|~hBOOL(hAPP(X2,esk275_3(X1,X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.25 cnf(c_0_12022, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk276_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk273_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.25 cnf(c_0_12023, plain, (X3=c_Big__Operators_Olattice__class_OSup__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_6276]), ['final']). 6.97/7.25 cnf(c_0_12024, plain, (X3=c_Big__Operators_Olinorder__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_6247]), ['final']). 6.97/7.25 cnf(c_0_12025, plain, (X1=X2|c_Fun_Ofun__upd(X3,X4,c_Fun_Ofun__upd(X3,X4,X5,X2,X6),X1,X7)=c_Fun_Ofun__upd(X3,X4,c_Fun_Ofun__upd(X3,X4,X5,X1,X7),X2,X6)), inference(split_conjunct,[status(thm)],[c_0_7240]), ['final']). 6.97/7.25 cnf(c_0_12026, 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_7241]), ['final']). 6.97/7.25 cnf(c_0_12027, 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_7242, c_0_4413]), c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_12028, 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_7181]), ['final']). 6.97/7.25 cnf(c_0_12029, 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_7243, c_0_4742]), ['final']). 6.97/7.25 cnf(c_0_12030, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4)),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),c_List_Olists(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_7244]), ['final']). 6.97/7.25 cnf(c_0_12031, 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_7245, c_0_4977])])]), c_0_7246]), c_0_7247]), ['final']). 6.97/7.25 cnf(c_0_12032, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,esk403_5(X3,X4,X5,X2,X1),esk404_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_6741]), ['final']). 6.97/7.25 cnf(c_0_12033, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,esk38_5(X3,X4,X5,X2,X1),esk39_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_7164]), ['final']). 6.97/7.25 cnf(c_0_12034, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk530_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_7248]), ['final']). 6.97/7.25 cnf(c_0_12035, 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))|hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X4),X1)!=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3))), inference(rw,[status(thm)],[c_0_7249, c_0_6030]), ['final']). 6.97/7.25 cnf(c_0_12036, plain, (hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X2))=c_Random__Sequence_ORandom(X2,X3,X1,X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), inference(split_conjunct,[status(thm)],[c_0_5893]), ['final']). 6.97/7.25 cnf(c_0_12037, 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_7250, c_0_4415]), c_0_4415]), c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_12038, plain, (hAPP(X6,X7)=hAPP(hAPP(X3,hAPP(X6,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))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X8),X7))), inference(split_conjunct,[status(thm)],[c_0_7251]), ['final']). 6.97/7.25 cnf(c_0_12039, 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),esk32_4(X4,X3,X2,X1))))), inference(split_conjunct,[status(thm)],[c_0_6725]), ['final']). 6.97/7.25 cnf(c_0_12040, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk527_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_7252]), ['final']). 6.97/7.25 cnf(c_0_12041, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk242_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_7253]), ['final']). 6.97/7.25 cnf(c_0_12042, 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_7254, c_0_7255]), ['final']). 6.97/7.25 cnf(c_0_12043, 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_7256]), ['final']). 6.97/7.25 cnf(c_0_12044, 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_7257]), ['final']). 6.97/7.25 cnf(c_0_12045, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|c_Big__Operators_Olattice__class_OSup__fin(X1,X2)=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))|~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_7258]), ['final']). 6.97/7.25 cnf(c_0_12046, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|c_Big__Operators_Olinorder__class_OMin(X1,X2)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olinorder__class_OMin(X1,X3)),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_7259]), ['final']). 6.97/7.25 cnf(c_0_12047, 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_7070]), ['final']). 6.97/7.25 cnf(c_0_12048, 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_7078]), ['final']). 6.97/7.25 cnf(c_0_12049, 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)),esk332_3(X1,X3,X2)),hAPP(hAPP(c_Set_Oinsert(X2),esk331_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_7260]), ['final']). 6.97/7.25 cnf(c_0_12050, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk26_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_7261]), ['final']). 6.97/7.25 cnf(c_0_12051, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|c_Big__Operators_Olattice__class_OInf__fin(X1,X2)=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))|~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_7262]), ['final']). 6.97/7.25 cnf(c_0_12052, 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_7263]), ['final']). 6.97/7.25 cnf(c_0_12053, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2))=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))|~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_7264]), ['final']). 6.97/7.25 cnf(c_0_12054, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk146_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_7037]), ['final']). 6.97/7.25 cnf(c_0_12055, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk451_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_7265, c_0_5174]), ['final']). 6.97/7.25 cnf(c_0_12056, 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_7266]), ['final']). 6.97/7.25 cnf(c_0_12057, 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_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_6997]), ['final']). 6.97/7.25 cnf(c_0_12058, 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_7267]), ['final']). 6.97/7.25 cnf(c_0_12059, 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_7268, c_0_5002]), c_0_5002]), c_0_5002]), ['final']). 6.97/7.25 cnf(c_0_12060, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk255_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_12061, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Inductive_Ocomplete__lattice__class_Ogfp(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(X4,X3)))), inference(split_conjunct,[status(thm)],[c_0_7269]), ['final']). 6.97/7.25 cnf(c_0_12062, 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_6154]), ['final']). 6.97/7.25 cnf(c_0_12063, 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_6150]), ['final']). 6.97/7.25 cnf(c_0_12064, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk480_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_7270]), ['final']). 6.97/7.25 cnf(c_0_12065, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|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)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7271]), ['final']). 6.97/7.25 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)),esk255_3(X2,X3,X1)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,esk257_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_12067, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk516_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)))), inference(split_conjunct,[status(thm)],[c_0_6993]), ['final']). 6.97/7.25 cnf(c_0_12068, 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_7272]), ['final']). 6.97/7.25 cnf(c_0_12069, 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_7273]), ['final']). 6.97/7.25 cnf(c_0_12070, 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),esk26_3(X2,X3,X1)),esk26_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_7261]), ['final']). 6.97/7.25 cnf(c_0_12071, 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),esk146_3(X2,X3,X1)),esk146_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_7037]), ['final']). 6.97/7.25 cnf(c_0_12072, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk216_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),esk217_3(X2,X3,X1)),esk217_3(X2,X3,X1))),X2))), inference(split_conjunct,[status(thm)],[c_0_4503]), ['final']). 6.97/7.25 cnf(c_0_12073, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|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))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)|~class_Fields_Ofield__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7274]), ['final']). 6.97/7.25 cnf(c_0_12074, 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_7273]), ['final']). 6.97/7.25 cnf(c_0_12075, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk255_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_12076, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk255_3(X2,X3,X1)))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,esk257_3(X2,X3,X1)))|~hBOOL(hAPP(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_12077, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk246_4(X2,X3,X4,X1)),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|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_7275]), ['final']). 6.97/7.25 cnf(c_0_12078, 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_7276]), ['final']). 6.97/7.25 cnf(c_0_12079, 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_7277]), ['final']). 6.97/7.25 cnf(c_0_12080, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X4),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))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(X5,X2)))), inference(split_conjunct,[status(thm)],[c_0_7278]), ['final']). 6.97/7.25 cnf(c_0_12081, plain, (hBOOL(hAPP(X1,esk120_2(X1,X2)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk118_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk119_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,esk118_2(X1,X2)))|~hBOOL(hAPP(X1,X3))), inference(rw,[status(thm)],[c_0_7279, c_0_6285]), ['final']). 6.97/7.25 cnf(c_0_12082, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk339_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_7280]), ['final']). 6.97/7.25 cnf(c_0_12083, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk67_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),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5472]), ['final']). 6.97/7.25 cnf(c_0_12084, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk280_4(X2,X3,X4,X1)),X4))|c_Wellfounded_Omax__extp(X1,X2,X4,X3)|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),X4))), inference(split_conjunct,[status(thm)],[c_0_7281]), ['final']). 6.97/7.25 cnf(c_0_12085, 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_7282]), ['final']). 6.97/7.25 cnf(c_0_12086, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk499_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_7283]), ['final']). 6.97/7.25 cnf(c_0_12087, plain, (X3=X5|X4=X2|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_5072]), ['final']). 6.97/7.25 cnf(c_0_12088, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk126_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_7284]), ['final']). 6.97/7.25 cnf(c_0_12089, plain, (X4=hAPP(c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3)),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_7285]), ['final']). 6.97/7.25 cnf(c_0_12090, plain, (hAPP(c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))=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_7286]), ['final']). 6.97/7.25 cnf(c_0_12091, 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_6860]), ['final']). 6.97/7.25 cnf(c_0_12092, 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_7287]), ['final']). 6.97/7.25 cnf(c_0_12093, plain, (hAPP(c_Groups_Oabs__class_Oabs(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),hAPP(hAPP(c_COMBB(X1,X1,X2),c_Groups_Oabs__class_Oabs(X1)),X3)),X4)|~class_Fields_Olinordered__field(X1)), inference(split_conjunct,[status(thm)],[c_0_7288]), ['final']). 6.97/7.25 cnf(c_0_12094, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X3),hAPP(hAPP(c_COMBC(X2,X4,X1),X5),X6))=hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X4,X1)),X3),X5),X6)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7289]), ['final']). 6.97/7.25 cnf(c_0_12095, 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_7290]), ['final']). 6.97/7.25 cnf(c_0_12096, plain, (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))=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)|~class_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7291]), ['final']). 6.97/7.25 cnf(c_0_12097, 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),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7292]), ['final']). 6.97/7.25 cnf(c_0_12098, 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_7293]), ['final']). 6.97/7.25 cnf(c_0_12099, 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_7294]), ['final']). 6.97/7.25 cnf(c_0_12100, plain, (hAPP(hAPP(c_List_Oappend(X1),esk428_3(X2,X3,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),esk429_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_7295]), ['final']). 6.97/7.25 cnf(c_0_12101, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),esk210_3(X1,X3,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk211_3(X1,X3,X2)))|~hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_7296]), ['final']). 6.97/7.25 cnf(c_0_12102, 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_7297, c_0_6909]), c_0_6910]), ['final']). 6.97/7.25 cnf(c_0_12103, 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_7298]), ['final']). 6.97/7.25 cnf(c_0_12104, 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_6869]), ['final']). 6.97/7.25 cnf(c_0_12105, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|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_Lattices_Oab__semigroup__idem__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7299]), ['final']). 6.97/7.25 cnf(c_0_12106, plain, (X3=hAPP(hAPP(c_List_Oappend(X1),esk522_3(X3,X2,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk523_3(X3,X2,X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_5752]), ['final']). 6.97/7.25 cnf(c_0_12107, 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_7300, c_0_5174]), ['final']). 6.97/7.25 cnf(c_0_12108, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)), inference(split_conjunct,[status(thm)],[c_0_7062]), ['final']). 6.97/7.25 cnf(c_0_12109, 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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_7301, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), ['final']). 6.97/7.25 cnf(c_0_12110, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_7302, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), ['final']). 6.97/7.25 cnf(c_0_12111, 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_6719]), ['final']). 6.97/7.25 cnf(c_0_12112, plain, (c_List_Olist_ONil(X1)=X2|hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_OSuc,X3)),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)))), inference(split_conjunct,[status(thm)],[c_0_7303]), ['final']). 6.97/7.25 cnf(c_0_12113, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk60_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_7182]), ['final']). 6.97/7.25 cnf(c_0_12114, plain, (X3=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)|~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))), inference(split_conjunct,[status(thm)],[c_0_5221]), ['final']). 6.97/7.25 cnf(c_0_12115, 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_7304]), ['final']). 6.97/7.25 cnf(c_0_12116, plain, (c_Fun_Obij__betw(X1,X3,X5,X6,X8)|~c_Fun_Obij__betw(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5),X6,X7)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X3,X5),X6)),X8))|~c_Fun_Obij__betw(X3,X2,X4,X8,X7)), inference(split_conjunct,[status(thm)],[c_0_7305]), ['final']). 6.97/7.25 cnf(c_0_12117, 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_6941]), ['final']). 6.97/7.25 cnf(c_0_12118, 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_6692]), ['final']). 6.97/7.25 cnf(c_0_12119, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|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_7306]), ['final']). 6.97/7.25 cnf(c_0_12120, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk59_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_7182]), ['final']). 6.97/7.25 cnf(c_0_12121, 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(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|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)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.25 cnf(c_0_12122, 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_7307, c_0_5002]), c_0_5002]), c_0_5002]), ['final']). 6.97/7.25 cnf(c_0_12123, 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_7308, c_0_4467]), ['final']). 6.97/7.25 cnf(c_0_12124, 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_7309]), ['final']). 6.97/7.25 cnf(c_0_12125, 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_6943]), ['final']). 6.97/7.25 cnf(c_0_12126, 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)), inference(split_conjunct,[status(thm)],[c_0_7310]), ['final']). 6.97/7.25 cnf(c_0_12127, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),hAPP(c_List_Oset(X2),X3))=hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X4),X3))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_List_Odistinct(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7311]), ['final']). 6.97/7.25 cnf(c_0_12128, 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_7312]), ['final']). 6.97/7.25 cnf(c_0_12129, 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_7313]), ['final']). 6.97/7.25 cnf(c_0_12130, 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_7314]), ['final']). 6.97/7.25 cnf(c_0_12131, 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_7315]), ['final']). 6.97/7.25 cnf(c_0_12132, 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_7316]), ['final']). 6.97/7.25 cnf(c_0_12133, 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_7317]), ['final']). 6.97/7.25 cnf(c_0_12134, 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_7318]), ['final']). 6.97/7.25 cnf(c_0_12135, 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,esk50_4(X2,X1,X3,X4))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), inference(split_conjunct,[status(thm)],[c_0_6913]), ['final']). 6.97/7.25 cnf(c_0_12136, 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_7319]), ['final']). 6.97/7.25 cnf(c_0_12137, 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),esk255_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_12138, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk257_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_12139, 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)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3))|~class_Orderings_Olinorder(X4)), inference(split_conjunct,[status(thm)],[c_0_7320]), ['final']). 6.97/7.25 cnf(c_0_12140, plain, (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_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_7321]), ['final']). 6.97/7.25 cnf(c_0_12141, plain, (hAPP(c_Set_Oimage(X1,X2,c_Hilbert__Choice_Oinv__into(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X3)),X4)=hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X4),X3)|~c_Fun_Obij__betw(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)))), inference(rw,[status(thm)],[c_0_7322, c_0_4768]), ['final']). 6.97/7.25 cnf(c_0_12142, 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_7323]), ['final']). 6.97/7.25 cnf(c_0_12143, 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_7324]), ['final']). 6.97/7.25 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|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)), inference(split_conjunct,[status(thm)],[c_0_5766]), ['final']). 6.97/7.25 cnf(c_0_12145, 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_7325]), ['final']). 6.97/7.25 cnf(c_0_12146, 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))), inference(split_conjunct,[status(thm)],[c_0_5367]), ['final']). 6.97/7.25 cnf(c_0_12147, 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_7326]), ['final']). 6.97/7.25 cnf(c_0_12148, 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_7327]), ['final']). 6.97/7.25 cnf(c_0_12149, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)),X1)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),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))), inference(split_conjunct,[status(thm)],[c_0_7328]), ['final']). 6.97/7.25 cnf(c_0_12150, 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_7329, c_0_4467]), c_0_4467]), ['final']). 6.97/7.25 cnf(c_0_12151, 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_7330, c_0_5560]), ['final']). 6.97/7.25 cnf(c_0_12152, 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_7331]), ['final']). 6.97/7.25 cnf(c_0_12153, 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_7332]), ['final']). 6.97/7.25 cnf(c_0_12154, 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_7333]), ['final']). 6.97/7.25 cnf(c_0_12155, 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_7334, c_0_4632]), ['final']). 6.97/7.25 cnf(c_0_12156, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk374_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_7335]), ['final']). 6.97/7.25 cnf(c_0_12157, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk331_3(X2,X3,X1)),esk332_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_7260]), ['final']). 6.97/7.25 cnf(c_0_12158, 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_7336, c_0_4471]), c_0_4471]), ['final']). 6.97/7.25 cnf(c_0_12159, 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),esk27_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))), inference(rw,[status(thm)],[c_0_7337, c_0_4813]), ['final']). 6.97/7.25 cnf(c_0_12160, 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_7338]), ['final']). 6.97/7.25 cnf(c_0_12161, 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),esk233_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_6645]), ['final']). 6.97/7.25 cnf(c_0_12162, 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_7339]), ['final']). 6.97/7.25 cnf(c_0_12163, 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_5111]), ['final']). 6.97/7.25 cnf(c_0_12164, 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_7340]), ['final']). 6.97/7.25 cnf(c_0_12165, plain, (c_Relation_Otrans(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_Relation_Otrans(X1,X2)|~c_Relation_Oantisym(X1,X2)), inference(rw,[status(thm)],[c_0_7341, c_0_5560]), ['final']). 6.97/7.25 cnf(c_0_12166, 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_7342]), ['final']). 6.97/7.25 cnf(c_0_12167, 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_7343]), ['final']). 6.97/7.25 cnf(c_0_12168, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk353_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_6949]), ['final']). 6.97/7.25 cnf(c_0_12169, 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_7344]), ['final']). 6.97/7.25 cnf(c_0_12170, plain, (hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,X1)),X4),X5),X6)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(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_7345]), ['final']). 6.97/7.25 cnf(c_0_12171, plain, (hAPP(hAPP(X4,X1),X3)=hAPP(hAPP(X4,X2),X3)|hAPP(X1,esk300_7(X1,X2,X3,X4,X5,X6,X7))!=hAPP(X2,esk300_7(X1,X2,X3,X4,X5,X6,X7))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X3))|~c_Finite__Set_Ofolding__image(X8,X7,X6,X5,X4)), inference(split_conjunct,[status(thm)],[c_0_6948]), ['final']). 6.97/7.25 cnf(c_0_12172, 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,esk529_5(X4,X2,X3,X3,X1))!=hAPP(X4,esk529_5(X4,X2,X3,X3,X1))|~class_Groups_Ocomm__monoid__mult(X1)|~class_Groups_Ocomm__monoid__add(X1)|~c_Nat__Transfer_Onat__set(X3)), inference(er,[status(thm)],[c_0_7346]), ['final']). 6.97/7.25 cnf(c_0_12173, 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),esk255_3(X1,X2,X3)),X1))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_12174, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_List_Odrop(X2),X1),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4))=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))),X4)), inference(split_conjunct,[status(thm)],[c_0_7347]), ['final']). 6.97/7.25 cnf(c_0_12175, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk170_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_7348]), ['final']). 6.97/7.25 cnf(c_0_12176, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),esk222_5(X3,X4,X1,X5,X2)),X3)|hAPP(hAPP(c_List_Olist_OCons(X2),X5),X1)=X3|hAPP(hAPP(c_List_Olist_OCons(X2),X5),X1)!=hAPP(hAPP(c_List_Oappend(X2),X4),X3)), inference(split_conjunct,[status(thm)],[c_0_5751]), ['final']). 6.97/7.25 cnf(c_0_12177, plain, (X1=hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)|X4=hAPP(hAPP(c_List_Oappend(X2),esk490_5(X4,X3,X1,X5,X2)),X1)|hAPP(hAPP(c_List_Oappend(X2),X5),X1)!=hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)), inference(split_conjunct,[status(thm)],[c_0_7349]), ['final']). 6.97/7.25 cnf(c_0_12178, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk257_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_12179, 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,esk561_5(X2,X4,X3,X3,X1))!=hAPP(X4,esk561_5(X2,X4,X3,X3,X1))|~class_Groups_Ocomm__monoid__mult(X1)|~class_Groups_Ocomm__monoid__add(X1)|~c_Nat__Transfer_Onat__set(X3)), inference(er,[status(thm)],[c_0_7350]), ['final']). 6.97/7.25 cnf(c_0_12180, 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)),X2))|~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(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))), inference(split_conjunct,[status(thm)],[c_0_7351]), ['final']). 6.97/7.25 cnf(c_0_12181, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk229_2(X2,X1)),esk229_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_7352, c_0_5560]), ['final']). 6.97/7.25 cnf(c_0_12182, 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)), inference(split_conjunct,[status(thm)],[c_0_7353]), ['final']). 6.97/7.25 cnf(c_0_12183, plain, (X1=hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk222_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_5751]), ['final']). 6.97/7.25 cnf(c_0_12184, plain, (X1=hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)|X5=hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk490_5(X4,X3,X1,X5,X2))|hAPP(hAPP(c_List_Oappend(X2),X5),X1)!=hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)), inference(split_conjunct,[status(thm)],[c_0_7349]), ['final']). 6.97/7.25 cnf(c_0_12185, plain, (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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_6997]), ['final']). 6.97/7.25 cnf(c_0_12186, 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_7266]), ['final']). 6.97/7.25 cnf(c_0_12187, 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_7266]), ['final']). 6.97/7.25 cnf(c_0_12188, 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))|~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_6997]), ['final']). 6.97/7.25 cnf(c_0_12189, 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_7354, c_0_4413]), c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_12190, 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_7355]), ['final']). 6.97/7.25 cnf(c_0_12191, 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_7356]), ['final']). 6.97/7.25 cnf(c_0_12192, 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_7357]), ['final']). 6.97/7.25 cnf(c_0_12193, 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_7358, c_0_5202]), c_0_7359]), c_0_4742]), ['final']). 6.97/7.25 cnf(c_0_12194, 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_7360]), ['final']). 6.97/7.25 cnf(c_0_12195, 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),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__cancel__semiring(X1)), inference(split_conjunct,[status(thm)],[c_0_7361]), ['final']). 6.97/7.25 cnf(c_0_12196, 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_7211]), ['final']). 6.97/7.25 cnf(c_0_12197, 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_7362]), ['final']). 6.97/7.25 cnf(c_0_12198, 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),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__cancel__semiring(X1)), inference(split_conjunct,[status(thm)],[c_0_7361]), ['final']). 6.97/7.25 cnf(c_0_12199, 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_7362]), ['final']). 6.97/7.25 cnf(c_0_12200, 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_7363]), ['final']). 6.97/7.25 cnf(c_0_12201, 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_7364]), ['final']). 6.97/7.25 cnf(c_0_12202, 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_7365]), ['final']). 6.97/7.25 cnf(c_0_12203, 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_7366]), ['final']). 6.97/7.25 cnf(c_0_12204, plain, (c_List_Olist_ONil(X1)=X2|hAPP(c_List_Orotate1(X1),X2)=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)))), inference(split_conjunct,[status(thm)],[c_0_7367]), ['final']). 6.97/7.25 cnf(c_0_12205, 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_7368]), ['final']). 6.97/7.25 cnf(c_0_12206, 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_7369]), ['final']). 6.97/7.25 cnf(c_0_12207, 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_7370]), ['final']). 6.97/7.25 cnf(c_0_12208, 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_7371]), ['final']). 6.97/7.25 cnf(c_0_12209, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X1),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin),X2))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))), inference(rw,[status(thm)],[c_0_7372, c_0_4741]), ['final']). 6.97/7.25 cnf(c_0_12210, 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_7373]), ['final']). 6.97/7.25 cnf(c_0_12211, 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_7374]), ['final']). 6.97/7.25 cnf(c_0_12212, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),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))))), inference(split_conjunct,[status(thm)],[c_0_5860]), ['final']). 6.97/7.25 cnf(c_0_12213, 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_7375]), ['final']). 6.97/7.25 cnf(c_0_12214, 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_7376]), ['final']). 6.97/7.25 cnf(c_0_12215, 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_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_7377]), ['final']). 6.97/7.25 cnf(c_0_12216, 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)))|~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_7378]), ['final']). 6.97/7.25 cnf(c_0_12217, 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)))|~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_7379]), ['final']). 6.97/7.25 cnf(c_0_12218, 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_7380]), ['final']). 6.97/7.25 cnf(c_0_12219, 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_7381]), ['final']). 6.97/7.25 cnf(c_0_12220, 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_7382]), ['final']). 6.97/7.25 cnf(c_0_12221, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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_Rings_Odvd__class_Odvd(X1),X2),X3))|~class_Rings_Oidom(X1)), inference(split_conjunct,[status(thm)],[c_0_5256]), ['final']). 6.97/7.25 cnf(c_0_12222, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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_Rings_Odvd__class_Odvd(X1),X2),X3))|~class_Rings_Oidom(X1)), inference(split_conjunct,[status(thm)],[c_0_5254]), ['final']). 6.97/7.25 cnf(c_0_12223, 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_7383]), ['final']). 6.97/7.25 cnf(c_0_12224, 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_7384]), ['final']). 6.97/7.25 cnf(c_0_12225, 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_7385]), ['final']). 6.97/7.25 cnf(c_0_12226, 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)))|~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_7378]), ['final']). 6.97/7.25 cnf(c_0_12227, 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_7379]), ['final']). 6.97/7.25 cnf(c_0_12228, 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_7386]), ['final']). 6.97/7.25 cnf(c_0_12229, 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_7387, c_0_4415]), c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_12230, 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_7388]), ['final']). 6.97/7.25 cnf(c_0_12231, 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_7389]), ['final']). 6.97/7.25 cnf(c_0_12232, 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_7390]), ['final']). 6.97/7.25 cnf(c_0_12233, 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_7391]), ['final']). 6.97/7.25 cnf(c_0_12234, 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_7392]), ['final']). 6.97/7.25 cnf(c_0_12235, plain, (X5=X6|hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X5)!=hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X6)|~hBOOL(hAPP(hAPP(c_member(X2),X6),hAPP(c_Set_Oimage(X1,X2,X4),X3)))|~hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Set_Oimage(X1,X2,X4),X3)))), inference(split_conjunct,[status(thm)],[c_0_7393]), ['final']). 6.97/7.25 cnf(c_0_12236, 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_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_7394]), ['final']). 6.97/7.25 cnf(c_0_12237, 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_7395]), ['final']). 6.97/7.25 cnf(c_0_12238, 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_7396]), ['final']). 6.97/7.25 cnf(c_0_12239, 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_7397]), ['final']). 6.97/7.25 cnf(c_0_12240, 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_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_7398]), ['final']). 6.97/7.25 cnf(c_0_12241, 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_7399]), ['final']). 6.97/7.25 cnf(c_0_12242, 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_7400]), ['final']). 6.97/7.25 cnf(c_0_12243, plain, (hAPP(X4,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))|~c_Finite__Set_Ofolding__one(X1,X5,X4)), inference(split_conjunct,[status(thm)],[c_0_6177]), ['final']). 6.97/7.25 cnf(c_0_12244, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk414_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_7401]), ['final']). 6.97/7.25 cnf(c_0_12245, plain, (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__idem(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_7402]), ['final']). 6.97/7.25 cnf(c_0_12246, 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_Int_Onumber__ring(X1)|~class_Fields_Ofield(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7403, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), ['final']). 6.97/7.25 cnf(c_0_12247, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X2,X3,X1)),X2))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,esk257_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_12248, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk485_3(X2,X3,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)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X2)), inference(split_conjunct,[status(thm)],[c_0_5288]), ['final']). 6.97/7.25 cnf(c_0_12249, 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_7404]), ['final']). 6.97/7.25 cnf(c_0_12250, 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_7405]), ['final']). 6.97/7.25 cnf(c_0_12251, 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_7406, c_0_7407]), ['final']). 6.97/7.25 cnf(c_0_12252, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk257_3(X1,X2,X3)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk255_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_12253, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk350_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))), inference(split_conjunct,[status(thm)],[c_0_7408]), ['final']). 6.97/7.25 cnf(c_0_12254, plain, (hAPP(c_Finite__Set_Ocard(tc_sum(X1,X3)),c_Sum__Type_OPlus(X1,X3,X2,X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7409]), ['final']). 6.97/7.25 cnf(c_0_12255, 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_6169]), ['final']). 6.97/7.25 cnf(c_0_12256, plain, (c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__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_6174]), ['final']). 6.97/7.25 cnf(c_0_12257, 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,esk327_5(X3,X2,X1,X4,X5))),X3))), inference(split_conjunct,[status(thm)],[c_0_6701]), ['final']). 6.97/7.25 cnf(c_0_12258, 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_7410]), ['final']). 6.97/7.25 cnf(c_0_12259, 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_6965]), ['final']). 6.97/7.25 cnf(c_0_12260, 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_7411]), ['final']). 6.97/7.25 cnf(c_0_12261, 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_7412]), ['final']). 6.97/7.25 cnf(c_0_12262, 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,esk252_5(X3,X2,X4,X5,X1))),X3))), inference(split_conjunct,[status(thm)],[c_0_6704]), ['final']). 6.97/7.25 cnf(c_0_12263, 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,esk155_5(X3,X4,X5,X2,X1))))), inference(split_conjunct,[status(thm)],[c_0_6707]), ['final']). 6.97/7.25 cnf(c_0_12264, 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,esk107_5(X3,X2,X1,X4,X5))))), inference(split_conjunct,[status(thm)],[c_0_6711]), ['final']). 6.97/7.25 cnf(c_0_12265, 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_7413]), ['final']). 6.97/7.25 cnf(c_0_12266, 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_7414, c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_12267, 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_7415, c_0_4798]), ['final']). 6.97/7.25 cnf(c_0_12268, 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_7208]), ['final']). 6.97/7.25 cnf(c_0_12269, 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)),esk437_3(X2,X3,X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_7023]), ['final']). 6.97/7.25 cnf(c_0_12270, plain, (hAPP(X6,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))|~hBOOL(hAPP(hAPP(c_member(X2),X8),X7))), inference(split_conjunct,[status(thm)],[c_0_7416]), ['final']). 6.97/7.25 cnf(c_0_12271, 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_7417]), ['final']). 6.97/7.25 cnf(c_0_12272, 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_7418, c_0_7419]), ['final']). 6.97/7.25 cnf(c_0_12273, plain, (c_Groups_Oone__class_Oone(X1)=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)!=hAPP(X2,esk93_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_6812]), ['final']). 6.97/7.25 cnf(c_0_12274, 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_7420])]), ['final']). 6.97/7.25 cnf(c_0_12275, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|X2=hAPP(hAPP(c_Set_Oinsert(X1),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(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))), inference(split_conjunct,[status(thm)],[c_0_7421]), ['final']). 6.97/7.25 cnf(c_0_12276, plain, (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),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_6838]), ['final']). 6.97/7.25 cnf(c_0_12277, 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_6839]), ['final']). 6.97/7.25 cnf(c_0_12278, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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_Groups_Otimes__class_Otimes(X1),X4),X2)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6835]), ['final']). 6.97/7.25 cnf(c_0_12279, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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_Groups_Otimes__class_Otimes(X1),X4),X2)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6837]), ['final']). 6.97/7.25 cnf(c_0_12280, 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_7422]), ['final']). 6.97/7.25 cnf(c_0_12281, plain, (hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,X1)),X3),X4),X5)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(X3,X5)),hAPP(X4,X5))|~class_Groups_Ominus(X1)), inference(split_conjunct,[status(thm)],[c_0_7423]), ['final']). 6.97/7.25 cnf(c_0_12282, plain, (hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,X1)),X3),X4),X5)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(X3,X5)),hAPP(X4,X5))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7424]), ['final']). 6.97/7.25 cnf(c_0_12283, 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_7425]), ['final']). 6.97/7.25 cnf(c_0_12284, 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)), inference(split_conjunct,[status(thm)],[c_0_7426]), ['final']). 6.97/7.25 cnf(c_0_12285, 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_5742]), ['final']). 6.97/7.25 cnf(c_0_12286, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk454_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_7427]), ['final']). 6.97/7.25 cnf(c_0_12287, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(X2,X3)),hAPP(X4,X3))=hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,X1)),X2),X4),X3)|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7428]), ['final']). 6.97/7.25 cnf(c_0_12288, 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)), inference(split_conjunct,[status(thm)],[c_0_7429]), ['final']). 6.97/7.25 cnf(c_0_12289, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)=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)|~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_7430, c_0_4471]), ['final']). 6.97/7.25 cnf(c_0_12290, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|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))), inference(split_conjunct,[status(thm)],[c_0_7431]), ['final']). 6.97/7.25 cnf(c_0_12291, 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_7432]), ['final']). 6.97/7.25 cnf(c_0_12292, 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_7433, c_0_4415]), c_0_5002]), c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_12293, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk458_3(X3,X2,X1)))=X1|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),X3),X1))), inference(split_conjunct,[status(thm)],[c_0_7434]), ['final']). 6.97/7.25 cnf(c_0_12294, 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_7435]), ['final']). 6.97/7.25 cnf(c_0_12295, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X2,X3,X1)),X2))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,esk257_3(X2,X3,X1)))|~hBOOL(hAPP(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_12296, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk257_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk255_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_12297, 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_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin)))=c_Lazy__Sequence_Osmall__lazy_H(X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))), inference(rw,[status(thm)],[c_0_7436, c_0_4741]), ['final']). 6.97/7.25 cnf(c_0_12298, 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_7437]), ['final']). 6.97/7.25 cnf(c_0_12299, plain, (c_List_Olist__all2(X2,X5,X1,X3,X4)|~hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk436_5(X1,X4,X5,X3,X2))),hAPP(hAPP(c_List_Onth(X5),X4),esk436_5(X1,X4,X5,X3,X2))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_7094]), ['final']). 6.97/7.25 cnf(c_0_12300, plain, (c_List_Olist__all2(X2,X5,X1,X3,X4)|~hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk89_5(X4,X3,X1,X5,X2))),hAPP(hAPP(c_List_Onth(X5),X4),esk89_5(X4,X3,X1,X5,X2))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_7099]), ['final']). 6.97/7.25 cnf(c_0_12301, plain, (hAPP(X3,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X5))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),hAPP(X3,X4)),hAPP(X3,X5))|~class_Orderings_Olinorder(X1)|~class_Orderings_Olinorder(X2)|~c_Orderings_Oorder__class_Omono(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_7438]), ['final']). 6.97/7.25 cnf(c_0_12302, 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_7439, c_0_4415]), c_0_4415]), c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_12303, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3))|~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))), inference(split_conjunct,[status(thm)],[c_0_7440]), ['final']). 6.97/7.25 cnf(c_0_12304, plain, (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(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_4569]), ['final']). 6.97/7.25 cnf(c_0_12305, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk13_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_7236]), ['final']). 6.97/7.25 cnf(c_0_12306, 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_6971]), ['final']). 6.97/7.25 cnf(c_0_12307, 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_7441]), ['final']). 6.97/7.25 cnf(c_0_12308, 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))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7442, c_0_4813]), c_0_4813]), ['final']). 6.97/7.25 cnf(c_0_12309, plain, (hAPP(X3,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X5))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X2),hAPP(X3,X4)),hAPP(X3,X5))|~class_Orderings_Olinorder(X1)|~class_Orderings_Olinorder(X2)|~c_Orderings_Oorder__class_Omono(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_7443]), ['final']). 6.97/7.25 cnf(c_0_12310, 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_7444]), ['final']). 6.97/7.25 cnf(c_0_12311, 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),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)), inference(split_conjunct,[status(thm)],[c_0_7444]), ['final']). 6.97/7.25 cnf(c_0_12312, 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),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_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7445]), ['final']). 6.97/7.25 cnf(c_0_12313, 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),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_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7445]), ['final']). 6.97/7.25 cnf(c_0_12314, plain, (hAPP(c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3)),hAPP(c_Set_Oimage(X1,X2,X3),X5))=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_7446]), ['final']). 6.97/7.25 cnf(c_0_12315, plain, (X4=X2|~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_7447]), ['final']). 6.97/7.25 cnf(c_0_12316, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk349_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_Orderings_Olinorder(X5)|~class_Complete__Lattice_Ocomplete__lattice(X5)), inference(split_conjunct,[status(thm)],[c_0_7100]), ['final']). 6.97/7.25 cnf(c_0_12317, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk133_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_7101]), ['final']). 6.97/7.25 cnf(c_0_12318, 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_7448, c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_12319, 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_7449]), ['final']). 6.97/7.25 cnf(c_0_12320, 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_7450]), ['final']). 6.97/7.25 cnf(c_0_12321, 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_7451]), ['final']). 6.97/7.25 cnf(c_0_12322, 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_7452]), ['final']). 6.97/7.25 cnf(c_0_12323, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk99_4(X2,X3,X4,X1)),c_Quotient_ORespects(X1,X4)))|~hBOOL(hAPP(X3,X5))|~hBOOL(hAPP(X2,esk98_4(X2,X3,X4,X1)))|~c_Equiv__Relations_Oequivp(X1,X4)), inference(split_conjunct,[status(thm)],[c_0_7068]), ['final']). 6.97/7.25 cnf(c_0_12324, 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_7453]), ['final']). 6.97/7.25 cnf(c_0_12325, 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_7454]), ['final']). 6.97/7.25 cnf(c_0_12326, 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_7455]), ['final']). 6.97/7.25 cnf(c_0_12327, plain, (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)))|~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_7456]), ['final']). 6.97/7.25 cnf(c_0_12328, 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_7457]), ['final']). 6.97/7.25 cnf(c_0_12329, plain, (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)))|~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_7456]), ['final']). 6.97/7.25 cnf(c_0_12330, plain, (hAPP(X1,X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X2=esk231_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_7458, c_0_4742]), ['final']). 6.97/7.25 cnf(c_0_12331, plain, (hBOOL(hAPP(hAPP(hAPP(X1,esk196_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_6981]), ['final']). 6.97/7.25 cnf(c_0_12332, plain, (hBOOL(hAPP(hAPP(hAPP(X1,esk90_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_7459]), ['final']). 6.97/7.25 cnf(c_0_12333, 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,esk367_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_6396]), ['final']). 6.97/7.25 cnf(c_0_12334, 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_7457]), ['final']). 6.97/7.25 cnf(c_0_12335, 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_List_Oset(X1),X2)),hAPP(c_List_Oset(X1),X3))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_7460]), ['final']). 6.97/7.25 cnf(c_0_12336, 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_7461]), ['final']). 6.97/7.25 cnf(c_0_12337, 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_7462]), ['final']). 6.97/7.25 cnf(c_0_12338, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk412_2(X2,X1)),esk412_2(X2,X1))),X2))|c_Relation_Oirrefl(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7463]), ['final']). 6.97/7.25 cnf(c_0_12339, plain, (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,esk316_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_6397]), ['final']). 6.97/7.25 cnf(c_0_12340, plain, (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,esk183_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_6402]), ['final']). 6.97/7.25 cnf(c_0_12341, plain, (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),X4)|c_Groups_Oone__class_Oone(X1)!=hAPP(X2,esk524_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__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_6395]), ['final']). 6.97/7.25 cnf(c_0_12342, 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_7464]), ['final']). 6.97/7.25 cnf(c_0_12343, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk597_2(X2,X1)),esk596_2(X2,X1))),X2))|c_Relation_Oantisym(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7465]), ['final']). 6.97/7.25 cnf(c_0_12344, 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_7466, c_0_4415]), c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_12345, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk516_3(X1,X2,X3))),X2))|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_6993]), ['final']). 6.97/7.25 cnf(c_0_12346, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk37_3(X3,X2,X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7467]), ['final']). 6.97/7.25 cnf(c_0_12347, 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_7468]), ['final']). 6.97/7.25 cnf(c_0_12348, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk596_2(X2,X1)),esk597_2(X2,X1))),X2))|c_Relation_Oantisym(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7465]), ['final']). 6.97/7.25 cnf(c_0_12349, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk531_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_7469]), ['final']). 6.97/7.25 cnf(c_0_12350, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk500_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_7470]), ['final']). 6.97/7.25 cnf(c_0_12351, 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_6623]), ['final']). 6.97/7.25 cnf(c_0_12352, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk261_4(X3,X4,X2,X1)),esk260_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_6770]), ['final']). 6.97/7.25 cnf(c_0_12353, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk563_2(X2,X1)),esk564_2(X2,X1))),X2))|c_Relation_Otrans(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7471]), ['final']). 6.97/7.25 cnf(c_0_12354, 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_7472]), ['final']). 6.97/7.25 cnf(c_0_12355, plain, (c_Hilbert__Choice_Oinv__into(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3))=X3|~c_Fun_Obij__betw(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_7473]), ['final']). 6.97/7.25 cnf(c_0_12356, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk562_2(X2,X1)),esk563_2(X2,X1))),X2))|c_Relation_Otrans(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7471]), ['final']). 6.97/7.25 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),X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_6997]), ['final']). 6.97/7.25 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_7266]), ['final']). 6.97/7.25 cnf(c_0_12359, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk312_2(X2,X1)),esk313_2(X2,X1))),X2))|c_Relation_Osym(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_6959]), ['final']). 6.97/7.25 cnf(c_0_12360, 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_7474]), ['final']). 6.97/7.25 cnf(c_0_12361, 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_7475]), ['final']). 6.97/7.25 cnf(c_0_12362, plain, (hAPP(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,X2),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_7476]), ['final']). 6.97/7.25 cnf(c_0_12363, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk82_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_7477]), ['final']). 6.97/7.25 cnf(c_0_12364, 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_7478, c_0_5065]), ['final']). 6.97/7.25 cnf(c_0_12365, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|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_7479]), ['final']). 6.97/7.25 cnf(c_0_12366, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,esk349_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_Orderings_Olinorder(X1)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7100]), ['final']). 6.97/7.25 cnf(c_0_12367, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(X3,esk133_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_7101]), ['final']). 6.97/7.25 cnf(c_0_12368, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)=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)))))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7480]), ['final']). 6.97/7.25 cnf(c_0_12369, 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_7481]), ['final']). 6.97/7.25 cnf(c_0_12370, 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_7482]), ['final']). 6.97/7.25 cnf(c_0_12371, 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_7483]), ['final']). 6.97/7.25 cnf(c_0_12372, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk340_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_7484]), ['final']). 6.97/7.25 cnf(c_0_12373, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)=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)))))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7485]), ['final']). 6.97/7.25 cnf(c_0_12374, 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),esk32_4(X1,X3,X2,X4))))), inference(split_conjunct,[status(thm)],[c_0_6725]), ['final']). 6.97/7.25 cnf(c_0_12375, plain, (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))|~c_List_Olist__all2(X1,X2,X3,X4,X5)|~hBOOL(hAPP(hAPP(X3,X6),X7))), inference(split_conjunct,[status(thm)],[c_0_7486]), ['final']). 6.97/7.25 cnf(c_0_12376, 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_7487]), ['final']). 6.97/7.25 cnf(c_0_12377, plain, (hAPP(hAPP(X5,X7),X6)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,X3),X7),X4),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_7488]), ['final']). 6.97/7.25 cnf(c_0_12378, 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_7489]), ['final']). 6.97/7.25 cnf(c_0_12379, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk540_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_7490]), ['final']). 6.97/7.25 cnf(c_0_12380, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk139_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_7491]), ['final']). 6.97/7.25 cnf(c_0_12381, 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_7492]), ['final']). 6.97/7.25 cnf(c_0_12382, plain, (hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)=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))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7493]), ['final']). 6.97/7.25 cnf(c_0_12383, 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_7494]), ['final']). 6.97/7.25 cnf(c_0_12384, 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']). 6.97/7.25 cnf(c_0_12385, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk187_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_4960]), ['final']). 6.97/7.25 cnf(c_0_12386, 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_7495])]), ['final']). 6.97/7.25 cnf(c_0_12387, 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_7496]), ['final']). 6.97/7.25 cnf(c_0_12388, plain, (hAPP(hAPP(c_List_Olist_OCons(X3),X2),hAPP(c_List_Ofilter(X3,X1),X4))=hAPP(c_List_Ofilter(X3,X1),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_7497]), ['final']). 6.97/7.25 cnf(c_0_12389, 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_7498]), ['final']). 6.97/7.25 cnf(c_0_12390, 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_7499]), ['final']). 6.97/7.25 cnf(c_0_12391, 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))), inference(split_conjunct,[status(thm)],[c_0_7500]), ['final']). 6.97/7.25 cnf(c_0_12392, 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_7501]), ['final']). 6.97/7.25 cnf(c_0_12393, 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_7502]), ['final']). 6.97/7.25 cnf(c_0_12394, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk295_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_7097]), ['final']). 6.97/7.25 cnf(c_0_12395, plain, (X5=X6|~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_7503]), ['final']). 6.97/7.25 cnf(c_0_12396, 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_7504]), ['final']). 6.97/7.25 cnf(c_0_12397, 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)), inference(split_conjunct,[status(thm)],[c_0_7505]), ['final']). 6.97/7.25 cnf(c_0_12398, 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_7506]), ['final']). 6.97/7.25 cnf(c_0_12399, 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_7507]), ['final']). 6.97/7.25 cnf(c_0_12400, 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_7282]), ['final']). 6.97/7.25 cnf(c_0_12401, 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_7508, c_0_4742]), ['final']). 6.97/7.25 cnf(c_0_12402, 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_7509]), ['final']). 6.97/7.25 cnf(c_0_12403, 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_7510]), ['final']). 6.97/7.25 cnf(c_0_12404, 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_7511]), ['final']). 6.97/7.25 cnf(c_0_12405, 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_7512]), ['final']). 6.97/7.25 cnf(c_0_12406, 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_7513, c_0_7514]), ['final']). 6.97/7.25 cnf(c_0_12407, 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_7515]), ['final']). 6.97/7.25 cnf(c_0_12408, 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_7516, c_0_7517]), ['final']). 6.97/7.25 cnf(c_0_12409, plain, (hBOOL(hAPP(hAPP(X1,esk449_1(X1)),esk449_1(X1)))|hBOOL(hAPP(hAPP(X1,esk448_1(X1)),esk449_1(X1)))|c_Equiv__Relations_Opart__equivp(X3,X1)|~hBOOL(hAPP(hAPP(X1,X2),X2))), inference(split_conjunct,[status(thm)],[c_0_7518]), ['final']). 6.97/7.25 cnf(c_0_12410, plain, (hBOOL(hAPP(hAPP(X1,esk448_1(X1)),esk448_1(X1)))|hBOOL(hAPP(hAPP(X1,esk448_1(X1)),esk449_1(X1)))|c_Equiv__Relations_Opart__equivp(X3,X1)|~hBOOL(hAPP(hAPP(X1,X2),X2))), inference(split_conjunct,[status(thm)],[c_0_7518]), ['final']). 6.97/7.25 cnf(c_0_12411, 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_7519, c_0_4798]), ['final']). 6.97/7.25 cnf(c_0_12412, 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_7520, c_0_4415]), c_0_5002]), c_0_4742]), c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_12413, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(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)),hAPP(c_List_Oset(X1),X2)),hAPP(c_List_Oset(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7460]), ['final']). 6.97/7.25 cnf(c_0_12414, plain, (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)=c_List_Obutlast(X2,hAPP(hAPP(c_List_Otake(X2),X1),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_7521]), ['final']). 6.97/7.25 cnf(c_0_12415, 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),X3),X2)),hAPP(hAPP(c_List_Olist_OCons(X5),X4),X1))),c_List_Olistrel1(X5,X6)))), inference(split_conjunct,[status(thm)],[c_0_6216]), ['final']). 6.97/7.25 cnf(c_0_12416, plain, (X2=esk262_3(X4,X3,X1)|hAPP(X4,X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|c_Groups_Oone__class_Oone(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_7127]), ['final']). 6.97/7.25 cnf(c_0_12417, 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_7522]), ['final']). 6.97/7.25 cnf(c_0_12418, plain, (hAPP(c_Fun_Ocomp(X2,X1,X1,X3),c_Hilbert__Choice_Oinv__into(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X3))=c_Fun_Oid(X1)|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_7523]), ['final']). 6.97/7.25 cnf(c_0_12419, 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_7524]), ['final']). 6.97/7.25 cnf(c_0_12420, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk373_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_7335]), ['final']). 6.97/7.25 cnf(c_0_12421, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk243_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))), inference(split_conjunct,[status(thm)],[c_0_7525]), ['final']). 6.97/7.25 cnf(c_0_12422, 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_7526]), ['final']). 6.97/7.25 cnf(c_0_12423, 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_7527]), ['final']). 6.97/7.25 cnf(c_0_12424, 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_7528]), ['final']). 6.97/7.25 cnf(c_0_12425, 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_7529]), ['final']). 6.97/7.25 cnf(c_0_12426, plain, (c_Relation_Oantisym(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_Relation_Oantisym(X1,X2)), inference(rw,[status(thm)],[c_0_7530, c_0_5560]), ['final']). 6.97/7.25 cnf(c_0_12427, plain, (c_Relation_Otrans(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_Relation_Otrans(X1,X2)), inference(rw,[status(thm)],[c_0_7531, c_0_5560]), ['final']). 6.97/7.25 cnf(c_0_12428, 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_7532, c_0_7533]), c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_12429, plain, (c_Fun_Obij__betw(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)))|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|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_7534]), ['final']). 6.97/7.25 cnf(c_0_12430, 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_7535]), ['final']). 6.97/7.25 cnf(c_0_12431, 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_7535]), ['final']). 6.97/7.25 cnf(c_0_12432, 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_7536]), ['final']). 6.97/7.25 cnf(c_0_12433, 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_7537]), ['final']). 6.97/7.25 cnf(c_0_12434, 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_Groups_Omonoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_7538]), ['final']). 6.97/7.25 cnf(c_0_12435, 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_7539]), ['final']). 6.97/7.25 cnf(c_0_12436, 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_7540]), ['final']). 6.97/7.25 cnf(c_0_12437, 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_7541, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), ['final']). 6.97/7.25 cnf(c_0_12438, 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_7033]), ['final']). 6.97/7.25 cnf(c_0_12439, 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_7542]), ['final']). 6.97/7.25 cnf(c_0_12440, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|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)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7543]), ['final']). 6.97/7.25 cnf(c_0_12441, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk355_3(X2,X3,X1)),X3))|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),X3)),X2))), inference(split_conjunct,[status(thm)],[c_0_7544]), ['final']). 6.97/7.25 cnf(c_0_12442, 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_7181]), ['final']). 6.97/7.25 cnf(c_0_12443, 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,esk353_3(X1,X2,X3))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))), inference(split_conjunct,[status(thm)],[c_0_6949]), ['final']). 6.97/7.25 cnf(c_0_12444, 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,esk170_3(X1,X2,X3))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7348]), ['final']). 6.97/7.25 cnf(c_0_12445, 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),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7362]), ['final']). 6.97/7.25 cnf(c_0_12446, 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),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7362]), ['final']). 6.97/7.25 cnf(c_0_12447, 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),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7362]), ['final']). 6.97/7.25 cnf(c_0_12448, 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),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7362]), ['final']). 6.97/7.25 cnf(c_0_12449, 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)), inference(split_conjunct,[status(thm)],[c_0_7545]), ['final']). 6.97/7.25 cnf(c_0_12450, 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_7546]), ['final']). 6.97/7.25 cnf(c_0_12451, 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_7547]), ['final']). 6.97/7.25 cnf(c_0_12452, 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_7548]), ['final']). 6.97/7.25 cnf(c_0_12453, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk468_3(X2,X3,X1)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)))), inference(split_conjunct,[status(thm)],[c_0_7549]), ['final']). 6.97/7.25 cnf(c_0_12454, 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_7550]), ['final']). 6.97/7.25 cnf(c_0_12455, plain, (c_Big__Operators_Olinorder__class_OMin(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_6226]), ['final']). 6.97/7.25 cnf(c_0_12456, plain, (X3=c_Big__Operators_Olinorder__class_OMax(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_6192]), ['final']). 6.97/7.25 cnf(c_0_12457, 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_7551, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), ['final']). 6.97/7.25 cnf(c_0_12458, 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_7552]), ['final']). 6.97/7.25 cnf(c_0_12459, plain, (c_Fun_Oinj__on(X1,X2,c_Hilbert__Choice_Oinv__into(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X3),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(X2,X1,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_7553]), ['final']). 6.97/7.25 cnf(c_0_12460, 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_6735]), ['final']). 6.97/7.25 cnf(c_0_12461, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk386_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_7554]), ['final']). 6.97/7.25 cnf(c_0_12462, 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_7555]), ['final']). 6.97/7.25 cnf(c_0_12463, 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_6218]), ['final']). 6.97/7.25 cnf(c_0_12464, plain, (X3=c_Big__Operators_Olattice__class_OInf__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_6210]), ['final']). 6.97/7.25 cnf(c_0_12465, 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_7378]), ['final']). 6.97/7.25 cnf(c_0_12466, 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_7378]), ['final']). 6.97/7.25 cnf(c_0_12467, 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_7556]), ['final']). 6.97/7.25 cnf(c_0_12468, 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_7557]), ['final']). 6.97/7.25 cnf(c_0_12469, 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_7558]), ['final']). 6.97/7.25 cnf(c_0_12470, 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_7559]), ['final']). 6.97/7.25 cnf(c_0_12471, 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_7560]), ['final']). 6.97/7.25 cnf(c_0_12472, 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_7561]), ['final']). 6.97/7.25 cnf(c_0_12473, 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_7378]), ['final']). 6.97/7.25 cnf(c_0_12474, 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_7378]), ['final']). 6.97/7.25 cnf(c_0_12475, 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_7562, c_0_4734]), c_0_4734]), ['final']). 6.97/7.25 cnf(c_0_12476, 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_7563]), ['final']). 6.97/7.25 cnf(c_0_12477, 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_7564]), ['final']). 6.97/7.25 cnf(c_0_12478, 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_7565]), ['final']). 6.97/7.25 cnf(c_0_12479, 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_7566]), ['final']). 6.97/7.25 cnf(c_0_12480, 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_7567]), ['final']). 6.97/7.25 cnf(c_0_12481, 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_7568, c_0_6829]), c_0_6829]), ['final']). 6.97/7.25 cnf(c_0_12482, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk481_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_7270]), ['final']). 6.97/7.25 cnf(c_0_12483, 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_7569]), ['final']). 6.97/7.25 cnf(c_0_12484, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X1),c_Fun_Oid(X1)),hAPP(c_Set_Oimage(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_7570]), ['final']). 6.97/7.25 cnf(c_0_12485, 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_7571]), ['final']). 6.97/7.25 cnf(c_0_12486, 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_7572]), ['final']). 6.97/7.25 cnf(c_0_12487, 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_7573]), ['final']). 6.97/7.25 cnf(c_0_12488, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7574, c_0_4409]), c_0_4410]), c_0_4411]), ['final']). 6.97/7.25 cnf(c_0_12489, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),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_7575, c_0_4413]), c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_12490, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)))|~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),X3),X4))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7576]), ['final']). 6.97/7.25 cnf(c_0_12491, 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_6773]), ['final']). 6.97/7.25 cnf(c_0_12492, 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),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_7577, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_6506]), ['final']). 6.97/7.25 cnf(c_0_12493, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_7578, c_0_4409]), c_0_4410]), c_0_4411]), ['final']). 6.97/7.25 cnf(c_0_12494, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),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_7579, c_0_4413]), c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_12495, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7580, c_0_4415]), c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_12496, 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_7581]), ['final']). 6.97/7.25 cnf(c_0_12497, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|~class_Int_Onumber__ring(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)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7582, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4821]), ['final']). 6.97/7.25 cnf(c_0_12498, 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_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_7394]), ['final']). 6.97/7.25 cnf(c_0_12499, 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_7583]), ['final']). 6.97/7.25 cnf(c_0_12500, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(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),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_7584, c_0_4409]), c_0_4410]), c_0_4411]), ['final']). 6.97/7.25 cnf(c_0_12501, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(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),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7585, c_0_4413]), c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_12502, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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),X1)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7586, c_0_4409]), c_0_4410]), c_0_4411]), ['final']). 6.97/7.25 cnf(c_0_12503, 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_Ominus__class_Ominus(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),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7587, c_0_4413]), c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_12504, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,esk531_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_7469]), ['final']). 6.97/7.25 cnf(c_0_12505, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,esk500_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_7470]), ['final']). 6.97/7.25 cnf(c_0_12506, plain, (hBOOL(hAPP(hAPP(c_member(X3),hAPP(c_Hilbert__Choice_Oinv__into(X3,X1,X5,X4),X2)),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Set_Oimage(X3,X1,X4),X5)))), inference(split_conjunct,[status(thm)],[c_0_7588]), ['final']). 6.97/7.25 cnf(c_0_12507, 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_7589]), ['final']). 6.97/7.25 cnf(c_0_12508, 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_7590]), ['final']). 6.97/7.25 cnf(c_0_12509, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7591]), ['final']). 6.97/7.25 cnf(c_0_12510, 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)],[c_0_7592, c_0_4410]), c_0_4410]), ['final']). 6.97/7.25 cnf(c_0_12511, plain, (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))|c_List_Olast(X2,X3)=c_List_Olast(X2,hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X4))|c_List_Olist_ONil(X2)=X3), inference(split_conjunct,[status(thm)],[c_0_5315]), ['final']). 6.97/7.25 cnf(c_0_12512, 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_7593]), ['final']). 6.97/7.25 cnf(c_0_12513, 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_7142]), ['final']). 6.97/7.25 cnf(c_0_12514, 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,esk267_3(X2,X1,X3)),esk268_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_5034]), ['final']). 6.97/7.25 cnf(c_0_12515, 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_7594, c_0_4415]), c_0_4415]), c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_12516, 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_7595]), ['final']). 6.97/7.25 cnf(c_0_12517, 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_7596]), ['final']). 6.97/7.25 cnf(c_0_12518, 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_7597]), ['final']). 6.97/7.25 cnf(c_0_12519, 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_7598, c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_12520, 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,esk495_3(X2,X1,X3)),esk496_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_5035]), ['final']). 6.97/7.25 cnf(c_0_12521, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X2))|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)),X4)), inference(split_conjunct,[status(thm)],[c_0_6713]), ['final']). 6.97/7.25 cnf(c_0_12522, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk196_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_6981]), ['final']). 6.97/7.25 cnf(c_0_12523, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk90_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_7459]), ['final']). 6.97/7.25 cnf(c_0_12524, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk545_3(X1,X2,X3))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_7599]), ['final']). 6.97/7.25 cnf(c_0_12525, 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)],[c_0_7600, c_0_4410]), c_0_4410]), ['final']). 6.97/7.25 cnf(c_0_12526, 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_7601]), ['final']). 6.97/7.25 cnf(c_0_12527, 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_7602]), ['final']). 6.97/7.25 cnf(c_0_12528, 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_7603]), ['final']). 6.97/7.25 cnf(c_0_12529, 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),esk397_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_7604]), ['final']). 6.97/7.25 cnf(c_0_12530, 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_7605]), ['final']). 6.97/7.25 cnf(c_0_12531, 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),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7444]), ['final']). 6.97/7.25 cnf(c_0_12532, 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),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7445]), ['final']). 6.97/7.25 cnf(c_0_12533, 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),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7444]), ['final']). 6.97/7.25 cnf(c_0_12534, 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_7606]), ['final']). 6.97/7.25 cnf(c_0_12535, 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_7607]), ['final']). 6.97/7.25 cnf(c_0_12536, 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_7608]), ['final']). 6.97/7.25 cnf(c_0_12537, 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),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7444]), ['final']). 6.97/7.25 cnf(c_0_12538, 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),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7445]), ['final']). 6.97/7.25 cnf(c_0_12539, 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),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7445]), ['final']). 6.97/7.25 cnf(c_0_12540, 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),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7444]), ['final']). 6.97/7.25 cnf(c_0_12541, 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))|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_7609]), ['final']). 6.97/7.25 cnf(c_0_12542, 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_7344]), ['final']). 6.97/7.25 cnf(c_0_12543, 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_7340]), ['final']). 6.97/7.25 cnf(c_0_12544, plain, (c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X3),X2)|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7610]), ['final']). 6.97/7.25 cnf(c_0_12545, 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),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7445]), ['final']). 6.97/7.25 cnf(c_0_12546, 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_7456]), ['final']). 6.97/7.25 cnf(c_0_12547, 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_7456]), ['final']). 6.97/7.25 cnf(c_0_12548, 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_7456]), ['final']). 6.97/7.25 cnf(c_0_12549, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2))|~class_Fields_Olinordered__field(X1)), inference(split_conjunct,[status(thm)],[c_0_7611]), ['final']). 6.97/7.25 cnf(c_0_12550, plain, (c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),X2)|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7612]), ['final']). 6.97/7.25 cnf(c_0_12551, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),c_Complete__Lattice_OInf__class_OInf(X1,X2))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),X2)|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7613]), ['final']). 6.97/7.25 cnf(c_0_12552, 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),X2)),X2))|~c_Relation_Otrans(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7614]), ['final']). 6.97/7.25 cnf(c_0_12553, 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_7022]), ['final']). 6.97/7.25 cnf(c_0_12554, 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_7456]), ['final']). 6.97/7.25 cnf(c_0_12555, 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_7457]), ['final']). 6.97/7.25 cnf(c_0_12556, 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_7457]), ['final']). 6.97/7.25 cnf(c_0_12557, 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_7457]), ['final']). 6.97/7.25 cnf(c_0_12558, 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_7615]), ['final']). 6.97/7.25 cnf(c_0_12559, plain, (hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),X1),c_Nat_OSuc)))=c_Orderings_Oord__class_OLeast(tc_Nat_Onat,X1)|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_7616]), ['final']). 6.97/7.25 cnf(c_0_12560, 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_7617, c_0_4415]), c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_12561, 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_7457]), ['final']). 6.97/7.25 cnf(c_0_12562, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(X2,esk194_5(X3,X2,X4,X5,X1))))|c_Groups_Ozero__class_Ozero(X1)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X4)|~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_7128]), ['final']). 6.97/7.25 cnf(c_0_12563, 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_7618]), ['final']). 6.97/7.25 cnf(c_0_12564, 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_7619]), ['final']). 6.97/7.25 cnf(c_0_12565, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[c_0_7620, c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_12566, 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_7621]), ['final']). 6.97/7.25 cnf(c_0_12567, 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_7622]), ['final']). 6.97/7.25 cnf(c_0_12568, 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_7623]), ['final']). 6.97/7.25 cnf(c_0_12569, 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_7624]), ['final']). 6.97/7.25 cnf(c_0_12570, 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_7625]), ['final']). 6.97/7.25 cnf(c_0_12571, 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_7626]), ['final']). 6.97/7.25 cnf(c_0_12572, plain, (hBOOL(hAPP(hAPP(c_member(X2),hAPP(hAPP(c_List_Onth(X2),X3),X1)),hAPP(c_List_Oset(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_7627]), ['final']). 6.97/7.25 cnf(c_0_12573, 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_7628]), ['final']). 6.97/7.25 cnf(c_0_12574, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk557_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_7629]), ['final']). 6.97/7.25 cnf(c_0_12575, 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_7630]), ['final']). 6.97/7.25 cnf(c_0_12576, plain, (hAPP(c_Set_Oimage(X1,X4,X5),X3)=hAPP(hAPP(c_Set_Oinsert(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_7631]), ['final']). 6.97/7.25 cnf(c_0_12577, 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_7632]), ['final']). 6.97/7.25 cnf(c_0_12578, 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_7633]), ['final']). 6.97/7.25 cnf(c_0_12579, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk237_5(X2,X3,X4,X5,X1)),X5))|hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X5),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_7634]), ['final']). 6.97/7.25 cnf(c_0_12580, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))=hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7635]), ['final']). 6.97/7.25 cnf(c_0_12581, plain, (hAPP(hAPP(c_List_Onth(X2),X3),X1)=hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Oappend(X2),X3),X4)),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_6702]), ['final']). 6.97/7.25 cnf(c_0_12582, plain, (c_List_Olist_ONil(X1)=X2|hAPP(hAPP(c_List_Onth(X1),X2),X3)=hAPP(c_List_Ohd(X1),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)))), inference(split_conjunct,[status(thm)],[c_0_7636]), ['final']). 6.97/7.25 cnf(c_0_12583, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk506_2(X2,X1)),hAPP(c_Relation_OImage(X1,X1,X2),esk506_2(X2,X1))))|c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7637]), ['final']). 6.97/7.25 cnf(c_0_12584, 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_7638]), ['final']). 6.97/7.25 cnf(c_0_12585, 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_7639]), ['final']). 6.97/7.25 cnf(c_0_12586, 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_7120]), ['final']). 6.97/7.25 cnf(c_0_12587, 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_6329]), ['final']). 6.97/7.25 cnf(c_0_12588, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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)))|~class_Rings_Oidom(X1)), inference(er,[status(thm)],[c_0_7640]), ['final']). 6.97/7.25 cnf(c_0_12589, 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_7641, c_0_4565]), ['final']). 6.97/7.25 cnf(c_0_12590, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk114_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))|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_7642]), ['final']). 6.97/7.25 cnf(c_0_12591, 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_7417]), ['final']). 6.97/7.25 cnf(c_0_12592, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),c_Groups_Ozero__class_Ozero(X1))))|~class_Rings_Oidom(X1)), inference(er,[status(thm)],[c_0_7643]), ['final']). 6.97/7.25 cnf(c_0_12593, 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_7644]), ['final']). 6.97/7.25 cnf(c_0_12594, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X4),X3)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X4),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_7645]), ['final']). 6.97/7.25 cnf(c_0_12595, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X3)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Oplus__class_Oplus(X1)),X4),c_Groups_Ozero__class_Ozero(X1)),X3)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7646]), ['final']). 6.97/7.25 cnf(c_0_12596, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk351_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))), inference(split_conjunct,[status(thm)],[c_0_7408]), ['final']). 6.97/7.25 cnf(c_0_12597, 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)), inference(split_conjunct,[status(thm)],[c_0_7647]), ['final']). 6.97/7.25 cnf(c_0_12598, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olinorder__class_OMax(X1,X2))=c_Big__Operators_Olinorder__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_7648]), ['final']). 6.97/7.25 cnf(c_0_12599, 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_7649]), ['final']). 6.97/7.25 cnf(c_0_12600, 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)), inference(split_conjunct,[status(thm)],[c_0_7650]), ['final']). 6.97/7.25 cnf(c_0_12601, plain, (esk358_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_7651]), c_0_7652])]), ['final']). 6.97/7.25 cnf(c_0_12602, 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_7653]), ['final']). 6.97/7.25 cnf(c_0_12603, plain, (hBOOL(hAPP(X1,X4))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),esk480_4(X1,X3,X4,X2)),esk481_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_7270]), ['final']). 6.97/7.25 cnf(c_0_12604, 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_7654]), ['final']). 6.97/7.25 cnf(c_0_12605, 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_7655]), ['final']). 6.97/7.25 cnf(c_0_12606, 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_7656]), ['final']). 6.97/7.25 cnf(c_0_12607, 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)), inference(split_conjunct,[status(thm)],[c_0_7657]), ['final']). 6.97/7.25 cnf(c_0_12608, 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)))), inference(split_conjunct,[status(thm)],[c_0_7658]), ['final']). 6.97/7.25 cnf(c_0_12609, 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_Olistrel(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_6233]), ['final']). 6.97/7.25 cnf(c_0_12610, 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_7659]), ['final']). 6.97/7.25 cnf(c_0_12611, 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_7660]), ['final']). 6.97/7.25 cnf(c_0_12612, 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_7661]), ['final']). 6.97/7.25 cnf(c_0_12613, 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_7662]), ['final']). 6.97/7.25 cnf(c_0_12614, plain, (hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Set_Oimage(X1,X2,X3),X4)))|c_Fun_Oinj__on(X1,X2,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_7663]), ['final']). 6.97/7.25 cnf(c_0_12615, 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_7323]), ['final']). 6.97/7.25 cnf(c_0_12616, 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_7324]), ['final']). 6.97/7.25 cnf(c_0_12617, 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_7664]), ['final']). 6.97/7.25 cnf(c_0_12618, 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_7665]), ['final']). 6.97/7.25 cnf(c_0_12619, 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_7666]), ['final']). 6.97/7.25 cnf(c_0_12620, 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_7667]), ['final']). 6.97/7.25 cnf(c_0_12621, 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)), inference(split_conjunct,[status(thm)],[c_0_7668]), ['final']). 6.97/7.25 cnf(c_0_12622, 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_7669]), ['final']). 6.97/7.25 cnf(c_0_12623, 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_7670]), ['final']). 6.97/7.25 cnf(c_0_12624, 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_7671]), ['final']). 6.97/7.25 cnf(c_0_12625, 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_7672]), ['final']). 6.97/7.25 cnf(c_0_12626, 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),esk457_2(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_List_Oset(tc_Nat_Onat),X1)))), inference(er,[status(thm)],[c_0_7673]), ['final']). 6.97/7.25 cnf(c_0_12627, 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_7674, c_0_4768]), ['final']). 6.97/7.25 cnf(c_0_12628, 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_7675, c_0_4768]), ['final']). 6.97/7.25 cnf(c_0_12629, plain, (X3=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))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7676]), ['final']). 6.97/7.25 cnf(c_0_12630, 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_7677]), ['final']). 6.97/7.25 cnf(c_0_12631, 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))|hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1)))|~hBOOL(hAPP(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_12632, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk306_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_7678]), ['final']). 6.97/7.25 cnf(c_0_12633, 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_7333]), ['final']). 6.97/7.25 cnf(c_0_12634, 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_7338]), ['final']). 6.97/7.25 cnf(c_0_12635, 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_7679]), ['final']). 6.97/7.25 cnf(c_0_12636, 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_7680]), ['final']). 6.97/7.25 cnf(c_0_12637, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),X4)))|~c_Fun_Obij__betw(X1,X2,X4,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(rw,[status(thm)],[c_0_7681, c_0_4768]), ['final']). 6.97/7.25 cnf(c_0_12638, plain, (hAPP(X1,esk448_1(X1))=hAPP(X1,esk449_1(X1))|hBOOL(hAPP(hAPP(X1,esk448_1(X1)),esk449_1(X1)))|c_Equiv__Relations_Opart__equivp(X3,X1)|~hBOOL(hAPP(hAPP(X1,X2),X2))), inference(split_conjunct,[status(thm)],[c_0_7518]), ['final']). 6.97/7.25 cnf(c_0_12639, 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_7682]), ['final']). 6.97/7.25 cnf(c_0_12640, 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_7683]), ['final']). 6.97/7.25 cnf(c_0_12641, plain, (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))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oremove1(X1,X2,X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_7684]), ['final']). 6.97/7.25 cnf(c_0_12642, plain, (X1=hAPP(hAPP(X2,X3),esk463_7(X3,X1,X4,X5,X2,X6,X7))|~hBOOL(hAPP(hAPP(c_member(X7),X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X6,X2,X5,X4),X1))|~c_Finite__Set_Ofun__left__comm(X7,X6,X2)), inference(split_conjunct,[status(thm)],[c_0_6302]), ['final']). 6.97/7.25 cnf(c_0_12643, 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))|X6=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))|~c_Fun_Oinj__on(X1,X2,X3,hAPP(X4,esk482_6(X4,X3,X2,X1,X5,X6)))), inference(split_conjunct,[status(thm)],[c_0_6683]), ['final']). 6.97/7.25 cnf(c_0_12644, 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,esk366_4(X2,X1,X3,X4))),hAPP(X2,esk366_4(X2,X1,X3,X4))))), inference(split_conjunct,[status(thm)],[c_0_6862]), ['final']). 6.97/7.25 cnf(c_0_12645, 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_7685]), ['final']). 6.97/7.25 cnf(c_0_12646, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~c_Fun_Obij__betw(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_7686, c_0_4768]), ['final']). 6.97/7.25 cnf(c_0_12647, 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_7687, c_0_4768]), ['final']). 6.97/7.25 cnf(c_0_12648, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(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_Lattices_Osemilattice__sup(X1)), inference(split_conjunct,[status(thm)],[c_0_7688]), ['final']). 6.97/7.25 cnf(c_0_12649, 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_7689, c_0_4768]), ['final']). 6.97/7.25 cnf(c_0_12650, 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_7690, c_0_4768]), ['final']). 6.97/7.25 cnf(c_0_12651, 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_7691, c_0_4768]), ['final']). 6.97/7.25 cnf(c_0_12652, 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_7692, c_0_4768]), ['final']). 6.97/7.25 cnf(c_0_12653, 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_7693, c_0_4768]), ['final']). 6.97/7.25 cnf(c_0_12654, 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))), inference(split_conjunct,[status(thm)],[c_0_7694]), ['final']). 6.97/7.25 cnf(c_0_12655, 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_7695]), ['final']). 6.97/7.25 cnf(c_0_12656, 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_7696]), ['final']). 6.97/7.25 cnf(c_0_12657, 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_7697, c_0_4768]), ['final']). 6.97/7.25 cnf(c_0_12658, 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_7698]), ['final']). 6.97/7.25 cnf(c_0_12659, plain, (hBOOL(hAPP(X1,esk99_4(X1,X2,X3,X4)))|hBOOL(hAPP(X2,esk98_4(X1,X2,X3,X4)))|~hBOOL(hAPP(X2,X5))|~c_Equiv__Relations_Oequivp(X4,X3)), inference(split_conjunct,[status(thm)],[c_0_7068]), ['final']). 6.97/7.25 cnf(c_0_12660, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X2)), inference(split_conjunct,[status(thm)],[c_0_7699]), ['final']). 6.97/7.25 cnf(c_0_12661, 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_7700, c_0_5002]), c_0_5941]), ['final']). 6.97/7.25 cnf(c_0_12662, 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_7701]), ['final']). 6.97/7.25 cnf(c_0_12663, 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_7702]), ['final']). 6.97/7.25 cnf(c_0_12664, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk205_3(X2,X3,X1)),c_List_Olists(X1,X2)))|X3=c_List_Olist_ONil(X1)|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_7703]), ['final']). 6.97/7.25 cnf(c_0_12665, plain, (X3=X4|~c_Relation_Oantisym(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_7704]), ['final']). 6.97/7.25 cnf(c_0_12666, 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_7705, c_0_4742]), c_0_4742]), ['final']). 6.97/7.25 cnf(c_0_12667, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|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))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7706]), ['final']). 6.97/7.25 cnf(c_0_12668, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|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))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7707]), ['final']). 6.97/7.25 cnf(c_0_12669, 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_7708]), ['final']). 6.97/7.25 cnf(c_0_12670, 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),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_7709]), ['final']). 6.97/7.25 cnf(c_0_12671, plain, (X1=X2|X3=X2|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))))!=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))))), inference(split_conjunct,[status(thm)],[c_0_7709]), ['final']). 6.97/7.25 cnf(c_0_12672, 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_7710]), ['final']). 6.97/7.25 cnf(c_0_12673, 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)), inference(split_conjunct,[status(thm)],[c_0_7711]), ['final']). 6.97/7.25 cnf(c_0_12674, 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_7712]), ['final']). 6.97/7.25 cnf(c_0_12675, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)=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))), inference(split_conjunct,[status(thm)],[c_0_7713]), ['final']). 6.97/7.25 cnf(c_0_12676, 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,esk409_7(X2,X3,X4,X5,X1,X6,X7)),X5),X4))), inference(split_conjunct,[status(thm)],[c_0_7091]), ['final']). 6.97/7.25 cnf(c_0_12677, 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,esk526_7(X2,X3,X1,X4,X5,X6,X7)),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7088]), ['final']). 6.97/7.25 cnf(c_0_12678, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7714]), ['final']). 6.97/7.25 cnf(c_0_12679, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7715]), ['final']). 6.97/7.25 cnf(c_0_12680, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7716]), ['final']). 6.97/7.25 cnf(c_0_12681, 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_6835]), ['final']). 6.97/7.25 cnf(c_0_12682, 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_6837]), ['final']). 6.97/7.25 cnf(c_0_12683, 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_6838]), ['final']). 6.97/7.25 cnf(c_0_12684, 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_6839]), ['final']). 6.97/7.25 cnf(c_0_12685, plain, (X1=c_List_Olist_ONil(X2)|hAPP(hAPP(c_List_Onth(X2),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_List_Olast(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_7717]), ['final']). 6.97/7.25 cnf(c_0_12686, 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_7718, c_0_5539]), ['final']). 6.97/7.25 cnf(c_0_12687, 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_7719]), ['final']). 6.97/7.25 cnf(c_0_12688, 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_7720]), ['final']). 6.97/7.25 cnf(c_0_12689, 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_7721, c_0_6542]), ['final']). 6.97/7.25 cnf(c_0_12690, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(X3,X4)),hAPP(X3,X5)))|~class_Orderings_Oorder(X1)|~class_Orderings_Oorder(X2)|~c_Orderings_Oorder__class_Ostrict__mono(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_7722]), ['final']). 6.97/7.25 cnf(c_0_12691, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(X5,X2)),hAPP(X5,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~c_Orderings_Oorder__class_Ostrict__mono(X1,X4,X5)|~class_Orderings_Olinorder(X1)|~class_Orderings_Oorder(X4)), inference(split_conjunct,[status(thm)],[c_0_7723]), ['final']). 6.97/7.25 cnf(c_0_12692, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(X3,X4)),hAPP(X3,X5)))|~class_Orderings_Oorder(X1)|~class_Orderings_Oorder(X2)|~c_Orderings_Oorder__class_Omono(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_7724]), ['final']). 6.97/7.25 cnf(c_0_12693, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(X5,X2)),hAPP(X5,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~c_Orderings_Oorder__class_Ostrict__mono(X1,X4,X5)|~class_Orderings_Oorder(X4)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7725]), ['final']). 6.97/7.25 cnf(c_0_12694, plain, (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)=X5|X3=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_7726]), ['final']). 6.97/7.25 cnf(c_0_12695, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),esk277_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_7727]), ['final']). 6.97/7.25 cnf(c_0_12696, plain, (X1=hAPP(X2,esk358_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_5257]), ['final']). 6.97/7.25 cnf(c_0_12697, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X2)),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_7728]), ['final']). 6.97/7.25 cnf(c_0_12698, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)|c_Groups_Ozero__class_Ozero(X1)=X3|X5=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_7726]), ['final']). 6.97/7.25 cnf(c_0_12699, 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_7729]), ['final']). 6.97/7.25 cnf(c_0_12700, 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_7730]), ['final']). 6.97/7.25 cnf(c_0_12701, 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_7731]), ['final']). 6.97/7.25 cnf(c_0_12702, 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_7732]), ['final']). 6.97/7.25 cnf(c_0_12703, plain, (c_Equiv__Relations_Opart__equivp(X3,X1)|~hBOOL(hAPP(hAPP(X1,esk449_1(X1)),esk449_1(X1)))|hAPP(X1,esk448_1(X1))!=hAPP(X1,esk449_1(X1))|~hBOOL(hAPP(hAPP(X1,esk448_1(X1)),esk448_1(X1)))|~hBOOL(hAPP(hAPP(X1,esk448_1(X1)),esk449_1(X1)))|~hBOOL(hAPP(hAPP(X1,X2),X2))), inference(split_conjunct,[status(thm)],[c_0_7518]), ['final']). 6.97/7.25 cnf(c_0_12704, 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_7733]), ['final']). 6.97/7.25 cnf(c_0_12705, 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_7734]), ['final']). 6.97/7.25 cnf(c_0_12706, 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))))), inference(split_conjunct,[status(thm)],[c_0_7735]), ['final']). 6.97/7.25 cnf(c_0_12707, 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_7736]), ['final']). 6.97/7.25 cnf(c_0_12708, 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_7737]), ['final']). 6.97/7.25 cnf(c_0_12709, 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_7738]), ['final']). 6.97/7.25 cnf(c_0_12710, 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_7739]), ['final']). 6.97/7.25 cnf(c_0_12711, 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,esk232_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))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7740, c_0_4742]), c_0_4742]), ['final']). 6.97/7.25 cnf(c_0_12712, 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_7741]), ['final']). 6.97/7.25 cnf(c_0_12713, 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_7742]), ['final']). 6.97/7.25 cnf(c_0_12714, 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_7743]), ['final']). 6.97/7.25 cnf(c_0_12715, 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_5228]), ['final']). 6.97/7.25 cnf(c_0_12716, plain, (hBOOL(hAPP(X1,X5))|~hBOOL(hAPP(X1,esk535_4(X1,X2,X3,X4)))|~hBOOL(hAPP(X1,esk534_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_6414]), ['final']). 6.97/7.25 cnf(c_0_12717, plain, (hBOOL(hAPP(X1,esk481_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_7270]), ['final']). 6.97/7.25 cnf(c_0_12718, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Complete__Lattice_OInf__class_OInf(X1,X3)),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))|~class_Orderings_Olinorder(X1)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7744]), ['final']). 6.97/7.25 cnf(c_0_12719, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Complete__Lattice_OSup__class_OSup(X1,X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X4))|~class_Orderings_Olinorder(X1)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7745]), ['final']). 6.97/7.25 cnf(c_0_12720, 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_7746, c_0_5174]), ['final']). 6.97/7.25 cnf(c_0_12721, 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_7747, c_0_5174]), ['final']). 6.97/7.25 cnf(c_0_12722, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(c_Set_Oimage(X1,X4,c_Fun_Ofun__upd(X1,X4,X5,X2,X6)),X3)=hAPP(c_Set_Oimage(X1,X4,X5),X3)), inference(split_conjunct,[status(thm)],[c_0_6265]), ['final']). 6.97/7.25 cnf(c_0_12723, 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_7748, c_0_5002]), c_0_5002]), c_0_5002]), ['final']). 6.97/7.25 cnf(c_0_12724, 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_7749, c_0_5002]), ['final']). 6.97/7.25 cnf(c_0_12725, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)=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)))|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_4452]), ['final']). 6.97/7.25 cnf(c_0_12726, 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_7750]), ['final']). 6.97/7.25 cnf(c_0_12727, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk380_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_7751]), ['final']). 6.97/7.25 cnf(c_0_12728, 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_7752]), ['final']). 6.97/7.25 cnf(c_0_12729, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk244_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_7525]), ['final']). 6.97/7.25 cnf(c_0_12730, plain, (X1=hAPP(hAPP(c_List_Olist_OCons(X2),esk204_3(X3,X1,X2)),esk205_3(X3,X1,X2))|X1=c_List_Olist_ONil(X2)|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X1),c_List_Olists(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_7703]), ['final']). 6.97/7.25 cnf(c_0_12731, plain, (hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X1),c_List_Oupto(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin),X2))=c_List_Oupto(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[c_0_7753, c_0_4741]), ['final']). 6.97/7.25 cnf(c_0_12732, 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_7754]), ['final']). 6.97/7.25 cnf(c_0_12733, 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_7755, c_0_7756]), ['final']). 6.97/7.25 cnf(c_0_12734, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk444_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_7029]), ['final']). 6.97/7.25 cnf(c_0_12735, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk323_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_7030]), ['final']). 6.97/7.25 cnf(c_0_12736, plain, (c_List_OtakeWhile(X4,X1,hAPP(hAPP(c_List_Oappend(X4),X3),X2))=hAPP(hAPP(c_List_Oappend(X4),X3),c_List_OtakeWhile(X4,X1,X2))|~hBOOL(hAPP(X1,esk153_4(X2,X1,X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_7159]), ['final']). 6.97/7.25 cnf(c_0_12737, 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_7757, c_0_7756]), ['final']). 6.97/7.25 cnf(c_0_12738, 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_7758]), ['final']). 6.97/7.25 cnf(c_0_12739, 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_7759]), ['final']). 6.97/7.25 cnf(c_0_12740, 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_7760]), ['final']). 6.97/7.25 cnf(c_0_12741, 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_7761]), ['final']). 6.97/7.25 cnf(c_0_12742, 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_7762]), ['final']). 6.97/7.25 cnf(c_0_12743, 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)), inference(split_conjunct,[status(thm)],[c_0_7763]), ['final']). 6.97/7.25 cnf(c_0_12744, 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)),X3),X4)|~class_Divides_Oring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7764]), ['final']). 6.97/7.25 cnf(c_0_12745, 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_7765]), ['final']). 6.97/7.25 cnf(c_0_12746, 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_7766]), ['final']). 6.97/7.25 cnf(c_0_12747, 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_7767]), ['final']). 6.97/7.25 cnf(c_0_12748, 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,esk27_3(X2,X1,X3)))), inference(rw,[status(thm)],[c_0_7768, c_0_4813]), ['final']). 6.97/7.25 cnf(c_0_12749, 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_7769, c_0_5002]), c_0_7770]), ['final']). 6.97/7.25 cnf(c_0_12750, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk162_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_7771]), ['final']). 6.97/7.25 cnf(c_0_12751, 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_7772]), ['final']). 6.97/7.25 cnf(c_0_12752, 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_7678]), ['final']). 6.97/7.25 cnf(c_0_12753, 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_7773]), ['final']). 6.97/7.25 cnf(c_0_12754, 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_7774]), ['final']). 6.97/7.25 cnf(c_0_12755, 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_7775]), ['final']). 6.97/7.25 cnf(c_0_12756, 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_7776]), ['final']). 6.97/7.25 cnf(c_0_12757, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk359_3(X2,X3,X1)),X3))|X2=c_Big__Operators_Olinorder__class_OMin(X1,X3)|~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_7777]), ['final']). 6.97/7.25 cnf(c_0_12758, 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_7181]), ['final']). 6.97/7.25 cnf(c_0_12759, 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_7778]), ['final']). 6.97/7.25 cnf(c_0_12760, plain, (c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),c_SetInterval_Oord__class_OatLeastAtMost(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_7779]), ['final']). 6.97/7.25 cnf(c_0_12761, 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),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7780]), ['final']). 6.97/7.25 cnf(c_0_12762, 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_7272]), ['final']). 6.97/7.25 cnf(c_0_12763, 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_7781]), ['final']). 6.97/7.25 cnf(c_0_12764, 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(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_7782, c_0_7533]), c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_12765, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),esk222_5(X3,X4,X1,X5,X2)),X3)|c_List_Olist_ONil(X2)=X4|hAPP(hAPP(c_List_Olist_OCons(X2),X5),X1)!=hAPP(hAPP(c_List_Oappend(X2),X4),X3)), inference(split_conjunct,[status(thm)],[c_0_5751]), ['final']). 6.97/7.25 cnf(c_0_12766, plain, (X1=c_List_Olist_ONil(X2)|X3=hAPP(hAPP(c_List_Oappend(X2),esk490_5(X3,X4,X5,X1,X2)),X5)|hAPP(hAPP(c_List_Oappend(X2),X1),X5)!=hAPP(hAPP(c_List_Olist_OCons(X2),X4),X3)), inference(split_conjunct,[status(thm)],[c_0_7349]), ['final']). 6.97/7.25 cnf(c_0_12767, plain, (X1=hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk222_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_5751]), ['final']). 6.97/7.25 cnf(c_0_12768, plain, (X1=c_List_Olist_ONil(X2)|X1=hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk490_5(X4,X3,X5,X1,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_7349]), ['final']). 6.97/7.25 cnf(c_0_12769, 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_7344]), ['final']). 6.97/7.25 cnf(c_0_12770, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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)))|~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_7783]), ['final']). 6.97/7.25 cnf(c_0_12771, 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_7340]), ['final']). 6.97/7.25 cnf(c_0_12772, 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_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5149]), ['final']). 6.97/7.25 cnf(c_0_12773, 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_7784]), ['final']). 6.97/7.25 cnf(c_0_12774, plain, (hAPP(c_Fun_Ocomp(X2,X1,X1,c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3)),X3)=c_Fun_Oid(X1)|~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_7785]), ['final']). 6.97/7.25 cnf(c_0_12775, 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_7786, c_0_5065]), ['final']). 6.97/7.25 cnf(c_0_12776, 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_7787]), ['final']). 6.97/7.25 cnf(c_0_12777, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|X4=X6|~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_7788]), ['final']). 6.97/7.25 cnf(c_0_12778, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|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_7789]), ['final']). 6.97/7.25 cnf(c_0_12779, plain, (c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X2|c_Wellfounded_Omax__extp(X4,X1,X3,X2)|~hBOOL(hAPP(hAPP(X1,esk246_4(X2,X3,X1,X4)),X5))|~hBOOL(hAPP(hAPP(c_member(X4),X5),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), inference(split_conjunct,[status(thm)],[c_0_7275]), ['final']). 6.97/7.25 cnf(c_0_12780, plain, (c_Wellfounded_Omax__extp(X4,X1,X3,X2)|X2=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(X1,esk280_4(X1,X2,X3,X4)),X5))|~hBOOL(hAPP(hAPP(c_member(X4),X5),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), inference(split_conjunct,[status(thm)],[c_0_7281]), ['final']). 6.97/7.25 cnf(c_0_12781, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,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,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))), inference(split_conjunct,[status(thm)],[c_0_7790]), ['final']). 6.97/7.25 cnf(c_0_12782, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_7791]), ['final']). 6.97/7.25 cnf(c_0_12783, 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_7792, c_0_5002]), c_0_5002]), c_0_5002]), ['final']). 6.97/7.25 cnf(c_0_12784, 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_7793, c_0_5002]), c_0_5002]), c_0_5002]), ['final']). 6.97/7.25 cnf(c_0_12785, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3))=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))|~class_Groups_Omonoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7794]), ['final']). 6.97/7.25 cnf(c_0_12786, 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))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_7795]), ['final']). 6.97/7.25 cnf(c_0_12787, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))|c_Wellfounded_Omax__extp(X4,X1,X3,X2)|~hBOOL(hAPP(hAPP(X1,esk67_4(X2,X3,X1,X4)),X5))|~hBOOL(hAPP(hAPP(c_member(X4),X5),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))), inference(split_conjunct,[status(thm)],[c_0_5472]), ['final']). 6.97/7.25 cnf(c_0_12788, 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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),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)],[c_0_7796, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), ['final']). 6.97/7.25 cnf(c_0_12789, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|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,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_7797]), ['final']). 6.97/7.25 cnf(c_0_12790, 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_7798]), ['final']). 6.97/7.25 cnf(c_0_12791, 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)), inference(split_conjunct,[status(thm)],[c_0_7799]), ['final']). 6.97/7.25 cnf(c_0_12792, 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_7800]), ['final']). 6.97/7.25 cnf(c_0_12793, 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_7801]), ['final']). 6.97/7.25 cnf(c_0_12794, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),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)],[c_0_7802, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), ['final']). 6.97/7.25 cnf(c_0_12795, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_7803, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), ['final']). 6.97/7.25 cnf(c_0_12796, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_7804, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), ['final']). 6.97/7.25 cnf(c_0_12797, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X4),X3)=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Ocomm__semiring__1(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|hAPP(X4,X5)!=c_Groups_Ozero__class_Ozero(X1)|~hBOOL(hAPP(hAPP(c_member(X2),X5),X3))), inference(split_conjunct,[status(thm)],[c_0_7805]), ['final']). 6.97/7.25 cnf(c_0_12798, 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_7806]), ['final']). 6.97/7.25 cnf(c_0_12799, 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_7807]), ['final']). 6.97/7.25 cnf(c_0_12800, 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_7808]), ['final']). 6.97/7.25 cnf(c_0_12801, 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_7809, c_0_5002]), c_0_5002]), c_0_5002]), ['final']). 6.97/7.25 cnf(c_0_12802, 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_7810]), ['final']). 6.97/7.25 cnf(c_0_12803, 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_7811]), ['final']). 6.97/7.25 cnf(c_0_12804, 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_7000]), ['final']). 6.97/7.25 cnf(c_0_12805, 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_7812]), ['final']). 6.97/7.25 cnf(c_0_12806, 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_7813]), ['final']). 6.97/7.25 cnf(c_0_12807, 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_7814]), ['final']). 6.97/7.25 cnf(c_0_12808, 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_7008]), ['final']). 6.97/7.25 cnf(c_0_12809, 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_7815]), ['final']). 6.97/7.25 cnf(c_0_12810, 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_7816]), ['final']). 6.97/7.25 cnf(c_0_12811, 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_7017]), ['final']). 6.97/7.25 cnf(c_0_12812, 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_7817]), ['final']). 6.97/7.25 cnf(c_0_12813, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(c_Set_Oimage(X1,X3,hAPP(c_COMBK(X3,X1),X4)),X2)=hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_7818]), ['final']). 6.97/7.25 cnf(c_0_12814, 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),esk485_3(X3,X2,X1))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(rw,[status(thm)],[c_0_7819, c_0_5999]), ['final']). 6.97/7.25 cnf(c_0_12815, 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)), inference(split_conjunct,[status(thm)],[c_0_7820]), ['final']). 6.97/7.25 cnf(c_0_12816, 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_7821]), ['final']). 6.97/7.25 cnf(c_0_12817, 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)), inference(split_conjunct,[status(thm)],[c_0_7822]), ['final']). 6.97/7.25 cnf(c_0_12818, 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)), inference(split_conjunct,[status(thm)],[c_0_7823]), ['final']). 6.97/7.25 cnf(c_0_12819, 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)), inference(split_conjunct,[status(thm)],[c_0_7824]), ['final']). 6.97/7.25 cnf(c_0_12820, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))=hAPP(X4,X5)|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)),X3),X4)|~hBOOL(hAPP(hAPP(c_member(X2),X5),X3))), inference(split_conjunct,[status(thm)],[c_0_7825]), ['final']). 6.97/7.25 cnf(c_0_12821, 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_7826]), ['final']). 6.97/7.25 cnf(c_0_12822, plain, (c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__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_7827]), ['final']). 6.97/7.25 cnf(c_0_12823, 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_7828]), ['final']). 6.97/7.25 cnf(c_0_12824, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk544_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_7829]), ['final']). 6.97/7.25 cnf(c_0_12825, 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),X3)!=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_7830, c_0_4821]), ['final']). 6.97/7.25 cnf(c_0_12826, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X1,esk341_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_7831]), ['final']). 6.97/7.25 cnf(c_0_12827, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk406_4(X2,X3,X4,X1)),X3))|c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X2)), inference(split_conjunct,[status(thm)],[c_0_7832]), ['final']). 6.97/7.25 cnf(c_0_12828, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),X2)=c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__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_7833]), ['final']). 6.97/7.25 cnf(c_0_12829, plain, (X4=X3|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_7834]), ['final']). 6.97/7.25 cnf(c_0_12830, plain, (hBOOL(hAPP(X2,X4))|~hBOOL(hAPP(hAPP(c_member(X1),esk480_4(X2,X3,X4,X1)),esk481_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_7270]), ['final']). 6.97/7.25 cnf(c_0_12831, 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_7835]), ['final']). 6.97/7.25 cnf(c_0_12832, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk41_4(X2,X3,X1,X4)),X3))|c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X2)), inference(split_conjunct,[status(thm)],[c_0_7825]), ['final']). 6.97/7.25 cnf(c_0_12833, 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_7836]), ['final']). 6.97/7.25 cnf(c_0_12834, 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_7837]), ['final']). 6.97/7.25 cnf(c_0_12835, 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_7838, c_0_5002]), c_0_5002]), ['final']). 6.97/7.25 cnf(c_0_12836, 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_7839]), ['final']). 6.97/7.25 cnf(c_0_12837, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk184_4(X2,X3,X4,X1)),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_7840]), ['final']). 6.97/7.25 cnf(c_0_12838, 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_7841]), ['final']). 6.97/7.25 cnf(c_0_12839, 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_7842]), ['final']). 6.97/7.25 cnf(c_0_12840, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk145_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_7826]), ['final']). 6.97/7.25 cnf(c_0_12841, 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_7843]), ['final']). 6.97/7.25 cnf(c_0_12842, 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_7844, c_0_4467]), ['final']). 6.97/7.25 cnf(c_0_12843, 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_7065]), ['final']). 6.97/7.25 cnf(c_0_12844, 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_7067]), ['final']). 6.97/7.25 cnf(c_0_12845, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk247_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_7845]), ['final']). 6.97/7.25 cnf(c_0_12846, 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_7846, c_0_5746]), ['final']). 6.97/7.25 cnf(c_0_12847, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|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)))|~hBOOL(hAPP(X1,esk275_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.25 cnf(c_0_12848, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|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)))|~hBOOL(hAPP(X1,esk273_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.25 cnf(c_0_12849, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|X3=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X4,tc_HOL_Obool)),X1),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7847]), ['final']). 6.97/7.25 cnf(c_0_12850, 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,esk536_4(X2,X3,X4,X1))))|~class_Rings_Olinordered__semidom(X1)), inference(split_conjunct,[status(thm)],[c_0_6952]), ['final']). 6.97/7.25 cnf(c_0_12851, 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,esk156_4(X2,X3,X4,X1))))|~class_Rings_Olinordered__semidom(X1)), inference(split_conjunct,[status(thm)],[c_0_6953]), ['final']). 6.97/7.25 cnf(c_0_12852, 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_7848]), ['final']). 6.97/7.25 cnf(c_0_12853, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|X3=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X4,tc_HOL_Obool)),X1),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5722]), ['final']). 6.97/7.25 cnf(c_0_12854, 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_7849, c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_12855, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk270_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)))), inference(split_conjunct,[status(thm)],[c_0_5135]), ['final']). 6.97/7.25 cnf(c_0_12856, 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_7850]), ['final']). 6.97/7.25 cnf(c_0_12857, 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),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_7851]), ['final']). 6.97/7.25 cnf(c_0_12858, 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_7431]), ['final']). 6.97/7.25 cnf(c_0_12859, plain, (c_Fun_Obij__betw(tc_Nat_Onat,X1,esk477_2(X2,X1),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),X2)),X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7852]), ['final']). 6.97/7.25 cnf(c_0_12860, plain, (c_Fun_Obij__betw(X1,tc_Nat_Onat,esk223_2(X2,X1),X2,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(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_7853]), ['final']). 6.97/7.25 cnf(c_0_12861, 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_7854, c_0_5794]), ['final']). 6.97/7.25 cnf(c_0_12862, 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_Int_Onumber__ring(X1)|~class_Fields_Ofield__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7855]), ['final']). 6.97/7.25 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,esk322_5(X3,X2,X1,X4,X5))))), inference(split_conjunct,[status(thm)],[c_0_6855]), ['final']). 6.97/7.25 cnf(c_0_12864, 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,esk102_5(X3,X4,X5,X2,X1))))), inference(split_conjunct,[status(thm)],[c_0_6860]), ['final']). 6.97/7.25 cnf(c_0_12865, plain, (c_List_Osublist(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2)),X1)=hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(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_7856]), ['final']). 6.97/7.25 cnf(c_0_12866, 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_7857]), ['final']). 6.97/7.25 cnf(c_0_12867, 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_7858]), ['final']). 6.97/7.25 cnf(c_0_12868, 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_7859]), ['final']). 6.97/7.25 cnf(c_0_12869, 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_7860]), ['final']). 6.97/7.25 cnf(c_0_12870, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|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_7861]), ['final']). 6.97/7.25 cnf(c_0_12871, 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_7862]), ['final']). 6.97/7.25 cnf(c_0_12872, 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_7863]), ['final']). 6.97/7.25 cnf(c_0_12873, 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_7864]), ['final']). 6.97/7.25 cnf(c_0_12874, plain, (hAPP(hAPP(c_List_Onth(X3),X4),X1)=hAPP(hAPP(c_List_Onth(X3),hAPP(hAPP(c_List_Otake(X3),X2),X4)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7865]), ['final']). 6.97/7.25 cnf(c_0_12875, plain, (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(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X1)))|~hBOOL(hAPP(X2,esk275_3(X1,X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.25 cnf(c_0_12876, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk94_3(X2,X3,X1)),esk94_3(X2,X3,X1))=X3|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X3),c_Relation_OId__on(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_7866]), ['final']). 6.97/7.25 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_7867]), ['final']). 6.97/7.25 cnf(c_0_12878, 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_7491]), ['final']). 6.97/7.25 cnf(c_0_12879, plain, (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)))|hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X1)))|~hBOOL(hAPP(X2,esk273_3(X1,X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.25 cnf(c_0_12880, 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_7868, c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_12881, 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_7869]), ['final']). 6.97/7.25 cnf(c_0_12882, 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_7870]), ['final']). 6.97/7.25 cnf(c_0_12883, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk270_3(X1,X2,X3)),X1))|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(split_conjunct,[status(thm)],[c_0_5135]), ['final']). 6.97/7.25 cnf(c_0_12884, 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_7871]), ['final']). 6.97/7.25 cnf(c_0_12885, 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_7872]), ['final']). 6.97/7.25 cnf(c_0_12886, plain, (hAPP(hAPP(c_List_Omap(X5,X4),X2),X3)=hAPP(hAPP(c_List_Omap(X5,X4),X1),X3)|hAPP(X1,esk117_5(X2,X3,X1,X4,X5))!=hAPP(X2,esk117_5(X2,X3,X1,X4,X5))), inference(split_conjunct,[status(thm)],[c_0_7120]), ['final']). 6.97/7.25 cnf(c_0_12887, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|X3=X4|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2)), inference(er,[status(thm)],[c_0_7873]), ['final']). 6.97/7.25 cnf(c_0_12888, 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_7874]), ['final']). 6.97/7.25 cnf(c_0_12889, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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_7591]), ['final']). 6.97/7.25 cnf(c_0_12890, 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_7875, c_0_4798]), ['final']). 6.97/7.25 cnf(c_0_12891, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk475_3(X2,X1,X3)),esk473_2(X2,X1)))|c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),esk473_2(X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_7123]), ['final']). 6.97/7.25 cnf(c_0_12892, plain, (hAPP(hAPP(X4,X5),X6)=hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),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_7876]), ['final']). 6.97/7.25 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_7877, c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_12894, 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_7878]), ['final']). 6.97/7.25 cnf(c_0_12895, 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_5466]), ['final']). 6.97/7.25 cnf(c_0_12896, 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_5382]), ['final']). 6.97/7.25 cnf(c_0_12897, 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_7879]), ['final']). 6.97/7.25 cnf(c_0_12898, plain, (c_Divides_Odiv__class_Omod(X1,X2,X3)=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)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7880]), ['final']). 6.97/7.25 cnf(c_0_12899, 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_7881, c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_12900, 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_5466]), ['final']). 6.97/7.25 cnf(c_0_12901, plain, (hAPP(X3,hAPP(c_Fun_Othe__inv__into(X1,X2,X4,X3),X5))=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_7882]), ['final']). 6.97/7.25 cnf(c_0_12902, plain, (X2=hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X3),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(rw,[status(thm)],[c_0_7883, c_0_5794]), ['final']). 6.97/7.25 cnf(c_0_12903, 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_7884]), ['final']). 6.97/7.25 cnf(c_0_12904, 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_7885]), ['final']). 6.97/7.25 cnf(c_0_12905, 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_7886]), ['final']). 6.97/7.25 cnf(c_0_12906, 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_7887]), ['final']). 6.97/7.25 cnf(c_0_12907, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~class_Rings_Oidom(X1)), inference(split_conjunct,[status(thm)],[c_0_5254]), ['final']). 6.97/7.25 cnf(c_0_12908, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4))|c_Groups_Ozero__class_Ozero(X1)=X3|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~class_Rings_Oidom(X1)), inference(split_conjunct,[status(thm)],[c_0_5256]), ['final']). 6.97/7.25 cnf(c_0_12909, 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_7888]), ['final']). 6.97/7.25 cnf(c_0_12910, 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_7889]), ['final']). 6.97/7.25 cnf(c_0_12911, 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_7890]), ['final']). 6.97/7.25 cnf(c_0_12912, 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_7891]), ['final']). 6.97/7.25 cnf(c_0_12913, 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_7892, c_0_6208]), ['final']). 6.97/7.25 cnf(c_0_12914, 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_7893, c_0_6208]), ['final']). 6.97/7.25 cnf(c_0_12915, 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_7894]), ['final']). 6.97/7.25 cnf(c_0_12916, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk552_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_7895]), ['final']). 6.97/7.25 cnf(c_0_12917, 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_7896]), ['final']). 6.97/7.25 cnf(c_0_12918, 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_7897]), ['final']). 6.97/7.25 cnf(c_0_12919, 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_7898]), ['final']). 6.97/7.25 cnf(c_0_12920, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk545_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)))), inference(split_conjunct,[status(thm)],[c_0_7599]), ['final']). 6.97/7.25 cnf(c_0_12921, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk417_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_7899]), ['final']). 6.97/7.25 cnf(c_0_12922, 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_7900, c_0_4467]), c_0_4467]), ['final']). 6.97/7.25 cnf(c_0_12923, 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_7220]), ['final']). 6.97/7.25 cnf(c_0_12924, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),esk397_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_7604]), ['final']). 6.97/7.25 cnf(c_0_12925, 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_7901]), ['final']). 6.97/7.25 cnf(c_0_12926, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk487_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_7902]), ['final']). 6.97/7.25 cnf(c_0_12927, 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_7903]), ['final']). 6.97/7.25 cnf(c_0_12928, plain, (hAPP(X3,X4)=hAPP(hAPP(X2,X5),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_7904]), ['final']). 6.97/7.25 cnf(c_0_12929, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk379_3(X2,X3,X1)),X3))|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_7905]), ['final']). 6.97/7.25 cnf(c_0_12930, plain, (X4=hAPP(X3,hAPP(c_Hilbert__Choice_Oinv__into(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X3),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_7906]), ['final']). 6.97/7.25 cnf(c_0_12931, 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_7907, c_0_5746]), ['final']). 6.97/7.25 cnf(c_0_12932, 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_7908]), ['final']). 6.97/7.25 cnf(c_0_12933, 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_7909]), ['final']). 6.97/7.25 cnf(c_0_12934, 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_7684]), ['final']). 6.97/7.25 cnf(c_0_12935, 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_7910, c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_12936, 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_7911, c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_12937, 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_7912, c_0_5002]), c_0_5002]), ['final']). 6.97/7.25 cnf(c_0_12938, 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_7913, c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_12939, plain, (hBOOL(hAPP(c_List_Odistinct(X3),hAPP(hAPP(c_List_Omap(X1,X3),X4),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))|~c_Fun_Oinj__on(X1,X3,X4,hAPP(c_List_Oset(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7914]), ['final']). 6.97/7.25 cnf(c_0_12940, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk132_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)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Rings_Ocomm__semiring__1(X4)|~class_Rings_Ono__zero__divisors(X4)), inference(split_conjunct,[status(thm)],[c_0_7915]), ['final']). 6.97/7.25 cnf(c_0_12941, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|X3=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X4)),X1)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X3),X1)!=hAPP(c_Int_Onumber__class_Onumber__of(X2),X4)|~class_Fields_Ofield__inverse__zero(X2)|~class_Int_Onumber(X2)), inference(split_conjunct,[status(thm)],[c_0_5223]), ['final']). 6.97/7.25 cnf(c_0_12942, 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_7916, c_0_5002]), c_0_5002]), ['final']). 6.97/7.25 cnf(c_0_12943, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk377_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_7917]), ['final']). 6.97/7.25 cnf(c_0_12944, 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_7918]), ['final']). 6.97/7.25 cnf(c_0_12945, 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_7919]), ['final']). 6.97/7.25 cnf(c_0_12946, plain, (hAPP(c_Set_Oimage(X2,X3,X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))|hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X1),esk10_3(X1,X3,X2)))!=esk10_3(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_7920]), ['final']). 6.97/7.25 cnf(c_0_12947, 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_7921])]), ['final']). 6.97/7.25 cnf(c_0_12948, 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_7922]), ['final']). 6.97/7.25 cnf(c_0_12949, 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_7922]), ['final']). 6.97/7.25 cnf(c_0_12950, 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_7923]), ['final']). 6.97/7.25 cnf(c_0_12951, 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_7924]), ['final']). 6.97/7.25 cnf(c_0_12952, plain, (X3=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)),X2)|~class_Divides_Osemiring__div(X1)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7925]), ['final']). 6.97/7.25 cnf(c_0_12953, plain, (X3=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2))|~class_Divides_Osemiring__div(X1)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7926]), ['final']). 6.97/7.25 cnf(c_0_12954, 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_7927, c_0_4813]), ['final']). 6.97/7.25 cnf(c_0_12955, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X3),X2),X4)))|~hBOOL(hAPP(X1,esk169_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_6857]), ['final']). 6.97/7.25 cnf(c_0_12956, 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_7928]), ['final']). 6.97/7.25 cnf(c_0_12957, 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_7929]), ['final']). 6.97/7.25 cnf(c_0_12958, 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_7930]), ['final']). 6.97/7.25 cnf(c_0_12959, 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_7559]), ['final']). 6.97/7.25 cnf(c_0_12960, 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_7931]), ['final']). 6.97/7.25 cnf(c_0_12961, 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_7932]), ['final']). 6.97/7.25 cnf(c_0_12962, 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_7933]), ['final']). 6.97/7.25 cnf(c_0_12963, 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_7565]), ['final']). 6.97/7.25 cnf(c_0_12964, 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_7573]), ['final']). 6.97/7.25 cnf(c_0_12965, 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_7934]), ['final']). 6.97/7.25 cnf(c_0_12966, 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_7935]), ['final']). 6.97/7.25 cnf(c_0_12967, 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_7936]), ['final']). 6.97/7.25 cnf(c_0_12968, 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_7937]), ['final']). 6.97/7.25 cnf(c_0_12969, 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_7938]), ['final']). 6.97/7.25 cnf(c_0_12970, plain, (hBOOL(hAPP(X1,esk527_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_7252]), ['final']). 6.97/7.25 cnf(c_0_12971, plain, (hBOOL(hAPP(X1,esk242_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_7253]), ['final']). 6.97/7.25 cnf(c_0_12972, 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_6623]), ['final']). 6.97/7.25 cnf(c_0_12973, 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_7939]), ['final']). 6.97/7.25 cnf(c_0_12974, 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_7940]), ['final']). 6.97/7.25 cnf(c_0_12975, 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_7941]), ['final']). 6.97/7.25 cnf(c_0_12976, 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_7942]), ['final']). 6.97/7.25 cnf(c_0_12977, 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_7943]), ['final']). 6.97/7.25 cnf(c_0_12978, 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_7944]), ['final']). 6.97/7.25 cnf(c_0_12979, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))|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_Orderings_Oord__class_Omin(X1),X2),X3)),X4))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7945]), ['final']). 6.97/7.25 cnf(c_0_12980, 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_7946]), ['final']). 6.97/7.25 cnf(c_0_12981, 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_Lattices_Oboolean__algebra(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7947]), ['final']). 6.97/7.25 cnf(c_0_12982, 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_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7948]), ['final']). 6.97/7.25 cnf(c_0_12983, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|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_Omax(X1),X3),X4)))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7949]), ['final']). 6.97/7.25 cnf(c_0_12984, 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_7950]), ['final']). 6.97/7.25 cnf(c_0_12985, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X1,X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,esk309_5(X3,X2,X1,X4,X5))),X3))), inference(split_conjunct,[status(thm)],[c_0_6939]), ['final']). 6.97/7.25 cnf(c_0_12986, plain, (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))=c_List_Olist_ONil(X2)|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_7951]), ['final']). 6.97/7.25 cnf(c_0_12987, 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)), inference(split_conjunct,[status(thm)],[c_0_7952]), ['final']). 6.97/7.25 cnf(c_0_12988, 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_7953]), ['final']). 6.97/7.25 cnf(c_0_12989, 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_OgreaterThanLessThan(X1,X3,X4))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7954]), ['final']). 6.97/7.25 cnf(c_0_12990, 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_7955]), ['final']). 6.97/7.25 cnf(c_0_12991, 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_7956]), ['final']). 6.97/7.25 cnf(c_0_12992, plain, (hBOOL(hAPP(X1,X7))|~hBOOL(hAPP(X1,esk140_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_6443]), ['final']). 6.97/7.25 cnf(c_0_12993, 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)),X2),X4)),hAPP(c_List_Olexn(X1,X5),X3)))), inference(split_conjunct,[status(thm)],[c_0_7957]), ['final']). 6.97/7.25 cnf(c_0_12994, 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_7957]), ['final']). 6.97/7.25 cnf(c_0_12995, 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_7958]), ['final']). 6.97/7.25 cnf(c_0_12996, 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_7959]), ['final']). 6.97/7.25 cnf(c_0_12997, 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)), inference(split_conjunct,[status(thm)],[c_0_7960]), ['final']). 6.97/7.25 cnf(c_0_12998, 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)), inference(split_conjunct,[status(thm)],[c_0_7961]), ['final']). 6.97/7.25 cnf(c_0_12999, 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)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7962]), ['final']). 6.97/7.25 cnf(c_0_13000, plain, (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)))|~c_Fun_Obij__betw(X1,X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_7963]), ['final']). 6.97/7.25 cnf(c_0_13001, 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_7462]), ['final']). 6.97/7.25 cnf(c_0_13002, 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_7964]), ['final']). 6.97/7.25 cnf(c_0_13003, 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_7965]), ['final']). 6.97/7.25 cnf(c_0_13004, 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)), inference(split_conjunct,[status(thm)],[c_0_7966]), ['final']). 6.97/7.25 cnf(c_0_13005, 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_7967]), ['final']). 6.97/7.25 cnf(c_0_13006, 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)|esk232_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_7968, c_0_4742]), c_0_4742]), ['final']). 6.97/7.25 cnf(c_0_13007, 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,esk422_5(X3,X2,X4,X5,X1))),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_6941]), ['final']). 6.97/7.25 cnf(c_0_13008, 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,esk83_5(X3,X2,X4,X5,X1))),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_6942]), ['final']). 6.97/7.25 cnf(c_0_13009, 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,esk71_5(X3,X4,X5,X2,X1))))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_6943]), ['final']). 6.97/7.25 cnf(c_0_13010, 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_7969]), ['final']). 6.97/7.25 cnf(c_0_13011, 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__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_7970]), ['final']). 6.97/7.25 cnf(c_0_13012, 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_7971]), ['final']). 6.97/7.25 cnf(c_0_13013, 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_7972]), ['final']). 6.97/7.25 cnf(c_0_13014, 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,esk33_5(X3,X2,X4,X5,X1))))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_6944]), ['final']). 6.97/7.25 cnf(c_0_13015, 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_7028]), ['final']). 6.97/7.25 cnf(c_0_13016, plain, (X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))=X4|hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5732]), ['final']). 6.97/7.25 cnf(c_0_13017, 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_7973, c_0_4413]), c_0_4456]), ['final']). 6.97/7.25 cnf(c_0_13018, 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,esk430_4(X2,X1,X3,X4))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), inference(split_conjunct,[status(thm)],[c_0_6911]), ['final']). 6.97/7.25 cnf(c_0_13019, 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,esk1_4(X2,X1,X3,X4))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), inference(split_conjunct,[status(thm)],[c_0_6912]), ['final']). 6.97/7.25 cnf(c_0_13020, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X2)),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~c_Orderings_Oorder__class_Omono(X1,X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X2)),X3))),X3))), inference(split_conjunct,[status(thm)],[c_0_7974]), ['final']). 6.97/7.25 cnf(c_0_13021, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X2)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~c_Orderings_Oorder__class_Omono(X1,X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X2)))))), inference(split_conjunct,[status(thm)],[c_0_7975]), ['final']). 6.97/7.25 cnf(c_0_13022, 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_7976, c_0_4413]), c_0_7977]), c_0_7978]), ['final']). 6.97/7.25 cnf(c_0_13023, plain, (c_Fun_Obij__betw(tc_Nat_Onat,X1,esk305_2(X2,X1),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7979]), ['final']). 6.97/7.25 cnf(c_0_13024, 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_7980, c_0_7756]), ['final']). 6.97/7.25 cnf(c_0_13025, 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_7981, c_0_7756]), ['final']). 6.97/7.25 cnf(c_0_13026, 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_4569]), ['final']). 6.97/7.25 cnf(c_0_13027, 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_7982]), ['final']). 6.97/7.25 cnf(c_0_13028, 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_7983]), ['final']). 6.97/7.25 cnf(c_0_13029, 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_7984]), ['final']). 6.97/7.25 cnf(c_0_13030, 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_7985, c_0_7756]), ['final']). 6.97/7.25 cnf(c_0_13031, 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_7986, c_0_7756]), ['final']). 6.97/7.25 cnf(c_0_13032, plain, (c_Groups_Ozero__class_Ozero(X1)=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))|~class_Groups_Omonoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7987]), ['final']). 6.97/7.25 cnf(c_0_13033, plain, (hBOOL(hAPP(X1,hAPP(c_Nat_OSuc,esk238_2(X2,X1))))|hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,X2))), inference(rw,[status(thm)],[c_0_7988, c_0_6030]), ['final']). 6.97/7.25 cnf(c_0_13034, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk453_2(X3,X1)),X2))|X3=c_List_Olist_ONil(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk452_2(X3,X1))))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5212]), ['final']). 6.97/7.25 cnf(c_0_13035, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X1),X2)|hAPP(X1,esk263_4(X1,X2,X3,X4))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(X1,X4)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X3),X4),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7127]), ['final']). 6.97/7.25 cnf(c_0_13036, 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_7989]), ['final']). 6.97/7.25 cnf(c_0_13037, 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_7990]), ['final']). 6.97/7.25 cnf(c_0_13038, 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_7991]), ['final']). 6.97/7.25 cnf(c_0_13039, 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_7992]), ['final']). 6.97/7.25 cnf(c_0_13040, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk402_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_7993]), ['final']). 6.97/7.25 cnf(c_0_13041, plain, (hAPP(c_Hilbert__Choice_Oinv__into(X2,X1,X5,c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3)),X6)=hAPP(X3,X6)|~c_Fun_Obij__betw(X1,X2,X3,X4,X5)|~hBOOL(hAPP(hAPP(c_member(X1),X6),X4))), inference(split_conjunct,[status(thm)],[c_0_7994]), ['final']). 6.97/7.25 cnf(c_0_13042, plain, (c_Fun_Oinj__on(X1,X2,esk440_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_6822]), ['final']). 6.97/7.25 cnf(c_0_13043, 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_7995]), ['final']). 6.97/7.25 cnf(c_0_13044, 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_7996, c_0_4415]), c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_13045, 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_7997]), ['final']). 6.97/7.25 cnf(c_0_13046, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk40_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_7998]), ['final']). 6.97/7.25 cnf(c_0_13047, 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_7999]), ['final']). 6.97/7.25 cnf(c_0_13048, 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_8000]), ['final']). 6.97/7.25 cnf(c_0_13049, 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_Power_Opower(X1)), inference(split_conjunct,[status(thm)],[c_0_8001]), ['final']). 6.97/7.25 cnf(c_0_13050, 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_7997]), ['final']). 6.97/7.25 cnf(c_0_13051, 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_8002, c_0_5002]), ['final']). 6.97/7.25 cnf(c_0_13052, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk138_3(X2,X3,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)),X3),X2)), inference(split_conjunct,[status(thm)],[c_0_5363]), ['final']). 6.97/7.25 cnf(c_0_13053, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X1)),X2),X4))|~class_Orderings_Oord(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,esk600_4(X3,X4,X2,X1))),hAPP(X4,esk600_4(X3,X4,X2,X1))))), inference(split_conjunct,[status(thm)],[c_0_8003]), ['final']). 6.97/7.25 cnf(c_0_13054, 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,esk456_4(X3,X2,X4,X1))),hAPP(X3,esk456_4(X3,X2,X4,X1))))|~class_Orderings_Oord(X1)), inference(split_conjunct,[status(thm)],[c_0_7903]), ['final']). 6.97/7.25 cnf(c_0_13055, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk137_3(X2,X3,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)),X3),X2)), inference(split_conjunct,[status(thm)],[c_0_5363]), ['final']). 6.97/7.25 cnf(c_0_13056, 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_8004]), ['final']). 6.97/7.25 cnf(c_0_13057, 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_8005]), ['final']). 6.97/7.25 cnf(c_0_13058, 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_8006]), ['final']). 6.97/7.25 cnf(c_0_13059, 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_8007]), ['final']). 6.97/7.25 cnf(c_0_13060, plain, (hBOOL(hAPP(X1,X6))|~hBOOL(hAPP(X1,esk142_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_6443]), ['final']). 6.97/7.25 cnf(c_0_13061, plain, (c_Fun_Obij__betw(X6,X2,hAPP(c_Fun_Ocomp(X1,X2,X6,X3),X7),X8,X5)|~c_Fun_Obij__betw(X1,X2,X3,X4,X5)|~c_Fun_Obij__betw(X6,X1,X7,X8,X4)), inference(split_conjunct,[status(thm)],[c_0_8008]), ['final']). 6.97/7.25 cnf(c_0_13062, plain, (hAPP(X4,X5)=hAPP(X4,X6)|~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_8009]), ['final']). 6.97/7.25 cnf(c_0_13063, 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_8010]), ['final']). 6.97/7.25 cnf(c_0_13064, 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_8011]), ['final']). 6.97/7.25 cnf(c_0_13065, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk259_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_8012]), ['final']). 6.97/7.25 cnf(c_0_13066, 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_8013]), ['final']). 6.97/7.25 cnf(c_0_13067, 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_8014]), ['final']). 6.97/7.25 cnf(c_0_13068, plain, (hBOOL(hAPP(X1,esk101_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_8015]), ['final']). 6.97/7.25 cnf(c_0_13069, 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,esk408_5(X3,X2,X4,X5,X1))))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7136]), ['final']). 6.97/7.25 cnf(c_0_13070, plain, (~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk472_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_7123]), ['final']). 6.97/7.25 cnf(c_0_13071, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,X3)),hAPP(X2,X4)))|~c_Orderings_Oorder__class_Ostrict__mono(X5,X1,X2)|~class_Orderings_Olinorder(X5)|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7723]), ['final']). 6.97/7.25 cnf(c_0_13072, 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_8016, c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_13073, plain, (hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=X3|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_8017]), ['final']). 6.97/7.25 cnf(c_0_13074, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk443_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_8018]), ['final']). 6.97/7.25 cnf(c_0_13075, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),hAPP(X2,X4)))|~c_Orderings_Oorder__class_Ostrict__mono(X5,X1,X2)|~class_Orderings_Oorder(X1)|~class_Orderings_Olinorder(X5)), inference(split_conjunct,[status(thm)],[c_0_7725]), ['final']). 6.97/7.25 cnf(c_0_13076, 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))), inference(split_conjunct,[status(thm)],[c_0_8019]), ['final']). 6.97/7.25 cnf(c_0_13077, plain, (hBOOL(hAPP(X4,X2))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X5)!=c_List_Opartition(X1,X4,X6)), inference(split_conjunct,[status(thm)],[c_0_8020]), ['final']). 6.97/7.25 cnf(c_0_13078, plain, (c_Groups_Ozero__class_Ozero(X1)=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))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)|~class_Rings_Odivision__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_8021]), ['final']). 6.97/7.25 cnf(c_0_13079, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk182_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_7999]), ['final']). 6.97/7.25 cnf(c_0_13080, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk42_3(X2,X3,X1)),X3))|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)), inference(split_conjunct,[status(thm)],[c_0_8022]), ['final']). 6.97/7.25 cnf(c_0_13081, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk72_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_8000]), ['final']). 6.97/7.25 cnf(c_0_13082, 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_7929]), ['final']). 6.97/7.25 cnf(c_0_13083, plain, (c_SetInterval_Oord__class_OgreaterThanLessThan(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)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X2))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8023]), ['final']). 6.97/7.25 cnf(c_0_13084, plain, (c_SetInterval_Oord__class_OatLeastAtMost(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)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X2))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8024]), ['final']). 6.97/7.25 cnf(c_0_13085, 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_8025]), ['final']). 6.97/7.25 cnf(c_0_13086, plain, (X1=hAPP(c_Set_Oimage(X2,X3,X4),esk530_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_7248]), ['final']). 6.97/7.25 cnf(c_0_13087, 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|c_List_Olist_ONil(X1)=X2), inference(er,[status(thm)],[c_0_8026]), ['final']). 6.97/7.25 cnf(c_0_13088, 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_8027, c_0_6448]), ['final']). 6.97/7.25 cnf(c_0_13089, 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_8028, c_0_5538]), ['final']). 6.97/7.25 cnf(c_0_13090, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk410_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_8029]), ['final']). 6.97/7.25 cnf(c_0_13091, plain, (X3=hAPP(c_Relation_OImage(X1,X1,c_Transitive__Closure_Ortrancl(X1,X2)),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_8030]), ['final']). 6.97/7.25 cnf(c_0_13092, 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_8031]), ['final']). 6.97/7.25 cnf(c_0_13093, 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_8032]), ['final']). 6.97/7.25 cnf(c_0_13094, 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))|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|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_8033]), ['final']). 6.97/7.25 cnf(c_0_13095, 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))|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|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_8033]), ['final']). 6.97/7.25 cnf(c_0_13096, 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_8034]), ['final']). 6.97/7.25 cnf(c_0_13097, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X3),X2)=c_Big__Operators_Olinorder__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_8035]), ['final']). 6.97/7.25 cnf(c_0_13098, 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_8036, c_0_5002]), c_0_5002]), ['final']). 6.97/7.25 cnf(c_0_13099, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk332_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_7260]), ['final']). 6.97/7.25 cnf(c_0_13100, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=hAPP(c_Product__Type_Osnd(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_8037]), ['final']). 6.97/7.25 cnf(c_0_13101, 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_8038]), ['final']). 6.97/7.25 cnf(c_0_13102, 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_8039]), ['final']). 6.97/7.25 cnf(c_0_13103, 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_8040]), ['final']). 6.97/7.25 cnf(c_0_13104, plain, (X3=hAPP(hAPP(c_Orderings_Oord__class_Omax(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_8041]), ['final']). 6.97/7.25 cnf(c_0_13105, 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_8042]), ['final']). 6.97/7.25 cnf(c_0_13106, 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_8043]), ['final']). 6.97/7.25 cnf(c_0_13107, plain, (hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X2),tc_List_Olist(X2)),X1),c_List_Orotate1(X2)),X3)=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_8044, c_0_5794]), ['final']). 6.97/7.25 cnf(c_0_13108, plain, (X2=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,esk7_2(X2,X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5787]), ['final']). 6.97/7.25 cnf(c_0_13109, plain, (X1=X2|hAPP(hAPP(c_List_Onth(X3),hAPP(hAPP(c_List_Olist__update(X3,X4),X1),X5)),X2)=hAPP(hAPP(c_List_Onth(X3),X4),X2)), inference(split_conjunct,[status(thm)],[c_0_8045]), ['final']). 6.97/7.25 cnf(c_0_13110, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk393_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_8046]), ['final']). 6.97/7.25 cnf(c_0_13111, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk227_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_7550]), ['final']). 6.97/7.25 cnf(c_0_13112, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk224_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_7034]), ['final']). 6.97/7.25 cnf(c_0_13113, plain, (c_Equiv__Relations_Ocongruent2(X6,X4,X2,X5,X3,X1)|hAPP(hAPP(X1,esk382_6(X2,X1,X3,X4,X5,X6)),esk384_6(X2,X1,X3,X4,X5,X6))!=hAPP(hAPP(X1,esk381_6(X2,X1,X3,X4,X5,X6)),esk383_6(X2,X1,X3,X4,X5,X6))), inference(split_conjunct,[status(thm)],[c_0_6576]), ['final']). 6.97/7.25 cnf(c_0_13114, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|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_8047]), ['final']). 6.97/7.25 cnf(c_0_13115, plain, (hBOOL(hAPP(X1,X2))|~c_Orderings_Oorder__class_Omono(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X4)|~hBOOL(hAPP(X1,esk53_5(X1,X2,X4,X3,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X3,tc_HOL_Obool),X4))))|~hBOOL(hAPP(hAPP(c_member(X3),X2),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X3,tc_HOL_Obool),X4)))), inference(er,[status(thm)],[c_0_8048]), ['final']). 6.97/7.25 cnf(c_0_13116, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))=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)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[c_0_8049, c_0_4471]), ['final']). 6.97/7.25 cnf(c_0_13117, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,esk257_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_13118, plain, (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|hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1)))|~hBOOL(hAPP(X2,esk255_3(X1,X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_13119, 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_8050, c_0_4742]), c_0_4742]), ['final']). 6.97/7.25 cnf(c_0_13120, 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_8051]), ['final']). 6.97/7.25 cnf(c_0_13121, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)),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_8052]), ['final']). 6.97/7.25 cnf(c_0_13122, 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)), inference(split_conjunct,[status(thm)],[c_0_8053]), ['final']). 6.97/7.25 cnf(c_0_13123, 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_8054, c_0_4742]), c_0_4742]), ['final']). 6.97/7.25 cnf(c_0_13124, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk416_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_8055]), ['final']). 6.97/7.25 cnf(c_0_13125, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),esk505_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_8056]), ['final']). 6.97/7.25 cnf(c_0_13126, 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_7902]), ['final']). 6.97/7.25 cnf(c_0_13127, plain, (hAPP(X2,X4)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|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))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7905]), ['final']). 6.97/7.25 cnf(c_0_13128, 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_8057]), ['final']). 6.97/7.25 cnf(c_0_13129, plain, (hBOOL(hAPP(hAPP(c_member(X6),X3),c_SetInterval_Oord_OatLeastLessThan(X6,X1,X4,X2,X5)))|~hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(X4,X3),X5))), inference(split_conjunct,[status(thm)],[c_0_8058]), ['final']). 6.97/7.25 cnf(c_0_13130, 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_8059]), ['final']). 6.97/7.25 cnf(c_0_13131, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),esk416_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_8055]), ['final']). 6.97/7.25 cnf(c_0_13132, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),hAPP(X2,hAPP(c_Nat_OSuc,X3))))|~c_Orderings_Oorder__class_Omono(tc_Nat_Onat,X1,X2)|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8060]), ['final']). 6.97/7.25 cnf(c_0_13133, 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_8061]), ['final']). 6.97/7.25 cnf(c_0_13134, plain, (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)))|hAPP(c_Fun_Ocomp(X1,X2,X2,X3),c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3))!=c_Fun_Oid(X2)), inference(split_conjunct,[status(thm)],[c_0_7523]), ['final']). 6.97/7.25 cnf(c_0_13135, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk94_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_7866]), ['final']). 6.97/7.25 cnf(c_0_13136, 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_8062]), ['final']). 6.97/7.25 cnf(c_0_13137, plain, (c_List_Olist__ex(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_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),X1),X2,X3)), inference(rw,[status(thm)],[c_0_8063, c_0_4471]), ['final']). 6.97/7.25 cnf(c_0_13138, plain, (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)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))|~class_Fields_Ofield__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_8064]), ['final']). 6.97/7.25 cnf(c_0_13139, 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_8065]), ['final']). 6.97/7.25 cnf(c_0_13140, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,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(X2),X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))), inference(split_conjunct,[status(thm)],[c_0_8066]), ['final']). 6.97/7.25 cnf(c_0_13141, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk361_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_5164]), ['final']). 6.97/7.25 cnf(c_0_13142, plain, (hAPP(hAPP(c_List_Otake(X2),X1),c_List_Obutlast(X2,X3))=hAPP(hAPP(c_List_Otake(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_8067]), ['final']). 6.97/7.25 cnf(c_0_13143, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk239_3(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X1)))|c_List_Oall__interval__nat(X3,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_8068]), ['final']). 6.97/7.25 cnf(c_0_13144, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,esk257_3(X2,X3,X1)))|~hBOOL(hAPP(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_13145, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1)))|~hBOOL(hAPP(X2,esk255_3(X1,X3,X2)))|~hBOOL(hAPP(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_13146, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk361_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_5164]), ['final']). 6.97/7.25 cnf(c_0_13147, 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_8069]), ['final']). 6.97/7.25 cnf(c_0_13148, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk569_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_8070]), ['final']). 6.97/7.25 cnf(c_0_13149, 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),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk355_3(X2,X3,X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_7544]), ['final']). 6.97/7.25 cnf(c_0_13150, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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(X1,tc_HOL_Obool)),X2),esk468_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_7549]), ['final']). 6.97/7.25 cnf(c_0_13151, 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_8071]), ['final']). 6.97/7.25 cnf(c_0_13152, 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_7162]), ['final']). 6.97/7.25 cnf(c_0_13153, 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_8072]), ['final']). 6.97/7.25 cnf(c_0_13154, 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_8073]), ['final']). 6.97/7.25 cnf(c_0_13155, 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_8074]), ['final']). 6.97/7.25 cnf(c_0_13156, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~class_Rings_Ocomm__semiring__1(X1)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8075]), ['final']). 6.97/7.25 cnf(c_0_13157, 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_8076]), ['final']). 6.97/7.25 cnf(c_0_13158, 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_7933]), ['final']). 6.97/7.25 cnf(c_0_13159, 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_7644]), ['final']). 6.97/7.25 cnf(c_0_13160, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk578_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_8077]), ['final']). 6.97/7.25 cnf(c_0_13161, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2))|~class_Rings_Odivision__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_8078]), ['final']). 6.97/7.25 cnf(c_0_13162, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~class_Rings_Ocomm__semiring__1(X1)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8079]), ['final']). 6.97/7.25 cnf(c_0_13163, 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_8080]), ['final']). 6.97/7.25 cnf(c_0_13164, 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_8081]), ['final']). 6.97/7.25 cnf(c_0_13165, 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_8082]), ['final']). 6.97/7.25 cnf(c_0_13166, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk245_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_7275]), ['final']). 6.97/7.25 cnf(c_0_13167, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk68_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_5472]), ['final']). 6.97/7.25 cnf(c_0_13168, plain, (X5=c_List_Olinorder__class_Oinsort__insert__key(X4,X1,X2,X3,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_8083]), ['final']). 6.97/7.25 cnf(c_0_13169, 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_8084]), ['final']). 6.97/7.25 cnf(c_0_13170, 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_8085]), ['final']). 6.97/7.25 cnf(c_0_13171, 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_5111]), ['final']). 6.97/7.25 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__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_7282]), ['final']). 6.97/7.25 cnf(c_0_13173, 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_5111]), ['final']). 6.97/7.25 cnf(c_0_13174, 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_8086]), ['final']). 6.97/7.25 cnf(c_0_13175, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk204_3(X2,X3,X1)),X2))|X3=c_List_Olist_ONil(X1)|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_7703]), ['final']). 6.97/7.25 cnf(c_0_13176, 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_Int_Onumber__ring(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)))), inference(rw,[status(thm)],[c_0_8087, c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_13177, 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_7282]), ['final']). 6.97/7.25 cnf(c_0_13178, 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_5224]), ['final']). 6.97/7.25 cnf(c_0_13179, 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_5224]), ['final']). 6.97/7.25 cnf(c_0_13180, 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_Int_Onumber__ring(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)))), inference(rw,[status(thm)],[c_0_8088, c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_13181, 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_Int_Onumber__ring(X1)|~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))), inference(rw,[status(thm)],[c_0_8089, c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_13182, 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_Int_Onumber__ring(X1)|~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))), inference(rw,[status(thm)],[c_0_8090, c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_13183, 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_8091]), ['final']). 6.97/7.25 cnf(c_0_13184, 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_8092]), ['final']). 6.97/7.25 cnf(c_0_13185, plain, (hAPP(X4,hAPP(c_Hilbert__Choice_Oinv__into(X3,X1,X5,X4),X2))=X2|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Set_Oimage(X3,X1,X4),X5)))), inference(split_conjunct,[status(thm)],[c_0_8093]), ['final']). 6.97/7.25 cnf(c_0_13186, 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_8094, c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_13187, 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_8095]), ['final']). 6.97/7.25 cnf(c_0_13188, 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_8096]), ['final']). 6.97/7.25 cnf(c_0_13189, 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_6035]), ['final']). 6.97/7.25 cnf(c_0_13190, 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_8097, c_0_5002]), ['final']). 6.97/7.25 cnf(c_0_13191, 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_8098]), ['final']). 6.97/7.25 cnf(c_0_13192, 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_8099]), ['final']). 6.97/7.25 cnf(c_0_13193, 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_8100]), ['final']). 6.97/7.25 cnf(c_0_13194, 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_8101]), ['final']). 6.97/7.25 cnf(c_0_13195, 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))|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|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_8033]), ['final']). 6.97/7.25 cnf(c_0_13196, 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_8102]), ['final']). 6.97/7.25 cnf(c_0_13197, plain, (hAPP(c_Hilbert__Choice_Oinv__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_8103]), ['final']). 6.97/7.25 cnf(c_0_13198, 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_8104]), ['final']). 6.97/7.25 cnf(c_0_13199, 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_8105]), ['final']). 6.97/7.25 cnf(c_0_13200, 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_8106]), ['final']). 6.97/7.25 cnf(c_0_13201, 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_8107]), ['final']). 6.97/7.25 cnf(c_0_13202, 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_8108]), ['final']). 6.97/7.25 cnf(c_0_13203, 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,esk502_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_8109]), ['final']). 6.97/7.25 cnf(c_0_13204, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[c_0_8110, c_0_4741]), ['final']). 6.97/7.25 cnf(c_0_13205, 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_8111]), ['final']). 6.97/7.25 cnf(c_0_13206, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk368_4(X2,X3,X4,X1)),X3))|c_Equiv__Relations_Ocongruent(X1,X4,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_6039]), ['final']). 6.97/7.25 cnf(c_0_13207, 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)), inference(split_conjunct,[status(thm)],[c_0_8112]), ['final']). 6.97/7.25 cnf(c_0_13208, 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_8113]), ['final']). 6.97/7.25 cnf(c_0_13209, 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_8114]), ['final']). 6.97/7.25 cnf(c_0_13210, 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_8115]), ['final']). 6.97/7.25 cnf(c_0_13211, 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_8116]), ['final']). 6.97/7.25 cnf(c_0_13212, 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_8117]), ['final']). 6.97/7.25 cnf(c_0_13213, 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_8118, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), ['final']). 6.97/7.25 cnf(c_0_13214, 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_8119, c_0_4798]), ['final']). 6.97/7.25 cnf(c_0_13215, 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,esk8_4(X3,X2,X1,X4))), inference(split_conjunct,[status(thm)],[c_0_7176]), ['final']). 6.97/7.25 cnf(c_0_13216, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk492_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_8120]), ['final']). 6.97/7.25 cnf(c_0_13217, 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_8121])]), ['final']). 6.97/7.25 cnf(c_0_13218, 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_5294]), ['final']). 6.97/7.25 cnf(c_0_13219, 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_8122]), ['final']). 6.97/7.25 cnf(c_0_13220, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(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_8123, c_0_4741]), ['final']). 6.97/7.25 cnf(c_0_13221, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk491_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_8120]), ['final']). 6.97/7.25 cnf(c_0_13222, 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),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_5103]), ['final']). 6.97/7.25 cnf(c_0_13223, 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_5103]), ['final']). 6.97/7.25 cnf(c_0_13224, 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_8124]), ['final']). 6.97/7.25 cnf(c_0_13225, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|c_List_Olist_ONil(X2)=c_List_Osublist(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2)),X1)), inference(split_conjunct,[status(thm)],[c_0_7856]), ['final']). 6.97/7.25 cnf(c_0_13226, plain, (X2=X3|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__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8125]), ['final']). 6.97/7.25 cnf(c_0_13227, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[c_0_8126, c_0_4741]), ['final']). 6.97/7.25 cnf(c_0_13228, 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_8127, c_0_5038]), ['final']). 6.97/7.25 cnf(c_0_13229, 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_8128, c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_13230, plain, (hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk200_1(X1))))|~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))), inference(split_conjunct,[status(thm)],[c_0_8129]), ['final']). 6.97/7.25 cnf(c_0_13231, 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_8130]), ['final']). 6.97/7.25 cnf(c_0_13232, plain, (hBOOL(hAPP(X1,X4))|~hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk168_3(X1,X3,X2))))|~hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_6857]), ['final']). 6.97/7.25 cnf(c_0_13233, 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_8131]), ['final']). 6.97/7.25 cnf(c_0_13234, 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_8132])]), ['final']). 6.97/7.25 cnf(c_0_13235, 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_7944]), ['final']). 6.97/7.25 cnf(c_0_13236, 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_7944]), ['final']). 6.97/7.25 cnf(c_0_13237, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X4),X3)))|~hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(c_List_Olistsp(X1,X2),X4))), inference(split_conjunct,[status(thm)],[c_0_8133]), ['final']). 6.97/7.25 cnf(c_0_13238, 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_8134]), ['final']). 6.97/7.25 cnf(c_0_13239, 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_8135]), ['final']). 6.97/7.25 cnf(c_0_13240, plain, (hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(hAPP(X1,esk497_3(X1,X2,X3)),esk498_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_4968]), ['final']). 6.97/7.25 cnf(c_0_13241, 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_7945]), ['final']). 6.97/7.25 cnf(c_0_13242, 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_8136]), ['final']). 6.97/7.25 cnf(c_0_13243, plain, (hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(hAPP(X1,esk438_3(X1,X2,X3)),esk439_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_4482]), ['final']). 6.97/7.25 cnf(c_0_13244, plain, (hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(hAPP(X1,esk290_3(X1,X2,X3)),esk291_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_4488]), ['final']). 6.97/7.25 cnf(c_0_13245, plain, (hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(hAPP(X1,esk250_3(X1,X2,X3)),esk251_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_4997]), ['final']). 6.97/7.25 cnf(c_0_13246, plain, (hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(hAPP(X1,esk122_3(X1,X2,X3)),esk123_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_6552]), ['final']). 6.97/7.25 cnf(c_0_13247, 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_8137]), ['final']). 6.97/7.25 cnf(c_0_13248, 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_8138]), ['final']). 6.97/7.25 cnf(c_0_13249, 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_8139]), ['final']). 6.97/7.25 cnf(c_0_13250, plain, (hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(hAPP(X1,esk48_3(X1,X2,X3)),esk49_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_6490]), ['final']). 6.97/7.25 cnf(c_0_13251, plain, (c_Fun_Obij__betw(X3,X1,esk189_4(X2,X1,X4,X3),X4,X2)|hAPP(c_Finite__Set_Ocard(X1),X2)!=hAPP(c_Finite__Set_Ocard(X3),X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8140]), ['final']). 6.97/7.25 cnf(c_0_13252, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk231_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_8141, c_0_4742]), ['final']). 6.97/7.25 cnf(c_0_13253, plain, (hAPP(hAPP(c_List_Olist_OCons(X3),X2),c_List_OtakeWhile(X3,X1,X4))=c_List_OtakeWhile(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_8142]), ['final']). 6.97/7.25 cnf(c_0_13254, 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_8143]), ['final']). 6.97/7.25 cnf(c_0_13255, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7949]), ['final']). 6.97/7.25 cnf(c_0_13256, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8144]), ['final']). 6.97/7.25 cnf(c_0_13257, plain, (hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(X1,esk494_4(X1,X2,X3,X4)))|~c_Orderings_Oorder__class_Omono(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X2)|~hBOOL(hAPP(hAPP(c_member(X4),X3),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X4,tc_HOL_Obool),X2)))), inference(split_conjunct,[status(thm)],[c_0_4959]), ['final']). 6.97/7.25 cnf(c_0_13258, 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_8145, c_0_4645]), ['final']). 6.97/7.25 cnf(c_0_13259, 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_7810]), ['final']). 6.97/7.25 cnf(c_0_13260, 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_8146, c_0_4411]), ['final']). 6.97/7.25 cnf(c_0_13261, 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_8147]), ['final']). 6.97/7.25 cnf(c_0_13262, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_8148, c_0_4409]), c_0_4410]), c_0_4411]), ['final']). 6.97/7.25 cnf(c_0_13263, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk356_3(X2,X3,X1)),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_8149]), ['final']). 6.97/7.25 cnf(c_0_13264, 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_8150, c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_13265, 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_8070]), ['final']). 6.97/7.25 cnf(c_0_13266, 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_8151]), ['final']). 6.97/7.25 cnf(c_0_13267, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8152, c_0_4413]), c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_13268, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8153, c_0_4413]), c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_13269, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_8154, c_0_4409]), c_0_4410]), c_0_4411]), ['final']). 6.97/7.25 cnf(c_0_13270, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Ominus__class_Ominus(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)],[c_0_8155, c_0_4415]), c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_13271, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(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)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8156]), ['final']). 6.97/7.25 cnf(c_0_13272, plain, (c_Fun_Obij__betw(X1,X2,X3,X4,hAPP(c_Set_Oimage(X1,X2,X3),X4))|~c_Fun_Obij__betw(X1,X2,X3,X5,X6)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5))), inference(er,[status(thm)],[c_0_8157]), ['final']). 6.97/7.25 cnf(c_0_13273, 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_Ominus__class_Ominus(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_8158, c_0_4409]), c_0_4410]), c_0_4411]), ['final']). 6.97/7.25 cnf(c_0_13274, 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_Ominus__class_Ominus(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_8159, c_0_4409]), c_0_4410]), c_0_4411]), ['final']). 6.97/7.25 cnf(c_0_13275, 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_Ominus__class_Ominus(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)],[c_0_8160, c_0_4413]), c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_13276, 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_8161]), ['final']). 6.97/7.25 cnf(c_0_13277, 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_8162]), ['final']). 6.97/7.25 cnf(c_0_13278, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk405_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|c_List_OtakeWhile(X1,X3,X2)=X2), inference(split_conjunct,[status(thm)],[c_0_8163]), ['final']). 6.97/7.25 cnf(c_0_13279, 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_8164]), ['final']). 6.97/7.25 cnf(c_0_13280, 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_Ominus__class_Ominus(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)],[c_0_8165, c_0_4413]), c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_13281, 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_7972]), ['final']). 6.97/7.25 cnf(c_0_13282, 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_7971]), ['final']). 6.97/7.25 cnf(c_0_13283, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|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),X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_8061]), ['final']). 6.97/7.25 cnf(c_0_13284, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk116_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_8166, c_0_5002]), ['final']). 6.97/7.25 cnf(c_0_13285, 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_8162]), ['final']). 6.97/7.25 cnf(c_0_13286, 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_8167]), ['final']). 6.97/7.25 cnf(c_0_13287, 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_8168]), ['final']). 6.97/7.25 cnf(c_0_13288, 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))))|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))), inference(split_conjunct,[status(thm)],[c_0_8169]), ['final']). 6.97/7.25 cnf(c_0_13289, 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_8170]), ['final']). 6.97/7.25 cnf(c_0_13290, 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_8171, c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_13291, 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_8172]), ['final']). 6.97/7.25 cnf(c_0_13292, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk297_3(X2,X3,X1)),c_Quotient_ORespects(X1,X3)))|~hBOOL(hAPP(X2,X4))|~c_Equiv__Relations_Oequivp(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_8173]), ['final']). 6.97/7.25 cnf(c_0_13293, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk334_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_8174]), ['final']). 6.97/7.25 cnf(c_0_13294, 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_7590]), ['final']). 6.97/7.25 cnf(c_0_13295, plain, (hBOOL(hAPP(hAPP(X1,esk44_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_7956]), ['final']). 6.97/7.25 cnf(c_0_13296, 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)), inference(split_conjunct,[status(thm)],[c_0_8175]), ['final']). 6.97/7.25 cnf(c_0_13297, 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_8176]), ['final']). 6.97/7.25 cnf(c_0_13298, 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_8177]), ['final']). 6.97/7.25 cnf(c_0_13299, 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_8178]), ['final']). 6.97/7.25 cnf(c_0_13300, 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_8179]), ['final']). 6.97/7.25 cnf(c_0_13301, plain, (hBOOL(hAPP(hAPP(X1,X2),esk44_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_7956]), ['final']). 6.97/7.25 cnf(c_0_13302, 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_8180]), ['final']). 6.97/7.25 cnf(c_0_13303, plain, (X2=hAPP(c_Set_Oimage(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)),hAPP(c_Set_Oimage(X1,X1,X3),X2)),X2))|~c_Fun_Oinj__on(X1,X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_8181]), ['final']). 6.97/7.25 cnf(c_0_13304, 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_8182]), ['final']). 6.97/7.25 cnf(c_0_13305, 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_8183]), ['final']). 6.97/7.25 cnf(c_0_13306, 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_8184]), ['final']). 6.97/7.25 cnf(c_0_13307, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk459_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_6854]), ['final']). 6.97/7.25 cnf(c_0_13308, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk5_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_8185]), ['final']). 6.97/7.25 cnf(c_0_13309, 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_8186, c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_13310, 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_8187]), ['final']). 6.97/7.25 cnf(c_0_13311, plain, (hBOOL(hAPP(hAPP(c_member(X5),X2),c_SetInterval_Oord_OgreaterThanLessThan(X5,X1,X4,X3)))|~hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(X1,X4),X2))), inference(split_conjunct,[status(thm)],[c_0_8188]), ['final']). 6.97/7.25 cnf(c_0_13312, 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_8189]), ['final']). 6.97/7.25 cnf(c_0_13313, 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_8190]), ['final']). 6.97/7.25 cnf(c_0_13314, 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_8191]), ['final']). 6.97/7.25 cnf(c_0_13315, plain, (hBOOL(hAPP(X1,esk351_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))), inference(split_conjunct,[status(thm)],[c_0_7408]), ['final']). 6.97/7.25 cnf(c_0_13316, plain, (c_Big__Operators_Olinorder__class_OMax(X1,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))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8192]), ['final']). 6.97/7.25 cnf(c_0_13317, 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_8193]), ['final']). 6.97/7.25 cnf(c_0_13318, plain, (c_Big__Operators_Olinorder__class_OMin(X1,X2)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),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_8194]), ['final']). 6.97/7.25 cnf(c_0_13319, 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_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8195]), ['final']). 6.97/7.25 cnf(c_0_13320, 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))), inference(split_conjunct,[status(thm)],[c_0_8196]), ['final']). 6.97/7.25 cnf(c_0_13321, 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_8197, c_0_5002]), c_0_5002]), ['final']). 6.97/7.25 cnf(c_0_13322, 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_8198]), ['final']). 6.97/7.25 cnf(c_0_13323, 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_8199]), ['final']). 6.97/7.25 cnf(c_0_13324, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X1),X2)|esk263_4(X1,X2,X3,X4)!=X4|hAPP(X1,X4)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X3),X4),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7127]), ['final']). 6.97/7.25 cnf(c_0_13325, 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_7148]), ['final']). 6.97/7.25 cnf(c_0_13326, 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_7148]), ['final']). 6.97/7.25 cnf(c_0_13327, 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_8200]), ['final']). 6.97/7.25 cnf(c_0_13328, 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)), inference(split_conjunct,[status(thm)],[c_0_8201]), ['final']). 6.97/7.25 cnf(c_0_13329, 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_7244]), ['final']). 6.97/7.25 cnf(c_0_13330, 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_8202]), ['final']). 6.97/7.25 cnf(c_0_13331, 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_8203]), ['final']). 6.97/7.25 cnf(c_0_13332, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk262_3(X2,X3,X1)),X3))|c_Groups_Oone__class_Oone(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_7127]), ['final']). 6.97/7.25 cnf(c_0_13333, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk178_1(X1)))|hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))), inference(split_conjunct,[status(thm)],[c_0_8204]), ['final']). 6.97/7.25 cnf(c_0_13334, 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_8205]), ['final']). 6.97/7.25 cnf(c_0_13335, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk84_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_8206]), ['final']). 6.97/7.25 cnf(c_0_13336, plain, (hBOOL(hAPP(X1,esk332_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_7260]), ['final']). 6.97/7.25 cnf(c_0_13337, 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_5029]), ['final']). 6.97/7.25 cnf(c_0_13338, 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_8207]), ['final']). 6.97/7.25 cnf(c_0_13339, 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_8208, c_0_4742]), c_0_4742]), c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_13340, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,c_Inductive_Ocomplete__lattice__class_Olfp(X1,X2))),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X2)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~c_Orderings_Oorder__class_Omono(X1,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8209]), ['final']). 6.97/7.25 cnf(c_0_13341, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X2))),c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X2)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~c_Orderings_Oorder__class_Omono(X1,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8210]), ['final']). 6.97/7.25 cnf(c_0_13342, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X2)),hAPP(X2,c_Inductive_Ocomplete__lattice__class_Olfp(X1,X2))))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~c_Orderings_Oorder__class_Omono(X1,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8211]), ['final']). 6.97/7.25 cnf(c_0_13343, plain, (X1=X2|c_List_Oremove1(X3,X2,hAPP(hAPP(c_List_Olist_OCons(X3),X1),X4))=hAPP(hAPP(c_List_Olist_OCons(X3),X1),c_List_Oremove1(X3,X2,X4))), inference(split_conjunct,[status(thm)],[c_0_5838]), ['final']). 6.97/7.25 cnf(c_0_13344, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))|~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)), inference(split_conjunct,[status(thm)],[c_0_7383]), ['final']). 6.97/7.25 cnf(c_0_13345, 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_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)), inference(split_conjunct,[status(thm)],[c_0_7389]), ['final']). 6.97/7.25 cnf(c_0_13346, plain, (hBOOL(hAPP(X1,X2))|hAPP(c_List_Ofilter(X3,X1),X4)=hAPP(c_List_Ofilter(X3,X1),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_7497]), ['final']). 6.97/7.25 cnf(c_0_13347, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X2)),hAPP(X2,c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X2))))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~c_Orderings_Oorder__class_Omono(X1,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8212]), ['final']). 6.97/7.25 cnf(c_0_13348, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk352_3(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X2,X1)))|c_List_Oall__interval__int(X3,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_8213]), ['final']). 6.97/7.25 cnf(c_0_13349, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk591_2(X1,X2)),c_Int_OInteg))|hBOOL(hAPP(X2,X1))), inference(split_conjunct,[status(thm)],[c_0_8214]), ['final']). 6.97/7.25 cnf(c_0_13350, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk513_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))|c_List_Olist__all(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8215]), ['final']). 6.97/7.25 cnf(c_0_13351, 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_7391]), ['final']). 6.97/7.25 cnf(c_0_13352, 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_8216]), ['final']). 6.97/7.25 cnf(c_0_13353, plain, (hAPP(X3,X5)=hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X3,X5)),hAPP(X3,X5))|~c_Finite__Set_Ofolding__idem(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8217]), ['final']). 6.97/7.25 cnf(c_0_13354, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk461_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|c_List_Olist__all(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_8218]), ['final']). 6.97/7.25 cnf(c_0_13355, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk423_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|c_List_Olist__all(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_8219]), ['final']). 6.97/7.25 cnf(c_0_13356, plain, (hAPP(hAPP(c_Set_Oinsert(X1),esk80_3(X2,X3,X1)),esk81_3(X2,X3,X1))=X3|hAPP(c_Finite__Set_Ocard(X1),X3)!=hAPP(c_Nat_OSuc,X2)), inference(split_conjunct,[status(thm)],[c_0_5303]), ['final']). 6.97/7.25 cnf(c_0_13357, 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)))|~hBOOL(hAPP(X2,esk275_3(X1,X3,X2)))|~hBOOL(hAPP(X2,esk273_3(X1,X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.25 cnf(c_0_13358, 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_8220]), ['final']). 6.97/7.25 cnf(c_0_13359, 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,esk593_3(X2,X1,X3)))),hAPP(X3,esk593_3(X2,X1,X3)))),X2))), inference(split_conjunct,[status(thm)],[c_0_6871]), ['final']). 6.97/7.25 cnf(c_0_13360, 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_8221]), ['final']). 6.97/7.25 cnf(c_0_13361, 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,esk537_3(X3,X2,X1)))),hAPP(X3,esk537_3(X3,X2,X1)))),X2))), inference(split_conjunct,[status(thm)],[c_0_8222]), ['final']). 6.97/7.25 cnf(c_0_13362, plain, (hBOOL(hAPP(hAPP(X1,esk393_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_8046]), ['final']). 6.97/7.25 cnf(c_0_13363, plain, (hBOOL(hAPP(hAPP(X1,esk227_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_7550]), ['final']). 6.97/7.25 cnf(c_0_13364, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk472_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_7123]), ['final']). 6.97/7.25 cnf(c_0_13365, plain, (c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))=X3|X4=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X3),hAPP(c_COMBK(X1,X2),X4))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8223]), ['final']). 6.97/7.25 cnf(c_0_13366, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X3,X2),esk310_3(X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8224]), ['final']). 6.97/7.25 cnf(c_0_13367, 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_8225, c_0_4742]), c_0_5002]), ['final']). 6.97/7.25 cnf(c_0_13368, 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_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)],[c_0_8226, c_0_4410]), ['final']). 6.97/7.25 cnf(c_0_13369, 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)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8227, c_0_5656]), c_0_5657]), ['final']). 6.97/7.25 cnf(c_0_13370, 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_8228]), ['final']). 6.97/7.25 cnf(c_0_13371, 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),X4),X5)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8229]), ['final']). 6.97/7.25 cnf(c_0_13372, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X1),X2),hAPP(c_COMBK(X1,X3),X4))=X4|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8230]), ['final']). 6.97/7.25 cnf(c_0_13373, 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)), inference(split_conjunct,[status(thm)],[c_0_8231]), ['final']). 6.97/7.25 cnf(c_0_13374, 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_8232]), ['final']). 6.97/7.25 cnf(c_0_13375, 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_8233]), ['final']). 6.97/7.25 cnf(c_0_13376, plain, (hAPP(c_SetInterval_Oord__class_OatLeast(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_OatMost(X1),X2))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8234]), ['final']). 6.97/7.25 cnf(c_0_13377, 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)|c_Orderings_Otop__class_Otop(X1)!=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_8235]), ['final']). 6.97/7.25 cnf(c_0_13378, 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)],[c_0_8236, c_0_4410]), c_0_4410]), ['final']). 6.97/7.25 cnf(c_0_13379, 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_7162]), ['final']). 6.97/7.25 cnf(c_0_13380, plain, (X1=c_List_Olist_ONil(X2)|hAPP(c_List_Ohd(X3),hAPP(hAPP(c_List_Omap(X2,X3),X4),X1))=hAPP(X4,hAPP(c_List_Ohd(X2),X1))), inference(split_conjunct,[status(thm)],[c_0_8237]), ['final']). 6.97/7.25 cnf(c_0_13381, 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_8238]), ['final']). 6.97/7.25 cnf(c_0_13382, 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_8239]), ['final']). 6.97/7.25 cnf(c_0_13383, 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_8240]), ['final']). 6.97/7.25 cnf(c_0_13384, 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_8241]), ['final']). 6.97/7.25 cnf(c_0_13385, 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,X1))), inference(rw,[status(thm)],[c_0_8242, c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_13386, 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_8071]), ['final']). 6.97/7.25 cnf(c_0_13387, 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_7597]), ['final']). 6.97/7.25 cnf(c_0_13388, 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)],[c_0_8243, c_0_4410]), c_0_4410]), ['final']). 6.97/7.25 cnf(c_0_13389, plain, (hAPP(hAPP(c_List_Onth(X1),X2),esk491_2(X2,X1))=hAPP(hAPP(c_List_Onth(X1),X2),esk492_2(X2,X1))|hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8120]), ['final']). 6.97/7.25 cnf(c_0_13390, 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_8244]), ['final']). 6.97/7.25 cnf(c_0_13391, 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_8245]), ['final']). 6.97/7.25 cnf(c_0_13392, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|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_8246]), ['final']). 6.97/7.25 cnf(c_0_13393, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|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_8247]), ['final']). 6.97/7.25 cnf(c_0_13394, 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_7608]), ['final']). 6.97/7.25 cnf(c_0_13395, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X2)),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),X3))), inference(split_conjunct,[status(thm)],[c_0_8248]), ['final']). 6.97/7.25 cnf(c_0_13396, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X3)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_8249]), ['final']). 6.97/7.25 cnf(c_0_13397, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X7)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)|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_8250]), ['final']). 6.97/7.25 cnf(c_0_13398, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk341_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_7831]), ['final']). 6.97/7.25 cnf(c_0_13399, 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_8251]), ['final']). 6.97/7.25 cnf(c_0_13400, plain, (hAPP(X4,esk426_3(X4,X3,X2))=X2|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Set_Oimage(X3,X1,X4),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))))), inference(split_conjunct,[status(thm)],[c_0_8252]), ['final']). 6.97/7.25 cnf(c_0_13401, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X2))|~c_Nat__Transfer_Ois__nat(X1)|~c_Nat__Transfer_Onat__set(X2)|~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_8253, c_0_5002]), ['final']). 6.97/7.25 cnf(c_0_13402, 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_8254, c_0_6164]), ['final']). 6.97/7.25 cnf(c_0_13403, 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,esk397_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_7604]), ['final']). 6.97/7.25 cnf(c_0_13404, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))|hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(X1,esk545_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_7599]), ['final']). 6.97/7.25 cnf(c_0_13405, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|X2=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_8255]), ['final']). 6.97/7.25 cnf(c_0_13406, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk427_3(X2,X3,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Complete__Lattice_OInf__class_OInf(X1,X3)),X2))|~class_Orderings_Olinorder(X1)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7744]), ['final']). 6.97/7.25 cnf(c_0_13407, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk427_3(X2,X3,X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Complete__Lattice_OInf__class_OInf(X1,X3)),X2))|~class_Orderings_Olinorder(X1)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7744]), ['final']). 6.97/7.25 cnf(c_0_13408, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk115_3(X2,X3,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Complete__Lattice_OSup__class_OSup(X1,X2)))|~class_Orderings_Olinorder(X1)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7745]), ['final']). 6.97/7.25 cnf(c_0_13409, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),esk115_3(X3,X2,X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Complete__Lattice_OSup__class_OSup(X1,X3)))|~class_Orderings_Olinorder(X1)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7745]), ['final']). 6.97/7.25 cnf(c_0_13410, 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_8256]), ['final']). 6.97/7.25 cnf(c_0_13411, plain, (X3=hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Relation_Oconverse(X1,X1),X3)),X3)|~c_Equiv__Relations_Oequiv(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8257]), ['final']). 6.97/7.25 cnf(c_0_13412, plain, (hBOOL(hAPP(X1,esk247_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_7845]), ['final']). 6.97/7.25 cnf(c_0_13413, plain, (X3=X2|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_8258]), ['final']). 6.97/7.25 cnf(c_0_13414, plain, (hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),esk333_3(X1,X3,X2)),esk334_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_8174]), ['final']). 6.97/7.25 cnf(c_0_13415, 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_8259]), ['final']). 6.97/7.25 cnf(c_0_13416, 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_8260]), ['final']). 6.97/7.25 cnf(c_0_13417, 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))), inference(split_conjunct,[status(thm)],[c_0_8261]), ['final']). 6.97/7.25 cnf(c_0_13418, 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_8262]), ['final']). 6.97/7.25 cnf(c_0_13419, 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_7504]), ['final']). 6.97/7.25 cnf(c_0_13420, 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_8263, c_0_5002]), c_0_5002]), ['final']). 6.97/7.25 cnf(c_0_13421, 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_8264]), ['final']). 6.97/7.25 cnf(c_0_13422, 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_8265, c_0_4415]), c_0_5038]), ['final']). 6.97/7.25 cnf(c_0_13423, 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_8266, c_0_4415]), c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_13424, 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_8267, c_0_5002]), c_0_5002]), ['final']). 6.97/7.25 cnf(c_0_13425, plain, (hBOOL(hAPP(X1,esk298_3(X1,X4,X3)))|~hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),c_Quotient_ORespects(X3,X4)))|~c_Equiv__Relations_Oequivp(X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8173]), ['final']). 6.97/7.25 cnf(c_0_13426, plain, (hBOOL(hAPP(hAPP(X1,X2),esk245_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_7275]), ['final']). 6.97/7.25 cnf(c_0_13427, plain, (hBOOL(hAPP(hAPP(X1,X2),esk68_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_5472]), ['final']). 6.97/7.25 cnf(c_0_13428, 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_8268]), ['final']). 6.97/7.25 cnf(c_0_13429, 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)],[c_0_8269, c_0_4410]), ['final']). 6.97/7.25 cnf(c_0_13430, 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)],[c_0_8270, c_0_4413]), c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_13431, 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)],[c_0_8271, c_0_4410]), ['final']). 6.97/7.25 cnf(c_0_13432, 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_8272]), ['final']). 6.97/7.25 cnf(c_0_13433, 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),esk59_3(X2,X3,X1)),esk60_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_7182]), ['final']). 6.97/7.25 cnf(c_0_13434, 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_8273]), ['final']). 6.97/7.25 cnf(c_0_13435, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|c_Groups_Osgn__class_Osgn(X1,X2)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))|X2=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Osgn__if(X1)), inference(split_conjunct,[status(thm)],[c_0_8274]), ['final']). 6.97/7.25 cnf(c_0_13436, 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)],[c_0_8275, c_0_4413]), c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_13437, 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)],[c_0_8276, c_0_4415]), c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_13438, 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_8277, c_0_4565]), ['final']). 6.97/7.25 cnf(c_0_13439, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X1,X3)),c_Sum__Type_OPlus(X1,X3,X2,X4)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8278]), ['final']). 6.97/7.25 cnf(c_0_13440, 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_8279]), ['final']). 6.97/7.25 cnf(c_0_13441, plain, (X3=X2|hAPP(hAPP(c_List_Onth(X1),X2),esk114_3(X1,X3,X2))!=hAPP(hAPP(c_List_Onth(X1),X3),esk114_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_7642]), ['final']). 6.97/7.25 cnf(c_0_13442, 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_8280]), ['final']). 6.97/7.25 cnf(c_0_13443, 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_8281]), ['final']). 6.97/7.25 cnf(c_0_13444, 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_8282]), ['final']). 6.97/7.25 cnf(c_0_13445, 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_8283]), ['final']). 6.97/7.25 cnf(c_0_13446, 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_8284]), ['final']). 6.97/7.25 cnf(c_0_13447, 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_8285]), ['final']). 6.97/7.25 cnf(c_0_13448, 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_8286]), ['final']). 6.97/7.25 cnf(c_0_13449, plain, (hBOOL(hAPP(X1,esk244_2(X1,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_7525]), ['final']). 6.97/7.25 cnf(c_0_13450, plain, (X1=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_8287, c_0_4409]), c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), c_0_4411]), ['final']). 6.97/7.25 cnf(c_0_13451, 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_8288]), ['final']). 6.97/7.25 cnf(c_0_13452, plain, (X1=X2|hAPP(hAPP(c_List_Oappend(X3),X4),hAPP(hAPP(c_List_Olist_OCons(X3),X2),c_List_Olist_ONil(X3)))!=hAPP(hAPP(c_List_Oappend(X3),X5),hAPP(hAPP(c_List_Olist_OCons(X3),X1),c_List_Olist_ONil(X3)))), inference(split_conjunct,[status(thm)],[c_0_8288]), ['final']). 6.97/7.25 cnf(c_0_13453, plain, (hAPP(X1,esk432_1(X1))=hAPP(X1,esk431_1(X1))|hBOOL(hAPP(hAPP(X1,esk431_1(X1)),esk432_1(X1)))|c_Equiv__Relations_Oequivp(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_8289]), ['final']). 6.97/7.25 cnf(c_0_13454, 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_8290]), ['final']). 6.97/7.25 cnf(c_0_13455, 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)],[c_0_8291, c_0_4410]), ['final']). 6.97/7.25 cnf(c_0_13456, 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)],[c_0_8292, c_0_4413]), c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_13457, plain, (X3=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)|X2=X3|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_5398]), ['final']). 6.97/7.25 cnf(c_0_13458, plain, (hBOOL(hAPP(X1,X5))|~hBOOL(hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X4),esk69_5(X5,X1,X4,X3,X2))))|~c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_6927]), ['final']). 6.97/7.25 cnf(c_0_13459, 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)],[c_0_8293, c_0_4410]), ['final']). 6.97/7.25 cnf(c_0_13460, 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)],[c_0_8294, c_0_4413]), c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_13461, 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_8295]), ['final']). 6.97/7.25 cnf(c_0_13462, 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_8296]), ['final']). 6.97/7.25 cnf(c_0_13463, 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_8297]), ['final']). 6.97/7.25 cnf(c_0_13464, 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_8298]), ['final']). 6.97/7.25 cnf(c_0_13465, 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_8299]), ['final']). 6.97/7.25 cnf(c_0_13466, 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)), inference(split_conjunct,[status(thm)],[c_0_8300]), ['final']). 6.97/7.25 cnf(c_0_13467, 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_8301, c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_13468, plain, (X1=hAPP(c_List_Ofilter(X2,X3),esk131_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_4995]), ['final']). 6.97/7.25 cnf(c_0_13469, plain, (X1=hAPP(c_List_Ofilter(X2,X3),esk88_5(X1,X4,X5,X3,X2))|hAPP(hAPP(c_List_Olist_OCons(X2),X4),X1)!=hAPP(c_List_Ofilter(X2,X3),X5)), inference(split_conjunct,[status(thm)],[c_0_4996]), ['final']). 6.97/7.25 cnf(c_0_13470, 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_8302]), ['final']). 6.97/7.25 cnf(c_0_13471, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk455_2(X1,X2)),X1))|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1)))), inference(split_conjunct,[status(thm)],[c_0_8303]), ['final']). 6.97/7.25 cnf(c_0_13472, plain, (c_List_Olist_ONil(X1)=X2|hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_List_Ohd(X1),X2)),hAPP(c_List_Oset(X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_8304]), ['final']). 6.97/7.25 cnf(c_0_13473, 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_8305]), ['final']). 6.97/7.25 cnf(c_0_13474, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)|~class_Int_Onumber__ring(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)))), inference(rw,[status(thm)],[c_0_8306, c_0_4821]), ['final']). 6.97/7.25 cnf(c_0_13475, 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_8307]), ['final']). 6.97/7.25 cnf(c_0_13476, 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_8308]), ['final']). 6.97/7.25 cnf(c_0_13477, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|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_8309]), ['final']). 6.97/7.25 cnf(c_0_13478, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|X3=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X2)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_8310]), ['final']). 6.97/7.25 cnf(c_0_13479, 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_8311]), ['final']). 6.97/7.25 cnf(c_0_13480, plain, (X5=X6|~c_Fun_Oinj__on(X1,X2,X3,X4)|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X6),X4))|hAPP(X3,X6)!=hAPP(X3,X5)), inference(split_conjunct,[status(thm)],[c_0_8312]), ['final']). 6.97/7.25 cnf(c_0_13481, 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_8313]), ['final']). 6.97/7.25 cnf(c_0_13482, 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_8314]), ['final']). 6.97/7.25 cnf(c_0_13483, 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_8315]), ['final']). 6.97/7.25 cnf(c_0_13484, 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_8316, c_0_4467]), ['final']). 6.97/7.25 cnf(c_0_13485, 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_5837]), ['final']). 6.97/7.25 cnf(c_0_13486, 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),esk514_5(X3,X4,X5,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_6472]), ['final']). 6.97/7.25 cnf(c_0_13487, 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),esk240_5(X4,X5,X3,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_6474]), ['final']). 6.97/7.25 cnf(c_0_13488, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X3),X2),X4)))|~hBOOL(hAPP(X1,esk434_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_7025]), ['final']). 6.97/7.25 cnf(c_0_13489, 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)))|~hBOOL(hAPP(X1,esk275_3(X2,X3,X1)))|~hBOOL(hAPP(X1,esk273_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_4962]), ['final']). 6.97/7.25 cnf(c_0_13490, 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_8317]), ['final']). 6.97/7.25 cnf(c_0_13491, plain, (c_List_Olast(X2,hAPP(hAPP(c_List_Odrop(X2),X1),X3))=c_List_Olast(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_8318]), ['final']). 6.97/7.25 cnf(c_0_13492, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk528_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|~c_List_Olist__ex1(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_7252]), ['final']). 6.97/7.25 cnf(c_0_13493, plain, (c_List_Olist_ONil(X1)=X2|c_List_Obutlast(X1,hAPP(hAPP(c_List_Oappend(X1),X3),X2))=hAPP(hAPP(c_List_Oappend(X1),X3),c_List_Obutlast(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_8319]), ['final']). 6.97/7.25 cnf(c_0_13494, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X4,X2))|hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),X3)!=c_List_Opartition(X1,X4,X6)), inference(split_conjunct,[status(thm)],[c_0_8020]), ['final']). 6.97/7.25 cnf(c_0_13495, 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_8320]), ['final']). 6.97/7.25 cnf(c_0_13496, 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_8321]), ['final']). 6.97/7.25 cnf(c_0_13497, 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_8322, c_0_5746]), ['final']). 6.97/7.25 cnf(c_0_13498, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk335_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))|~c_List_Olist__ex(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8323]), ['final']). 6.97/7.25 cnf(c_0_13499, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk241_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|~c_List_Olist__ex1(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_7253]), ['final']). 6.97/7.25 cnf(c_0_13500, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk181_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|~c_List_Olist__ex(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_8324]), ['final']). 6.97/7.25 cnf(c_0_13501, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk66_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|~c_List_Olist__ex(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_8325]), ['final']). 6.97/7.25 cnf(c_0_13502, plain, (c_List_Olist_ONil(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),c_List_Olist_ONil(X1))),c_List_Olistrel(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_8326]), ['final']). 6.97/7.25 cnf(c_0_13503, plain, (hAPP(c_List_Ofilter(X2,X3),c_List_Olinorder__class_Osort__key(X2,X1,X4,X5))=c_List_Olinorder__class_Osort__key(X2,X1,X4,hAPP(c_List_Ofilter(X2,X3),X5))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8327]), ['final']). 6.97/7.25 cnf(c_0_13504, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(X2,esk132_4(X2,X3,X4,X1))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X1),X2),X3)!=c_Groups_Ozero__class_Ozero(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))|~class_Rings_Ocomm__semiring__1(X1)|~class_Rings_Ono__zero__divisors(X1)), inference(split_conjunct,[status(thm)],[c_0_7915]), ['final']). 6.97/7.25 cnf(c_0_13505, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),esk410_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_8029]), ['final']). 6.97/7.25 cnf(c_0_13506, 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_8328, c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_13507, 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_8329]), ['final']). 6.97/7.25 cnf(c_0_13508, plain, (hAPP(c_Finite__Set_Ocard(X1),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_member(X1),esk504_2(X2,X1)),X2))), inference(csr,[status(thm)],[c_0_8330, c_0_8331]), ['final']). 6.97/7.25 cnf(c_0_13509, 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,esk247_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_7845]), ['final']). 6.97/7.25 cnf(c_0_13510, 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_7440]), ['final']). 6.97/7.25 cnf(c_0_13511, 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_4927]), ['final']). 6.97/7.25 cnf(c_0_13512, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1),X1)=c_Divides_Odiv__class_Omod(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_8332]), ['final']). 6.97/7.25 cnf(c_0_13513, 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_8333]), ['final']). 6.97/7.25 cnf(c_0_13514, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk271_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_5799]), ['final']). 6.97/7.25 cnf(c_0_13515, plain, (hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(X1,esk13_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_7236]), ['final']). 6.97/7.25 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_8334]), ['final']). 6.97/7.25 cnf(c_0_13517, plain, (X3=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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_8335]), ['final']). 6.97/7.25 cnf(c_0_13518, 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))), inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_8336]), c_0_4977]), ['final']). 6.97/7.25 cnf(c_0_13519, plain, (c_Relation_Otrans(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~c_Relation_Otrans(X1,X2)|~c_Relation_Otrans(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_8337]), ['final']). 6.97/7.25 cnf(c_0_13520, plain, (c_Relation_Osym(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~c_Relation_Osym(X1,X2)|~c_Relation_Osym(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_8338]), ['final']). 6.97/7.25 cnf(c_0_13521, 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_6714]), ['final']). 6.97/7.25 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_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_6715]), ['final']). 6.97/7.25 cnf(c_0_13523, plain, (hBOOL(hAPP(X1,esk334_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_8174]), ['final']). 6.97/7.25 cnf(c_0_13524, plain, (hAPP(X1,esk231_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_8339, c_0_4742]), c_0_4742]), ['final']). 6.97/7.25 cnf(c_0_13525, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),esk453_2(X2,X1)),esk452_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_5212]), ['final']). 6.97/7.25 cnf(c_0_13526, plain, (c_Relation_Osym(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~c_Relation_Osym(X1,X2)|~c_Relation_Osym(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_8340]), ['final']). 6.97/7.25 cnf(c_0_13527, 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),esk377_2(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_7917]), ['final']). 6.97/7.25 cnf(c_0_13528, 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_7858]), ['final']). 6.97/7.25 cnf(c_0_13529, 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_8341]), ['final']). 6.97/7.25 cnf(c_0_13530, 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_8342]), ['final']). 6.97/7.25 cnf(c_0_13531, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|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_8343]), ['final']). 6.97/7.25 cnf(c_0_13532, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Nat_OSuc,X2))|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8344]), ['final']). 6.97/7.25 cnf(c_0_13533, 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_Ominus__class_Ominus(tc_Int_Oint),X2),c_Int_OMin)))), inference(rw,[status(thm)],[c_0_8345, c_0_4741]), ['final']). 6.97/7.25 cnf(c_0_13534, 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_8346, c_0_5002]), ['final']). 6.97/7.25 cnf(c_0_13535, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|X3=c_List_Oremove1(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8347]), ['final']). 6.97/7.25 cnf(c_0_13536, 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_8348]), ['final']). 6.97/7.25 cnf(c_0_13537, plain, (hAPP(hAPP(X3,X4),X5)=hAPP(hAPP(X3,X4),hAPP(hAPP(X3,X4),X5))|~c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8349]), ['final']). 6.97/7.25 cnf(c_0_13538, 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_8350]), ['final']). 6.97/7.25 cnf(c_0_13539, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|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_8351]), ['final']). 6.97/7.25 cnf(c_0_13540, 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_8352]), ['final']). 6.97/7.25 cnf(c_0_13541, 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_8353]), ['final']). 6.97/7.25 cnf(c_0_13542, 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_8354]), ['final']). 6.97/7.25 cnf(c_0_13543, 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_7836]), ['final']). 6.97/7.25 cnf(c_0_13544, 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_7837]), ['final']). 6.97/7.25 cnf(c_0_13545, 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_8355]), ['final']). 6.97/7.25 cnf(c_0_13546, plain, (hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X2,tc_HOL_Obool)),X4),X1),X3))|~hBOOL(hAPP(hAPP(X1,esk237_5(X2,X3,X1,X4,X5)),X3))), inference(split_conjunct,[status(thm)],[c_0_7634]), ['final']). 6.97/7.25 cnf(c_0_13547, 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,esk557_5(X2,X1,X3,X4,X5)),X2))), inference(split_conjunct,[status(thm)],[c_0_7629]), ['final']). 6.97/7.25 cnf(c_0_13548, 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_7754]), ['final']). 6.97/7.25 cnf(c_0_13549, 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_7762]), ['final']). 6.97/7.25 cnf(c_0_13550, 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_8356]), ['final']). 6.97/7.25 cnf(c_0_13551, 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_8357]), ['final']). 6.97/7.25 cnf(c_0_13552, plain, (hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X4),X3),c_List_Olist_ONil(X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8358]), ['final']). 6.97/7.25 cnf(c_0_13553, 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_7760]), ['final']). 6.97/7.25 cnf(c_0_13554, 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_7761]), ['final']). 6.97/7.25 cnf(c_0_13555, 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_7759]), ['final']). 6.97/7.25 cnf(c_0_13556, 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_5259]), ['final']). 6.97/7.25 cnf(c_0_13557, plain, (X2=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))))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8359]), ['final']). 6.97/7.25 cnf(c_0_13558, plain, (X2=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))))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8360]), ['final']). 6.97/7.25 cnf(c_0_13559, 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_5342]), ['final']). 6.97/7.25 cnf(c_0_13560, 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_8361]), ['final']). 6.97/7.25 cnf(c_0_13561, 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_8362]), ['final']). 6.97/7.25 cnf(c_0_13562, plain, (X1=hAPP(X2,esk552_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_7895]), ['final']). 6.97/7.25 cnf(c_0_13563, plain, (X1=hAPP(X2,esk417_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_7899]), ['final']). 6.97/7.25 cnf(c_0_13564, 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_8363]), ['final']). 6.97/7.25 cnf(c_0_13565, plain, (hBOOL(hAPP(X1,esk516_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)))), inference(split_conjunct,[status(thm)],[c_0_6993]), ['final']). 6.97/7.25 cnf(c_0_13566, plain, (c_List_Oremdups(X1,X3)=c_List_Oremdups(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_7680]), ['final']). 6.97/7.25 cnf(c_0_13567, 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_8364]), ['final']). 6.97/7.25 cnf(c_0_13568, 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_7884]), ['final']). 6.97/7.25 cnf(c_0_13569, 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_7885]), ['final']). 6.97/7.25 cnf(c_0_13570, 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_8365, c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_13571, 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_8366, c_0_7533]), c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_13572, 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_8367]), ['final']). 6.97/7.25 cnf(c_0_13573, 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_8368]), ['final']). 6.97/7.25 cnf(c_0_13574, 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_8369]), ['final']). 6.97/7.25 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_7886]), ['final']). 6.97/7.25 cnf(c_0_13576, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X3,X2),X4),X5)))|~hBOOL(hAPP(X1,esk583_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_8370]), ['final']). 6.97/7.25 cnf(c_0_13577, 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_7889]), ['final']). 6.97/7.25 cnf(c_0_13578, 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_7896]), ['final']). 6.97/7.25 cnf(c_0_13579, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk144_4(X2,X3,X4,X1)),X2))|c_Fun_Oinj__on(X1,X4,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_8312]), ['final']). 6.97/7.25 cnf(c_0_13580, 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_8371]), ['final']). 6.97/7.25 cnf(c_0_13581, 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_5452]), ['final']). 6.97/7.25 cnf(c_0_13582, 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_8372, c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_13583, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk143_4(X2,X3,X4,X1)),X2))|c_Fun_Oinj__on(X1,X4,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_8312]), ['final']). 6.97/7.25 cnf(c_0_13584, plain, (esk528_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_7252]), ['final']). 6.97/7.25 cnf(c_0_13585, plain, (esk241_3(X4,X1,X3)=X2|~hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X4)))|~c_List_Olist__ex1(X3,X1,X4)), inference(split_conjunct,[status(thm)],[c_0_7253]), ['final']). 6.97/7.25 cnf(c_0_13586, plain, (hBOOL(hAPP(hAPP(X2,X3),X5))|~c_Equiv__Relations_Opart__equivp(X1,X2)|~hBOOL(hAPP(hAPP(X2,X3),X4))|~hBOOL(hAPP(hAPP(X2,X4),X5))), inference(split_conjunct,[status(thm)],[c_0_8373]), ['final']). 6.97/7.25 cnf(c_0_13587, plain, (hBOOL(hAPP(hAPP(X2,X3),X5))|~c_Predicate_Otransp(X1,X2)|~hBOOL(hAPP(hAPP(X2,X3),X4))|~hBOOL(hAPP(hAPP(X2,X4),X5))), inference(split_conjunct,[status(thm)],[c_0_8374]), ['final']). 6.97/7.25 cnf(c_0_13588, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|hAPP(c_Finite__Set_Ocard(tc_sum(X1,X3)),c_Sum__Type_OPlus(X1,X3,X2,X4))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_7409]), ['final']). 6.97/7.25 cnf(c_0_13589, plain, (X3=X2|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),X3))), inference(split_conjunct,[status(thm)],[c_0_4570]), ['final']). 6.97/7.25 cnf(c_0_13590, 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_8375, c_0_4467]), ['final']). 6.97/7.25 cnf(c_0_13591, plain, (c_Relation_Otrans(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))|~c_Predicate_Otransp(X1,X2)), inference(rw,[status(thm)],[c_0_8376, c_0_4467]), ['final']). 6.97/7.25 cnf(c_0_13592, plain, (c_Relation_Osym(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))|~c_Predicate_Osymp(X1,X2)), inference(rw,[status(thm)],[c_0_8377, c_0_4467]), ['final']). 6.97/7.25 cnf(c_0_13593, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|hAPP(c_Finite__Set_Ocard(tc_sum(X3,X1)),c_Sum__Type_OPlus(X3,X1,X4,X2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_7409]), ['final']). 6.97/7.25 cnf(c_0_13594, 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_8378]), ['final']). 6.97/7.25 cnf(c_0_13595, 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_8379]), ['final']). 6.97/7.25 cnf(c_0_13596, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk425_1(X1)),hAPP(c_List_Oset(tc_Nat_Onat),X1)))|hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_8380]), ['final']). 6.97/7.25 cnf(c_0_13597, 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_8381, c_0_4467]), ['final']). 6.97/7.25 cnf(c_0_13598, 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_8382, c_0_4415]), ['final']). 6.97/7.25 cnf(c_0_13599, plain, (X4=hAPP(X3,hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~c_Finite__Set_Ofolding__one(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8383]), ['final']). 6.97/7.25 cnf(c_0_13600, 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),esk460_2(X2,X1))),hAPP(hAPP(c_List_Onth(X1),X2),esk459_2(X2,X1))))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6854]), ['final']). 6.97/7.25 cnf(c_0_13601, 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),esk4_2(X2,X1))),hAPP(hAPP(c_List_Onth(X1),X2),esk5_2(X2,X1))))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8185]), ['final']). 6.97/7.25 cnf(c_0_13602, plain, (hBOOL(hAPP(X2,X3))|~hBOOL(hAPP(hAPP(c_member(X1),esk333_3(X2,X3,X1)),esk334_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_8174]), ['final']). 6.97/7.25 cnf(c_0_13603, plain, (hAPP(c_Hilbert__Choice_Oinv__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_8384]), ['final']). 6.97/7.25 cnf(c_0_13604, 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_8385])]), ['final']). 6.97/7.25 cnf(c_0_13605, 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)), inference(split_conjunct,[status(thm)],[c_0_8386]), ['final']). 6.97/7.25 cnf(c_0_13606, plain, (c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X2)=hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8387]), ['final']). 6.97/7.25 cnf(c_0_13607, 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_8388]), ['final']). 6.97/7.25 cnf(c_0_13608, plain, (X5=hAPP(c_Fun_Othe__inv__into(X1,X2,X4,X3),hAPP(X3,X5))|~c_Fun_Oinj__on(X1,X2,X3,X4)|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4))), inference(split_conjunct,[status(thm)],[c_0_8389]), ['final']). 6.97/7.25 cnf(c_0_13609, plain, (X1=X3|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__eq(tc_Nat_Onat),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8390]), ['final']). 6.97/7.25 cnf(c_0_13610, 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_8391]), ['final']). 6.97/7.25 cnf(c_0_13611, 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_8392]), ['final']). 6.97/7.25 cnf(c_0_13612, 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_8392]), ['final']). 6.97/7.25 cnf(c_0_13613, 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_8393]), ['final']). 6.97/7.25 cnf(c_0_13614, plain, (c_Fun_Obij__betw(X3,X2,X4,X8,X7)|~c_Fun_Obij__betw(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5),X6,X7)|~c_Fun_Obij__betw(X1,X3,X5,X6,X8)), inference(split_conjunct,[status(thm)],[c_0_8008]), ['final']). 6.97/7.25 cnf(c_0_13615, plain, (hBOOL(hAPP(X1,esk560_4(X1,X2,X3,X4)))|~hBOOL(hAPP(hAPP(c_member(X4),X5),X2))|~hBOOL(hAPP(X1,X5))), inference(split_conjunct,[status(thm)],[c_0_6508]), ['final']). 6.97/7.25 cnf(c_0_13616, plain, (hBOOL(hAPP(X1,esk560_4(X1,X2,X3,X4)))|~hBOOL(hAPP(hAPP(c_member(X4),X5),X3))|~hBOOL(hAPP(X1,X5))), inference(split_conjunct,[status(thm)],[c_0_6508]), ['final']). 6.97/7.25 cnf(c_0_13617, 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_8394]), ['final']). 6.97/7.25 cnf(c_0_13618, 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)|esk590_2(X1,X2)!=c_List_Olist_ONil(X2)), inference(rw,[status(thm)],[c_0_8395, c_0_4645]), ['final']). 6.97/7.25 cnf(c_0_13619, 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_7914]), ['final']). 6.97/7.25 cnf(c_0_13620, plain, (hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(X1,esk373_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_7335]), ['final']). 6.97/7.25 cnf(c_0_13621, plain, (hAPP(X1,esk144_4(X2,X1,X3,X4))=hAPP(X1,esk143_4(X2,X1,X3,X4))|c_Fun_Oinj__on(X4,X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8312]), ['final']). 6.97/7.25 cnf(c_0_13622, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X3)=X2|c_Groups_Ozero__class_Ozero(X1)=X3|~class_Rings_Odivision__ring(X1)), inference(er,[status(thm)],[c_0_8396]), ['final']). 6.97/7.25 cnf(c_0_13623, 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)|c_List_Olist_ONil(X1)!=esk462_2(X2,X1)), inference(rw,[status(thm)],[c_0_8397, c_0_4645]), ['final']). 6.97/7.25 cnf(c_0_13624, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(c_COMBK(X1,X2),c_Groups_Oone__class_Oone(X1))),X3)|~class_Groups_Ocomm__monoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_8398]), ['final']). 6.97/7.25 cnf(c_0_13625, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(c_COMBK(X1,X2),c_Groups_Ozero__class_Ozero(X1))),X3)|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8399]), ['final']). 6.97/7.25 cnf(c_0_13626, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk238_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_5312]), ['final']). 6.97/7.25 cnf(c_0_13627, 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_7817]), ['final']). 6.97/7.25 cnf(c_0_13628, 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_7850]), ['final']). 6.97/7.25 cnf(c_0_13629, plain, (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),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_8400]), ['final']). 6.97/7.25 cnf(c_0_13630, 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,esk435_1(X1))))=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_8401]), ['final']). 6.97/7.25 cnf(c_0_13631, 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_8402]), ['final']). 6.97/7.25 cnf(c_0_13632, 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)), inference(split_conjunct,[status(thm)],[c_0_8403]), ['final']). 6.97/7.25 cnf(c_0_13633, 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_8404]), ['final']). 6.97/7.25 cnf(c_0_13634, 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_8405]), ['final']). 6.97/7.25 cnf(c_0_13635, 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),esk416_3(X2,X3,X1)),X3)),X2))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_8055]), ['final']). 6.97/7.25 cnf(c_0_13636, plain, (hBOOL(hAPP(X1,esk99_4(X1,X2,X3,X4)))|~hBOOL(hAPP(X2,X5))|~hBOOL(hAPP(X1,esk98_4(X1,X2,X3,X4)))|~c_Equiv__Relations_Oequivp(X4,X3)), inference(split_conjunct,[status(thm)],[c_0_7068]), ['final']). 6.97/7.25 cnf(c_0_13637, 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_5111]), ['final']). 6.97/7.25 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_8406]), ['final']). 6.97/7.25 cnf(c_0_13639, 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_8407, c_0_5202]), c_0_5202]), ['final']). 6.97/7.25 cnf(c_0_13640, 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_8408]), ['final']). 6.97/7.25 cnf(c_0_13641, 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_8409]), ['final']). 6.97/7.25 cnf(c_0_13642, 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),esk505_3(X3,X2,X1))))|~class_Fields_Olinordered__field(X1)), inference(split_conjunct,[status(thm)],[c_0_8056]), ['final']). 6.97/7.25 cnf(c_0_13643, plain, (hBOOL(hAPP(hAPP(X3,hAPP(X4,X5)),hAPP(X4,X6)))|~c_Predicate_Oinv__imagep(X1,X2,X3,X4,X5,X6)), inference(split_conjunct,[status(thm)],[c_0_8410]), ['final']). 6.97/7.25 cnf(c_0_13644, 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_8411]), ['final']). 6.97/7.25 cnf(c_0_13645, 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_8412, c_0_5202]), c_0_5202]), ['final']). 6.97/7.25 cnf(c_0_13646, 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_8413]), ['final']). 6.97/7.25 cnf(c_0_13647, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,esk257_3(X2,X3,X1)))|~hBOOL(hAPP(X1,esk255_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.25 cnf(c_0_13648, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk177_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_8204]), ['final']). 6.97/7.25 cnf(c_0_13649, 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_8414]), ['final']). 6.97/7.25 cnf(c_0_13650, plain, (hAPP(hAPP(c_List_Onth(X1),X2),esk544_3(X2,X3,X1))=X3|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_7829]), ['final']). 6.97/7.25 cnf(c_0_13651, 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_8415]), ['final']). 6.97/7.25 cnf(c_0_13652, 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_8416]), ['final']). 6.97/7.25 cnf(c_0_13653, plain, (X3=X4|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_8417]), ['final']). 6.97/7.25 cnf(c_0_13654, 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_8418, c_0_5174]), ['final']). 6.97/7.25 cnf(c_0_13655, plain, (c_Fun_Oinj__on(X2,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))|hAPP(c_Fun_Ocomp(X1,X2,X2,c_Hilbert__Choice_Oinv__into(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X3)),X3)!=c_Fun_Oid(X2)), inference(split_conjunct,[status(thm)],[c_0_8419]), ['final']). 6.97/7.25 cnf(c_0_13656, 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_8184]), ['final']). 6.97/7.25 cnf(c_0_13657, 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_8420]), ['final']). 6.97/7.25 cnf(c_0_13658, 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_8421]), ['final']). 6.97/7.25 cnf(c_0_13659, 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_8422]), ['final']). 6.97/7.25 cnf(c_0_13660, 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_8423]), ['final']). 6.97/7.25 cnf(c_0_13661, 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_8424]), ['final']). 6.97/7.25 cnf(c_0_13662, plain, (c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),X1),X2,X3)|c_List_Olist__ex(tc_Int_Oint,X1,c_List_Oupto(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_8425]), ['final']). 6.97/7.25 cnf(c_0_13663, 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),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))!=hAPP(c_Finite__Set_Ocard(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_8426]), ['final']). 6.97/7.25 cnf(c_0_13664, 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_8427, c_0_5560]), ['final']). 6.97/7.25 cnf(c_0_13665, 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_7181]), ['final']). 6.97/7.25 cnf(c_0_13666, 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_8428]), ['final']). 6.97/7.25 cnf(c_0_13667, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk134_3(X2,X3,X1)),X2))|hBOOL(hAPP(c_Predicate_OPowp(X1,X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8429]), ['final']). 6.97/7.25 cnf(c_0_13668, 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_7564]), ['final']). 6.97/7.25 cnf(c_0_13669, 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_7564]), ['final']). 6.97/7.25 cnf(c_0_13670, 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),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_8430]), ['final']). 6.97/7.25 cnf(c_0_13671, 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_8431, c_0_5746]), ['final']). 6.97/7.25 cnf(c_0_13672, 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),esk92_3(X2,X3,X1)),esk91_3(X2,X3,X1))),X2))), inference(split_conjunct,[status(thm)],[c_0_6223]), ['final']). 6.97/7.25 cnf(c_0_13673, 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),esk91_3(X2,X3,X1)),esk92_3(X2,X3,X1))),X2))), inference(split_conjunct,[status(thm)],[c_0_6223]), ['final']). 6.97/7.25 cnf(c_0_13674, 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_8432, c_0_5560]), ['final']). 6.97/7.25 cnf(c_0_13675, 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_8433]), ['final']). 6.97/7.25 cnf(c_0_13676, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(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),X2))|~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_8033]), ['final']). 6.97/7.25 cnf(c_0_13677, plain, (X5=hAPP(c_Set_Oimage(X1,X2,X3),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_8434]), ['final']). 6.97/7.25 cnf(c_0_13678, 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_8435, c_0_5174]), ['final']). 6.97/7.25 cnf(c_0_13679, plain, (c_Fun_Oinj__on(X1,X3,c_Hilbert__Choice_Oinv__into(X3,X1,X5,X4),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)))), inference(split_conjunct,[status(thm)],[c_0_8436]), ['final']). 6.97/7.25 cnf(c_0_13680, 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_8437]), ['final']). 6.97/7.25 cnf(c_0_13681, 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_8438]), ['final']). 6.97/7.25 cnf(c_0_13682, 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_8439]), ['final']). 6.97/7.25 cnf(c_0_13683, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(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_8440, c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_13684, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(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_8441, c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_13685, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~class_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(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_8442, c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_13686, 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_8443]), ['final']). 6.97/7.25 cnf(c_0_13687, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk460_2(X1,X2)),esk459_2(X1,X2)))|c_List_Olinorder__class_Osorted(X2,X1)|~class_Orderings_Olinorder(X2)), inference(split_conjunct,[status(thm)],[c_0_6854]), ['final']). 6.97/7.25 cnf(c_0_13688, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk4_2(X1,X2)),esk5_2(X1,X2)))|c_List_Olinorder__class_Osorted(X2,X1)|~class_Orderings_Olinorder(X2)), inference(split_conjunct,[status(thm)],[c_0_8185]), ['final']). 6.97/7.25 cnf(c_0_13689, 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_8444]), ['final']). 6.97/7.25 cnf(c_0_13690, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~class_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(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_8445, c_0_4413]), ['final']). 6.97/7.25 cnf(c_0_13691, plain, (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)|~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_8446]), ['final']). 6.97/7.25 cnf(c_0_13692, 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_Oorder(X2)|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_4999]), ['final']). 6.97/7.25 cnf(c_0_13693, 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),esk380_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_7751]), ['final']). 6.97/7.25 cnf(c_0_13694, plain, (c_Divides_OnegDivAlg(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)),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_7211]), ['final']). 6.97/7.25 cnf(c_0_13695, plain, (hAPP(c_Finite__Set_Ocard(X1),X4)=hAPP(c_Finite__Set_Ocard(X2),hAPP(c_Set_Oimage(X1,X2,X3),X4))|~c_Fun_Oinj__on(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8447]), ['final']). 6.97/7.25 cnf(c_0_13696, plain, (hBOOL(hAPP(X1,esk73_3(X2,X1,X3)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X4)))|~class_Rings_Osemiring__0(X3)|~class_Rings_Odvd(X3)), inference(split_conjunct,[status(thm)],[c_0_7174]), ['final']). 6.97/7.25 cnf(c_0_13697, 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_8448]), ['final']). 6.97/7.25 cnf(c_0_13698, plain, (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))=c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(X2,X1),X3)|~class_Lazy__Sequence_Osmall__lazy(X1)|~class_Lazy__Sequence_Osmall__lazy(X2)), inference(split_conjunct,[status(thm)],[c_0_8449]), ['final']). 6.97/7.25 cnf(c_0_13699, 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_8450]), ['final']). 6.97/7.25 cnf(c_0_13700, plain, (c_Complete__Lattice_OSup__class_OSup(X1,hAPP(c_List_Oset(X1),X2))=hAPP(c_List_Ofoldl(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8451]), ['final']). 6.97/7.25 cnf(c_0_13701, plain, (c_Complete__Lattice_OInf__class_OInf(X1,hAPP(c_List_Oset(X1),X2))=hAPP(c_List_Ofoldl(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Otop__class_Otop(X1)),X2)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8452]), ['final']). 6.97/7.25 cnf(c_0_13702, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk84_3(X3,X1,X2))))|~c_List_Olist__ex(X2,X1,X3)), inference(split_conjunct,[status(thm)],[c_0_8206]), ['final']). 6.97/7.25 cnf(c_0_13703, 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_8453]), ['final']). 6.97/7.25 cnf(c_0_13704, plain, (X2=X3|~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),X2)!=hAPP(c_List_Oset(X1),X3)), inference(split_conjunct,[status(thm)],[c_0_8454]), ['final']). 6.97/7.25 cnf(c_0_13705, plain, (hBOOL(hAPP(X1,esk365_4(X2,X3,X1,X4)))|c_HOL_OThe(X3,X1)=c_FunDef_OTHE__default(X3,X2,X1)|~hBOOL(hAPP(X1,X4))), inference(split_conjunct,[status(thm)],[c_0_8455]), ['final']). 6.97/7.25 cnf(c_0_13706, plain, (X1=c_List_Olist_ONil(X2)|hBOOL(hAPP(hAPP(c_member(X2),c_List_Olast(X2,X1)),hAPP(c_List_Oset(X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_8456]), ['final']). 6.97/7.25 cnf(c_0_13707, 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_8457, c_0_4471]), ['final']). 6.97/7.25 cnf(c_0_13708, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk301_2(X2,X1)))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5806]), ['final']). 6.97/7.25 cnf(c_0_13709, 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_8458, c_0_5002]), c_0_5002]), c_0_5002]), ['final']). 6.97/7.25 cnf(c_0_13710, 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_8459]), ['final']). 6.97/7.25 cnf(c_0_13711, 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_8460]), ['final']). 6.97/7.25 cnf(c_0_13712, 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_8460]), ['final']). 6.97/7.25 cnf(c_0_13713, plain, (c_Wellfounded_Owf(tc_prod(X3,X1),c_Recdef_Osame__fst(X3,X1,X4,X2))|~c_Wellfounded_Owf(X1,hAPP(X2,esk101_4(X3,X2,X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_8015]), ['final']). 6.97/7.25 cnf(c_0_13714, plain, (c_Big__Operators_Olinorder__class_OMax(X1,X3)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk162_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_7771]), ['final']). 6.97/7.25 cnf(c_0_13715, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk201_1(X1)))|~hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))), inference(split_conjunct,[status(thm)],[c_0_8129]), ['final']). 6.97/7.25 cnf(c_0_13716, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8461]), ['final']). 6.97/7.25 cnf(c_0_13717, 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_8462]), ['final']). 6.97/7.25 cnf(c_0_13718, 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_7244]), ['final']). 6.97/7.25 cnf(c_0_13719, 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,esk145_4(X1,X2,X3,X4))!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_7826]), ['final']). 6.97/7.25 cnf(c_0_13720, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))=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))!=hAPP(X2,esk406_4(X2,X3,X1,X4))), inference(split_conjunct,[status(thm)],[c_0_7832]), ['final']). 6.97/7.25 cnf(c_0_13721, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))=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))!=hAPP(X2,esk41_4(X2,X3,X4,X1))), inference(split_conjunct,[status(thm)],[c_0_7825]), ['final']). 6.97/7.25 cnf(c_0_13722, plain, (c_List_Olist_ONil(X1)=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(X1)),X2)))), inference(split_conjunct,[status(thm)],[c_0_8463]), ['final']). 6.97/7.25 cnf(c_0_13723, 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_8464]), ['final']). 6.97/7.25 cnf(c_0_13724, 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_8465]), ['final']). 6.97/7.25 cnf(c_0_13725, 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_8466]), ['final']). 6.97/7.25 cnf(c_0_13726, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X1,tc_HOL_Obool)),X3),X2)|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=hAPP(X2,esk184_4(X2,X3,X1,X4))), inference(split_conjunct,[status(thm)],[c_0_7840]), ['final']). 6.97/7.25 cnf(c_0_13727, 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_7477]), ['final']). 6.97/7.25 cnf(c_0_13728, 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_7401]), ['final']). 6.97/7.25 cnf(c_0_13729, 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_7939]), ['final']). 6.97/7.25 cnf(c_0_13730, 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_8467]), ['final']). 6.97/7.25 cnf(c_0_13731, 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_8468]), ['final']). 6.97/7.25 cnf(c_0_13732, 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_8469]), ['final']). 6.97/7.25 cnf(c_0_13733, 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_7940]), ['final']). 6.97/7.25 cnf(c_0_13734, plain, (X2=c_Big__Operators_Olinorder__class_OMin(X1,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk359_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_7777]), ['final']). 6.97/7.25 cnf(c_0_13735, 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_7942]), ['final']). 6.97/7.25 cnf(c_0_13736, 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_8470]), ['final']). 6.97/7.25 cnf(c_0_13737, 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_8471]), ['final']). 6.97/7.25 cnf(c_0_13738, 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_8472]), ['final']). 6.97/7.25 cnf(c_0_13739, 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_8473, c_0_5002]), ['final']). 6.97/7.25 cnf(c_0_13740, 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_4577]), ['final']). 6.97/7.25 cnf(c_0_13741, 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_8474, c_0_5002]), ['final']). 6.97/7.25 cnf(c_0_13742, 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_7948]), ['final']). 6.97/7.25 cnf(c_0_13743, 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_8475]), ['final']). 6.97/7.25 cnf(c_0_13744, 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)), inference(split_conjunct,[status(thm)],[c_0_8476]), ['final']). 6.97/7.25 cnf(c_0_13745, 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)), inference(split_conjunct,[status(thm)],[c_0_8477]), ['final']). 6.97/7.25 cnf(c_0_13746, 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,esk116_2(X1,X2)))), inference(rw,[status(thm)],[c_0_8478, c_0_5002]), ['final']). 6.97/7.25 cnf(c_0_13747, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),esk3_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_8479]), ['final']). 6.97/7.25 cnf(c_0_13748, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),esk392_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_8480]), ['final']). 6.97/7.25 cnf(c_0_13749, 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_8481]), ['final']). 6.97/7.25 cnf(c_0_13750, 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_8240]), ['final']). 6.97/7.25 cnf(c_0_13751, 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_8241]), ['final']). 6.97/7.25 cnf(c_0_13752, 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_8244]), ['final']). 6.97/7.25 cnf(c_0_13753, 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_8245]), ['final']). 6.97/7.25 cnf(c_0_13754, 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_8482, c_0_5963]), ['final']). 6.97/7.25 cnf(c_0_13755, 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_8483]), ['final']). 6.97/7.25 cnf(c_0_13756, 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_8484]), ['final']). 6.97/7.25 cnf(c_0_13757, 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_8485]), ['final']). 6.97/7.25 cnf(c_0_13758, 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_8486]), ['final']). 6.97/7.25 cnf(c_0_13759, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8487]), ['final']). 6.97/7.25 cnf(c_0_13760, 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_8488]), ['final']). 6.97/7.25 cnf(c_0_13761, plain, (hBOOL(hAPP(X1,esk586_1(X1)))|~hBOOL(hAPP(X1,X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_8489, c_0_8490])]), ['final']). 6.97/7.25 cnf(c_0_13762, 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_8491]), ['final']). 6.97/7.25 cnf(c_0_13763, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk87_5(X3,X4,X5,X6,X1))))|~hBOOL(hAPP(X6,X2))|hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3)!=hAPP(c_List_Ofilter(X1,X6),X5)), inference(split_conjunct,[status(thm)],[c_0_4996]), ['final']). 6.97/7.25 cnf(c_0_13764, 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_8492, c_0_8493]), ['final']). 6.97/7.25 cnf(c_0_13765, 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_8494]), ['final']). 6.97/7.25 cnf(c_0_13766, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8495]), ['final']). 6.97/7.25 cnf(c_0_13767, 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_8496]), ['final']). 6.97/7.25 cnf(c_0_13768, 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_8497]), ['final']). 6.97/7.25 cnf(c_0_13769, 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_8498]), ['final']). 6.97/7.25 cnf(c_0_13770, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk130_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_4995]), ['final']). 6.97/7.25 cnf(c_0_13771, plain, (hBOOL(hAPP(X1,X4))|~hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk499_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_7283]), ['final']). 6.97/7.25 cnf(c_0_13772, 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_8005]), ['final']). 6.97/7.25 cnf(c_0_13773, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_8499]), ['final']). 6.97/7.25 cnf(c_0_13774, 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_8500]), ['final']). 6.97/7.26 cnf(c_0_13775, 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_8501]), ['final']). 6.97/7.26 cnf(c_0_13776, 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_8502]), ['final']). 6.97/7.26 cnf(c_0_13777, 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_8503]), ['final']). 6.97/7.26 cnf(c_0_13778, 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_8504]), ['final']). 6.97/7.26 cnf(c_0_13779, 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_8007]), ['final']). 6.97/7.26 cnf(c_0_13780, 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_8006]), ['final']). 6.97/7.26 cnf(c_0_13781, 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),esk386_2(X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X2))), inference(split_conjunct,[status(thm)],[c_0_7554]), ['final']). 6.97/7.26 cnf(c_0_13782, 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_8505]), ['final']). 6.97/7.26 cnf(c_0_13783, plain, (c_Relation_Osym(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))|~c_Relation_Osym(X1,X2)), inference(rw,[status(thm)],[c_0_8506, c_0_5174]), ['final']). 6.97/7.26 cnf(c_0_13784, plain, (X1=X2|c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3,X1)!=hAPP(c_fequal,X2)), inference(rw,[status(thm)],[c_0_8507, c_0_5539]), ['final']). 6.97/7.26 cnf(c_0_13785, plain, (X1=X2|c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2,X1)!=hAPP(c_fequal,X3)), inference(rw,[status(thm)],[c_0_8508, c_0_5539]), ['final']). 6.97/7.26 cnf(c_0_13786, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|X3=X2|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_8280]), ['final']). 6.97/7.26 cnf(c_0_13787, 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_8509, c_0_5174]), ['final']). 6.97/7.26 cnf(c_0_13788, 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_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin)),X2))), inference(rw,[status(thm)],[c_0_8510, c_0_4741]), ['final']). 6.97/7.26 cnf(c_0_13789, 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_8111]), ['final']). 6.97/7.26 cnf(c_0_13790, plain, (esk469_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_8511]), c_0_8512])]), ['final']). 6.97/7.26 cnf(c_0_13791, plain, (X7=X6|~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_8513]), ['final']). 6.97/7.26 cnf(c_0_13792, 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_8514]), ['final']). 6.97/7.26 cnf(c_0_13793, 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_8116]), ['final']). 6.97/7.26 cnf(c_0_13794, 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_8515]), ['final']). 6.97/7.26 cnf(c_0_13795, 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_8176]), ['final']). 6.97/7.26 cnf(c_0_13796, 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_8177]), ['final']). 6.97/7.26 cnf(c_0_13797, 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_8178]), ['final']). 6.97/7.26 cnf(c_0_13798, 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_8117]), ['final']). 6.97/7.26 cnf(c_0_13799, 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_8122]), ['final']). 6.97/7.26 cnf(c_0_13800, 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_8516, c_0_5038]), ['final']). 6.97/7.26 cnf(c_0_13801, 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_Ominus__class_Ominus(tc_Int_Oint),X2),c_Int_OMin)))), inference(rw,[status(thm)],[c_0_8517, c_0_4741]), ['final']). 6.97/7.26 cnf(c_0_13802, 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_8179]), ['final']). 6.97/7.26 cnf(c_0_13803, 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_7735]), ['final']). 6.97/7.26 cnf(c_0_13804, 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_7735]), ['final']). 6.97/7.26 cnf(c_0_13805, 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_8518]), ['final']). 6.97/7.26 cnf(c_0_13806, 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_8519, c_0_6506]), ['final']). 6.97/7.26 cnf(c_0_13807, 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_8520, c_0_4742]), c_0_5002]), ['final']). 6.97/7.26 cnf(c_0_13808, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|hAPP(c_Nat_OSuc,X2)=X1|~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_8521]), ['final']). 6.97/7.26 cnf(c_0_13809, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X4=c_Divides_Odiv__class_Omod(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_8522]), ['final']). 6.97/7.26 cnf(c_0_13810, plain, (esk137_3(X1,X2,X3)=esk138_3(X1,X2,X3)|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)), inference(split_conjunct,[status(thm)],[c_0_5363]), ['final']). 6.97/7.26 cnf(c_0_13811, 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_5211]), ['final']). 6.97/7.26 cnf(c_0_13812, 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),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_5211]), ['final']). 6.97/7.26 cnf(c_0_13813, 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_7440]), ['final']). 6.97/7.26 cnf(c_0_13814, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X3),X4)!=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_8523, c_0_4471]), ['final']). 6.97/7.26 cnf(c_0_13815, plain, (hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,X1)),X3),X4)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(X3,X4))|~class_Groups_Ouminus(X1)), inference(split_conjunct,[status(thm)],[c_0_8524]), ['final']). 6.97/7.26 cnf(c_0_13816, 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_8525]), ['final']). 6.97/7.26 cnf(c_0_13817, 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_8526]), ['final']). 6.97/7.26 cnf(c_0_13818, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),c_Groups_Ozero__class_Ozero(X1))=hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)|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_8527]), ['final']). 6.97/7.26 cnf(c_0_13819, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_Olinorder__class_Osort__key(X2,X1,X3,X4))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8528]), ['final']). 6.97/7.26 cnf(c_0_13820, 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_8529]), ['final']). 6.97/7.26 cnf(c_0_13821, 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_7540]), ['final']). 6.97/7.26 cnf(c_0_13822, 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_8530]), ['final']). 6.97/7.26 cnf(c_0_13823, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)=X3|~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_8531]), ['final']). 6.97/7.26 cnf(c_0_13824, 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_8206]), ['final']). 6.97/7.26 cnf(c_0_13825, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Onumber__ring(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8532, c_0_4413]), c_0_4456]), ['final']). 6.97/7.26 cnf(c_0_13826, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Onumber__ring(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_8533, c_0_4413]), c_0_7977]), c_0_7978]), ['final']). 6.97/7.26 cnf(c_0_13827, 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_8012]), ['final']). 6.97/7.26 cnf(c_0_13828, plain, (c_Orderings_Oorder__class_Omono(tc_Nat_Onat,X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,esk16_2(X2,X1))),hAPP(X2,hAPP(c_Nat_OSuc,esk16_2(X2,X1)))))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8060]), ['final']). 6.97/7.26 cnf(c_0_13829, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=X1|X2=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=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_8534, c_0_4742]), c_0_4742]), c_0_4742]), ['final']). 6.97/7.26 cnf(c_0_13830, 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_8535]), ['final']). 6.97/7.26 cnf(c_0_13831, 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_8536]), ['final']). 6.97/7.26 cnf(c_0_13832, 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_8537]), ['final']). 6.97/7.26 cnf(c_0_13833, plain, (hBOOL(hAPP(hAPP(c_member(X3),X2),c_Quotient_ORespects(X3,X1)))|~hBOOL(hAPP(hAPP(X1,X2),X2))), inference(split_conjunct,[status(thm)],[c_0_8538]), ['final']). 6.97/7.26 cnf(c_0_13834, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(X1),esk515_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_7137]), ['final']). 6.97/7.26 cnf(c_0_13835, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(X1),esk203_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_7140]), ['final']). 6.97/7.26 cnf(c_0_13836, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(X1),esk43_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_7146]), ['final']). 6.97/7.26 cnf(c_0_13837, plain, (hAPP(X1,esk262_3(X1,X2,X3))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Oone__class_Oone(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_7127]), ['final']). 6.97/7.26 cnf(c_0_13838, plain, (X2=hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))|X2=c_Groups_Oone__class_Oone(X1)|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_5412]), ['final']). 6.97/7.26 cnf(c_0_13839, 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_8539, c_0_5963]), ['final']). 6.97/7.26 cnf(c_0_13840, plain, (hBOOL(hAPP(X1,esk516_3(X2,X3,X1)))|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_6993]), ['final']). 6.97/7.26 cnf(c_0_13841, 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_8077]), ['final']). 6.97/7.26 cnf(c_0_13842, 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_7576]), ['final']). 6.97/7.26 cnf(c_0_13843, 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),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8540]), ['final']). 6.97/7.26 cnf(c_0_13844, 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_8541]), ['final']). 6.97/7.26 cnf(c_0_13845, plain, (~hBOOL(hAPP(hAPP(c_member(X1),esk403_5(X2,X3,X4,X5,X1)),esk404_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_6741]), ['final']). 6.97/7.26 cnf(c_0_13846, 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_8542]), ['final']). 6.97/7.26 cnf(c_0_13847, plain, (~class_Int_Onumber__ring(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_8543, c_0_4740]), ['final']). 6.97/7.26 cnf(c_0_13848, plain, (~hBOOL(hAPP(hAPP(c_member(X1),esk38_5(X2,X3,X4,X5,X1)),esk39_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_7164]), ['final']). 6.97/7.26 cnf(c_0_13849, 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_8544]), ['final']). 6.97/7.26 cnf(c_0_13850, 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_8545]), ['final']). 6.97/7.26 cnf(c_0_13851, 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_8546]), ['final']). 6.97/7.26 cnf(c_0_13852, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X3)|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8547]), ['final']). 6.97/7.26 cnf(c_0_13853, plain, (c_Divides_Odiv__class_Omod(X1,X2,X3)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X3)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_8548]), ['final']). 6.97/7.26 cnf(c_0_13854, 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_8549]), ['final']). 6.97/7.26 cnf(c_0_13855, 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_8550]), ['final']). 6.97/7.26 cnf(c_0_13856, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~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_8551]), ['final']). 6.97/7.26 cnf(c_0_13857, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4))|~class_Rings_Ocomm__semiring__1(X1)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))), inference(split_conjunct,[status(thm)],[c_0_8552]), ['final']). 6.97/7.26 cnf(c_0_13858, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X4))|~class_Rings_Ocomm__semiring__1(X1)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))), inference(split_conjunct,[status(thm)],[c_0_8553]), ['final']). 6.97/7.26 cnf(c_0_13859, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin))|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_8554]), ['final']). 6.97/7.26 cnf(c_0_13860, 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_8555]), ['final']). 6.97/7.26 cnf(c_0_13861, 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_8556]), ['final']). 6.97/7.26 cnf(c_0_13862, 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,esk19_1(X1)))), inference(rw,[status(thm)],[c_0_8557, c_0_5002]), ['final']). 6.97/7.26 cnf(c_0_13863, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk18_1(X1)))|hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5403]), ['final']). 6.97/7.26 cnf(c_0_13864, 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_7688]), ['final']). 6.97/7.26 cnf(c_0_13865, 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_7688]), ['final']). 6.97/7.26 cnf(c_0_13866, 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_8558]), ['final']). 6.97/7.26 cnf(c_0_13867, 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_8559]), ['final']). 6.97/7.26 cnf(c_0_13868, 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_8560]), ['final']). 6.97/7.26 cnf(c_0_13869, plain, (X1=c_List_Olist_ONil(X2)|hAPP(c_List_Ohd(X2),X1)=hAPP(c_List_Ohd(X2),hAPP(hAPP(c_List_Oappend(X2),X1),X3))), inference(split_conjunct,[status(thm)],[c_0_8561]), ['final']). 6.97/7.26 cnf(c_0_13870, 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_8562]), ['final']). 6.97/7.26 cnf(c_0_13871, 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_8562]), ['final']). 6.97/7.26 cnf(c_0_13872, plain, (hBOOL(hAPP(hAPP(X1,esk532_3(X2,X1,X3)),X2))|hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8563]), ['final']). 6.97/7.26 cnf(c_0_13873, 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_8564]), ['final']). 6.97/7.26 cnf(c_0_13874, 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_8565]), ['final']). 6.97/7.26 cnf(c_0_13875, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk116_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_8566, c_0_5002]), ['final']). 6.97/7.26 cnf(c_0_13876, plain, (hBOOL(hAPP(hAPP(X1,esk396_3(X2,X1,X3)),X2))|hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8567]), ['final']). 6.97/7.26 cnf(c_0_13877, 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_8568]), ['final']). 6.97/7.26 cnf(c_0_13878, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(X1),esk306_3(X2,X3,X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_7678]), ['final']). 6.97/7.26 cnf(c_0_13879, 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),esk540_3(X3,X2,X1)))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7490]), ['final']). 6.97/7.26 cnf(c_0_13880, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk474_2(X2,X1)),esk473_2(X2,X1)))|c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7123]), ['final']). 6.97/7.26 cnf(c_0_13881, 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_8569]), ['final']). 6.97/7.26 cnf(c_0_13882, 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),esk340_3(X2,X3,X1)))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7484]), ['final']). 6.97/7.26 cnf(c_0_13883, 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),esk139_3(X3,X2,X1)))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7491]), ['final']). 6.97/7.26 cnf(c_0_13884, 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_8570, c_0_4813]), ['final']). 6.97/7.26 cnf(c_0_13885, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Rings_Odvd(X1)), inference(er,[status(thm)],[c_0_8571]), ['final']). 6.97/7.26 cnf(c_0_13886, plain, (c_Relation_Oantisym(X1,X2)|~c_Relation_Oantisym(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_8572, c_0_5560]), ['final']). 6.97/7.26 cnf(c_0_13887, 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_8573, c_0_5794]), ['final']). 6.97/7.26 cnf(c_0_13888, 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_8574]), ['final']). 6.97/7.26 cnf(c_0_13889, plain, (X3=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~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']). 6.97/7.26 cnf(c_0_13890, 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']). 6.97/7.26 cnf(c_0_13891, 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_8577]), ['final']). 6.97/7.26 cnf(c_0_13892, plain, (~class_Int_Oring__char__0(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(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)), inference(split_conjunct,[status(thm)],[c_0_8578]), ['final']). 6.97/7.26 cnf(c_0_13893, 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)), inference(split_conjunct,[status(thm)],[c_0_8579]), ['final']). 6.97/7.26 cnf(c_0_13894, 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_8580]), ['final']). 6.97/7.26 cnf(c_0_13895, plain, (X2=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)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_8581]), ['final']). 6.97/7.26 cnf(c_0_13896, 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_8582, c_0_5002]), ['final']). 6.97/7.26 cnf(c_0_13897, plain, (c_Groups_Osgn__class_Osgn(X1,X2)=c_Groups_Oone__class_Oone(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_Osgn__if(X1)), inference(split_conjunct,[status(thm)],[c_0_8274]), ['final']). 6.97/7.26 cnf(c_0_13898, 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_8583]), ['final']). 6.97/7.26 cnf(c_0_13899, 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_8584]), ['final']). 6.97/7.26 cnf(c_0_13900, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),c_Groups_Ozero__class_Ozero(X1))!=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber(X1)), inference(er,[status(thm)],[c_0_8585]), ['final']). 6.97/7.26 cnf(c_0_13901, 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_8586]), ['final']). 6.97/7.26 cnf(c_0_13902, 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_8584]), ['final']). 6.97/7.26 cnf(c_0_13903, 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_8587]), ['final']). 6.97/7.26 cnf(c_0_13904, 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_8588]), ['final']). 6.97/7.26 cnf(c_0_13905, 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_8589]), ['final']). 6.97/7.26 cnf(c_0_13906, 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_8590]), ['final']). 6.97/7.26 cnf(c_0_13907, 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_8591]), ['final']). 6.97/7.26 cnf(c_0_13908, plain, (hBOOL(hAPP(X1,X4))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk584_3(X3,X2,X1)),esk585_3(X3,X2,X1))))), inference(split_conjunct,[status(thm)],[c_0_8370]), ['final']). 6.97/7.26 cnf(c_0_13909, 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_7486]), ['final']). 6.97/7.26 cnf(c_0_13910, 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_8592]), ['final']). 6.97/7.26 cnf(c_0_13911, 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_8593]), ['final']). 6.97/7.26 cnf(c_0_13912, 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)],[c_0_8594, c_0_4413]), c_0_4413]), ['final']). 6.97/7.26 cnf(c_0_13913, 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)],[c_0_8595, c_0_4410]), ['final']). 6.97/7.26 cnf(c_0_13914, 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_8596]), ['final']). 6.97/7.26 cnf(c_0_13915, 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_8597]), ['final']). 6.97/7.26 cnf(c_0_13916, 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)],[c_0_8598, c_0_4410]), ['final']). 6.97/7.26 cnf(c_0_13917, 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)],[c_0_8599, c_0_4413]), c_0_4413]), ['final']). 6.97/7.26 cnf(c_0_13918, 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)],[c_0_8600, c_0_4415]), c_0_4415]), ['final']). 6.97/7.26 cnf(c_0_13919, 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_8601, c_0_4565]), ['final']). 6.97/7.26 cnf(c_0_13920, 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),esk443_3(X2,X3,X1)),X2))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8018]), ['final']). 6.97/7.26 cnf(c_0_13921, 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),esk182_3(X2,X3,X1)),X2))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7999]), ['final']). 6.97/7.26 cnf(c_0_13922, plain, (hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,esk257_3(X2,X3,X1)))|~hBOOL(hAPP(X1,esk255_3(X2,X3,X1)))|~hBOOL(hAPP(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_4980]), ['final']). 6.97/7.26 cnf(c_0_13923, 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_8602]), ['final']). 6.97/7.26 cnf(c_0_13924, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(X1,esk269_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5135]), ['final']). 6.97/7.26 cnf(c_0_13925, 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)],[c_0_8603, c_0_4410]), ['final']). 6.97/7.26 cnf(c_0_13926, 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)],[c_0_8604, c_0_4410]), ['final']). 6.97/7.26 cnf(c_0_13927, 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)],[c_0_8605, c_0_4413]), c_0_4413]), ['final']). 6.97/7.26 cnf(c_0_13928, 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),esk72_3(X3,X2,X1)))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8000]), ['final']). 6.97/7.26 cnf(c_0_13929, 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),esk42_3(X2,X3,X1)))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8022]), ['final']). 6.97/7.26 cnf(c_0_13930, 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_8311]), ['final']). 6.97/7.26 cnf(c_0_13931, 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_8313]), ['final']). 6.97/7.26 cnf(c_0_13932, 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_8606]), ['final']). 6.97/7.26 cnf(c_0_13933, 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)],[c_0_8607, c_0_4413]), c_0_4413]), ['final']). 6.97/7.26 cnf(c_0_13934, 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_8608, c_0_5002]), c_0_5002]), ['final']). 6.97/7.26 cnf(c_0_13935, 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_8609, c_0_5002]), ['final']). 6.97/7.26 cnf(c_0_13936, 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_8357]), ['final']). 6.97/7.26 cnf(c_0_13937, plain, (hBOOL(hAPP(X1,X4))|~c_List_Oall__interval__nat(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_8068]), ['final']). 6.97/7.26 cnf(c_0_13938, 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_8314]), ['final']). 6.97/7.26 cnf(c_0_13939, 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_8315]), ['final']). 6.97/7.26 cnf(c_0_13940, plain, (hBOOL(hAPP(X1,esk350_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))|~hBOOL(hAPP(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_7408]), ['final']). 6.97/7.26 cnf(c_0_13941, 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_8610]), ['final']). 6.97/7.26 cnf(c_0_13942, plain, (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)|~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_8611]), ['final']). 6.97/7.26 cnf(c_0_13943, plain, (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),X2),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_8611]), ['final']). 6.97/7.26 cnf(c_0_13944, plain, (c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X1|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_8612, c_0_5202]), c_0_7359]), ['final']). 6.97/7.26 cnf(c_0_13945, plain, (hBOOL(hAPP(X1,esk243_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))|~hBOOL(hAPP(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_7525]), ['final']). 6.97/7.26 cnf(c_0_13946, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)=hAPP(c_Groups_Oabs__class_Oabs(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_8505]), ['final']). 6.97/7.26 cnf(c_0_13947, 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_8613]), ['final']). 6.97/7.26 cnf(c_0_13948, 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_8614]), ['final']). 6.97/7.26 cnf(c_0_13949, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk92_3(X2,X3,X1)),X3))|c_Relation_Ototal__on(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_6223]), ['final']). 6.97/7.26 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_Osemilattice__sup(X1)), inference(split_conjunct,[status(thm)],[c_0_8615]), ['final']). 6.97/7.26 cnf(c_0_13951, 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_8616]), ['final']). 6.97/7.26 cnf(c_0_13952, 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_8617]), ['final']). 6.97/7.26 cnf(c_0_13953, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk91_3(X2,X3,X1)),X3))|c_Relation_Ototal__on(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_6223]), ['final']). 6.97/7.26 cnf(c_0_13954, 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_7524]), ['final']). 6.97/7.26 cnf(c_0_13955, 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),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_8618]), ['final']). 6.97/7.26 cnf(c_0_13956, 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_8618]), ['final']). 6.97/7.26 cnf(c_0_13957, plain, (hAPP(X3,X4)=hAPP(c_Finite__Set_Ofold1(X1,X2),X4)|~c_Finite__Set_Ofolding__one(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_8619]), ['final']). 6.97/7.26 cnf(c_0_13958, 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_8620]), ['final']). 6.97/7.26 cnf(c_0_13959, 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_8621]), ['final']). 6.97/7.26 cnf(c_0_13960, 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_8622]), ['final']). 6.97/7.26 cnf(c_0_13961, 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_8623]), ['final']). 6.97/7.26 cnf(c_0_13962, plain, (X3=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(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_8624]), ['final']). 6.97/7.26 cnf(c_0_13963, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk549_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_8625]), ['final']). 6.97/7.26 cnf(c_0_13964, plain, (hBOOL(hAPP(X1,X2))|c_List_OtakeWhile(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))=c_List_Olist_ONil(X3)), inference(split_conjunct,[status(thm)],[c_0_8142]), ['final']). 6.97/7.26 cnf(c_0_13965, plain, (hAPP(X3,X4)=hAPP(c_Finite__Set_Ofold1(X1,X2),X4)|~c_Big__Operators_Osemilattice__big(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_8626]), ['final']). 6.97/7.26 cnf(c_0_13966, 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_8627, c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_13967, 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_8628, c_0_4471]), ['final']). 6.97/7.26 cnf(c_0_13968, 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_8629]), ['final']). 6.97/7.26 cnf(c_0_13969, 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_8630]), ['final']). 6.97/7.26 cnf(c_0_13970, 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_7728]), ['final']). 6.97/7.26 cnf(c_0_13971, 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_7728]), ['final']). 6.97/7.26 cnf(c_0_13972, 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_7729]), ['final']). 6.97/7.26 cnf(c_0_13973, 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_8631]), ['final']). 6.97/7.26 cnf(c_0_13974, 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_8632]), ['final']). 6.97/7.26 cnf(c_0_13975, 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_8633]), ['final']). 6.97/7.26 cnf(c_0_13976, 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_8634]), ['final']). 6.97/7.26 cnf(c_0_13977, 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_7729]), ['final']). 6.97/7.26 cnf(c_0_13978, 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_8635]), ['final']). 6.97/7.26 cnf(c_0_13979, 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_8636, c_0_4413]), ['final']). 6.97/7.26 cnf(c_0_13980, 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_8637]), ['final']). 6.97/7.26 cnf(c_0_13981, 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)), inference(split_conjunct,[status(thm)],[c_0_8638]), ['final']). 6.97/7.26 cnf(c_0_13982, 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_8639]), ['final']). 6.97/7.26 cnf(c_0_13983, plain, (X2=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))))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8640]), ['final']). 6.97/7.26 cnf(c_0_13984, 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_8641]), ['final']). 6.97/7.26 cnf(c_0_13985, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(X1,esk269_3(X2,X3,X1)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_5135]), ['final']). 6.97/7.26 cnf(c_0_13986, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,X2))|~class_Power_Opower(X1)|~class_Rings_Osemiring__0(X1)), inference(split_conjunct,[status(thm)],[c_0_8642]), ['final']). 6.97/7.26 cnf(c_0_13987, 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)), inference(split_conjunct,[status(thm)],[c_0_8643]), ['final']). 6.97/7.26 cnf(c_0_13988, 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_8644]), ['final']). 6.97/7.26 cnf(c_0_13989, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)=hAPP(c_Finite__Set_Ocard(X1),hAPP(c_List_Oset(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8645]), ['final']). 6.97/7.26 cnf(c_0_13990, 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_8646]), ['final']). 6.97/7.26 cnf(c_0_13991, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(X1,esk545_3(X2,X3,X1)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_7599]), ['final']). 6.97/7.26 cnf(c_0_13992, 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,esk397_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_7604]), ['final']). 6.97/7.26 cnf(c_0_13993, 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_7730]), ['final']). 6.97/7.26 cnf(c_0_13994, 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_7730]), ['final']). 6.97/7.26 cnf(c_0_13995, 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)), inference(split_conjunct,[status(thm)],[c_0_8647]), ['final']). 6.97/7.26 cnf(c_0_13996, 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_8648]), ['final']). 6.97/7.26 cnf(c_0_13997, plain, (hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8649]), ['final']). 6.97/7.26 cnf(c_0_13998, 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_7734]), ['final']). 6.97/7.26 cnf(c_0_13999, 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_7734]), ['final']). 6.97/7.26 cnf(c_0_14000, 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_8650]), ['final']). 6.97/7.26 cnf(c_0_14001, 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_8651]), ['final']). 6.97/7.26 cnf(c_0_14002, plain, (c_List_Olist__ex1(X4,X3,X2)|X1!=esk527_4(X2,X3,X4,X1)|~hBOOL(hAPP(hAPP(c_member(X4),X1),hAPP(c_List_Oset(X4),X2)))|~hBOOL(hAPP(X3,X1))), inference(split_conjunct,[status(thm)],[c_0_7252]), ['final']). 6.97/7.26 cnf(c_0_14003, plain, (c_List_Olist__ex1(X4,X3,X2)|X1!=esk242_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_7253]), ['final']). 6.97/7.26 cnf(c_0_14004, plain, (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))!=hAPP(c_List_Orev(X1),X3)), inference(split_conjunct,[status(thm)],[c_0_5790]), ['final']). 6.97/7.26 cnf(c_0_14005, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk391_2(X1,X2)),X1))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))), inference(split_conjunct,[status(thm)],[c_0_8480]), ['final']). 6.97/7.26 cnf(c_0_14006, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk2_2(X1,X2)),X1))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))), inference(split_conjunct,[status(thm)],[c_0_8479]), ['final']). 6.97/7.26 cnf(c_0_14007, 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_8652]), ['final']). 6.97/7.26 cnf(c_0_14008, 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_8653]), ['final']). 6.97/7.26 cnf(c_0_14009, 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_8448]), ['final']). 6.97/7.26 cnf(c_0_14010, 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_8654, c_0_5002]), ['final']). 6.97/7.26 cnf(c_0_14011, 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_8655]), ['final']). 6.97/7.26 cnf(c_0_14012, 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_8656]), ['final']). 6.97/7.26 cnf(c_0_14013, 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_8657]), ['final']). 6.97/7.26 cnf(c_0_14014, 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_8658]), ['final']). 6.97/7.26 cnf(c_0_14015, 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_8659]), ['final']). 6.97/7.26 cnf(c_0_14016, 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_8660]), ['final']). 6.97/7.26 cnf(c_0_14017, plain, (X3=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)|~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_8661]), ['final']). 6.97/7.26 cnf(c_0_14018, plain, (hBOOL(hAPP(X1,esk486_3(X2,X1,X3)))|c_Orderings_Oord__class_OLeast(X3,X1)=X2|~hBOOL(hAPP(X1,X2))|~class_Orderings_Oorder(X3)), inference(split_conjunct,[status(thm)],[c_0_8662]), ['final']). 6.97/7.26 cnf(c_0_14019, 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_8663]), ['final']). 6.97/7.26 cnf(c_0_14020, 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_8664]), ['final']). 6.97/7.26 cnf(c_0_14021, 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))|hAPP(hAPP(c_List_Odrop(X1),X2),X3)!=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_8665]), ['final']). 6.97/7.26 cnf(c_0_14022, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_member(X1),esk24_2(X2,X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_8666]), ['final']). 6.97/7.26 cnf(c_0_14023, 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_8667]), ['final']). 6.97/7.26 cnf(c_0_14024, plain, (hBOOL(hAPP(X2,X4))|c_List_OtakeWhile(X1,X2,X3)!=X3|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_8163]), ['final']). 6.97/7.26 cnf(c_0_14025, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk401_2(X2,X1)),X2))|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_8668]), ['final']). 6.97/7.26 cnf(c_0_14026, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))|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)), inference(rw,[status(thm)],[c_0_8669, c_0_4471]), ['final']). 6.97/7.26 cnf(c_0_14027, plain, (hAPP(hAPP(c_List_Odrop(X1),X3),X2)=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)),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_8670]), ['final']). 6.97/7.26 cnf(c_0_14028, plain, (c_Nitpick_Orefl_H(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk172_2(X2,X1)),esk172_2(X2,X1))),X2))), inference(split_conjunct,[status(thm)],[c_0_8011]), ['final']). 6.97/7.26 cnf(c_0_14029, plain, (c_Relation_Otrans(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk562_2(X2,X1)),esk564_2(X2,X1))),X2))), inference(split_conjunct,[status(thm)],[c_0_7471]), ['final']). 6.97/7.26 cnf(c_0_14030, plain, (c_Relation_Osym(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk313_2(X2,X1)),esk312_2(X2,X1))),X2))), inference(split_conjunct,[status(thm)],[c_0_6959]), ['final']). 6.97/7.26 cnf(c_0_14031, 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_Rings_Ozero__neq__one(X1)|~class_Rings_Ono__zero__divisors(X1)|~class_Rings_Omult__zero(X1)|~class_Power_Opower(X1)), inference(er,[status(thm)],[c_0_8671]), ['final']). 6.97/7.26 cnf(c_0_14032, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))=c_Groups_Oone__class_Oone(X1)|~class_Groups_Ocomm__monoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_8672]), ['final']). 6.97/7.26 cnf(c_0_14033, 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_8673]), ['final']). 6.97/7.26 cnf(c_0_14034, plain, (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)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)))), inference(split_conjunct,[status(thm)],[c_0_8674]), ['final']). 6.97/7.26 cnf(c_0_14035, 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_8361]), ['final']). 6.97/7.26 cnf(c_0_14036, 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_8363]), ['final']). 6.97/7.26 cnf(c_0_14037, plain, (hBOOL(hAPP(X1,esk56_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_8675, c_0_5002]), ['final']). 6.97/7.26 cnf(c_0_14038, 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']). 6.97/7.26 cnf(c_0_14039, 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,esk487_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_7902]), ['final']). 6.97/7.26 cnf(c_0_14040, plain, (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,esk379_3(X1,X2,X3))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7905]), ['final']). 6.97/7.26 cnf(c_0_14041, plain, (hBOOL(hAPP(X4,X2))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(X4,esk533_4(X4,X3,X5,X1)))), inference(split_conjunct,[status(thm)],[c_0_6414]), ['final']). 6.97/7.26 cnf(c_0_14042, plain, (hBOOL(hAPP(X4,X2))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(X4,esk533_4(X4,X5,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_6414]), ['final']). 6.97/7.26 cnf(c_0_14043, 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_8677]), ['final']). 6.97/7.26 cnf(c_0_14044, 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_8678]), ['final']). 6.97/7.26 cnf(c_0_14045, 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_8679]), ['final']). 6.97/7.26 cnf(c_0_14046, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2))|~hBOOL(hAPP(hAPP(c_member(X1),esk356_3(X2,X3,X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_8149]), ['final']). 6.97/7.26 cnf(c_0_14047, 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_8680]), ['final']). 6.97/7.26 cnf(c_0_14048, 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_7679]), ['final']). 6.97/7.26 cnf(c_0_14049, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=X1|c_Int_OMin=X1|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_8681, c_0_4415]), ['final']). 6.97/7.26 cnf(c_0_14050, 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_8682]), ['final']). 6.97/7.26 cnf(c_0_14051, 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_8683, c_0_5963]), ['final']). 6.97/7.26 cnf(c_0_14052, 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_8472]), ['final']). 6.97/7.26 cnf(c_0_14053, plain, (hBOOL(hAPP(hAPP(X3,esk548_2(X4,X3)),X4))|~hBOOL(hAPP(c_Predicate_ORangeP(X1,X2,X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8684]), ['final']). 6.97/7.26 cnf(c_0_14054, plain, (hBOOL(hAPP(hAPP(X3,X4),esk228_2(X4,X3)))|~hBOOL(hAPP(c_Predicate_ODomainP(X1,X2,X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8685]), ['final']). 6.97/7.26 cnf(c_0_14055, 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,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_8686]), ['final']). 6.97/7.26 cnf(c_0_14056, 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),esk454_4(hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),X1,X3,X2)))), inference(er,[status(thm)],[c_0_8687]), ['final']). 6.97/7.26 cnf(c_0_14057, 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_8688, c_0_5002]), ['final']). 6.97/7.26 cnf(c_0_14058, plain, (X2=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),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_8689]), ['final']). 6.97/7.26 cnf(c_0_14059, plain, (X3=X2|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_fequal),esk157_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_5291]), ['final']). 6.97/7.26 cnf(c_0_14060, plain, (c_List_Olist__all(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))|~hBOOL(hAPP(X1,X2))|~c_List_Olist__all(X3,X1,X4)), inference(split_conjunct,[status(thm)],[c_0_8690]), ['final']). 6.97/7.26 cnf(c_0_14061, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=X1|c_Int_OMin=X2|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_8691, c_0_4415]), ['final']). 6.97/7.26 cnf(c_0_14062, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|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_8692]), ['final']). 6.97/7.26 cnf(c_0_14063, 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_8693]), ['final']). 6.97/7.26 cnf(c_0_14064, 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_7486]), ['final']). 6.97/7.26 cnf(c_0_14065, 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_8694, c_0_5002]), c_0_5002]), ['final']). 6.97/7.26 cnf(c_0_14066, 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_8408]), ['final']). 6.97/7.26 cnf(c_0_14067, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=X1|X1=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_8695, c_0_4415]), ['final']). 6.97/7.26 cnf(c_0_14068, 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_8696, c_0_5202]), c_0_5202]), ['final']). 6.97/7.26 cnf(c_0_14069, 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_8697]), ['final']). 6.97/7.26 cnf(c_0_14070, 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_8413]), ['final']). 6.97/7.26 cnf(c_0_14071, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=X1|X2=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_8698, c_0_4415]), ['final']). 6.97/7.26 cnf(c_0_14072, 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_8699, c_0_5202]), c_0_5202]), ['final']). 6.97/7.26 cnf(c_0_14073, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|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),X2),hAPP(c_List_Oset(tc_Nat_Onat),X1)))), inference(split_conjunct,[status(thm)],[c_0_8380]), ['final']). 6.97/7.26 cnf(c_0_14074, plain, (X4=hAPP(hAPP(c_List_Onth(X1),X3),X2)|hAPP(hAPP(c_List_Odrop(X1),X2),X3)!=hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)), inference(split_conjunct,[status(thm)],[c_0_8700]), ['final']). 6.97/7.26 cnf(c_0_14075, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Groups_Oone__class_Oone(tc_Int_Oint)=X2|~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_8701]), ['final']). 6.97/7.26 cnf(c_0_14076, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|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_8702]), ['final']). 6.97/7.26 cnf(c_0_14077, 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_8703]), ['final']). 6.97/7.26 cnf(c_0_14078, 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_8704]), ['final']). 6.97/7.26 cnf(c_0_14079, 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_8705, c_0_6164]), ['final']). 6.97/7.26 cnf(c_0_14080, plain, (X2=hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))|~c_Relation_Otrans(X1,X2)), inference(rw,[status(thm)],[c_0_8706, c_0_5174]), ['final']). 6.97/7.26 cnf(c_0_14081, plain, (hBOOL(hAPP(X1,X4))|~c_List_Oall__interval__int(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_8213]), ['final']). 6.97/7.26 cnf(c_0_14082, 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),esk238_2(X2,X3)))|~hBOOL(hAPP(X3,X1))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_5312]), ['final']). 6.97/7.26 cnf(c_0_14083, 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_8707]), ['final']). 6.97/7.26 cnf(c_0_14084, 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),X1),X2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8708, c_0_4742]), c_0_4742]), ['final']). 6.97/7.26 cnf(c_0_14085, plain, (X1=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8709, c_0_4742]), c_0_4742]), ['final']). 6.97/7.26 cnf(c_0_14086, 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_8710]), ['final']). 6.97/7.26 cnf(c_0_14087, 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_8711]), ['final']). 6.97/7.26 cnf(c_0_14088, 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_7993]), ['final']). 6.97/7.26 cnf(c_0_14089, 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,esk208_2(X2,X1))))), inference(split_conjunct,[status(thm)],[c_0_8712]), ['final']). 6.97/7.26 cnf(c_0_14090, 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_8713]), ['final']). 6.97/7.26 cnf(c_0_14091, 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),X2),X2)))), inference(rw,[status(thm)],[c_0_8714, c_0_4410]), ['final']). 6.97/7.26 cnf(c_0_14092, 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_8715]), ['final']). 6.97/7.26 cnf(c_0_14093, 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_8716]), ['final']). 6.97/7.26 cnf(c_0_14094, plain, (hBOOL(hAPP(X1,esk82_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_7477]), ['final']). 6.97/7.26 cnf(c_0_14095, plain, (c_List_Olist__all(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_Oall__interval__nat(X1,X2,X3)), inference(rw,[status(thm)],[c_0_8717, c_0_4471]), ['final']). 6.97/7.26 cnf(c_0_14096, 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_8718, c_0_5002]), c_0_5002]), ['final']). 6.97/7.26 cnf(c_0_14097, plain, (hBOOL(hAPP(X1,esk36_3(X2,X1,X3)))|hAPP(c_List_Ofilter(X3,X1),X2)=c_List_OtakeWhile(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5051]), ['final']). 6.97/7.26 cnf(c_0_14098, 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_8719]), ['final']). 6.97/7.26 cnf(c_0_14099, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|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_8720]), ['final']). 6.97/7.26 cnf(c_0_14100, plain, (hBOOL(hAPP(X1,X2))|c_List_Olist_ONil(X3)=hAPP(c_List_Ofilter(X3,X1),c_List_Oreplicate(X3,X4,X2))), inference(split_conjunct,[status(thm)],[c_0_8693]), ['final']). 6.97/7.26 cnf(c_0_14101, plain, (X2=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)),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8721]), ['final']). 6.97/7.26 cnf(c_0_14102, 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_8722]), ['final']). 6.97/7.26 cnf(c_0_14103, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk109_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_5826]), ['final']). 6.97/7.26 cnf(c_0_14104, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Orderings_Oord__class_OLeast(X1,X2)),X3))|~class_Orderings_Owellorder(X1)|~hBOOL(hAPP(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_8723]), ['final']). 6.97/7.26 cnf(c_0_14105, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk55_1(X1)))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5417]), ['final']). 6.97/7.26 cnf(c_0_14106, 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_7604]), ['final']). 6.97/7.26 cnf(c_0_14107, 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_4518]), ['final']). 6.97/7.26 cnf(c_0_14108, 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_8724]), ['final']). 6.97/7.26 cnf(c_0_14109, 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)), inference(split_conjunct,[status(thm)],[c_0_8725]), ['final']). 6.97/7.26 cnf(c_0_14110, plain, (c_Groups_Ozero__class_Ozero(X1)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X3)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_8726]), ['final']). 6.97/7.26 cnf(c_0_14111, plain, (c_Predicate_Oinv__imagep(X5,X6,X1,X2,X3,X4)|~hBOOL(hAPP(hAPP(X1,hAPP(X2,X3)),hAPP(X2,X4)))), inference(split_conjunct,[status(thm)],[c_0_8410]), ['final']). 6.97/7.26 cnf(c_0_14112, 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_7850]), ['final']). 6.97/7.26 cnf(c_0_14113, 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_5827]), ['final']). 6.97/7.26 cnf(c_0_14114, 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(split_conjunct,[status(thm)],[c_0_8727]), ['final']). 6.97/7.26 cnf(c_0_14115, 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)), inference(split_conjunct,[status(thm)],[c_0_8728]), ['final']). 6.97/7.26 cnf(c_0_14116, 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_8729]), ['final']). 6.97/7.26 cnf(c_0_14117, 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_8730]), ['final']). 6.97/7.26 cnf(c_0_14118, plain, (X1=c_List_Olist_ONil(X2)|c_List_Olast(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X1))=c_List_Olast(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_8731]), ['final']). 6.97/7.26 cnf(c_0_14119, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~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)), inference(split_conjunct,[status(thm)],[c_0_8400]), ['final']). 6.97/7.26 cnf(c_0_14120, 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']). 6.97/7.26 cnf(c_0_14121, 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_8732]), ['final']). 6.97/7.26 cnf(c_0_14122, 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_8733]), ['final']). 6.97/7.26 cnf(c_0_14123, plain, (c_Orderings_Otop__class_Otop(X1)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_8734]), ['final']). 6.97/7.26 cnf(c_0_14124, plain, (hAPP(c_Nat_OSuc,esk455_2(X1,X2))=X2|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1)))), inference(split_conjunct,[status(thm)],[c_0_8303]), ['final']). 6.97/7.26 cnf(c_0_14125, 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_8735]), ['final']). 6.97/7.26 cnf(c_0_14126, 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_8736]), ['final']). 6.97/7.26 cnf(c_0_14127, 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_7211]), ['final']). 6.97/7.26 cnf(c_0_14128, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|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_5369]), ['final']). 6.97/7.26 cnf(c_0_14129, 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_8737]), ['final']). 6.97/7.26 cnf(c_0_14130, 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_8738]), ['final']). 6.97/7.26 cnf(c_0_14131, plain, (hAPP(c_Quotient_OBabs(X1,X4,X3,X5),X2)=hAPP(X5,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8739]), ['final']). 6.97/7.26 cnf(c_0_14132, 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_8740]), ['final']). 6.97/7.26 cnf(c_0_14133, 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_8741]), ['final']). 6.97/7.26 cnf(c_0_14134, 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_8742]), ['final']). 6.97/7.26 cnf(c_0_14135, 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_8743, c_0_4415]), ['final']). 6.97/7.26 cnf(c_0_14136, plain, (hAPP(hAPP(c_List_Otake(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)),X3))), inference(split_conjunct,[status(thm)],[c_0_8744]), ['final']). 6.97/7.26 cnf(c_0_14137, 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_8745]), ['final']). 6.97/7.26 cnf(c_0_14138, 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_8746]), ['final']). 6.97/7.26 cnf(c_0_14139, 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_8747]), ['final']). 6.97/7.26 cnf(c_0_14140, plain, (c_List_Olist__ex(X3,X1,X4)|~hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_8323]), ['final']). 6.97/7.26 cnf(c_0_14141, 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_5471]), ['final']). 6.97/7.26 cnf(c_0_14142, plain, (X1=X2|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),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8748]), ['final']). 6.97/7.26 cnf(c_0_14143, plain, (hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(X1,esk374_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7335]), ['final']). 6.97/7.26 cnf(c_0_14144, plain, (hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(X1,esk14_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7236]), ['final']). 6.97/7.26 cnf(c_0_14145, plain, (hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)=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_8749]), ['final']). 6.97/7.26 cnf(c_0_14146, 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_8750]), ['final']). 6.97/7.26 cnf(c_0_14147, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|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_8751]), ['final']). 6.97/7.26 cnf(c_0_14148, plain, (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)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[c_0_8752, c_0_4471]), ['final']). 6.97/7.26 cnf(c_0_14149, 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_8753]), ['final']). 6.97/7.26 cnf(c_0_14150, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(c_Code__Numeral_Onat__of,esk573_2(X1,X2))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_8754, c_0_8490])]), ['final']). 6.97/7.26 cnf(c_0_14151, plain, (c_List_Oremove1(X1,X3,c_List_Oremdups(X1,X2))=c_List_Oremdups(X1,c_List_Oremove1(X1,X3,X2))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8755]), ['final']). 6.97/7.26 cnf(c_0_14152, 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_8756, c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_14153, 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_8757]), ['final']). 6.97/7.26 cnf(c_0_14154, plain, (hBOOL(hAPP(hAPP(X1,esk299_2(X1,X2)),esk299_2(X1,X2)))|~c_Equiv__Relations_Opart__equivp(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_8758]), ['final']). 6.97/7.26 cnf(c_0_14155, plain, (hBOOL(hAPP(hAPP(X1,esk167_2(X1,X2)),esk167_2(X1,X2)))|~c_Equiv__Relations_Opart__equivp(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_8759]), ['final']). 6.97/7.26 cnf(c_0_14156, 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,esk361_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5164]), ['final']). 6.97/7.26 cnf(c_0_14157, 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_8415]), ['final']). 6.97/7.26 cnf(c_0_14158, 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_8423]), ['final']). 6.97/7.26 cnf(c_0_14159, 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_8422]), ['final']). 6.97/7.26 cnf(c_0_14160, 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_8424]), ['final']). 6.97/7.26 cnf(c_0_14161, 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_8760]), ['final']). 6.97/7.26 cnf(c_0_14162, plain, (hBOOL(hAPP(hAPP(X3,X2),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Quotient_ORespects(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_8538]), ['final']). 6.97/7.26 cnf(c_0_14163, 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_8429]), ['final']). 6.97/7.26 cnf(c_0_14164, 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_8761]), ['final']). 6.97/7.26 cnf(c_0_14165, 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_8762]), ['final']). 6.97/7.26 cnf(c_0_14166, plain, (X2=X1|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_8763]), ['final']). 6.97/7.26 cnf(c_0_14167, plain, (X2=X3|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_8764]), ['final']). 6.97/7.26 cnf(c_0_14168, plain, (c_Fun_Obij__betw(X2,X1,c_Fun_Othe__inv__into(X1,X2,X4,X3),X5,X4)|~c_Fun_Obij__betw(X1,X2,X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_8765]), ['final']). 6.97/7.26 cnf(c_0_14169, plain, (c_Fun_Obij__betw(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3),X5,X4)|~c_Fun_Obij__betw(X1,X2,X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_8766]), ['final']). 6.97/7.26 cnf(c_0_14170, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|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)), inference(split_conjunct,[status(thm)],[c_0_8767]), ['final']). 6.97/7.26 cnf(c_0_14171, 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_8768]), ['final']). 6.97/7.26 cnf(c_0_14172, 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_4518]), ['final']). 6.97/7.26 cnf(c_0_14173, 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_8769]), ['final']). 6.97/7.26 cnf(c_0_14174, 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_8770]), ['final']). 6.97/7.26 cnf(c_0_14175, 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_8771]), ['final']). 6.97/7.26 cnf(c_0_14176, plain, (X1=c_List_Olist_ONil(X2)|hBOOL(hAPP(c_List_Odistinct(X2),c_List_Obutlast(X2,X1)))|~hBOOL(hAPP(c_List_Odistinct(X2),X1))), inference(split_conjunct,[status(thm)],[c_0_8772]), ['final']). 6.97/7.26 cnf(c_0_14177, 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_8404]), ['final']). 6.97/7.26 cnf(c_0_14178, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|c_Partial__Function_Omk__less(X4,X1,X3,X2)|~hBOOL(hAPP(hAPP(X1,X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8773]), ['final']). 6.97/7.26 cnf(c_0_14179, 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_7998]), ['final']). 6.97/7.26 cnf(c_0_14180, 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_8774]), ['final']). 6.97/7.26 cnf(c_0_14181, 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_8775]), ['final']). 6.97/7.26 cnf(c_0_14182, plain, (c_Orderings_Oord__class_Omin(X1)=c_Orderings_Oord_Omax(X1,hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X1)))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8776]), ['final']). 6.97/7.26 cnf(c_0_14183, plain, (hBOOL(hAPP(hAPP(X1,X2),X2))|~hBOOL(hAPP(hAPP(X1,X2),X3))|~c_Equiv__Relations_Opart__equivp(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_7518]), ['final']). 6.97/7.26 cnf(c_0_14184, plain, (hBOOL(hAPP(hAPP(X1,X2),X2))|~hBOOL(hAPP(hAPP(X1,X3),X2))|~c_Equiv__Relations_Opart__equivp(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_7518]), ['final']). 6.97/7.26 cnf(c_0_14185, plain, (hBOOL(hAPP(hAPP(X2,X4),X3))|~c_Equiv__Relations_Opart__equivp(X1,X2)|~hBOOL(hAPP(hAPP(X2,X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8777]), ['final']). 6.97/7.26 cnf(c_0_14186, plain, (hBOOL(hAPP(hAPP(X2,X4),X3))|~c_Predicate_Osymp(X1,X2)|~hBOOL(hAPP(hAPP(X2,X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8778]), ['final']). 6.97/7.26 cnf(c_0_14187, 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_8779]), ['final']). 6.97/7.26 cnf(c_0_14188, 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_8780]), ['final']). 6.97/7.26 cnf(c_0_14189, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X2)=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_8781]), ['final']). 6.97/7.26 cnf(c_0_14190, 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))), inference(split_conjunct,[status(thm)],[c_0_8782]), ['final']). 6.97/7.26 cnf(c_0_14191, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(X1,esk307_1(X1)))), inference(rw,[status(thm)],[c_0_8783, c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_14192, plain, (X2=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Lattices_Osemilattice__inf(X1)), inference(split_conjunct,[status(thm)],[c_0_8784]), ['final']). 6.97/7.26 cnf(c_0_14193, 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_8785]), ['final']). 6.97/7.26 cnf(c_0_14194, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))|c_Nitpick_Ounknown(tc_HOL_Obool)|~c_Nitpick_Owf_H(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8786]), ['final']). 6.97/7.26 cnf(c_0_14195, plain, (c_Fun_Oinj__on(X2,X1,X3,X4)|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))), inference(split_conjunct,[status(thm)],[c_0_8787]), ['final']). 6.97/7.26 cnf(c_0_14196, 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_7679]), ['final']). 6.97/7.26 cnf(c_0_14197, plain, (c_Relation_Otrans(tc_prod(X1,X3),c_Wellfounded_Olex__prod(X1,X3,X2,X4))|~c_Relation_Otrans(X1,X2)|~c_Relation_Otrans(X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8788]), ['final']). 6.97/7.26 cnf(c_0_14198, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(X1,esk77_1(X1)))), inference(rw,[status(thm)],[c_0_8789, c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_14199, 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_8790]), ['final']). 6.97/7.26 cnf(c_0_14200, plain, (c_Big__Operators_Olinorder__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_8791]), ['final']). 6.97/7.26 cnf(c_0_14201, 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_8792]), ['final']). 6.97/7.26 cnf(c_0_14202, plain, (c_Big__Operators_Olattice__class_OInf__fin(X1,X2)=hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X2)|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8793]), ['final']). 6.97/7.26 cnf(c_0_14203, 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_8794]), ['final']). 6.97/7.26 cnf(c_0_14204, 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))), inference(split_conjunct,[status(thm)],[c_0_8795]), ['final']). 6.97/7.26 cnf(c_0_14205, 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__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_8796]), ['final']). 6.97/7.26 cnf(c_0_14206, plain, (esk81_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_8797]), c_0_4742]), ['final']). 6.97/7.26 cnf(c_0_14207, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=X1|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|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_8798, c_0_4742]), c_0_4742]), ['final']). 6.97/7.26 cnf(c_0_14208, 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_8799, c_0_4413]), ['final']). 6.97/7.26 cnf(c_0_14209, 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_8800]), ['final']). 6.97/7.26 cnf(c_0_14210, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)=X2|c_Groups_Ozero__class_Ozero(X1)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8801]), ['final']). 6.97/7.26 cnf(c_0_14211, 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_8802, c_0_4413]), ['final']). 6.97/7.26 cnf(c_0_14212, plain, (X1=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk284_2(X2,X1))|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_5841]), ['final']). 6.97/7.26 cnf(c_0_14213, plain, (X1=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk103_2(X2,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_5842]), ['final']). 6.97/7.26 cnf(c_0_14214, 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_8803]), ['final']). 6.97/7.26 cnf(c_0_14215, 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_7320]), ['final']). 6.97/7.26 cnf(c_0_14216, 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_7320]), ['final']). 6.97/7.26 cnf(c_0_14217, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8804, c_0_4409]), c_0_4410]), c_0_4411]), ['final']). 6.97/7.26 cnf(c_0_14218, 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_8805]), ['final']). 6.97/7.26 cnf(c_0_14219, 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_8806, c_0_8807]), ['final']). 6.97/7.26 cnf(c_0_14220, 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_8362]), ['final']). 6.97/7.26 cnf(c_0_14221, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk429_3(X3,X2,X1))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_7295]), ['final']). 6.97/7.26 cnf(c_0_14222, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk210_3(X3,X2,X1))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_7296]), ['final']). 6.97/7.26 cnf(c_0_14223, 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_8808]), ['final']). 6.97/7.26 cnf(c_0_14224, 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_8809]), ['final']). 6.97/7.26 cnf(c_0_14225, 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_8810]), ['final']). 6.97/7.26 cnf(c_0_14226, 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_8811]), ['final']). 6.97/7.26 cnf(c_0_14227, plain, (c_Relation_Oantisym(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~c_Relation_Oantisym(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_8812]), ['final']). 6.97/7.26 cnf(c_0_14228, 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_8813]), ['final']). 6.97/7.26 cnf(c_0_14229, plain, (hBOOL(hAPP(X1,esk40_3(X2,X1,X3)))|hAPP(c_List_Ofilter(X3,X1),X2)=c_List_Olist_ONil(X3)), inference(split_conjunct,[status(thm)],[c_0_7998]), ['final']). 6.97/7.26 cnf(c_0_14230, plain, (hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X4),X1),X2))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5847]), ['final']). 6.97/7.26 cnf(c_0_14231, 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_8814]), ['final']). 6.97/7.26 cnf(c_0_14232, plain, (X2=esk364_3(X3,X4,X1)|c_FunDef_OTHE__default(X4,X3,X1)=X3|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_8455]), ['final']). 6.97/7.26 cnf(c_0_14233, 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_8815]), ['final']). 6.97/7.26 cnf(c_0_14234, 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_8816]), ['final']). 6.97/7.26 cnf(c_0_14235, plain, (hAPP(c_Finite__Set_Ocard(X1),esk81_3(X2,X3,X1))=X2|hAPP(c_Finite__Set_Ocard(X1),X3)!=hAPP(c_Nat_OSuc,X2)), inference(split_conjunct,[status(thm)],[c_0_5303]), ['final']). 6.97/7.26 cnf(c_0_14236, 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_8817]), ['final']). 6.97/7.26 cnf(c_0_14237, plain, (X1=X2|hAPP(X3,X1)=hAPP(c_Fun_Ofun__upd(X4,X5,X3,X2,X6),X1)), inference(split_conjunct,[status(thm)],[c_0_8818]), ['final']). 6.97/7.26 cnf(c_0_14238, 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_8819, c_0_5002]), ['final']). 6.97/7.26 cnf(c_0_14239, 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_8820]), ['final']). 6.97/7.26 cnf(c_0_14240, 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_8820]), ['final']). 6.97/7.26 cnf(c_0_14241, 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_8814]), ['final']). 6.97/7.26 cnf(c_0_14242, 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_8821]), ['final']). 6.97/7.26 cnf(c_0_14243, 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_8822]), ['final']). 6.97/7.26 cnf(c_0_14244, 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_8823]), ['final']). 6.97/7.26 cnf(c_0_14245, plain, (X4=X3|hAPP(c_Product__Type_Ofst(X1,X2),X3)!=hAPP(c_Product__Type_Ofst(X1,X2),X4)|hAPP(c_Product__Type_Osnd(X1,X2),X3)!=hAPP(c_Product__Type_Osnd(X1,X2),X4)), inference(split_conjunct,[status(thm)],[c_0_8824]), ['final']). 6.97/7.26 cnf(c_0_14246, 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_8678]), ['final']). 6.97/7.26 cnf(c_0_14247, 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_8741]), ['final']). 6.97/7.26 cnf(c_0_14248, 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_8825]), ['final']). 6.97/7.26 cnf(c_0_14249, 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_6714]), ['final']). 6.97/7.26 cnf(c_0_14250, 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_6715]), ['final']). 6.97/7.26 cnf(c_0_14251, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ozero__class_Ozero(X2)),X1)=c_Groups_Ozero__class_Ozero(X2)|~class_Power_Opower(X2)|~class_Rings_Osemiring__0(X2)), inference(split_conjunct,[status(thm)],[c_0_8826]), ['final']). 6.97/7.26 cnf(c_0_14252, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),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_8827]), ['final']). 6.97/7.26 cnf(c_0_14253, 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_8828]), ['final']). 6.97/7.26 cnf(c_0_14254, 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_8086]), ['final']). 6.97/7.26 cnf(c_0_14255, 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_8086]), ['final']). 6.97/7.26 cnf(c_0_14256, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),X2)=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_8829]), ['final']). 6.97/7.26 cnf(c_0_14257, 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_8830]), ['final']). 6.97/7.26 cnf(c_0_14258, 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_8831]), ['final']). 6.97/7.26 cnf(c_0_14259, 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_8057]), ['final']). 6.97/7.26 cnf(c_0_14260, 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_8058]), ['final']). 6.97/7.26 cnf(c_0_14261, 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_8057]), ['final']). 6.97/7.26 cnf(c_0_14262, 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_8058]), ['final']). 6.97/7.26 cnf(c_0_14263, 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_8832]), ['final']). 6.97/7.26 cnf(c_0_14264, 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)), inference(split_conjunct,[status(thm)],[c_0_8833]), ['final']). 6.97/7.26 cnf(c_0_14265, 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_8834]), ['final']). 6.97/7.26 cnf(c_0_14266, plain, (c_Orderings_Oord__class_OLeast(X1,X3)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk486_3(X2,X3,X1)))|~hBOOL(hAPP(X3,X2))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8662]), ['final']). 6.97/7.26 cnf(c_0_14267, 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_7790]), ['final']). 6.97/7.26 cnf(c_0_14268, plain, (hBOOL(hAPP(c_Predicate_ORangeP(X4,X5,X1),X3))|~hBOOL(hAPP(hAPP(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8835]), ['final']). 6.97/7.26 cnf(c_0_14269, plain, (hBOOL(hAPP(c_Predicate_ODomainP(X4,X5,X1),X2))|~hBOOL(hAPP(hAPP(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8685]), ['final']). 6.97/7.26 cnf(c_0_14270, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)), inference(rw,[status(thm)],[c_0_8836, c_0_4742]), ['final']). 6.97/7.26 cnf(c_0_14271, 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_8837]), ['final']). 6.97/7.26 cnf(c_0_14272, 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_8838]), ['final']). 6.97/7.26 cnf(c_0_14273, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|c_Nitpick_Osetsum_H(X1,X3,X4,X2)=c_Groups_Ozero__class_Ozero(X3)|~class_Groups_Ocomm__monoid__add(X3)), inference(split_conjunct,[status(thm)],[c_0_4814]), ['final']). 6.97/7.26 cnf(c_0_14274, 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)), inference(split_conjunct,[status(thm)],[c_0_8839]), ['final']). 6.97/7.26 cnf(c_0_14275, 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_8840]), ['final']). 6.97/7.26 cnf(c_0_14276, 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_8841]), ['final']). 6.97/7.26 cnf(c_0_14277, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X2)|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8842]), ['final']). 6.97/7.26 cnf(c_0_14278, 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_8843]), ['final']). 6.97/7.26 cnf(c_0_14279, 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)), inference(split_conjunct,[status(thm)],[c_0_8844]), ['final']). 6.97/7.26 cnf(c_0_14280, 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_8845, c_0_5202]), c_0_5202]), ['final']). 6.97/7.26 cnf(c_0_14281, 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)), inference(split_conjunct,[status(thm)],[c_0_8846]), ['final']). 6.97/7.26 cnf(c_0_14282, 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))), inference(split_conjunct,[status(thm)],[c_0_8847]), ['final']). 6.97/7.26 cnf(c_0_14283, plain, (hBOOL(hAPP(X1,esk297_3(X1,X2,X3)))|~hBOOL(hAPP(X1,X4))|~c_Equiv__Relations_Oequivp(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_8173]), ['final']). 6.97/7.26 cnf(c_0_14284, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=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))), inference(split_conjunct,[status(thm)],[c_0_8848]), ['final']). 6.97/7.26 cnf(c_0_14285, 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)|esk457_2(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(er,[status(thm)],[c_0_8849]), ['final']). 6.97/7.26 cnf(c_0_14286, 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_8850]), ['final']). 6.97/7.26 cnf(c_0_14287, plain, (hBOOL(hAPP(X1,X2))|hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)!=hAPP(c_List_Ofilter(X3,X1),X5)), inference(split_conjunct,[status(thm)],[c_0_4996]), ['final']). 6.97/7.26 cnf(c_0_14288, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))=hAPP(c_Set_Oimage(X2,X1,X4),X5)|~c_Typedef_Otype__definition(X1,X2,X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_8851]), ['final']). 6.97/7.26 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_8852]), ['final']). 6.97/7.26 cnf(c_0_14290, plain, (hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))|~hBOOL(hAPP(X1,esk178_1(X1)))), inference(split_conjunct,[status(thm)],[c_0_8204]), ['final']). 6.97/7.26 cnf(c_0_14291, 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_8853]), ['final']). 6.97/7.26 cnf(c_0_14292, 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_8854]), ['final']). 6.97/7.26 cnf(c_0_14293, 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_8855]), ['final']). 6.97/7.26 cnf(c_0_14294, 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_8856]), ['final']). 6.97/7.26 cnf(c_0_14295, 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_8857]), ['final']). 6.97/7.26 cnf(c_0_14296, plain, (c_Relation_Otrans(X3,hAPP(hAPP(c_Relation_Oinv__image(X1,X3),X2),X4))|~c_Relation_Otrans(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8858]), ['final']). 6.97/7.26 cnf(c_0_14297, plain, (c_Relation_Osym(X3,hAPP(hAPP(c_Relation_Oinv__image(X1,X3),X2),X4))|~c_Relation_Osym(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8859]), ['final']). 6.97/7.26 cnf(c_0_14298, 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_8151]), ['final']). 6.97/7.26 cnf(c_0_14299, plain, (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)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)), inference(split_conjunct,[status(thm)],[c_0_8860]), ['final']). 6.97/7.26 cnf(c_0_14300, 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_8133]), ['final']). 6.97/7.26 cnf(c_0_14301, 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_8133]), ['final']). 6.97/7.26 cnf(c_0_14302, 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_8861]), ['final']). 6.97/7.26 cnf(c_0_14303, 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_8862]), ['final']). 6.97/7.26 cnf(c_0_14304, 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_8863]), ['final']). 6.97/7.26 cnf(c_0_14305, 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_8239]), ['final']). 6.97/7.26 cnf(c_0_14306, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Sum__Type_OPlus(X1,X3,X2,X4)!=c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X1,X3),tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5781]), ['final']). 6.97/7.26 cnf(c_0_14307, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|c_Sum__Type_OPlus(X3,X2,X4,X1)!=c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X3,X2),tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5781]), ['final']). 6.97/7.26 cnf(c_0_14308, plain, (hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2)))|~hBOOL(hAPP(X1,esk361_3(X2,X3,X1)))|~hBOOL(hAPP(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_5164]), ['final']). 6.97/7.26 cnf(c_0_14309, 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_8864]), ['final']). 6.97/7.26 cnf(c_0_14310, 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_8865]), ['final']). 6.97/7.26 cnf(c_0_14311, 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_8866]), ['final']). 6.97/7.26 cnf(c_0_14312, plain, (X1=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),X4),X4)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),X1),X2)|~class_Groups_Oab__group__add(X3)), inference(er,[status(thm)],[c_0_8867]), ['final']). 6.97/7.26 cnf(c_0_14313, 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_8868]), ['final']). 6.97/7.26 cnf(c_0_14314, 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_8869]), ['final']). 6.97/7.26 cnf(c_0_14315, 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_8870]), ['final']). 6.97/7.26 cnf(c_0_14316, 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_8871]), ['final']). 6.97/7.26 cnf(c_0_14317, 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_4577]), ['final']). 6.97/7.26 cnf(c_0_14318, 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_8814]), ['final']). 6.97/7.26 cnf(c_0_14319, 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_8872]), ['final']). 6.97/7.26 cnf(c_0_14320, 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_8873]), ['final']). 6.97/7.26 cnf(c_0_14321, 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_8874]), ['final']). 6.97/7.26 cnf(c_0_14322, 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_8875]), ['final']). 6.97/7.26 cnf(c_0_14323, 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)),X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_8876]), ['final']). 6.97/7.26 cnf(c_0_14324, 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)),X3),X1)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_8876]), ['final']). 6.97/7.26 cnf(c_0_14325, 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_8877]), ['final']). 6.97/7.26 cnf(c_0_14326, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=c_SetInterval_Oord__class_OgreaterThanAtMost(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_8878]), ['final']). 6.97/7.26 cnf(c_0_14327, 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), inference(split_conjunct,[status(thm)],[c_0_8433]), ['final']). 6.97/7.26 cnf(c_0_14328, 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_8879, c_0_4415]), ['final']). 6.97/7.26 cnf(c_0_14329, 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_8880, c_0_5002]), ['final']). 6.97/7.26 cnf(c_0_14330, plain, (hBOOL(hAPP(hAPP(X1,X3),X2))|hAPP(X1,X2)!=hAPP(X1,X3)|~c_Equiv__Relations_Oequivp(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_8289]), ['final']). 6.97/7.26 cnf(c_0_14331, 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_8187]), ['final']). 6.97/7.26 cnf(c_0_14332, 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_8188]), ['final']). 6.97/7.26 cnf(c_0_14333, 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_8187]), ['final']). 6.97/7.26 cnf(c_0_14334, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)=hAPP(c_Groups_Oabs__class_Oabs(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_8881]), ['final']). 6.97/7.26 cnf(c_0_14335, plain, (hBOOL(hAPP(c_List_Odistinct(X1),esk469_2(X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5396]), ['final']). 6.97/7.26 cnf(c_0_14336, 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_8882]), ['final']). 6.97/7.26 cnf(c_0_14337, 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_8883]), ['final']). 6.97/7.26 cnf(c_0_14338, 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_8188]), ['final']). 6.97/7.26 cnf(c_0_14339, 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_8884, c_0_5002])]), ['final']). 6.97/7.26 cnf(c_0_14340, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin))|~class_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8885]), ['final']). 6.97/7.26 cnf(c_0_14341, 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_Opreorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8108]), ['final']). 6.97/7.26 cnf(c_0_14342, plain, (X1=X2|hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))!=c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)|~class_Orderings_Oorder(X3)), inference(split_conjunct,[status(thm)],[c_0_8886]), ['final']). 6.97/7.26 cnf(c_0_14343, plain, (hBOOL(hAPP(hAPP(X1,esk450_1(X1)),esk450_1(X1)))|~c_Equiv__Relations_Opart__equivp(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_7518]), ['final']). 6.97/7.26 cnf(c_0_14344, plain, (X1=X2|hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))!=c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X1)|~class_Orderings_Oorder(X3)), inference(split_conjunct,[status(thm)],[c_0_8886]), ['final']). 6.97/7.26 cnf(c_0_14345, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|X3=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Ono__zero__divisors(X1)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)!=c_Groups_Ozero__class_Ozero(X1)), inference(split_conjunct,[status(thm)],[c_0_8887]), ['final']). 6.97/7.26 cnf(c_0_14346, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|X3=c_Groups_Ozero__class_Ozero(X1)|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_5442]), ['final']). 6.97/7.26 cnf(c_0_14347, 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)))), inference(split_conjunct,[status(thm)],[c_0_8888]), ['final']). 6.97/7.26 cnf(c_0_14348, plain, (X1=c_List_Olist_ONil(X2)|hAPP(c_List_Ohd(X2),X1)=hAPP(hAPP(c_List_Onth(X2),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_8889]), ['final']). 6.97/7.26 cnf(c_0_14349, 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)), inference(split_conjunct,[status(thm)],[c_0_8890]), ['final']). 6.97/7.26 cnf(c_0_14350, 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_8784]), ['final']). 6.97/7.26 cnf(c_0_14351, 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_8379]), ['final']). 6.97/7.26 cnf(c_0_14352, plain, (X4=X3|~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_5770]), ['final']). 6.97/7.26 cnf(c_0_14353, plain, (X1=c_List_Olist_ONil(X2)|hAPP(c_List_Ohd(X2),X1)=c_List_Olast(X2,hAPP(c_List_Orev(X2),X1))), inference(split_conjunct,[status(thm)],[c_0_8891]), ['final']). 6.97/7.26 cnf(c_0_14354, plain, (hBOOL(hAPP(X1,esk364_3(X2,X3,X1)))|c_FunDef_OTHE__default(X3,X2,X1)=X2), inference(split_conjunct,[status(thm)],[c_0_8455]), ['final']). 6.97/7.26 cnf(c_0_14355, 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_8354]), ['final']). 6.97/7.26 cnf(c_0_14356, 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_8892, c_0_5794]), ['final']). 6.97/7.26 cnf(c_0_14357, 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_8893]), ['final']). 6.97/7.26 cnf(c_0_14358, 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_8894]), ['final']). 6.97/7.26 cnf(c_0_14359, 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_8820]), ['final']). 6.97/7.26 cnf(c_0_14360, 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_8895]), ['final']). 6.97/7.26 cnf(c_0_14361, 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_8896]), ['final']). 6.97/7.26 cnf(c_0_14362, 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_8897]), ['final']). 6.97/7.26 cnf(c_0_14363, 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_8898]), ['final']). 6.97/7.26 cnf(c_0_14364, 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_8899]), ['final']). 6.97/7.26 cnf(c_0_14365, plain, (c_Equiv__Relations_Oequivp(X2,X1)|hAPP(X1,esk432_1(X1))!=hAPP(X1,esk431_1(X1))|~hBOOL(hAPP(hAPP(X1,esk431_1(X1)),esk432_1(X1)))), inference(split_conjunct,[status(thm)],[c_0_8289]), ['final']). 6.97/7.26 cnf(c_0_14366, 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,esk116_2(X2,X1)))), inference(rw,[status(thm)],[c_0_8900, c_0_5002]), ['final']). 6.97/7.26 cnf(c_0_14367, plain, (c_Nat__Transfer_Otsub(X2,X1)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8901]), ['final']). 6.97/7.26 cnf(c_0_14368, 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_8902]), ['final']). 6.97/7.26 cnf(c_0_14369, 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_7914]), ['final']). 6.97/7.26 cnf(c_0_14370, plain, (X2=c_Groups_Ozero__class_Ozero(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)))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_5385]), ['final']). 6.97/7.26 cnf(c_0_14371, 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_8903]), ['final']). 6.97/7.26 cnf(c_0_14372, 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_8904]), ['final']). 6.97/7.26 cnf(c_0_14373, plain, (c_Fun_Obij__betw(X1,X2,X3,X4,hAPP(c_Set_Oimage(X1,X2,X3),X4))|~c_Fun_Oinj__on(X1,X2,X3,X4)), inference(er,[status(thm)],[c_0_8905]), ['final']). 6.97/7.26 cnf(c_0_14374, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3)!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Omult__zero(X2)|~class_Rings_Ono__zero__divisors(X2)|~class_Rings_Ozero__neq__one(X2)|~class_Power_Opower(X2)), inference(split_conjunct,[status(thm)],[c_0_5416]), ['final']). 6.97/7.26 cnf(c_0_14375, plain, (~c_List_Olist__ex(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_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),X1),X2,X3)), inference(rw,[status(thm)],[c_0_8906, c_0_4471]), ['final']). 6.97/7.26 cnf(c_0_14376, 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_7463]), ['final']). 6.97/7.26 cnf(c_0_14377, 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_8907]), ['final']). 6.97/7.26 cnf(c_0_14378, 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_8908]), ['final']). 6.97/7.26 cnf(c_0_14379, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X3|hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,esk414_4(X1,X2,X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_7401]), ['final']). 6.97/7.26 cnf(c_0_14380, plain, (~hBOOL(hAPP(hAPP(c_member(X1),esk80_3(X2,X3,X1)),esk81_3(X2,X3,X1)))|hAPP(c_Finite__Set_Ocard(X1),X3)!=hAPP(c_Nat_OSuc,X2)), inference(split_conjunct,[status(thm)],[c_0_5303]), ['final']). 6.97/7.26 cnf(c_0_14381, 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_5399]), ['final']). 6.97/7.26 cnf(c_0_14382, plain, (X1=hAPP(c_List_Oset(X2),esk469_2(X1,X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))|~class_Orderings_Olinorder(X2)), inference(split_conjunct,[status(thm)],[c_0_5396]), ['final']). 6.97/7.26 cnf(c_0_14383, plain, (X1=hAPP(c_List_Oset(X2),c_List_Olinorder__class_Osorted__list__of__set(X2,X1))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))|~class_Orderings_Olinorder(X2)), inference(split_conjunct,[status(thm)],[c_0_8882]), ['final']). 6.97/7.26 cnf(c_0_14384, 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_8909]), ['final']). 6.97/7.26 cnf(c_0_14385, 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_8588]), ['final']). 6.97/7.26 cnf(c_0_14386, 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_8589]), ['final']). 6.97/7.26 cnf(c_0_14387, 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_8592]), ['final']). 6.97/7.26 cnf(c_0_14388, 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_8593]), ['final']). 6.97/7.26 cnf(c_0_14389, plain, (c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X2,X1)=c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5203]), ['final']). 6.97/7.26 cnf(c_0_14390, plain, (X3=hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8910]), ['final']). 6.97/7.26 cnf(c_0_14391, plain, (hBOOL(hAPP(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),esk55_1(X1))))|~hBOOL(hAPP(X1,X2))), inference(rw,[status(thm)],[c_0_8911, c_0_5002]), ['final']). 6.97/7.26 cnf(c_0_14392, plain, (X2=X1|~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_8912]), ['final']). 6.97/7.26 cnf(c_0_14393, plain, (hBOOL(hAPP(c_Quotient_ORespects(X3,X1),X2))|~hBOOL(hAPP(hAPP(X1,X2),X2))), inference(split_conjunct,[status(thm)],[c_0_8913]), ['final']). 6.97/7.26 cnf(c_0_14394, plain, (hBOOL(hAPP(hAPP(X2,X3),X3))|~hBOOL(hAPP(c_Quotient_ORespects(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8913]), ['final']). 6.97/7.26 cnf(c_0_14395, plain, (hBOOL(hAPP(X1,esk201_1(X1)))|~hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))), inference(split_conjunct,[status(thm)],[c_0_8129]), ['final']). 6.97/7.26 cnf(c_0_14396, 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_8914]), ['final']). 6.97/7.26 cnf(c_0_14397, 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_8915]), ['final']). 6.97/7.26 cnf(c_0_14398, 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)), inference(split_conjunct,[status(thm)],[c_0_8916]), ['final']). 6.97/7.26 cnf(c_0_14399, 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_8917]), ['final']). 6.97/7.26 cnf(c_0_14400, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X2)|~class_Groups_Omonoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_8918]), ['final']). 6.97/7.26 cnf(c_0_14401, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))=X3|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=hAPP(c_Relation_ODomain(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_5832]), ['final']). 6.97/7.26 cnf(c_0_14402, plain, (X3=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X1),tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=hAPP(c_Relation_ORange(X2,X1),X3)), inference(split_conjunct,[status(thm)],[c_0_5833]), ['final']). 6.97/7.26 cnf(c_0_14403, plain, (hBOOL(hAPP(X2,c_Orderings_Oord__class_OLeast(X1,X2)))|~class_Orderings_Owellorder(X1)|~hBOOL(hAPP(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_8919]), ['final']). 6.97/7.26 cnf(c_0_14404, 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_8920]), ['final']). 6.97/7.26 cnf(c_0_14405, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),c_Groups_Ozero__class_Ozero(X1)),X2)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_8921]), ['final']). 6.97/7.26 cnf(c_0_14406, 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_8922]), ['final']). 6.97/7.26 cnf(c_0_14407, plain, (c_Orderings_Obot__class_Obot(X1)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2)|~class_Lattices_Obounded__lattice__bot(X1)), inference(split_conjunct,[status(thm)],[c_0_8923]), ['final']). 6.97/7.26 cnf(c_0_14408, 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)), inference(split_conjunct,[status(thm)],[c_0_8924]), ['final']). 6.97/7.26 cnf(c_0_14409, 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_8827]), ['final']). 6.97/7.26 cnf(c_0_14410, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),X1))|X1!=hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),X3),X1)|~class_Orderings_Olinorder(X2)), inference(split_conjunct,[status(thm)],[c_0_8925]), ['final']). 6.97/7.26 cnf(c_0_14411, 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_6271]), ['final']). 6.97/7.26 cnf(c_0_14412, 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_6271]), ['final']). 6.97/7.26 cnf(c_0_14413, 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)), inference(split_conjunct,[status(thm)],[c_0_8926]), ['final']). 6.97/7.26 cnf(c_0_14414, 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)), inference(split_conjunct,[status(thm)],[c_0_8927]), ['final']). 6.97/7.26 cnf(c_0_14415, 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)), inference(split_conjunct,[status(thm)],[c_0_8928]), ['final']). 6.97/7.26 cnf(c_0_14416, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Odivision__ring__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_8929]), ['final']). 6.97/7.26 cnf(c_0_14417, plain, (c_Orderings_Obot__class_Obot(X1)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Orderings_Obot__class_Obot(X1))|~class_Lattices_Obounded__lattice__bot(X1)), inference(split_conjunct,[status(thm)],[c_0_8930]), ['final']). 6.97/7.26 cnf(c_0_14418, 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_8931]), ['final']). 6.97/7.26 cnf(c_0_14419, 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_8932]), ['final']). 6.97/7.26 cnf(c_0_14420, 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_8881]), ['final']). 6.97/7.26 cnf(c_0_14421, 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_8663]), ['final']). 6.97/7.26 cnf(c_0_14422, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|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))), inference(split_conjunct,[status(thm)],[c_0_5819]), ['final']). 6.97/7.26 cnf(c_0_14423, plain, (X7=hAPP(hAPP(X3,X7),X7)|~c_Finite__Set_Ofolding__image__simple__idem(X1,X2,X3,X4,X5,X6)), inference(split_conjunct,[status(thm)],[c_0_8933]), ['final']). 6.97/7.26 cnf(c_0_14424, 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_8934]), ['final']). 6.97/7.26 cnf(c_0_14425, 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_8935, c_0_4415]), ['final']). 6.97/7.26 cnf(c_0_14426, 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_8936]), ['final']). 6.97/7.26 cnf(c_0_14427, 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_8937]), ['final']). 6.97/7.26 cnf(c_0_14428, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_Nitpick_Onat__gcd(X2,X1)=c_Nitpick_Onat__gcd(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1))), inference(split_conjunct,[status(thm)],[c_0_5873]), ['final']). 6.97/7.26 cnf(c_0_14429, 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_8938]), ['final']). 6.97/7.26 cnf(c_0_14430, 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)), inference(split_conjunct,[status(thm)],[c_0_8847]), ['final']). 6.97/7.26 cnf(c_0_14431, plain, (X1=hAPP(c_Int_ORep__Integ,esk64_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_8939]), ['final']). 6.97/7.26 cnf(c_0_14432, 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_8940]), ['final']). 6.97/7.26 cnf(c_0_14433, plain, (X1=X2|hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X1),X3)!=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X4))), inference(rw,[status(thm)],[c_0_8941, c_0_4471]), ['final']). 6.97/7.26 cnf(c_0_14434, plain, (X2=X4|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_8942]), ['final']). 6.97/7.26 cnf(c_0_14435, 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_8943]), ['final']). 6.97/7.26 cnf(c_0_14436, 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_8944]), ['final']). 6.97/7.26 cnf(c_0_14437, 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_8945]), ['final']). 6.97/7.26 cnf(c_0_14438, plain, (X3=X4|~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_8946]), ['final']). 6.97/7.26 cnf(c_0_14439, plain, (X3=X4|~class_Groups_Ocancel__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_8947]), ['final']). 6.97/7.26 cnf(c_0_14440, plain, (X4=X2|hBOOL(hAPP(X3,X4))|~hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_5847]), ['final']). 6.97/7.26 cnf(c_0_14441, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Groups_Oone__class_Oone(X1)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X2)|~class_Rings_Odivision__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_8948]), ['final']). 6.97/7.26 cnf(c_0_14442, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8949]), ['final']). 6.97/7.26 cnf(c_0_14443, 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_8950]), ['final']). 6.97/7.26 cnf(c_0_14444, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk6_1(X1)),X1))|c_Nat__Transfer_Onat__set(X1)), inference(split_conjunct,[status(thm)],[c_0_8414]), ['final']). 6.97/7.26 cnf(c_0_14445, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_Groups_Oone__class_Oone(tc_Nat_Onat)=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=X1), inference(split_conjunct,[status(thm)],[c_0_8951]), ['final']). 6.97/7.26 cnf(c_0_14446, 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_7524]), ['final']). 6.97/7.26 cnf(c_0_14447, 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_7778]), ['final']). 6.97/7.26 cnf(c_0_14448, 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_7460]), ['final']). 6.97/7.26 cnf(c_0_14449, 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_7460]), ['final']). 6.97/7.26 cnf(c_0_14450, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|X2=hAPP(c_List_Ohd(X3),c_List_Oreplicate(X3,X1,X2))), inference(split_conjunct,[status(thm)],[c_0_8952]), ['final']). 6.97/7.26 cnf(c_0_14451, 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_8953]), ['final']). 6.97/7.26 cnf(c_0_14452, 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_5471]), ['final']). 6.97/7.26 cnf(c_0_14453, 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_7778]), ['final']). 6.97/7.26 cnf(c_0_14454, 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_8659]), ['final']). 6.97/7.26 cnf(c_0_14455, 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_8954]), ['final']). 6.97/7.26 cnf(c_0_14456, 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_8955]), ['final']). 6.97/7.26 cnf(c_0_14457, 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_8956]), ['final']). 6.97/7.26 cnf(c_0_14458, 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_8957]), ['final']). 6.97/7.26 cnf(c_0_14459, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|~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_5817]), ['final']). 6.97/7.26 cnf(c_0_14460, 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)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_8958]), ['final']). 6.97/7.26 cnf(c_0_14461, 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_8959]), ['final']). 6.97/7.26 cnf(c_0_14462, 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_8960]), ['final']). 6.97/7.26 cnf(c_0_14463, 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_8704]), ['final']). 6.97/7.26 cnf(c_0_14464, 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_8961]), ['final']). 6.97/7.26 cnf(c_0_14465, 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_8962]), ['final']). 6.97/7.26 cnf(c_0_14466, 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_8963]), ['final']). 6.97/7.26 cnf(c_0_14467, plain, (c_List_Olinorder__class_Osorted(X1,esk452_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_5212]), ['final']). 6.97/7.26 cnf(c_0_14468, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk2_2(X1,X2)),X2))), inference(split_conjunct,[status(thm)],[c_0_8479]), ['final']). 6.97/7.26 cnf(c_0_14469, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk391_2(X1,X2)),X2))), inference(split_conjunct,[status(thm)],[c_0_8480]), ['final']). 6.97/7.26 cnf(c_0_14470, plain, (hAPP(X1,X2)=hAPP(X1,X3)|~hBOOL(hAPP(hAPP(X1,X2),X3))|~c_Equiv__Relations_Opart__equivp(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_7518]), ['final']). 6.97/7.26 cnf(c_0_14471, plain, (hAPP(X1,X3)=hAPP(X1,X2)|~hBOOL(hAPP(hAPP(X1,X2),X3))|~c_Equiv__Relations_Oequivp(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_8289]), ['final']). 6.97/7.26 cnf(c_0_14472, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8964]), ['final']). 6.97/7.26 cnf(c_0_14473, plain, (X3=X2|X3=c_Groups_Ozero__class_Ozero(X1)|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_8965]), ['final']). 6.97/7.26 cnf(c_0_14474, 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_8966]), ['final']). 6.97/7.26 cnf(c_0_14475, 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_8967, c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_14476, plain, (c_Predicate_Otransp(X1,X2)|~c_Relation_Otrans(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))), inference(rw,[status(thm)],[c_0_8968, c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_14477, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2))|~class_Orderings_Oorder(X1)), inference(er,[status(thm)],[c_0_8969]), ['final']). 6.97/7.26 cnf(c_0_14478, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(c_Groups_Ouminus__class_Ouminus(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)), inference(split_conjunct,[status(thm)],[c_0_8970]), ['final']). 6.97/7.26 cnf(c_0_14479, plain, (c_Predicate_Osymp(X1,X2)|~c_Relation_Osym(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))), inference(rw,[status(thm)],[c_0_8971, c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_14480, 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_8972]), ['final']). 6.97/7.26 cnf(c_0_14481, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|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_8970]), ['final']). 6.97/7.26 cnf(c_0_14482, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk549_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_8625]), ['final']). 6.97/7.26 cnf(c_0_14483, 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_8973]), ['final']). 6.97/7.26 cnf(c_0_14484, 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_8620]), ['final']). 6.97/7.26 cnf(c_0_14485, plain, (X6=hAPP(X4,hAPP(X3,X6))|~c_Typedef_Otype__definition(X1,X2,X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_8974]), ['final']). 6.97/7.26 cnf(c_0_14486, plain, (c_List_Olist__all(X2,X1,X3)|~hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk569_3(X3,X1,X2))))), inference(split_conjunct,[status(thm)],[c_0_8070]), ['final']). 6.97/7.26 cnf(c_0_14487, 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_8975, c_0_5002]), ['final']). 6.97/7.26 cnf(c_0_14488, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=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_4704]), ['final']). 6.97/7.26 cnf(c_0_14489, plain, (X1=c_Int_OMin|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_8976, c_0_4409]), c_0_4410]), c_0_4411]), ['final']). 6.97/7.26 cnf(c_0_14490, 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_8977]), ['final']). 6.97/7.26 cnf(c_0_14491, plain, (hAPP(X1,c_Inductive_Ocomplete__lattice__class_Olfp(X2,X1))=c_Inductive_Ocomplete__lattice__class_Olfp(X2,X1)|~class_Complete__Lattice_Ocomplete__lattice(X2)|~c_Orderings_Oorder__class_Omono(X2,X2,X1)), inference(er,[status(thm)],[c_0_8978]), ['final']). 6.97/7.26 cnf(c_0_14492, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))|~hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk532_3(X3,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_8563]), ['final']). 6.97/7.26 cnf(c_0_14493, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))|~hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk396_3(X3,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_8567]), ['final']). 6.97/7.26 cnf(c_0_14494, plain, (hBOOL(hAPP(X2,esk518_2(X2,X1)))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X2))|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_8979]), ['final']). 6.97/7.26 cnf(c_0_14495, plain, (hBOOL(hAPP(X2,esk234_2(X2,X1)))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X2))|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_8980]), ['final']). 6.97/7.26 cnf(c_0_14496, plain, (hAPP(X1,c_Inductive_Ocomplete__lattice__class_Ogfp(X2,X1))=c_Inductive_Ocomplete__lattice__class_Ogfp(X2,X1)|~class_Complete__Lattice_Ocomplete__lattice(X2)|~c_Orderings_Oorder__class_Omono(X2,X2,X1)), inference(er,[status(thm)],[c_0_8981]), ['final']). 6.97/7.26 cnf(c_0_14497, 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_8982, c_0_8331]), ['final']). 6.97/7.26 cnf(c_0_14498, plain, (hAPP(c_Finite__Set_Ocard(X2),X5)=hAPP(c_Finite__Set_Ocard(X1),X4)|~c_Fun_Obij__betw(X1,X2,X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_8983]), ['final']). 6.97/7.26 cnf(c_0_14499, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X4|~c_Fun_Obij__betw(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_8984]), ['final']). 6.97/7.26 cnf(c_0_14500, 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_8985]), ['final']). 6.97/7.26 cnf(c_0_14501, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=X2|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8986]), ['final']). 6.97/7.26 cnf(c_0_14502, 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_8987]), ['final']). 6.97/7.26 cnf(c_0_14503, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Otop__class_Otop(X1)),X2)=X2|~class_Lattices_Obounded__lattice__top(X1)), inference(split_conjunct,[status(thm)],[c_0_8988]), ['final']). 6.97/7.26 cnf(c_0_14504, plain, (X4=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X4)), inference(split_conjunct,[status(thm)],[c_0_8989]), ['final']). 6.97/7.26 cnf(c_0_14505, 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_8239]), ['final']). 6.97/7.26 cnf(c_0_14506, plain, (X4=hAPP(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))|~c_Finite__Set_Ofolding__image__simple(X1,X2,X3,X4,X5,X6)), inference(split_conjunct,[status(thm)],[c_0_8990]), ['final']). 6.97/7.26 cnf(c_0_14507, 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_8991]), ['final']). 6.97/7.26 cnf(c_0_14508, 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_8992]), ['final']). 6.97/7.26 cnf(c_0_14509, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2)=X2|~class_Lattices_Obounded__lattice__bot(X1)), inference(split_conjunct,[status(thm)],[c_0_8993]), ['final']). 6.97/7.26 cnf(c_0_14510, 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_8994]), ['final']). 6.97/7.26 cnf(c_0_14511, 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_8995]), ['final']). 6.97/7.26 cnf(c_0_14512, 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_8996]), ['final']). 6.97/7.26 cnf(c_0_14513, 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_8997]), ['final']). 6.97/7.26 cnf(c_0_14514, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1))=X2|~class_Groups_Omonoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_8998]), ['final']). 6.97/7.26 cnf(c_0_14515, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1))=X2|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8999]), ['final']). 6.97/7.26 cnf(c_0_14516, 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_9000]), ['final']). 6.97/7.26 cnf(c_0_14517, 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_9001]), ['final']). 6.97/7.26 cnf(c_0_14518, plain, (X2=X3|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_9002]), ['final']). 6.97/7.26 cnf(c_0_14519, 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)],[c_0_9003, c_0_4410]), c_0_4410]), ['final']). 6.97/7.26 cnf(c_0_14520, 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_9004])]), ['final']). 6.97/7.26 cnf(c_0_14521, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))=X2|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_9005]), ['final']). 6.97/7.26 cnf(c_0_14522, plain, (X2=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_9006]), ['final']). 6.97/7.26 cnf(c_0_14523, plain, (X2=hAPP(hAPP(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_9007]), ['final']). 6.97/7.26 cnf(c_0_14524, 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_9008]), ['final']). 6.97/7.26 cnf(c_0_14525, plain, (X3=X1|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_9009]), ['final']). 6.97/7.26 cnf(c_0_14526, 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_9010]), ['final']). 6.97/7.26 cnf(c_0_14527, 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_9011]), ['final']). 6.97/7.26 cnf(c_0_14528, plain, (X2=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Orderings_Otop__class_Otop(X1))|~class_Lattices_Obounded__lattice__top(X1)), inference(split_conjunct,[status(thm)],[c_0_9012]), ['final']). 6.97/7.26 cnf(c_0_14529, plain, (X2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1))|~class_Groups_Ocomm__monoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_9013]), ['final']). 6.97/7.26 cnf(c_0_14530, 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_9014]), ['final']). 6.97/7.26 cnf(c_0_14531, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2))|c_Quickcheck_Obeyond(X1,X2)=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[c_0_9015]), ['final']). 6.97/7.26 cnf(c_0_14532, 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_5277]), ['final']). 6.97/7.26 cnf(c_0_14533, 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_9016]), ['final']). 6.97/7.26 cnf(c_0_14534, 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_9017]), ['final']). 6.97/7.26 cnf(c_0_14535, 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_9018]), ['final']). 6.97/7.26 cnf(c_0_14536, plain, (c_Quotient_OBabs(X1,X3,c_Quotient_ORespects(X1,X2),X4)=X4|~c_Equiv__Relations_Oequivp(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9019]), ['final']). 6.97/7.26 cnf(c_0_14537, 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_8901]), ['final']). 6.97/7.26 cnf(c_0_14538, 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_5340]), ['final']). 6.97/7.26 cnf(c_0_14539, plain, (c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))=X4|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X2,X1,X3),X4)), inference(split_conjunct,[status(thm)],[c_0_5830]), ['final']). 6.97/7.26 cnf(c_0_14540, 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_Rings_Ozero__neq__one(X1)|~class_Rings_Ono__zero__divisors(X1)|~class_Rings_Omult__zero(X1)|~class_Power_Opower(X1)), inference(er,[status(thm)],[c_0_9020]), ['final']). 6.97/7.26 cnf(c_0_14541, 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_9021]), ['final']). 6.97/7.26 cnf(c_0_14542, 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_9022]), ['final']). 6.97/7.26 cnf(c_0_14543, 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_9023]), ['final']). 6.97/7.26 cnf(c_0_14544, 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_9024]), ['final']). 6.97/7.26 cnf(c_0_14545, plain, (c_Equiv__Relations_Ocongruent(X4,X2,X3,X1)|hAPP(X1,esk286_4(X2,X1,X3,X4))!=hAPP(X1,esk285_4(X2,X1,X3,X4))), inference(split_conjunct,[status(thm)],[c_0_6919]), ['final']). 6.97/7.26 cnf(c_0_14546, 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_9025]), ['final']). 6.97/7.26 cnf(c_0_14547, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|c_List_Olist_ONil(X1)=X3|c_List_Olist_ONil(X1)!=hAPP(hAPP(c_List_Otake(X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_9026]), ['final']). 6.97/7.26 cnf(c_0_14548, 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_9027]), ['final']). 6.97/7.26 cnf(c_0_14549, plain, (hBOOL(hAPP(X1,esk528_3(X2,X1,X3)))|~c_List_Olist__ex1(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7252]), ['final']). 6.97/7.26 cnf(c_0_14550, plain, (hBOOL(hAPP(X1,esk335_3(X1,X2,X3)))|~c_List_Olist__ex(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8323]), ['final']). 6.97/7.26 cnf(c_0_14551, plain, (hBOOL(hAPP(X1,esk241_3(X2,X1,X3)))|~c_List_Olist__ex1(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7253]), ['final']). 6.97/7.26 cnf(c_0_14552, plain, (hBOOL(hAPP(X1,esk181_3(X2,X1,X3)))|~c_List_Olist__ex(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8324]), ['final']). 6.97/7.26 cnf(c_0_14553, plain, (hBOOL(hAPP(X1,esk66_3(X2,X1,X3)))|~c_List_Olist__ex(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8325]), ['final']). 6.97/7.26 cnf(c_0_14554, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|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_9028]), ['final']). 6.97/7.26 cnf(c_0_14555, 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_9029]), ['final']). 6.97/7.26 cnf(c_0_14556, 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_9030]), ['final']). 6.97/7.26 cnf(c_0_14557, plain, (hBOOL(hAPP(hAPP(c_member(X3),X2),X1))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_9031]), ['final']). 6.97/7.26 cnf(c_0_14558, plain, (hBOOL(hAPP(X1,esk587_2(X1,X2)))|~hBOOL(hAPP(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_5389]), ['final']). 6.97/7.26 cnf(c_0_14559, plain, (X1=X2|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))), inference(split_conjunct,[status(thm)],[c_0_5874]), ['final']). 6.97/7.26 cnf(c_0_14560, plain, (hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_9032]), ['final']). 6.97/7.26 cnf(c_0_14561, plain, (hBOOL(hAPP(X1,esk489_2(X2,X1)))|~hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_9033]), ['final']). 6.97/7.26 cnf(c_0_14562, 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_9034]), ['final']). 6.97/7.26 cnf(c_0_14563, 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_9035, c_0_4742]), ['final']). 6.97/7.26 cnf(c_0_14564, 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_9036]), ['final']). 6.97/7.26 cnf(c_0_14565, 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_8525]), ['final']). 6.97/7.26 cnf(c_0_14566, 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_9037]), ['final']). 6.97/7.26 cnf(c_0_14567, 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_9038]), ['final']). 6.97/7.26 cnf(c_0_14568, 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_9039]), ['final']). 6.97/7.26 cnf(c_0_14569, 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_9040]), ['final']). 6.97/7.26 cnf(c_0_14570, 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_8980]), ['final']). 6.97/7.26 cnf(c_0_14571, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X2=X3|c_List_Oreplicate(X4,X1,X2)!=c_List_Oreplicate(X4,X5,X3)), inference(split_conjunct,[status(thm)],[c_0_9041]), ['final']). 6.97/7.26 cnf(c_0_14572, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~c_Fun_Obij__betw(X1,X3,X5,X2,X4)), inference(split_conjunct,[status(thm)],[c_0_9042]), ['final']). 6.97/7.26 cnf(c_0_14573, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~c_Fun_Obij__betw(X3,X1,X5,X4,X2)), inference(split_conjunct,[status(thm)],[c_0_9042]), ['final']). 6.97/7.26 cnf(c_0_14574, 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_9043]), ['final']). 6.97/7.26 cnf(c_0_14575, 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_9044]), ['final']). 6.97/7.26 cnf(c_0_14576, 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_9045]), ['final']). 6.97/7.26 cnf(c_0_14577, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X2=c_List_Olast(X3,c_List_Oreplicate(X3,X1,X2))), inference(split_conjunct,[status(thm)],[c_0_9046]), ['final']). 6.97/7.26 cnf(c_0_14578, plain, (c_List_Oall__interval__nat(X1,X2,X3)|~c_List_Olist__all(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)))), inference(rw,[status(thm)],[c_0_9047, c_0_4471]), ['final']). 6.97/7.26 cnf(c_0_14579, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),esk18_1(X1))))), inference(rw,[status(thm)],[c_0_9048, c_0_5002]), ['final']). 6.97/7.26 cnf(c_0_14580, plain, (c_HOL_OThe(X2,X3)=c_FunDef_OTHE__default(X2,X1,X3)|esk365_4(X1,X2,X3,X4)!=X4|~hBOOL(hAPP(X3,X4))), inference(split_conjunct,[status(thm)],[c_0_8455]), ['final']). 6.97/7.26 cnf(c_0_14581, 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_9049]), ['final']). 6.97/7.26 cnf(c_0_14582, plain, (X2=c_Inductive_Ocomplete__lattice__class_Olfp(X1,hAPP(c_COMBK(X1,X1),X2))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9050]), ['final']). 6.97/7.26 cnf(c_0_14583, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2))|~class_Orderings_Opreorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9051]), ['final']). 6.97/7.26 cnf(c_0_14584, 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_9052]), ['final']). 6.97/7.26 cnf(c_0_14585, 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_9053]), ['final']). 6.97/7.26 cnf(c_0_14586, plain, (X1=X2|hAPP(hAPP(c_List_Olist_OCons(X3),X4),X1)!=hAPP(hAPP(c_List_Olist_OCons(X3),X5),X2)), inference(split_conjunct,[status(thm)],[c_0_9049]), ['final']). 6.97/7.26 cnf(c_0_14587, 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_9054]), ['final']). 6.97/7.26 cnf(c_0_14588, plain, (X3=X4|hAPP(hAPP(c_List_Oappend(X1),X2),X3)!=hAPP(hAPP(c_List_Oappend(X1),X2),X4)), inference(split_conjunct,[status(thm)],[c_0_9055]), ['final']). 6.97/7.26 cnf(c_0_14589, 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_6329]), ['final']). 6.97/7.26 cnf(c_0_14590, plain, (c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))|~c_Wellfounded_Oacyclic(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9056]), ['final']). 6.97/7.26 cnf(c_0_14591, 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_9057, c_0_4413]), ['final']). 6.97/7.26 cnf(c_0_14592, 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_9058, c_0_5002]), ['final']). 6.97/7.26 cnf(c_0_14593, plain, (c_Relation_Oantisym(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))|~c_Relation_Oantisym(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9059]), ['final']). 6.97/7.26 cnf(c_0_14594, plain, (c_Relation_Otrans(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))|~c_Relation_Otrans(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9060]), ['final']). 6.97/7.26 cnf(c_0_14595, plain, (c_Relation_Osym(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))|~c_Relation_Osym(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9061]), ['final']). 6.97/7.26 cnf(c_0_14596, 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_9062]), ['final']). 6.97/7.26 cnf(c_0_14597, 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_9063, c_0_5002]), ['final']). 6.97/7.26 cnf(c_0_14598, plain, (X2=X3|hAPP(X1,X2)!=hAPP(X1,X3)|~c_Orderings_Oorder__class_Ostrict__mono(X4,X5,X1)|~class_Orderings_Olinorder(X4)|~class_Orderings_Oorder(X5)), inference(split_conjunct,[status(thm)],[c_0_9064]), ['final']). 6.97/7.26 cnf(c_0_14599, 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_9065]), ['final']). 6.97/7.26 cnf(c_0_14600, plain, (X1=hAPP(c_Nat_OSuc,esk483_1(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_9066]), ['final']). 6.97/7.26 cnf(c_0_14601, plain, (c_Power_Opower__class_Opower(X1)=c_Power_Opower_Opower(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Otimes__class_Otimes(X1))|~class_Power_Opower(X1)), inference(split_conjunct,[status(thm)],[c_0_9067]), ['final']). 6.97/7.26 cnf(c_0_14602, 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_9068]), ['final']). 6.97/7.26 cnf(c_0_14603, 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)), inference(split_conjunct,[status(thm)],[c_0_9069]), ['final']). 6.97/7.26 cnf(c_0_14604, 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_8874]), ['final']). 6.97/7.26 cnf(c_0_14605, 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_8875]), ['final']). 6.97/7.26 cnf(c_0_14606, 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_9070]), ['final']). 6.97/7.26 cnf(c_0_14607, plain, (c_List_Olist_ONil(X1)=c_List_Olinorder__class_Osorted__list__of__set(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9071]), ['final']). 6.97/7.26 cnf(c_0_14608, 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_9072, c_0_5963]), ['final']). 6.97/7.26 cnf(c_0_14609, plain, (hAPP(hAPP(X2,X4),X4)=X4|~c_Finite__Set_Ofolding__one__idem(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_9073]), ['final']). 6.97/7.26 cnf(c_0_14610, 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_9074]), ['final']). 6.97/7.26 cnf(c_0_14611, 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_9075]), ['final']). 6.97/7.26 cnf(c_0_14612, 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_5259]), ['final']). 6.97/7.26 cnf(c_0_14613, plain, (c_Lazy__Sequence_Oempty(tc_Int_Oint)=c_Lazy__Sequence_Osmall__lazy_H(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5215]), ['final']). 6.97/7.26 cnf(c_0_14614, plain, (c_Orderings_Otop__class_Otop(X1)=X2|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)!=c_Orderings_Otop__class_Otop(X1)|~class_Lattices_Obounded__lattice__top(X1)), inference(split_conjunct,[status(thm)],[c_0_9076]), ['final']). 6.97/7.26 cnf(c_0_14615, 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_9076]), ['final']). 6.97/7.26 cnf(c_0_14616, 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_9077]), ['final']). 6.97/7.26 cnf(c_0_14617, 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_9078]), ['final']). 6.97/7.26 cnf(c_0_14618, 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_8488]), ['final']). 6.97/7.26 cnf(c_0_14619, plain, (c_Fun_Oinj__on(X2,X1,X3,X4)|~class_Orderings_Oorder(X1)|~class_Orderings_Olinorder(X2)|~c_Orderings_Oorder__class_Ostrict__mono(X2,X1,X3)), inference(split_conjunct,[status(thm)],[c_0_9079]), ['final']). 6.97/7.26 cnf(c_0_14620, plain, (X5=X4|~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_9080]), ['final']). 6.97/7.26 cnf(c_0_14621, 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_9081]), ['final']). 6.97/7.26 cnf(c_0_14622, plain, (c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_member(X1),esk294_2(X2,X1)),c_Wellfounded_Oacc(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_9082]), ['final']). 6.97/7.26 cnf(c_0_14623, plain, (X2=X3|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_9083]), ['final']). 6.97/7.26 cnf(c_0_14624, plain, (~c_List_Olist__ex(tc_Int_Oint,X1,c_List_Oupto(X2,X3))|~c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),X1),X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8425]), ['final']). 6.97/7.26 cnf(c_0_14625, plain, (hBOOL(hAPP(c_Predicate_OPowp(X3,X1),X2))|~hBOOL(hAPP(X1,esk134_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_8429]), ['final']). 6.97/7.26 cnf(c_0_14626, plain, (hBOOL(hAPP(c_List_Olistsp(X3,X1),X2))|~hBOOL(hAPP(X1,esk259_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_8012]), ['final']). 6.97/7.26 cnf(c_0_14627, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))|~c_Wellfounded_OwfP(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9084]), ['final']). 6.97/7.26 cnf(c_0_14628, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|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_9085]), ['final']). 6.97/7.26 cnf(c_0_14629, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X2)=X2|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9086]), ['final']). 6.97/7.26 cnf(c_0_14630, plain, (hBOOL(hAPP(hAPP(X2,X3),X3))|~c_Predicate_Oreflp(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9087]), ['final']). 6.97/7.26 cnf(c_0_14631, plain, (hBOOL(hAPP(hAPP(X2,X3),X3))|~c_Equiv__Relations_Oequivp(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9088]), ['final']). 6.97/7.26 cnf(c_0_14632, 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_8786]), ['final']). 6.97/7.26 cnf(c_0_14633, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X2)=X2|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9089]), ['final']). 6.97/7.26 cnf(c_0_14634, 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_9090]), ['final']). 6.97/7.26 cnf(c_0_14635, 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_9091]), ['final']). 6.97/7.26 cnf(c_0_14636, plain, (hAPP(c_Set_Oimage(X1,X2,X3),X4)=X5|~c_Fun_Obij__betw(X1,X2,X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_5440]), ['final']). 6.97/7.26 cnf(c_0_14637, plain, (hAPP(c_List_Ofilter(X3,X1),X2)=X2|~hBOOL(hAPP(X1,esk578_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_8077]), ['final']). 6.97/7.26 cnf(c_0_14638, 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_9092]), ['final']). 6.97/7.26 cnf(c_0_14639, 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_9093]), ['final']). 6.97/7.26 cnf(c_0_14640, 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_9094]), ['final']). 6.97/7.26 cnf(c_0_14641, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(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_8461]), ['final']). 6.97/7.26 cnf(c_0_14642, plain, (c_Equiv__Relations_Opart__equivp(X3,X1)|~hBOOL(hAPP(hAPP(X1,X2),X2))|~c_Predicate_Osymp(X3,X1)|~c_Predicate_Otransp(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_9095]), ['final']). 6.97/7.26 cnf(c_0_14643, 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_9096]), ['final']). 6.97/7.26 cnf(c_0_14644, 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_9097]), ['final']). 6.97/7.26 cnf(c_0_14645, plain, (c_List_Olinorder__class_Osorted(X1,esk469_2(X2,X1))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5396]), ['final']). 6.97/7.26 cnf(c_0_14646, 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_8882]), ['final']). 6.97/7.26 cnf(c_0_14647, 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_9098]), ['final']). 6.97/7.26 cnf(c_0_14648, 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_9099]), ['final']). 6.97/7.26 cnf(c_0_14649, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X2),X1))|~hBOOL(hAPP(X1,esk538_2(X1,X2)))|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_9100]), ['final']). 6.97/7.26 cnf(c_0_14650, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X2),X1))|~hBOOL(hAPP(X1,esk54_2(X1,X2)))|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_9092]), ['final']). 6.97/7.26 cnf(c_0_14651, 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_7205]), ['final']). 6.97/7.26 cnf(c_0_14652, 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)))), inference(split_conjunct,[status(thm)],[c_0_9101]), ['final']). 6.97/7.26 cnf(c_0_14653, 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_8690]), ['final']). 6.97/7.26 cnf(c_0_14654, 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_9102]), ['final']). 6.97/7.26 cnf(c_0_14655, 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_5441]), ['final']). 6.97/7.26 cnf(c_0_14656, plain, (c_Groups_Osgn__class_Osgn(X1,X2)=c_Groups_Osgn__class_Osgn(X1,c_Groups_Osgn__class_Osgn(X1,X2))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_9103]), ['final']). 6.97/7.26 cnf(c_0_14657, plain, (hBOOL(hAPP(hAPP(c_fconj,X1),X2))|~hBOOL(X1)|~hBOOL(X2)), inference(split_conjunct,[status(thm)],[c_0_9104]), ['final']). 6.97/7.26 cnf(c_0_14658, plain, (c_List_Olist__all(tc_Int_Oint,X1,c_List_Oupto(X2,X3))|~c_List_Oall__interval__int(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_9105]), ['final']). 6.97/7.26 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_9102]), ['final']). 6.97/7.26 cnf(c_0_14660, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|~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_9106]), ['final']). 6.97/7.26 cnf(c_0_14661, 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_8108]), ['final']). 6.97/7.26 cnf(c_0_14662, 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_9107]), ['final']). 6.97/7.26 cnf(c_0_14663, 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)), inference(split_conjunct,[status(thm)],[c_0_9108]), ['final']). 6.97/7.26 cnf(c_0_14664, 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)), inference(split_conjunct,[status(thm)],[c_0_9109]), ['final']). 6.97/7.26 cnf(c_0_14665, plain, (hAPP(c_Relation_Oconverse(X1,X1),X2)=X2|~c_Relation_Osym(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9110]), ['final']). 6.97/7.26 cnf(c_0_14666, 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_4842]), ['final']). 6.97/7.26 cnf(c_0_14667, 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_9111]), ['final']). 6.97/7.26 cnf(c_0_14668, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(c_Int_OAbs__Integ,esk591_2(X2,X1))))), inference(split_conjunct,[status(thm)],[c_0_8214]), ['final']). 6.97/7.26 cnf(c_0_14669, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),esk488_2(X2,X1))))), inference(rw,[status(thm)],[c_0_9112, c_0_5202]), ['final']). 6.97/7.26 cnf(c_0_14670, plain, (c_Wellfounded_Owf(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_9113]), ['final']). 6.97/7.26 cnf(c_0_14671, 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_9114]), ['final']). 6.97/7.26 cnf(c_0_14672, 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_9115]), ['final']). 6.97/7.26 cnf(c_0_14673, 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_8707]), ['final']). 6.97/7.26 cnf(c_0_14674, 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_8707]), ['final']). 6.97/7.26 cnf(c_0_14675, 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_8690]), ['final']). 6.97/7.26 cnf(c_0_14676, plain, (c_Groups_Ozero__class_Ozero(X1)=X3|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_5444]), ['final']). 6.97/7.26 cnf(c_0_14677, 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_9116]), ['final']). 6.97/7.26 cnf(c_0_14678, 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_9077]), ['final']). 6.97/7.26 cnf(c_0_14679, 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)), inference(split_conjunct,[status(thm)],[c_0_9117]), ['final']). 6.97/7.26 cnf(c_0_14680, plain, (X2=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9118]), ['final']). 6.97/7.26 cnf(c_0_14681, 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_9119]), ['final']). 6.97/7.26 cnf(c_0_14682, 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_9120]), ['final']). 6.97/7.26 cnf(c_0_14683, plain, (X2=X3|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_9121]), ['final']). 6.97/7.26 cnf(c_0_14684, 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_8768]), ['final']). 6.97/7.26 cnf(c_0_14685, plain, (X2=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9122]), ['final']). 6.97/7.26 cnf(c_0_14686, 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_9123]), ['final']). 6.97/7.26 cnf(c_0_14687, plain, (~class_Orderings_Owellorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Orderings_Oord__class_OLeast(X1,X3)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_9124]), ['final']). 6.97/7.26 cnf(c_0_14688, plain, (c_List_Oupto(X2,X1)=c_List_Olist_ONil(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9125]), ['final']). 6.97/7.26 cnf(c_0_14689, 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_7205]), ['final']). 6.97/7.26 cnf(c_0_14690, 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_8610]), ['final']). 6.97/7.26 cnf(c_0_14691, plain, (X2=X1|hAPP(X1,esk253_2(X2,X1))!=hAPP(X2,esk253_2(X2,X1))), inference(split_conjunct,[status(thm)],[c_0_9126]), ['final']). 6.97/7.26 cnf(c_0_14692, plain, (c_Fun_Oinj__on(X4,X3,X2,X1)|esk143_4(X1,X2,X3,X4)!=esk144_4(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8312]), ['final']). 6.97/7.26 cnf(c_0_14693, 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_9127]), ['final']). 6.97/7.26 cnf(c_0_14694, plain, (hBOOL(X1)|hBOOL(hAPP(hAPP(c_fimplies,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9128]), ['final']). 6.97/7.26 cnf(c_0_14695, plain, (c_Relation_Otrans(tc_List_Olist(X1),c_List_Olistrel(X1,X2))|~c_Relation_Otrans(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9129]), ['final']). 6.97/7.26 cnf(c_0_14696, plain, (c_Relation_Otrans(tc_List_Olist(X1),c_List_Olexord(X1,X2))|~c_Relation_Otrans(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9130]), ['final']). 6.97/7.26 cnf(c_0_14697, 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_7182]), ['final']). 6.97/7.26 cnf(c_0_14698, 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_7182]), ['final']). 6.97/7.26 cnf(c_0_14699, 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_7491]), ['final']). 6.97/7.26 cnf(c_0_14700, 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)), inference(split_conjunct,[status(thm)],[c_0_9131]), ['final']). 6.97/7.26 cnf(c_0_14701, plain, (c_Relation_Osym(tc_List_Olist(X1),c_List_Olistrel(X1,X2))|~c_Relation_Osym(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9132]), ['final']). 6.97/7.26 cnf(c_0_14702, 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_9133]), ['final']). 6.97/7.26 cnf(c_0_14703, 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_9134]), ['final']). 6.97/7.26 cnf(c_0_14704, 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)),esk6_1(X1)))), inference(split_conjunct,[status(thm)],[c_0_8414]), ['final']). 6.97/7.26 cnf(c_0_14705, plain, (c_Equiv__Relations_Oequiv(X1,X3,X2)|~c_Relation_Osym(X1,X2)|~c_Relation_Otrans(X1,X2)|~c_Relation_Orefl__on(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_9135]), ['final']). 6.97/7.26 cnf(c_0_14706, plain, (c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X2))|~c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9136]), ['final']). 6.97/7.26 cnf(c_0_14707, plain, (c_Wellfounded_Owf(X1,c_Wellfounded_Omlex__prod(X1,X3,X2))|~c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9137]), ['final']). 6.97/7.26 cnf(c_0_14708, 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)), inference(split_conjunct,[status(thm)],[c_0_9138]), ['final']). 6.97/7.26 cnf(c_0_14709, 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_9139]), ['final']). 6.97/7.26 cnf(c_0_14710, 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_9140]), ['final']). 6.97/7.26 cnf(c_0_14711, 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_9141]), ['final']). 6.97/7.26 cnf(c_0_14712, plain, (X1=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_9142]), ['final']). 6.97/7.26 cnf(c_0_14713, 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_9143]), ['final']). 6.97/7.26 cnf(c_0_14714, 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_9144]), ['final']). 6.97/7.26 cnf(c_0_14715, plain, (c_List_OtakeWhile(X3,X1,X2)=X2|~hBOOL(hAPP(X1,esk405_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_8163]), ['final']). 6.97/7.26 cnf(c_0_14716, plain, (c_List_Olist_ONil(X1)=X2|hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4)!=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_9145]), ['final']). 6.97/7.26 cnf(c_0_14717, 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_9146]), ['final']). 6.97/7.26 cnf(c_0_14718, plain, (X4=c_List_Olist_ONil(X1)|hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)!=c_List_Olist_ONil(X2)), inference(split_conjunct,[status(thm)],[c_0_9147]), ['final']). 6.97/7.26 cnf(c_0_14719, 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_9148]), ['final']). 6.97/7.26 cnf(c_0_14720, plain, (X3=X2|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_9149]), ['final']). 6.97/7.26 cnf(c_0_14721, 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_9150]), ['final']). 6.97/7.26 cnf(c_0_14722, 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_9151]), ['final']). 6.97/7.26 cnf(c_0_14723, 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_9152]), ['final']). 6.97/7.26 cnf(c_0_14724, 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_9153]), ['final']). 6.97/7.26 cnf(c_0_14725, 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_8664]), ['final']). 6.97/7.26 cnf(c_0_14726, 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_9154]), ['final']). 6.97/7.26 cnf(c_0_14727, plain, (X3=X2|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X3)))), inference(split_conjunct,[status(thm)],[c_0_5848]), ['final']). 6.97/7.26 cnf(c_0_14728, plain, (hBOOL(hAPP(X3,X2))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9031]), ['final']). 6.97/7.26 cnf(c_0_14729, plain, (X2=X3|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_9155]), ['final']). 6.97/7.26 cnf(c_0_14730, plain, (X2=X3|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_5443]), ['final']). 6.97/7.26 cnf(c_0_14731, 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_9156]), ['final']). 6.97/7.26 cnf(c_0_14732, plain, (hBOOL(hAPP(hAPP(c_fimplies,X1),X2))|~hBOOL(X2)), inference(split_conjunct,[status(thm)],[c_0_9157]), ['final']). 6.97/7.26 cnf(c_0_14733, plain, (hBOOL(hAPP(hAPP(c_fdisj,X1),X2))|~hBOOL(X1)), inference(split_conjunct,[status(thm)],[c_0_9158]), ['final']). 6.97/7.26 cnf(c_0_14734, plain, (hBOOL(hAPP(hAPP(c_fdisj,X2),X1))|~hBOOL(X1)), inference(split_conjunct,[status(thm)],[c_0_9159]), ['final']). 6.97/7.26 cnf(c_0_14735, 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_9160, c_0_4413]), ['final']). 6.97/7.26 cnf(c_0_14736, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~c_Partial__Function_Omk__less(X4,X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8773]), ['final']). 6.97/7.26 cnf(c_0_14737, 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_8937]), ['final']). 6.97/7.26 cnf(c_0_14738, 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_8940]), ['final']). 6.97/7.26 cnf(c_0_14739, plain, (X1=X2|c_Nitpick_Opair__box_OPairBox(X3,X4,X2,X5)!=c_Nitpick_Opair__box_OPairBox(X3,X4,X1,X6)), inference(split_conjunct,[status(thm)],[c_0_9161]), ['final']). 6.97/7.26 cnf(c_0_14740, plain, (X1=X2|c_Nitpick_Opair__box_OPairBox(X3,X4,X5,X2)!=c_Nitpick_Opair__box_OPairBox(X3,X4,X6,X1)), inference(split_conjunct,[status(thm)],[c_0_9161]), ['final']). 6.97/7.26 cnf(c_0_14741, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|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_9162]), ['final']). 6.97/7.26 cnf(c_0_14742, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Groups_Ozero__class_Ozero(X1)!=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_9163]), ['final']). 6.97/7.26 cnf(c_0_14743, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Groups_Ozero__class_Ozero(X1)!=hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)|~class_Int_Oring__char__0(X1)), inference(split_conjunct,[status(thm)],[c_0_5457]), ['final']). 6.97/7.26 cnf(c_0_14744, 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_9164]), ['final']). 6.97/7.26 cnf(c_0_14745, plain, (X5=hAPP(X1,X4)|X1!=c_Fun_Ofun__upd(X2,X3,X1,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_5857]), ['final']). 6.97/7.26 cnf(c_0_14746, plain, (c_Wellfounded_OwfP(X1,X2)|~hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk407_2(X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_9165]), ['final']). 6.97/7.26 cnf(c_0_14747, plain, (c_List_Oall__interval__nat(X1,X3,X2)|~hBOOL(hAPP(X1,esk239_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_8068]), ['final']). 6.97/7.26 cnf(c_0_14748, 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_9166]), ['final']). 6.97/7.26 cnf(c_0_14749, plain, (X1=c_List_Olist_ONil(X2)|c_List_Olist_ONil(X2)!=hAPP(hAPP(c_List_Oappend(X2),X1),X3)), inference(split_conjunct,[status(thm)],[c_0_9167]), ['final']). 6.97/7.26 cnf(c_0_14750, 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_9168]), ['final']). 6.97/7.26 cnf(c_0_14751, plain, (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),X2),X1)), inference(split_conjunct,[status(thm)],[c_0_9169]), ['final']). 6.97/7.26 cnf(c_0_14752, plain, (c_List_Olist__all(X3,X1,X2)|~hBOOL(hAPP(X1,esk513_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_8215]), ['final']). 6.97/7.26 cnf(c_0_14753, plain, (c_List_Olist__all(X3,X1,X2)|~hBOOL(hAPP(X1,esk461_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_8218]), ['final']). 6.97/7.26 cnf(c_0_14754, plain, (c_List_Olist__all(X3,X1,X2)|~hBOOL(hAPP(X1,esk423_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_8219]), ['final']). 6.97/7.26 cnf(c_0_14755, plain, (c_List_Oall__interval__int(X1,X3,X2)|~hBOOL(hAPP(X1,esk352_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_8213]), ['final']). 6.97/7.26 cnf(c_0_14756, plain, (X1=c_Groups_Ozero__class_Ozero(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_9169]), ['final']). 6.97/7.26 cnf(c_0_14757, plain, (X2=c_Quickcheck_Obeyond(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9015]), ['final']). 6.97/7.26 cnf(c_0_14758, plain, (hBOOL(X2)|hBOOL(X1)|~hBOOL(hAPP(hAPP(c_fdisj,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9170]), ['final']). 6.97/7.26 cnf(c_0_14759, 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_9171]), ['final']). 6.97/7.26 cnf(c_0_14760, 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_9172]), ['final']). 6.97/7.26 cnf(c_0_14761, 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_9173]), ['final']). 6.97/7.26 cnf(c_0_14762, 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_9029]), ['final']). 6.97/7.26 cnf(c_0_14763, 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_9030]), ['final']). 6.97/7.26 cnf(c_0_14764, plain, (hBOOL(hAPP(c_List_Odistinct(X2),X1))|esk492_2(X1,X2)!=esk491_2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8120]), ['final']). 6.97/7.26 cnf(c_0_14765, plain, (c_Divides_Odiv__class_Omod(X1,X2,X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_9174]), ['final']). 6.97/7.26 cnf(c_0_14766, plain, (X2=X3|hAPP(c_List_Orev(X1),X2)!=hAPP(c_List_Orev(X1),X3)), inference(split_conjunct,[status(thm)],[c_0_9175]), ['final']). 6.97/7.26 cnf(c_0_14767, plain, (c_Relation_Osym(X1,X2)|hAPP(c_Relation_Oconverse(X1,X1),X2)!=X2), inference(split_conjunct,[status(thm)],[c_0_9110]), ['final']). 6.97/7.26 cnf(c_0_14768, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~c_Wellfounded_Omax__extp(X1,X3,X2,X4)), inference(split_conjunct,[status(thm)],[c_0_5472]), ['final']). 6.97/7.26 cnf(c_0_14769, 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_9176]), ['final']). 6.97/7.26 cnf(c_0_14770, 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_9177]), ['final']). 6.97/7.26 cnf(c_0_14771, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~c_Wellfounded_Omax__extp(X1,X3,X4,X2)), inference(split_conjunct,[status(thm)],[c_0_5472]), ['final']). 6.97/7.26 cnf(c_0_14772, plain, (c_Fun_Oinj__on(X1,X2,X3,X4)|~c_Fun_Obij__betw(X1,X2,X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_5440]), ['final']). 6.97/7.26 cnf(c_0_14773, 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_9178]), ['final']). 6.97/7.26 cnf(c_0_14774, plain, (c_Orderings_Oorder__class_Omono(X2,X1,X3)|~class_Orderings_Oorder(X1)|~class_Orderings_Oorder(X2)|~c_Orderings_Oorder__class_Ostrict__mono(X2,X1,X3)), inference(split_conjunct,[status(thm)],[c_0_9179]), ['final']). 6.97/7.26 cnf(c_0_14775, plain, (c_List_Olist_ONil(X2)=X4|~c_List_Olist__all2(X1,X2,X3,c_List_Olist_ONil(X1),X4)), inference(split_conjunct,[status(thm)],[c_0_9180]), ['final']). 6.97/7.26 cnf(c_0_14776, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)!=X2|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_5459]), ['final']). 6.97/7.26 cnf(c_0_14777, plain, (c_List_Olist_ONil(X2)=X3|X1!=hAPP(hAPP(c_List_Oappend(X2),X1),X3)), inference(split_conjunct,[status(thm)],[c_0_9181]), ['final']). 6.97/7.26 cnf(c_0_14778, plain, (c_List_Olist_ONil(X1)=X4|~c_List_Olist__all2(X1,X2,X3,X4,c_List_Olist_ONil(X2))), inference(split_conjunct,[status(thm)],[c_0_5859]), ['final']). 6.97/7.26 cnf(c_0_14779, plain, (c_Relation_Ototal__on(X3,X2,X1)|esk92_3(X1,X2,X3)!=esk91_3(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_6223]), ['final']). 6.97/7.26 cnf(c_0_14780, plain, (X3=c_List_Olist_ONil(X2)|X1!=hAPP(hAPP(c_List_Oappend(X2),X3),X1)), inference(split_conjunct,[status(thm)],[c_0_9182]), ['final']). 6.97/7.26 cnf(c_0_14781, plain, (X2=c_List_Olist_ONil(X1)|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=hAPP(c_List_Oset(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_9183]), ['final']). 6.97/7.26 cnf(c_0_14782, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X1!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_9184]), ['final']). 6.97/7.26 cnf(c_0_14783, plain, (c_Relation_Osingle__valued(X3,X2,X1)|esk520_3(X1,X2,X3)!=esk521_3(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_7170]), ['final']). 6.97/7.26 cnf(c_0_14784, plain, (c_List_Oall__interval__int(X1,X2,X3)|~c_List_Olist__all(tc_Int_Oint,X1,c_List_Oupto(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_9105]), ['final']). 6.97/7.26 cnf(c_0_14785, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Finite__Set_Ofinite(X1)), inference(split_conjunct,[status(thm)],[c_0_9185]), ['final']). 6.97/7.26 cnf(c_0_14786, plain, (c_Relation_Oantisym(X1,c_Transitive__Closure_Ortrancl(X1,X2))|~c_Wellfounded_Oacyclic(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9186]), ['final']). 6.97/7.26 cnf(c_0_14787, plain, (X1=X2|c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X1,X4)!=c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X2,X5)), inference(split_conjunct,[status(thm)],[c_0_9187]), ['final']). 6.97/7.26 cnf(c_0_14788, 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_9187]), ['final']). 6.97/7.26 cnf(c_0_14789, plain, (X1=X2|c_List_Oreplicate(X3,X1,X4)!=c_List_Oreplicate(X3,X2,X5)), inference(split_conjunct,[status(thm)],[c_0_9041]), ['final']). 6.97/7.26 cnf(c_0_14790, plain, (c_Relation_Osym(X1,c_Transitive__Closure_Ortrancl(X1,X2))|~c_Relation_Osym(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9188]), ['final']). 6.97/7.26 cnf(c_0_14791, plain, (c_List_Olist_ONil(X1)=X2|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_9189]), ['final']). 6.97/7.26 cnf(c_0_14792, 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_9190]), ['final']). 6.97/7.26 cnf(c_0_14793, plain, (c_List_Olist_ONil(tc_List_Olist(X1))=c_List_Otranspose(X1,X2)|c_List_Olist_ONil(X1)!=esk402_2(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_7993]), ['final']). 6.97/7.26 cnf(c_0_14794, plain, (c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Osgn__if(X1)), inference(split_conjunct,[status(thm)],[c_0_9191]), ['final']). 6.97/7.26 cnf(c_0_14795, 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_9192]), ['final']). 6.97/7.26 cnf(c_0_14796, 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_9193]), ['final']). 6.97/7.26 cnf(c_0_14797, 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_9194]), ['final']). 6.97/7.26 cnf(c_0_14798, plain, (~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2))), inference(er,[status(thm)],[c_0_9195]), ['final']). 6.97/7.26 cnf(c_0_14799, plain, (c_Orderings_Oord__class_Omax(X1)=c_Orderings_Oord_Omax(X1,c_Orderings_Oord__class_Oless__eq(X1))|~class_Orderings_Oord(X1)), inference(split_conjunct,[status(thm)],[c_0_9196]), ['final']). 6.97/7.26 cnf(c_0_14800, 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_9197]), ['final']). 6.97/7.26 cnf(c_0_14801, 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_9198]), ['final']). 6.97/7.26 cnf(c_0_14802, 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_9199]), ['final']). 6.97/7.26 cnf(c_0_14803, 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_9200]), ['final']). 6.97/7.26 cnf(c_0_14804, plain, (~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2))), inference(er,[status(thm)],[c_0_9201]), ['final']). 6.97/7.26 cnf(c_0_14805, 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_9202]), ['final']). 6.97/7.26 cnf(c_0_14806, plain, (X2=c_List_Oremdups(X1,X2)|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9203]), ['final']). 6.97/7.26 cnf(c_0_14807, plain, (class_Lazy__Sequence_Osmall__lazy(tc_prod(X1,X2))|~class_Lazy__Sequence_Osmall__lazy(X1)|~class_Lazy__Sequence_Osmall__lazy(X2)), inference(split_conjunct,[status(thm)],[c_0_9204]), ['final']). 6.97/7.26 cnf(c_0_14808, 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_9205]), ['final']). 6.97/7.26 cnf(c_0_14809, 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_9206]), ['final']). 6.97/7.26 cnf(c_0_14810, 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_9207]), ['final']). 6.97/7.26 cnf(c_0_14811, plain, (class_Finite__Set_Ofinite(tc_fun(X1,X2))|~class_Finite__Set_Ofinite(X1)|~class_Finite__Set_Ofinite(X2)), inference(split_conjunct,[status(thm)],[c_0_9208]), ['final']). 6.97/7.26 cnf(c_0_14812, plain, (class_Enum_Oenum(tc_sum(X1,X2))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_9209]), ['final']). 6.97/7.26 cnf(c_0_14813, plain, (hBOOL(hAPP(c_List_Odistinct(X2),X1))|X1!=c_List_Oremdups(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_9203]), ['final']). 6.97/7.26 cnf(c_0_14814, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|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)],[c_0_9210, c_0_4413]), c_0_4413]), ['final']). 6.97/7.26 cnf(c_0_14815, plain, (class_Enum_Oenum(tc_prod(X2,X1))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_9211]), ['final']). 6.97/7.26 cnf(c_0_14816, plain, (class_Enum_Oenum(tc_fun(X1,X2))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_9212]), ['final']). 6.97/7.26 cnf(c_0_14817, 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_9213]), ['final']). 6.97/7.26 cnf(c_0_14818, 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_8945]), ['final']). 6.97/7.26 cnf(c_0_14819, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|esk425_1(X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_8380]), ['final']). 6.97/7.26 cnf(c_0_14820, plain, (c_Wellfounded_Oacyclic(X1,X2)|~c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9056]), ['final']). 6.97/7.26 cnf(c_0_14821, plain, (c_Relation_Oantisym(X1,X2)|~c_Relation_Oantisym(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9059]), ['final']). 6.97/7.26 cnf(c_0_14822, plain, (c_Relation_Otrans(X1,X2)|~c_Relation_Otrans(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9060]), ['final']). 6.97/7.26 cnf(c_0_14823, plain, (c_Relation_Osym(X1,X2)|~c_Relation_Osym(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9061]), ['final']). 6.97/7.26 cnf(c_0_14824, 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)), inference(split_conjunct,[status(thm)],[c_0_9214]), ['final']). 6.97/7.26 cnf(c_0_14825, plain, (hBOOL(X1)|~hBOOL(X2)|~hBOOL(hAPP(hAPP(c_fimplies,X2),X1))), inference(split_conjunct,[status(thm)],[c_0_9215]), ['final']). 6.97/7.26 cnf(c_0_14826, plain, (c_Equiv__Relations_Oequivp(X1,X2)|~c_Predicate_Oreflp(X1,X2)|~c_Predicate_Osymp(X1,X2)|~c_Predicate_Otransp(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9216]), ['final']). 6.97/7.26 cnf(c_0_14827, 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_9217]), ['final']). 6.97/7.26 cnf(c_0_14828, 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_9218]), ['final']). 6.97/7.26 cnf(c_0_14829, 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_9219]), ['final']). 6.97/7.26 cnf(c_0_14830, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|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_5460]), ['final']). 6.97/7.26 cnf(c_0_14831, 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_9171]), ['final']). 6.97/7.26 cnf(c_0_14832, plain, (c_List_Olist_ONil(X1)=X2|c_List_Olist_ONil(X1)!=hAPP(c_List_Orotate1(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_9220]), ['final']). 6.97/7.26 cnf(c_0_14833, 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_9221]), ['final']). 6.97/7.26 cnf(c_0_14834, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|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_9222]), ['final']). 6.97/7.26 cnf(c_0_14835, 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_8786]), ['final']). 6.97/7.26 cnf(c_0_14836, plain, (hBOOL(X1)|hBOOL(hAPP(c_fNot,X1))), inference(split_conjunct,[status(thm)],[c_0_9223]), ['final']). 6.97/7.26 cnf(c_0_14837, plain, (c_Relation_Orefl__on(X1,X2,X3)|~c_Equiv__Relations_Oequiv(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_9135]), ['final']). 6.97/7.26 cnf(c_0_14838, plain, (X2=X3|~c_Fun_Obij__betw(X1,X1,c_Fun_Oid(X1),X2,X3)), inference(split_conjunct,[status(thm)],[c_0_9224]), ['final']). 6.97/7.26 cnf(c_0_14839, plain, (X2=X1|hAPP(c_Code__Numeral_Onat__of,X1)!=hAPP(c_Code__Numeral_Onat__of,X2)), inference(split_conjunct,[status(thm)],[c_0_9225]), ['final']). 6.97/7.26 cnf(c_0_14840, plain, (X2=X1|hAPP(c_Nat_OSuc,X1)!=hAPP(c_Nat_OSuc,X2)), inference(split_conjunct,[status(thm)],[c_0_9226]), ['final']). 6.97/7.26 cnf(c_0_14841, plain, (X2=X1|hAPP(c_Int_ORep__Integ,X1)!=hAPP(c_Int_ORep__Integ,X2)), inference(split_conjunct,[status(thm)],[c_0_9227]), ['final']). 6.97/7.26 cnf(c_0_14842, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_fequal,X2),X1))), inference(split_conjunct,[status(thm)],[c_0_9228]), ['final']). 6.97/7.26 cnf(c_0_14843, plain, (c_Wellfounded_Owf(X2,X1)|esk506_2(X1,X2)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_7637]), ['final']). 6.97/7.26 cnf(c_0_14844, plain, (~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2))), inference(split_conjunct,[status(thm)],[c_0_9229]), ['final']). 6.97/7.26 cnf(c_0_14845, 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_9230, c_0_5202]), c_0_5202]), ['final']). 6.97/7.26 cnf(c_0_14846, plain, (c_Relation_Otrans(X1,X2)|~c_Equiv__Relations_Oequiv(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_9135]), ['final']). 6.97/7.26 cnf(c_0_14847, plain, (c_Relation_Osym(X1,X2)|~c_Equiv__Relations_Oequiv(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_9135]), ['final']). 6.97/7.26 cnf(c_0_14848, plain, (class_Orderings_Otop(tc_fun(X2,X1))|~class_Orderings_Otop(X1)), inference(split_conjunct,[status(thm)],[c_0_9231]), ['final']). 6.97/7.26 cnf(c_0_14849, plain, (class_Lattices_Obounded__lattice__bot(tc_fun(X2,X1))|~class_Lattices_Obounded__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9232]), ['final']). 6.97/7.26 cnf(c_0_14850, plain, (class_Groups_Ominus(tc_fun(X2,X1))|~class_Groups_Ominus(X1)), inference(split_conjunct,[status(thm)],[c_0_9233]), ['final']). 6.97/7.26 cnf(c_0_14851, plain, (class_Groups_Ouminus(tc_fun(X2,X1))|~class_Groups_Ouminus(X1)), inference(split_conjunct,[status(thm)],[c_0_9234]), ['final']). 6.97/7.26 cnf(c_0_14852, plain, (class_Lattices_Obounded__lattice(tc_fun(X2,X1))|~class_Lattices_Obounded__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9235]), ['final']). 6.97/7.26 cnf(c_0_14853, plain, (class_Orderings_Obot(tc_fun(X2,X1))|~class_Orderings_Obot(X1)), inference(split_conjunct,[status(thm)],[c_0_9236]), ['final']). 6.97/7.26 cnf(c_0_14854, plain, (class_Lattices_Oboolean__algebra(tc_fun(X2,X1))|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_9237]), ['final']). 6.97/7.26 cnf(c_0_14855, plain, (class_Orderings_Oord(tc_fun(X2,X1))|~class_Orderings_Oord(X1)), inference(split_conjunct,[status(thm)],[c_0_9238]), ['final']). 6.97/7.26 cnf(c_0_14856, plain, (class_Lattices_Obounded__lattice__top(tc_fun(X2,X1))|~class_Lattices_Obounded__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9239]), ['final']). 6.97/7.26 cnf(c_0_14857, plain, (class_Lattices_Osemilattice__inf(tc_fun(X2,X1))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9240]), ['final']). 6.97/7.26 cnf(c_0_14858, plain, (class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9241]), ['final']). 6.97/7.26 cnf(c_0_14859, plain, (class_Lattices_Osemilattice__sup(tc_fun(X2,X1))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9242]), ['final']). 6.97/7.26 cnf(c_0_14860, plain, (class_Orderings_Opreorder(tc_fun(X2,X1))|~class_Orderings_Opreorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9243]), ['final']). 6.97/7.26 cnf(c_0_14861, plain, (class_Orderings_Oorder(tc_fun(X2,X1))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9244]), ['final']). 6.97/7.26 cnf(c_0_14862, plain, (class_Lattices_Odistrib__lattice(tc_fun(X2,X1))|~class_Lattices_Odistrib__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9245]), ['final']). 6.97/7.26 cnf(c_0_14863, plain, (hBOOL(X1)|~hBOOL(hAPP(hAPP(c_fconj,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9246]), ['final']). 6.97/7.26 cnf(c_0_14864, plain, (hBOOL(X1)|~hBOOL(hAPP(hAPP(c_fconj,X2),X1))), inference(split_conjunct,[status(thm)],[c_0_9247]), ['final']). 6.97/7.26 cnf(c_0_14865, plain, (class_Lattices_Olattice(tc_fun(X2,X1))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9248]), ['final']). 6.97/7.26 cnf(c_0_14866, plain, (c_List_Olinorder__class_Osorted(X1,c_List_Olist_ONil(X1))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9249]), ['final']). 6.97/7.26 cnf(c_0_14867, plain, (c_Int_Oiszero(X1,c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_9250]), ['final']). 6.97/7.26 cnf(c_0_14868, 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_9251]), ['final']). 6.97/7.26 cnf(c_0_14869, plain, (X2=X3|~c_List_Olist__all2(X1,X1,c_fequal,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_5867]), ['final']). 6.97/7.26 cnf(c_0_14870, plain, (c_Relation_Oantisym(X2,X1)|esk597_2(X1,X2)!=esk596_2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7465]), ['final']). 6.97/7.26 cnf(c_0_14871, plain, (~hBOOL(hAPP(hAPP(X1,X2),X3))|~c_Partial__Function_Omk__less(X4,X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_8773]), ['final']). 6.97/7.26 cnf(c_0_14872, 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_9252, c_0_4413]), ['final']). 6.97/7.26 cnf(c_0_14873, plain, (X2=c_List_Olist_ONil(X1)|c_List_Olist_ONil(X1)!=c_List_Oremdups(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9253]), ['final']). 6.97/7.26 cnf(c_0_14874, 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_9202]), ['final']). 6.97/7.26 cnf(c_0_14875, 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_9254]), ['final']). 6.97/7.26 cnf(c_0_14876, plain, (c_Lattices_Osemilattice__sup__class_Osup(X1)=c_Orderings_Oord__class_Omax(X1)|~class_Orderings_Olinorder(X1)|~class_Lattices_Osemilattice__sup(X1)), inference(split_conjunct,[status(thm)],[c_0_9255]), ['final']). 6.97/7.26 cnf(c_0_14877, plain, (c_Lattices_Osemilattice__inf__class_Oinf(X1)=c_Orderings_Oord__class_Omin(X1)|~class_Orderings_Olinorder(X1)|~class_Lattices_Osemilattice__inf(X1)), inference(split_conjunct,[status(thm)],[c_0_9256]), ['final']). 6.97/7.26 cnf(c_0_14878, plain, (c_Equiv__Relations_Opart__equivp(X1,X2)|~c_Equiv__Relations_Oequivp(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9257]), ['final']). 6.97/7.26 cnf(c_0_14879, plain, (c_Predicate_Otransp(X1,X2)|~c_Equiv__Relations_Opart__equivp(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8759]), ['final']). 6.97/7.26 cnf(c_0_14880, plain, (c_Predicate_Otransp(X1,X2)|~c_Equiv__Relations_Oequivp(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9258]), ['final']). 6.97/7.26 cnf(c_0_14881, plain, (c_Predicate_Osymp(X1,X2)|~c_Equiv__Relations_Opart__equivp(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8759]), ['final']). 6.97/7.26 cnf(c_0_14882, plain, (c_Predicate_Osymp(X1,X2)|~c_Equiv__Relations_Oequivp(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9258]), ['final']). 6.97/7.26 cnf(c_0_14883, plain, (c_Predicate_Oreflp(X1,X2)|~c_Equiv__Relations_Oequivp(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9258]), ['final']). 6.97/7.26 cnf(c_0_14884, plain, (c_Wellfounded_Oacyclic(X1,X2)|~c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9259]), ['final']). 6.97/7.26 cnf(c_0_14885, plain, (class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X1))|~class_Lazy__Sequence_Osmall__lazy(X1)), inference(split_conjunct,[status(thm)],[c_0_9260]), ['final']). 6.97/7.26 cnf(c_0_14886, plain, (class_Finite__Set_Ofinite(tc_Option_Ooption(X1))|~class_Finite__Set_Ofinite(X1)), inference(split_conjunct,[status(thm)],[c_0_9261]), ['final']). 6.97/7.26 cnf(c_0_14887, plain, (class_Enum_Oenum(tc_Option_Ooption(X1))|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_9262]), ['final']). 6.97/7.26 cnf(c_0_14888, plain, (c_Wellfounded_Oacyclic(X1,X2)|~c_Nitpick_Owf_H(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8786]), ['final']). 6.97/7.26 cnf(c_0_14889, plain, (~hBOOL(X1)|~hBOOL(hAPP(c_fNot,X1))), inference(split_conjunct,[status(thm)],[c_0_9263]), ['final']). 6.97/7.26 cnf(c_0_14890, plain, (~class_Rings_Osemiring__1(X1)|~c_Int_Oiszero(X1,c_Groups_Oone__class_Oone(X1))), inference(split_conjunct,[status(thm)],[c_0_9264]), ['final']). 6.97/7.26 cnf(c_0_14891, 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_9265]), ['final']). 6.97/7.26 cnf(c_0_14892, 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_9266]), ['final']). 6.97/7.26 cnf(c_0_14893, 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_9267]), ['final']). 6.97/7.26 cnf(c_0_14894, 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_9268]), ['final']). 6.97/7.26 cnf(c_0_14895, 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_9269]), ['final']). 6.97/7.26 cnf(c_0_14896, 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_9270]), ['final']). 6.97/7.26 cnf(c_0_14897, 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_9271]), ['final']). 6.97/7.26 cnf(c_0_14898, 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_9272]), ['final']). 6.97/7.26 cnf(c_0_14899, 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_9273]), ['final']). 6.97/7.26 cnf(c_0_14900, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)!=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)],[c_0_9274, c_0_4409]), c_0_4410]), c_0_4410]), c_0_4411]), ['final']). 6.97/7.26 cnf(c_0_14901, 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_9275]), ['final']). 6.97/7.26 cnf(c_0_14902, 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_9276]), ['final']). 6.97/7.26 cnf(c_0_14903, 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_9277]), ['final']). 6.97/7.26 cnf(c_0_14904, 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_9278, c_0_5202]), c_0_7359])]), ['final']). 6.97/7.26 cnf(c_0_14905, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_9279, c_0_4413]), ['final']). 6.97/7.26 cnf(c_0_14906, 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_9280]), ['final']). 6.97/7.26 cnf(c_0_14907, 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_9281]), ['final']). 6.97/7.26 cnf(c_0_14908, 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_9282]), ['final']). 6.97/7.26 cnf(c_0_14909, 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_9283]), ['final']). 6.97/7.26 cnf(c_0_14910, 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_9284]), ['final']). 6.97/7.26 cnf(c_0_14911, 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_9285]), ['final']). 6.97/7.26 cnf(c_0_14912, 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_9286]), ['final']). 6.97/7.26 cnf(c_0_14913, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X2))), inference(er,[status(thm)],[c_0_9287]), ['final']). 6.97/7.26 cnf(c_0_14914, 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_9288, c_0_4467])]), ['final']). 6.97/7.26 cnf(c_0_14915, 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_9289]), ['final']). 6.97/7.26 cnf(c_0_14916, 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_9290, c_0_5202]), ['final']). 6.97/7.26 cnf(c_0_14917, 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_9291]), ['final']). 6.97/7.26 cnf(c_0_14918, 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_9292]), ['final']). 6.97/7.26 cnf(c_0_14919, 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_9293]), ['final']). 6.97/7.26 cnf(c_0_14920, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X1))), inference(er,[status(thm)],[c_0_9294]), ['final']). 6.97/7.26 cnf(c_0_14921, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_9295]), ['final']). 6.97/7.26 cnf(c_0_14922, 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_9296]), ['final']). 6.97/7.26 cnf(c_0_14923, 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_9297]), ['final']). 6.97/7.26 cnf(c_0_14924, 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_9298, c_0_4413]), ['final']). 6.97/7.26 cnf(c_0_14925, 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_9299, c_0_4413]), ['final']). 6.97/7.26 cnf(c_0_14926, 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_9300]), ['final']). 6.97/7.26 cnf(c_0_14927, 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_9301]), ['final']). 6.97/7.26 cnf(c_0_14928, plain, (c_Int_OMin!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)), inference(rw,[status(thm)],[c_0_9302, c_0_4410]), ['final']). 6.97/7.26 cnf(c_0_14929, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1))), inference(split_conjunct,[status(thm)],[c_0_9303]), ['final']). 6.97/7.26 cnf(c_0_14930, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)!=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_9304]), ['final']). 6.97/7.26 cnf(c_0_14931, plain, (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_9305]), ['final']). 6.97/7.26 cnf(c_0_14932, plain, (X1!=hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1)), inference(split_conjunct,[status(thm)],[c_0_9306]), ['final']). 6.97/7.26 cnf(c_0_14933, plain, (c_Lazy__Sequence_Olazy__sequence_OEmpty(X1)!=c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_9307]), ['final']). 6.97/7.26 cnf(c_0_14934, plain, (~hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_9308]), ['final']). 6.97/7.26 cnf(c_0_14935, plain, (~hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_9309]), ['final']). 6.97/7.26 cnf(c_0_14936, plain, (~c_List_Olist__ex1(X1,X2,c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_9310]), ['final']). 6.97/7.26 cnf(c_0_14937, plain, (~c_List_Olist__ex(X1,X2,c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_9311]), ['final']). 6.97/7.26 cnf(c_0_14938, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,X1)), inference(split_conjunct,[status(thm)],[c_0_9312]), ['final']). 6.97/7.26 cnf(c_0_14939, plain, (hAPP(c_Nat_OSuc,X1)!=X1), inference(split_conjunct,[status(thm)],[c_0_9313]), ['final']). 6.97/7.26 cnf(c_0_14940, 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']). 6.97/7.26 cnf(c_0_14941, plain, (c_Int_OMin!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_9314, c_0_4413]), ['final']). 6.97/7.26 cnf(c_0_14942, plain, (~hBOOL(c_fFalse)), inference(split_conjunct,[status(thm)],[c_0_9315]), ['final']). 6.97/7.26 cnf(c_0_14943, negated_conjecture, (~c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts)), inference(split_conjunct,[status(thm)],[c_0_9316]), ['final']). 6.97/7.26 cnf(c_0_14944, 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_9317, c_0_5929]), c_0_5929]), c_0_4806]), c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_14945, 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_9318, c_0_5929]), c_0_5929]), ['final']). 6.97/7.26 cnf(c_0_14946, plain, (hAPP(X1,hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X3),tc_HOL_Obool),tc_HOL_Obool,X3),c_HOL_OEx(tc_fun(X2,X3))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X3),tc_HOL_Obool),tc_fun(tc_fun(X2,X3),tc_HOL_Obool),X3),hAPP(c_COMBS(tc_fun(X2,X3),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X2,X3)),c_fconj),X4))),hAPP(hAPP(c_COMBC(X3,tc_fun(tc_fun(X2,X3),X3),tc_fun(tc_fun(X2,X3),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X2,X3),X3),tc_fun(tc_fun(X2,X3),tc_HOL_Obool)),X3),c_COMBB(X3,tc_HOL_Obool,tc_fun(X2,X3))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X2,X3),X2,X3),c_COMBI(tc_fun(X2,X3))),X5)))))=c_Partial__Function_Ofun__lub(X3,X6,X2,X1,X4,X5)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9319, c_0_4798]), c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_14947, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(c_Set_Oimage(X3,X1,X4),X5)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_Oimage(X3,X2,X6)),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__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),c_Set_Ovimage(X3,X1,X4)),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)))))),X5)))=hAPP(c_Set_Oimage(X3,tc_prod(X1,X2),hAPP(hAPP(c_COMBS(X3,X2,tc_prod(X1,X2)),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_prod(X1,X2)),X3),c_Product__Type_OPair(X1,X2)),X4)),X6)),X5)), inference(split_conjunct,[status(thm)],[c_0_9320]), ['final']). 6.97/7.26 cnf(c_0_14948, plain, (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),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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),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),X2),X3))))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9321, c_0_5539]), c_0_5539]), c_0_5539]), ['final']). 6.97/7.26 cnf(c_0_14949, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),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_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)],[c_0_9322, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), c_0_5941]), ['final']). 6.97/7.26 cnf(c_0_14950, 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_9323, c_0_4467]), c_0_5065]), c_0_4467]), c_0_5947]), ['final']). 6.97/7.26 cnf(c_0_14951, 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),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)))=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))))), inference(split_conjunct,[status(thm)],[c_0_9324]), ['final']). 6.97/7.26 cnf(c_0_14952, plain, (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))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),c_Divides_Odiv__class_Omod(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9325, c_0_4415]), c_0_4415]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), c_0_4415]), c_0_4415]), ['final']). 6.97/7.26 cnf(c_0_14953, plain, (hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X3,X4),hAPP(hAPP(c_Product__Type_Oscomp(X1,X5,X6,tc_prod(X2,X3)),X7),X8)),X9)=hAPP(hAPP(c_Product__Type_Oscomp(X1,X5,X6,X4),X7),hAPP(hAPP(c_COMBC(X5,tc_fun(X2,tc_fun(X3,X4)),tc_fun(X6,X4)),hAPP(hAPP(c_COMBB(tc_fun(X6,tc_prod(X2,X3)),tc_fun(tc_fun(X2,tc_fun(X3,X4)),tc_fun(X6,X4)),X5),c_Product__Type_Oscomp(X6,X2,X3,X4)),X8)),X9))), inference(split_conjunct,[status(thm)],[c_0_9326]), ['final']). 6.97/7.26 cnf(c_0_14954, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),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))=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)),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_9327]), ['final']). 6.97/7.26 cnf(c_0_14955, plain, (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),X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),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_Nat_Onat),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),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),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9328, c_0_4742]), c_0_5941]), ['final']). 6.97/7.26 cnf(c_0_14956, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),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(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5))), inference(split_conjunct,[status(thm)],[c_0_9329]), ['final']). 6.97/7.26 cnf(c_0_14957, 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_9330]), ['final']). 6.97/7.26 cnf(c_0_14958, 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__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool))),X4)),X5))=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))), inference(split_conjunct,[status(thm)],[c_0_9331]), ['final']). 6.97/7.26 cnf(c_0_14959, 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),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__sup__class_Osup(tc_fun(X2,tc_HOL_Obool))),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_9332]), ['final']). 6.97/7.26 cnf(c_0_14960, 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_9333, c_0_4978]), c_0_9334]), c_0_5538]), c_0_5539]), c_0_5065]), ['final']). 6.97/7.26 cnf(c_0_14961, 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_9335, c_0_4798]), c_0_4817]), c_0_4467]), ['final']). 6.97/7.26 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_9336])]), ['final']). 6.97/7.26 cnf(c_0_14963, 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_9337, c_0_4813]), c_0_4813]), ['final']). 6.97/7.26 cnf(c_0_14964, 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_9338, c_0_5929]), c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_14965, 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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,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)),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,X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4))),X3)), inference(rw,[status(thm)],[c_0_9339, c_0_6783]), ['final']). 6.97/7.26 cnf(c_0_14966, 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_9340, c_0_4632]), c_0_4632]), ['final']). 6.97/7.26 cnf(c_0_14967, 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)],[c_0_9341, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.26 cnf(c_0_14968, 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)],[c_0_9342, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.26 cnf(c_0_14969, 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_9343, c_0_5537]), ['final']). 6.97/7.26 cnf(c_0_14970, plain, (hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),X3),X6),hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)))=hAPP(hAPP(X3,X4),hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),X3),X6),hAPP(c_List_Orev(X1),X5)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9344, c_0_4632]), c_0_4632]), ['final']). 6.97/7.26 cnf(c_0_14971, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),hAPP(X3,hAPP(c_Product__Type_Ofst(X4,X5),X6))),hAPP(X7,hAPP(c_Product__Type_Osnd(X4,X5),X6)))=hAPP(c_Product__Type_Omap__pair(X1,X1,X5,X2,c_Fun_Oid(X1),X7),hAPP(c_Product__Type_Omap__pair(X4,X1,X5,X5,X3,c_Fun_Oid(X5)),X6))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9345, c_0_6829]), c_0_4734]), ['final']). 6.97/7.26 cnf(c_0_14972, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),hAPP(X3,hAPP(c_Product__Type_Ofst(X4,X5),X6))),hAPP(X7,hAPP(c_Product__Type_Osnd(X4,X5),X6)))=hAPP(c_Product__Type_Omap__pair(X4,X1,X2,X2,X3,c_Fun_Oid(X2)),hAPP(c_Product__Type_Omap__pair(X4,X4,X5,X2,c_Fun_Oid(X4),X7),X6))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9346, c_0_6829]), c_0_4734]), ['final']). 6.97/7.26 cnf(c_0_14973, 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(c_Product__Type_Omap__pair(X5,X3,X2,X2,X6,c_Fun_Oid(X2)),hAPP(c_Product__Type_Omap__pair(X5,X5,X1,X2,c_Fun_Oid(X5),X4),X7))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9347, c_0_6829]), c_0_6829]), c_0_4734]), c_0_4734]), ['final']). 6.97/7.26 cnf(c_0_14974, 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_9348]), ['final']). 6.97/7.26 cnf(c_0_14975, plain, (hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X4,X5,X6),hAPP(c_Product__Type_Omap__pair(X7,X1,X8,X3,X9,X10),X11))=hAPP(c_Product__Type_Omap__pair(X7,X2,X8,X4,hAPP(c_Fun_Ocomp(X1,X2,X7,X5),X9),hAPP(c_Fun_Ocomp(X3,X4,X8,X6),X10)),X11)), inference(split_conjunct,[status(thm)],[c_0_9349]), ['final']). 6.97/7.26 cnf(c_0_14976, plain, (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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)),X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9350, c_0_9351]), c_0_5815]), ['final']). 6.97/7.26 cnf(c_0_14977, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X4),c_List_Orotate1(X1)),X5))=hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X2),tc_List_Olist(X2)),X4),c_List_Orotate1(X2)),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9352, c_0_5794]), c_0_5794]), ['final']). 6.97/7.26 cnf(c_0_14978, 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_9353, c_0_4734]), c_0_4734]), c_0_4734]), ['final']). 6.97/7.26 cnf(c_0_14979, 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_9354, c_0_6829]), c_0_6829]), c_0_6829]), ['final']). 6.97/7.26 cnf(c_0_14980, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),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))),c_Int_OMin)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))), inference(rw,[status(thm)],[c_0_9355, c_0_5624]), ['final']). 6.97/7.26 cnf(c_0_14981, 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)],[c_0_9356, c_0_4410]), ['final']). 6.97/7.26 cnf(c_0_14982, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)),hAPP(hAPP(c_List_Olist_OCons(X2),X5),X6))=hAPP(hAPP(c_List_Olist_OCons(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X5)),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X6))), inference(split_conjunct,[status(thm)],[c_0_9357]), ['final']). 6.97/7.26 cnf(c_0_14983, 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_9358, c_0_5539]), ['final']). 6.97/7.26 cnf(c_0_14984, 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_9359]), ['final']). 6.97/7.26 cnf(c_0_14985, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(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_OINFI(X4,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X4,X6),X3)),X5)), inference(split_conjunct,[status(thm)],[c_0_9360]), ['final']). 6.97/7.26 cnf(c_0_14986, 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_9361]), ['final']). 6.97/7.26 cnf(c_0_14987, 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)),hAPP(hAPP(c_Set_Oinsert(X4),X3),X5)),X2)), inference(split_conjunct,[status(thm)],[c_0_9362]), ['final']). 6.97/7.26 cnf(c_0_14988, 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)),hAPP(hAPP(c_Set_Oinsert(X4),X3),X5)),X2)), inference(split_conjunct,[status(thm)],[c_0_9363]), ['final']). 6.97/7.26 cnf(c_0_14989, 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_9364]), ['final']). 6.97/7.26 cnf(c_0_14990, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X3,X1,X4),X5)),X6)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X2,tc_HOL_Obool)),X5),hAPP(c_Fun_Ocomp(X1,tc_fun(X2,tc_HOL_Obool),X3,X6),X4))), inference(split_conjunct,[status(thm)],[c_0_9365]), ['final']). 6.97/7.26 cnf(c_0_14991, 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)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,X3))=c_SetInterval_Oord__class_OatLeastAtMost(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_9366]), ['final']). 6.97/7.26 cnf(c_0_14992, plain, (hAPP(c_Fun_Ocomp(tc_prod(X1,X2),X1,tc_prod(X3,X4),c_Product__Type_Ofst(X1,X2)),c_Product__Type_Omap__pair(X3,X1,X4,X2,X5,X6))=hAPP(c_Fun_Ocomp(X3,X1,tc_prod(X3,X4),X5),c_Product__Type_Ofst(X3,X4))), inference(split_conjunct,[status(thm)],[c_0_9367]), ['final']). 6.97/7.26 cnf(c_0_14993, 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_9368]), ['final']). 6.97/7.26 cnf(c_0_14994, 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_9369]), ['final']). 6.97/7.26 cnf(c_0_14995, 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_9370]), ['final']). 6.97/7.26 cnf(c_0_14996, 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_9371]), ['final']). 6.97/7.26 cnf(c_0_14997, 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_9372]), ['final']). 6.97/7.26 cnf(c_0_14998, 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_9373]), ['final']). 6.97/7.26 cnf(c_0_14999, plain, (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))=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))), inference(rw,[status(thm)],[c_0_9374, c_0_4645]), ['final']). 6.97/7.26 cnf(c_0_15000, 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_9375]), ['final']). 6.97/7.26 cnf(c_0_15001, 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_9376, c_0_4742]), c_0_6021]), c_0_6030]), ['final']). 6.97/7.26 cnf(c_0_15002, 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_9377, c_0_4742]), c_0_6021]), c_0_6030]), ['final']). 6.97/7.26 cnf(c_0_15003, 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)],[c_0_9378, c_0_4410]), ['final']). 6.97/7.26 cnf(c_0_15004, 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_9379, c_0_4467]), c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15005, plain, (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),c_Fun_Ofun__upd(X1,X3,X5,X6,X7))), inference(split_conjunct,[status(thm)],[c_0_9380]), ['final']). 6.97/7.26 cnf(c_0_15006, 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_9381]), ['final']). 6.97/7.26 cnf(c_0_15007, 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_9382]), ['final']). 6.97/7.26 cnf(c_0_15008, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),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)),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))), inference(split_conjunct,[status(thm)],[c_0_9383]), ['final']). 6.97/7.26 cnf(c_0_15009, 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_9384]), ['final']). 6.97/7.26 cnf(c_0_15010, plain, (hAPP(c_Relation_ORange(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(X2,tc_HOL_Obool)),X3),c_Relation_ORange(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_9385]), ['final']). 6.97/7.26 cnf(c_0_15011, 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_9386]), ['final']). 6.97/7.26 cnf(c_0_15012, plain, (hAPP(c_Set_Oimage(X1,X2,X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X4))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X4),c_Set_Oimage(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_9387]), ['final']). 6.97/7.26 cnf(c_0_15013, 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),hAPP(hAPP(c_Set_Oinsert(X4),X3),X5))), inference(split_conjunct,[status(thm)],[c_0_9388]), ['final']). 6.97/7.26 cnf(c_0_15014, plain, (hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X1)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(X1),X2))=hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(X1),X2),X3),X4)), inference(split_conjunct,[status(thm)],[c_0_9389]), ['final']). 6.97/7.26 cnf(c_0_15015, 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_9390, c_0_7419]), ['final']). 6.97/7.26 cnf(c_0_15016, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(hAPP(c_List_Odrop(X1),X4),X5))=hAPP(hAPP(c_List_Odrop(X2),X4),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5))), inference(split_conjunct,[status(thm)],[c_0_9391]), ['final']). 6.97/7.26 cnf(c_0_15017, plain, (hAPP(hAPP(c_List_Otake(X1),X2),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5))=hAPP(hAPP(c_List_Omap(X3,X1),X4),hAPP(hAPP(c_List_Otake(X3),X2),X5))), inference(split_conjunct,[status(thm)],[c_0_9392]), ['final']). 6.97/7.26 cnf(c_0_15018, plain, (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)],[c_0_9393, c_0_9351]), ['final']). 6.97/7.26 cnf(c_0_15019, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),hAPP(hAPP(c_COMBB(X3,tc_HOL_Obool,X1),X4),X5)),X6)=hAPP(hAPP(c_COMBB(X3,tc_HOL_Obool,X2),X4),hAPP(c_Fun_Ocomp(X1,X3,X2,X5),X6))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9394, c_0_4768]), c_0_4768]), c_0_4768]), ['final']). 6.97/7.26 cnf(c_0_15020, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Oimage(X4,X1,X5),X6))=hAPP(c_Set_Oimage(X4,X2,hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5)),X6)), inference(split_conjunct,[status(thm)],[c_0_9395]), ['final']). 6.97/7.26 cnf(c_0_15021, 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_9396]), ['final']). 6.97/7.26 cnf(c_0_15022, 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_9397, c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15023, 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_9398]), ['final']). 6.97/7.26 cnf(c_0_15024, 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_9399]), ['final']). 6.97/7.26 cnf(c_0_15025, 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_9400, c_0_4768]), c_0_4768]), ['final']). 6.97/7.26 cnf(c_0_15026, 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_9401]), ['final']). 6.97/7.26 cnf(c_0_15027, plain, (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))=c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2))), inference(rw,[status(thm)],[c_0_9402, c_0_6164]), ['final']). 6.97/7.26 cnf(c_0_15028, 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_9403, c_0_4768]), ['final']). 6.97/7.26 cnf(c_0_15029, plain, (hAPP(hAPP(hAPP(X1,X2),X3),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X4,X5,X6,X1,X3))=c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X4,X5,X6,X1,c_Lazy__Sequence_Olazy__sequence_OInsert(X5,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_9404]), ['final']). 6.97/7.26 cnf(c_0_15030, 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_9405]), ['final']). 6.97/7.26 cnf(c_0_15031, 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_9406]), ['final']). 6.97/7.26 cnf(c_0_15032, plain, (c_List_Olist_Olist__size(X1,X2,hAPP(hAPP(c_List_Omap(X3,X1),X4),X5))=c_List_Olist_Olist__size(X3,hAPP(c_Fun_Ocomp(X1,tc_Nat_Onat,X3,X2),X4),X5)), inference(split_conjunct,[status(thm)],[c_0_9407]), ['final']). 6.97/7.26 cnf(c_0_15033, plain, (c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(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(hAPP(X3,X4),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X1,X2,X3,X4))), inference(rw,[status(thm)],[c_0_9408, c_0_5202]), ['final']). 6.97/7.26 cnf(c_0_15034, 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_9409]), ['final']). 6.97/7.26 cnf(c_0_15035, plain, (hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))=hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(c_List_Otl(X2),X4))), inference(split_conjunct,[status(thm)],[c_0_9410]), ['final']). 6.97/7.26 cnf(c_0_15036, 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_9411]), ['final']). 6.97/7.26 cnf(c_0_15037, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9412]), ['final']). 6.97/7.26 cnf(c_0_15038, plain, (hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X4)=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),X1),c_List_Olist_ONil(X2)),X4)), inference(er,[status(thm)],[c_0_9413]), ['final']). 6.97/7.26 cnf(c_0_15039, 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_9414]), ['final']). 6.97/7.26 cnf(c_0_15040, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_List_Oset(X1),X4))=hAPP(c_List_Oset(X2),hAPP(hAPP(c_List_Omap(X1,X2),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_9415]), ['final']). 6.97/7.26 cnf(c_0_15041, 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_9416]), ['final']). 6.97/7.26 cnf(c_0_15042, 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_9417]), ['final']). 6.97/7.26 cnf(c_0_15043, plain, (c_Lazy__Sequence_Omap(X1,X2,X3,c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X4,X5))=c_Lazy__Sequence_Olazy__sequence_OInsert(X2,hAPP(X3,X4),c_Lazy__Sequence_Omap(X1,X2,X3,X5))), inference(split_conjunct,[status(thm)],[c_0_9418]), ['final']). 6.97/7.26 cnf(c_0_15044, plain, (c_Random__Sequence_Oempty(X1,X2,X3)=hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X1)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X1))), inference(split_conjunct,[status(thm)],[c_0_9419]), ['final']). 6.97/7.26 cnf(c_0_15045, 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_9420]), ['final']). 6.97/7.26 cnf(c_0_15046, 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_9421, c_0_5560]), ['final']). 6.97/7.26 cnf(c_0_15047, 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_9422]), ['final']). 6.97/7.26 cnf(c_0_15048, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9423]), ['final']). 6.97/7.26 cnf(c_0_15049, 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_9424]), ['final']). 6.97/7.26 cnf(c_0_15050, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9425]), ['final']). 6.97/7.26 cnf(c_0_15051, plain, (c_List_Opartition(X1,X2,c_List_Olist_ONil(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))), inference(split_conjunct,[status(thm)],[c_0_9426]), ['final']). 6.97/7.26 cnf(c_0_15052, plain, (hAPP(c_List_Orev(X1),hAPP(c_List_Ofilter(X1,X2),X3))=hAPP(c_List_Ofilter(X1,X2),hAPP(c_List_Orev(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_9427]), ['final']). 6.97/7.26 cnf(c_0_15053, plain, (c_Enum_On__lists(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)=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_9428]), ['final']). 6.97/7.26 cnf(c_0_15054, 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_9429]), ['final']). 6.97/7.26 cnf(c_0_15055, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X1,X2)),c_Product__Type_OPair(X1,X2))=c_Fun_Oid(tc_prod(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_9430]), ['final']). 6.97/7.26 cnf(c_0_15056, 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_9431]), ['final']). 6.97/7.26 cnf(c_0_15057, 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_9432]), ['final']). 6.97/7.26 cnf(c_0_15058, 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_Osublists(X1,c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_9433]), ['final']). 6.97/7.26 cnf(c_0_15059, 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_9434, c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15060, 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_9435, c_0_4798]), c_0_4798]), c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15061, plain, (c_FunDef_Orp__inv__image(X1,X2)=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)))), inference(split_conjunct,[status(thm)],[c_0_9436]), ['final']). 6.97/7.26 cnf(c_0_15062, 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_9437, c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15063, 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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),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(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_9438, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), ['final']). 6.97/7.26 cnf(c_0_15064, 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_9439]), ['final']). 6.97/7.26 cnf(c_0_15065, 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_9440]), ['final']). 6.97/7.26 cnf(c_0_15066, 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_9441, c_0_4806]), c_0_5985]), c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15067, 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_9442, c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15068, 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_9443, c_0_4881]), c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15069, 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_9444, c_0_6208]), c_0_6208]), c_0_6208]), c_0_6208]), c_0_6208]), c_0_6208]), ['final']). 6.97/7.26 cnf(c_0_15070, 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)), inference(split_conjunct,[status(thm)],[c_0_9445]), ['final']). 6.97/7.26 cnf(c_0_15071, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),X3)),c_Int_OMin)))),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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),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)],[c_0_9446, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), c_0_4741]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), ['final']). 6.97/7.26 cnf(c_0_15072, 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_9447, c_0_4817]), c_0_4817]), c_0_4817]), ['final']). 6.97/7.26 cnf(c_0_15073, 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_9448, c_0_4798]), c_0_4817]), c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15074, 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_9449, c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15075, 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_9450, c_0_5537]), c_0_9451]), c_0_5537]), c_0_9452]), ['final']). 6.97/7.26 cnf(c_0_15076, plain, (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_9453]), ['final']). 6.97/7.26 cnf(c_0_15077, 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_9454]), ['final']). 6.97/7.26 cnf(c_0_15078, 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)))), inference(split_conjunct,[status(thm)],[c_0_9455]), ['final']). 6.97/7.26 cnf(c_0_15079, 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_9456, c_0_4415]), ['final']). 6.97/7.26 cnf(c_0_15080, 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_9457, c_0_4978]), c_0_4978]), c_0_4742]), c_0_5538]), c_0_5539]), c_0_5065]), c_0_4978]), c_0_4978]), c_0_9334]), ['final']). 6.97/7.26 cnf(c_0_15081, 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_9458, c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15082, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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(X5,tc_fun(X1,tc_HOL_Obool)),X6),X7))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(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_OSUPR(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__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool))),X4))),X7)))), inference(split_conjunct,[status(thm)],[c_0_9459]), ['final']). 6.97/7.26 cnf(c_0_15083, 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_9460]), ['final']). 6.97/7.26 cnf(c_0_15084, plain, (c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),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))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2)),c_fequal)),X4))))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9461, c_0_4798]), c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15085, plain, (c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),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))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2)),c_fequal)),X4))))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9462, c_0_4798]), c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15086, 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)), inference(split_conjunct,[status(thm)],[c_0_9463]), ['final']). 6.97/7.26 cnf(c_0_15087, 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_9464, c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15088, 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_9465, c_0_5002]), ['final']). 6.97/7.26 cnf(c_0_15089, 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_9466, c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15090, 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_9467, c_0_4798]), c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15091, 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_9468, c_0_9469]), ['final']). 6.97/7.26 cnf(c_0_15092, plain, (c_Nitpick_OFrac=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))))), inference(split_conjunct,[status(thm)],[fact_Nitpick_OFrac__def]), ['final']). 6.97/7.26 cnf(c_0_15093, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X3),X4),hAPP(hAPP(c_List_Ozip(X1,X2),X5),hAPP(hAPP(c_List_Omap(X6,X2),X7),X8)))=hAPP(hAPP(c_List_Omap(tc_prod(X1,X6),X3),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X6,X3),hAPP(hAPP(c_COMBB(tc_fun(X6,tc_prod(X1,X2)),tc_fun(X6,X3),X1),hAPP(c_COMBB(tc_prod(X1,X2),X3,X6),X4)),hAPP(hAPP(c_COMBC(X1,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))),X1),c_COMBB(X2,tc_prod(X1,X2),X6)),c_Product__Type_OPair(X1,X2))),X7)))),hAPP(hAPP(c_List_Ozip(X1,X6),X5),X8))), inference(split_conjunct,[status(thm)],[c_0_9470]), ['final']). 6.97/7.26 cnf(c_0_15094, 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_9471, c_0_4415]), ['final']). 6.97/7.26 cnf(c_0_15095, 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_9472, c_0_5954]), c_0_4817]), c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15096, 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_9473, c_0_9474]), ['final']). 6.97/7.26 cnf(c_0_15097, 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_9475, c_0_4415]), c_0_4978]), c_0_4978]), ['final']). 6.97/7.26 cnf(c_0_15098, 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_9476, c_0_5972]), ['final']). 6.97/7.26 cnf(c_0_15099, 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_9477, c_0_4415]), c_0_4881]), c_0_4881]), ['final']). 6.97/7.26 cnf(c_0_15100, 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_9478, c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15101, 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_9479, c_0_5539]), c_0_5539]), c_0_5539]), ['final']). 6.97/7.26 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_9480, c_0_4415]), ['final']). 6.97/7.26 cnf(c_0_15103, 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_9481, c_0_5539]), c_0_6253]), ['final']). 6.97/7.26 cnf(c_0_15104, 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_9482, c_0_5539]), c_0_6253]), ['final']). 6.97/7.26 cnf(c_0_15105, plain, (hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(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_fconj),X2))),c_member(X1)))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9483, c_0_4798]), c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15106, 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_9484, c_0_6208]), c_0_6208]), c_0_6208]), c_0_6208]), ['final']). 6.97/7.26 cnf(c_0_15107, 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_9485, c_0_4415]), c_0_4978]), c_0_4978]), ['final']). 6.97/7.26 cnf(c_0_15108, 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_9486, c_0_5537]), ['final']). 6.97/7.26 cnf(c_0_15109, 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_9487, c_0_4415]), c_0_4881]), c_0_4881]), ['final']). 6.97/7.26 cnf(c_0_15110, 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_9488]), ['final']). 6.97/7.26 cnf(c_0_15111, 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_9489, c_0_9469]), ['final']). 6.97/7.26 cnf(c_0_15112, 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_9490, c_0_9491]), ['final']). 6.97/7.26 cnf(c_0_15113, plain, (hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OEx(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_fconj),X3))),hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X4)))=hAPP(c_Relation_OImage(X1,X2,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X4)),X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9492, c_0_4798]), c_0_4467]), c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15114, 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_9493, c_0_5929]), ['final']). 6.97/7.26 cnf(c_0_15115, 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_9494]), ['final']). 6.97/7.26 cnf(c_0_15116, plain, (hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(X1,X2,X3,X4),X5),X6),X7)=c_New__DSequence_Oneg__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_9495]), ['final']). 6.97/7.26 cnf(c_0_15117, 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))), inference(split_conjunct,[status(thm)],[c_0_9496]), ['final']). 6.97/7.26 cnf(c_0_15118, 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))), inference(split_conjunct,[status(thm)],[c_0_9497]), ['final']). 6.97/7.26 cnf(c_0_15119, 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)],[c_0_9498, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.26 cnf(c_0_15120, 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_9499]), ['final']). 6.97/7.26 cnf(c_0_15121, 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_9500, c_0_4806]), ['final']). 6.97/7.26 cnf(c_0_15122, 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_9501, c_0_4806]), ['final']). 6.97/7.26 cnf(c_0_15123, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X5),X6)),X7)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),X4),c_Relation_Orel__comp(X1,X2,X3)),X6)),X7))), inference(split_conjunct,[status(thm)],[c_0_9502]), ['final']). 6.97/7.26 cnf(c_0_15124, 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)), inference(split_conjunct,[status(thm)],[c_0_9503]), ['final']). 6.97/7.26 cnf(c_0_15125, 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_9504]), ['final']). 6.97/7.26 cnf(c_0_15126, 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_9505]), ['final']). 6.97/7.26 cnf(c_0_15127, 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_9506, c_0_5929]), c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15128, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_9507, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_6097]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), ['final']). 6.97/7.26 cnf(c_0_15129, plain, (c_New__Random__Sequence_Opos__decr__bind(X1,X2,X3,X4,X5,X6,X7)=c_New__DSequence_Opos__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(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))))),X4),X5)),X6)),X7))), inference(split_conjunct,[status(thm)],[c_0_9508]), ['final']). 6.97/7.26 cnf(c_0_15130, 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_9509, c_0_4798]), c_0_4798]), c_0_4798]), c_0_4798]), ['final']). 6.97/7.26 cnf(c_0_15131, 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_9510, c_0_6252]), c_0_9511]), ['final']). 6.97/7.26 cnf(c_0_15132, 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)],[c_0_9512, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.26 cnf(c_0_15133, 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_9513, c_0_9514]), ['final']). 6.97/7.26 cnf(c_0_15134, 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_9515, c_0_4415]), ['final']). 6.97/7.26 cnf(c_0_15135, plain, (c_Relation_OId__on(X1,X2)=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))), inference(split_conjunct,[status(thm)],[c_0_9516]), ['final']). 6.97/7.26 cnf(c_0_15136, 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_9517]), ['final']). 6.97/7.26 cnf(c_0_15137, 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_9518, c_0_5929]), c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15138, 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)), inference(split_conjunct,[status(thm)],[c_0_9519]), ['final']). 6.97/7.26 cnf(c_0_15139, 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)), inference(split_conjunct,[status(thm)],[c_0_9520]), ['final']). 6.97/7.26 cnf(c_0_15140, 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_9521, c_0_9522]), ['final']). 6.97/7.26 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_9523, c_0_5202]), ['final']). 6.97/7.26 cnf(c_0_15142, 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_9524, c_0_5539]), c_0_5539]), ['final']). 6.97/7.26 cnf(c_0_15143, plain, (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))=hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_9525]), ['final']). 6.97/7.26 cnf(c_0_15144, 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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_9526, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), ['final']). 6.97/7.26 cnf(c_0_15145, 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_9527, c_0_4817]), c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15146, 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_9528]), ['final']). 6.97/7.26 cnf(c_0_15147, 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_9529, c_0_4768]), c_0_4768]), c_0_4768]), ['final']). 6.97/7.26 cnf(c_0_15148, 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_9530, c_0_4798]), c_0_4817]), ['final']). 6.97/7.26 cnf(c_0_15149, 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)), inference(split_conjunct,[status(thm)],[c_0_9531]), ['final']). 6.97/7.26 cnf(c_0_15150, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(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)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(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_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool))),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_9532]), ['final']). 6.97/7.26 cnf(c_0_15151, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(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__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool))),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_9533]), ['final']). 6.97/7.26 cnf(c_0_15152, 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_9534, c_0_5539]), c_0_5539]), ['final']). 6.97/7.26 cnf(c_0_15153, 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_9535]), ['final']). 6.97/7.26 cnf(c_0_15154, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))=hAPP(c_Set_Oimage(tc_prod(X2,X1),tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X2,X1,tc_prod(X1,X2)),hAPP(c_COMBC(X1,X2,tc_prod(X1,X2)),c_Product__Type_OPair(X1,X2)))),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_9536]), ['final']). 6.97/7.26 cnf(c_0_15155, 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))), inference(split_conjunct,[status(thm)],[c_0_9537]), ['final']). 6.97/7.26 cnf(c_0_15156, 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_9538]), ['final']). 6.97/7.26 cnf(c_0_15157, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),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),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))))), inference(rw,[status(thm)],[c_0_9539, c_0_5606]), ['final']). 6.97/7.26 cnf(c_0_15158, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),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),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9540, c_0_5624]), c_0_5606]), ['final']). 6.97/7.26 cnf(c_0_15159, 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_9541]), ['final']). 6.97/7.26 cnf(c_0_15160, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),c_Int_OMin))),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_9542, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), ['final']). 6.97/7.26 cnf(c_0_15161, 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_9543, c_0_5537]), ['final']). 6.97/7.26 cnf(c_0_15162, 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_9544]), ['final']). 6.97/7.26 cnf(c_0_15163, 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_9545, c_0_5606]), ['final']). 6.97/7.26 cnf(c_0_15164, 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_9546, c_0_6021]), ['final']). 6.97/7.26 cnf(c_0_15165, 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_9547]), ['final']). 6.97/7.26 cnf(c_0_15166, 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_9548, c_0_9549]), ['final']). 6.97/7.26 cnf(c_0_15167, plain, (hAPP(c_List_Orotate1(X1),X2)=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)), inference(split_conjunct,[status(thm)],[c_0_9550]), ['final']). 6.97/7.26 cnf(c_0_15168, 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_9551]), ['final']). 6.97/7.26 cnf(c_0_15169, 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))), inference(split_conjunct,[status(thm)],[c_0_9552]), ['final']). 6.97/7.26 cnf(c_0_15170, 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))), inference(split_conjunct,[status(thm)],[c_0_9553]), ['final']). 6.97/7.26 cnf(c_0_15171, 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_9554]), ['final']). 6.97/7.26 cnf(c_0_15172, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))=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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9555, c_0_5606]), c_0_9556]), ['final']). 6.97/7.26 cnf(c_0_15173, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9557, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), ['final']). 6.97/7.26 cnf(c_0_15174, 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_9558, c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15175, plain, (hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),hAPP(c_List_Orev(X1),X3))=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)),X3)),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_9559, c_0_5794]), c_0_5794]), ['final']). 6.97/7.26 cnf(c_0_15176, 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_9560]), ['final']). 6.97/7.26 cnf(c_0_15177, 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_9561, c_0_6208]), c_0_6208]), ['final']). 6.97/7.26 cnf(c_0_15178, 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9562, c_0_5538]), c_0_5065]), c_0_5946]), c_0_4467]), c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15179, 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)],[c_0_9563, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.26 cnf(c_0_15180, 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)), inference(split_conjunct,[status(thm)],[c_0_9564]), ['final']). 6.97/7.26 cnf(c_0_15181, 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_9565, c_0_4817]), c_0_4467]), c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15182, 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)), inference(split_conjunct,[status(thm)],[c_0_9566]), ['final']). 6.97/7.26 cnf(c_0_15183, 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_9567]), ['final']). 6.97/7.26 cnf(c_0_15184, 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_9568, c_0_4798]), c_0_4817]), c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15185, 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_9569]), ['final']). 6.97/7.26 cnf(c_0_15186, 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_9570]), ['final']). 6.97/7.26 cnf(c_0_15187, 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_9571]), ['final']). 6.97/7.26 cnf(c_0_15188, 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_9572, c_0_5174]), ['final']). 6.97/7.26 cnf(c_0_15189, 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)), inference(rw,[status(thm)],[c_0_9573, c_0_5794]), ['final']). 6.97/7.26 cnf(c_0_15190, 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_9574, c_0_5002]), c_0_5002]), c_0_9575]), c_0_5002]), c_0_5002]), ['final']). 6.97/7.26 cnf(c_0_15191, plain, (hAPP(c_Relation_Oconverse(X1,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X4),X5))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X1),tc_HOL_Obool),X3),c_Relation_Oconverse(X1,X2)),X5))), inference(split_conjunct,[status(thm)],[c_0_9576]), ['final']). 6.97/7.26 cnf(c_0_15192, plain, (hAPP(c_Relation_Oconverse(X1,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X4),X5))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X1),tc_HOL_Obool),X3),c_Relation_Oconverse(X1,X2)),X5))), inference(split_conjunct,[status(thm)],[c_0_9577]), ['final']). 6.97/7.26 cnf(c_0_15193, 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']). 6.97/7.26 cnf(c_0_15194, 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']). 6.97/7.26 cnf(c_0_15195, 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_9578]), ['final']). 6.97/7.26 cnf(c_0_15196, 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_9579]), ['final']). 6.97/7.26 cnf(c_0_15197, 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_9580]), ['final']). 6.97/7.26 cnf(c_0_15198, 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)],[c_0_9581, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.26 cnf(c_0_15199, 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_9582]), ['final']). 6.97/7.26 cnf(c_0_15200, 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_9583]), ['final']). 6.97/7.26 cnf(c_0_15201, 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_9584]), ['final']). 6.97/7.26 cnf(c_0_15202, 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)), inference(split_conjunct,[status(thm)],[c_0_9585]), ['final']). 6.97/7.26 cnf(c_0_15203, 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_9586]), ['final']). 6.97/7.26 cnf(c_0_15204, 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),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),X3)))=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)))), inference(split_conjunct,[status(thm)],[c_0_9587]), ['final']). 6.97/7.26 cnf(c_0_15205, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),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),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))), inference(rw,[status(thm)],[c_0_9588, c_0_5624]), ['final']). 6.97/7.26 cnf(c_0_15206, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),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))), 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_9589, c_0_5815]), c_0_4821]), c_0_5815]), c_0_4821]), c_0_5624]), c_0_9590]), ['final']). 6.97/7.26 cnf(c_0_15207, 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_9591]), ['final']). 6.97/7.26 cnf(c_0_15208, 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)), inference(split_conjunct,[status(thm)],[c_0_9592]), ['final']). 6.97/7.26 cnf(c_0_15209, 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)), inference(split_conjunct,[status(thm)],[c_0_9593]), ['final']). 6.97/7.26 cnf(c_0_15210, 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),esk420_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_9594]), ['final']). 6.97/7.26 cnf(c_0_15211, 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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),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_9595, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), ['final']). 6.97/7.26 cnf(c_0_15212, 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_9596]), ['final']). 6.97/7.26 cnf(c_0_15213, 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_9597]), ['final']). 6.97/7.26 cnf(c_0_15214, 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_9598, c_0_5539]), c_0_5002]), ['final']). 6.97/7.26 cnf(c_0_15215, 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_9599, c_0_4467]), c_0_4817]), c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15216, 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_9600]), ['final']). 6.97/7.26 cnf(c_0_15217, 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))), inference(split_conjunct,[status(thm)],[c_0_9601]), ['final']). 6.97/7.26 cnf(c_0_15218, 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_9602]), ['final']). 6.97/7.26 cnf(c_0_15219, 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))), inference(split_conjunct,[status(thm)],[c_0_9603]), ['final']). 6.97/7.26 cnf(c_0_15220, 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_9604]), ['final']). 6.97/7.26 cnf(c_0_15221, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(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_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_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2)),X5))), inference(split_conjunct,[status(thm)],[c_0_9605]), ['final']). 6.97/7.26 cnf(c_0_15222, plain, (c_Nat__Transfer_Ois__nat(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)),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9606, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), ['final']). 6.97/7.26 cnf(c_0_15223, 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_9607]), ['final']). 6.97/7.26 cnf(c_0_15224, 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_9608]), ['final']). 6.97/7.26 cnf(c_0_15225, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),X5),X6))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X4),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X4),X6))), inference(split_conjunct,[status(thm)],[c_0_9609]), ['final']). 6.97/7.26 cnf(c_0_15226, 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_9610, c_0_6909]), c_0_6909]), c_0_6910]), ['final']). 6.97/7.26 cnf(c_0_15227, 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_9611, c_0_5539]), ['final']). 6.97/7.26 cnf(c_0_15228, 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))), inference(split_conjunct,[status(thm)],[c_0_9612]), ['final']). 6.97/7.26 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_9613]), ['final']). 6.97/7.26 cnf(c_0_15230, 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)), inference(split_conjunct,[status(thm)],[c_0_9614]), ['final']). 6.97/7.26 cnf(c_0_15231, 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)), inference(split_conjunct,[status(thm)],[c_0_9615]), ['final']). 6.97/7.26 cnf(c_0_15232, 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_9616]), ['final']). 6.97/7.26 cnf(c_0_15233, 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)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9617, c_0_5794]), c_0_5794]), c_0_5794]), ['final']). 6.97/7.26 cnf(c_0_15234, plain, (hAPP(c_Set_OPow(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X3)),hAPP(c_Set_Oimage(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_Oinsert(X1),X2)),hAPP(c_Set_OPow(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_9618]), ['final']). 6.97/7.26 cnf(c_0_15235, 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_9619, c_0_5539]), ['final']). 6.97/7.26 cnf(c_0_15236, 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_9620, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_5891]), ['final']). 6.97/7.26 cnf(c_0_15237, plain, (c_Random__Sequence_Omap(X1,X2,X3,X4)=c_Random__Sequence_Obind(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_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),X1,c_Random__Sequence_Osingle(X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_9621]), ['final']). 6.97/7.26 cnf(c_0_15238, 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_9622, c_0_9623]), ['final']). 6.97/7.26 cnf(c_0_15239, 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_9624]), ['final']). 6.97/7.26 cnf(c_0_15240, 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_9625]), ['final']). 6.97/7.26 cnf(c_0_15241, 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_9626, c_0_9627]), c_0_9628]), ['final']). 6.97/7.26 cnf(c_0_15242, 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),esk566_1(X1)),esk567_1(X1)))))=X1), inference(rw,[status(thm)],[c_0_9629, c_0_5539]), ['final']). 6.97/7.26 cnf(c_0_15243, 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_9630, c_0_5065]), c_0_9631]), ['final']). 6.97/7.26 cnf(c_0_15244, 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_9632, c_0_4768]), ['final']). 6.97/7.26 cnf(c_0_15245, 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))), inference(split_conjunct,[status(thm)],[c_0_9633]), ['final']). 6.97/7.26 cnf(c_0_15246, 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_9634, c_0_4768]), ['final']). 6.97/7.26 cnf(c_0_15247, plain, (hAPP(c_Relation_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_Relation_OImage(X1,X2,X3)),X6))), inference(split_conjunct,[status(thm)],[c_0_9635]), ['final']). 6.97/7.26 cnf(c_0_15248, 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_9636]), ['final']). 6.97/7.26 cnf(c_0_15249, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(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_OINFI(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_9637]), ['final']). 6.97/7.26 cnf(c_0_15250, 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))), inference(split_conjunct,[status(thm)],[c_0_9638]), ['final']). 6.97/7.26 cnf(c_0_15251, 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_9639]), ['final']). 6.97/7.26 cnf(c_0_15252, plain, (hAPP(hAPP(c_List_Otake(X1),X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4))=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))), inference(split_conjunct,[status(thm)],[c_0_9640]), ['final']). 6.97/7.26 cnf(c_0_15253, 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_9641, c_0_4817]), c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15254, 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_9642, c_0_9643]), ['final']). 6.97/7.26 cnf(c_0_15255, 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)],[c_0_5647, c_0_9643]), ['final']). 6.97/7.26 cnf(c_0_15256, plain, (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),X3)),X4)=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),X4)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_9644]), ['final']). 6.97/7.26 cnf(c_0_15257, 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_9645]), ['final']). 6.97/7.26 cnf(c_0_15258, 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)),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),X4))), inference(split_conjunct,[status(thm)],[c_0_9646]), ['final']). 6.97/7.26 cnf(c_0_15259, 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))), inference(split_conjunct,[status(thm)],[c_0_9647]), ['final']). 6.97/7.26 cnf(c_0_15260, 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_9648]), ['final']). 6.97/7.26 cnf(c_0_15261, 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))), inference(split_conjunct,[status(thm)],[c_0_9649]), ['final']). 6.97/7.26 cnf(c_0_15262, 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_9650, c_0_4692]), ['final']). 6.97/7.26 cnf(c_0_15263, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),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))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9651, c_0_5624]), c_0_9590]), c_0_4413]), ['final']). 6.97/7.26 cnf(c_0_15264, 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),X4)),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_9652]), ['final']). 6.97/7.26 cnf(c_0_15265, 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_9653]), ['final']). 6.97/7.26 cnf(c_0_15266, 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)), inference(split_conjunct,[status(thm)],[c_0_9654]), ['final']). 6.97/7.26 cnf(c_0_15267, 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_9655]), ['final']). 6.97/7.26 cnf(c_0_15268, plain, (c_Random_Opick(X1,X2)=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))), inference(split_conjunct,[status(thm)],[c_0_9656]), ['final']). 6.97/7.26 cnf(c_0_15269, 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_9657]), ['final']). 6.97/7.26 cnf(c_0_15270, plain, (c_Random_Oselect__weight(X1,X2)=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))), inference(split_conjunct,[status(thm)],[c_0_9658]), ['final']). 6.97/7.26 cnf(c_0_15271, 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_9659]), ['final']). 6.97/7.26 cnf(c_0_15272, 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_9660, c_0_5537]), ['final']). 6.97/7.26 cnf(c_0_15273, 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)), inference(split_conjunct,[status(thm)],[c_0_9661]), ['final']). 6.97/7.26 cnf(c_0_15274, plain, (c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),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_9662, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), c_0_4741]), c_0_4415]), ['final']). 6.97/7.26 cnf(c_0_15275, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),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)),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_9663]), ['final']). 6.97/7.26 cnf(c_0_15276, 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_9664]), ['final']). 6.97/7.26 cnf(c_0_15277, 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_9665, c_0_4742]), c_0_6021]), c_0_6030]), c_0_7255]), ['final']). 6.97/7.26 cnf(c_0_15278, 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_9666, c_0_9667]), ['final']). 6.97/7.26 cnf(c_0_15279, 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)],[c_0_9668, c_0_4415]), c_0_4415]), c_0_4415]), c_0_4415]), ['final']). 6.97/7.26 cnf(c_0_15280, 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_9669, c_0_5065]), c_0_5065])]), ['final']). 6.97/7.26 cnf(c_0_15281, 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_9670, c_0_4817]), ['final']). 6.97/7.26 cnf(c_0_15282, 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_9671, c_0_5539]), ['final']). 6.97/7.26 cnf(c_0_15283, 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_9672, c_0_5539]), ['final']). 6.97/7.26 cnf(c_0_15284, 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_9673, c_0_9674]), ['final']). 6.97/7.26 cnf(c_0_15285, 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_9675]), ['final']). 6.97/7.26 cnf(c_0_15286, 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_9676]), ['final']). 6.97/7.26 cnf(c_0_15287, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),X3),c_List_OtakeWhile(X2,X4,X5))=c_List_OtakeWhile(tc_prod(X1,X2),hAPP(c_Fun_Ocomp(X2,tc_HOL_Obool,tc_prod(X1,X2),X4),c_Product__Type_Osnd(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X5))), inference(split_conjunct,[status(thm)],[c_0_9677]), ['final']). 6.97/7.26 cnf(c_0_15288, 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_9678]), ['final']). 6.97/7.26 cnf(c_0_15289, 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))), inference(split_conjunct,[status(thm)],[c_0_9679]), ['final']). 6.97/7.26 cnf(c_0_15290, 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_9680, c_0_5539]), c_0_5539]), ['final']). 6.97/7.26 cnf(c_0_15291, 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_9681]), ['final']). 6.97/7.26 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_9682]), ['final']). 6.97/7.26 cnf(c_0_15293, 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_9683, c_0_9628]), ['final']). 6.97/7.26 cnf(c_0_15294, 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_9684, c_0_4977]), ['final']). 6.97/7.26 cnf(c_0_15295, 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_9685, c_0_9686]), ['final']). 6.97/7.26 cnf(c_0_15296, 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_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__less)=c_FunDef_Opair__leq), inference(rw,[status(thm)],[c_0_9687, c_0_6253]), ['final']). 6.97/7.26 cnf(c_0_15297, 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_9688]), ['final']). 6.97/7.26 cnf(c_0_15298, 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)), inference(split_conjunct,[status(thm)],[c_0_9689]), ['final']). 6.97/7.26 cnf(c_0_15299, 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_9690, c_0_4978]), c_0_4978]), ['final']). 6.97/7.26 cnf(c_0_15300, 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_9691]), ['final']). 6.97/7.26 cnf(c_0_15301, 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_9692]), ['final']). 6.97/7.26 cnf(c_0_15302, 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_9693]), ['final']). 6.97/7.26 cnf(c_0_15303, 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_9694, c_0_5794]), c_0_5794]), ['final']). 6.97/7.26 cnf(c_0_15304, plain, (hAPP(hAPP(c_Nat_Ocompow(X1,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),X4)=hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(hAPP(c_Nat_Ocompow(X1,X1),X2),X4)),hAPP(hAPP(c_Nat_Ocompow(X1,X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_9695]), ['final']). 6.97/7.26 cnf(c_0_15305, 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_9696, c_0_4768]), c_0_4768]), c_0_4768]), ['final']). 6.97/7.26 cnf(c_0_15306, 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_9697]), ['final']). 6.97/7.26 cnf(c_0_15307, 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_9698, c_0_4768]), c_0_4768]), c_0_4768]), ['final']). 6.97/7.26 cnf(c_0_15308, 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_9699, c_0_4768]), c_0_4768]), c_0_4768]), ['final']). 6.97/7.26 cnf(c_0_15309, 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_9700, c_0_9701]), ['final']). 6.97/7.26 cnf(c_0_15310, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Int_OMin)=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),c_Int_OMin),c_Int_OMin))), inference(rw,[status(thm)],[c_0_9702, c_0_5624]), ['final']). 6.97/7.26 cnf(c_0_15311, 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_9703, c_0_5947]), ['final']). 6.97/7.26 cnf(c_0_15312, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(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),X1)),c_Int_OMin))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))), inference(rw,[status(thm)],[c_0_9704, c_0_5624]), ['final']). 6.97/7.26 cnf(c_0_15313, 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_9705]), ['final']). 6.97/7.26 cnf(c_0_15314, 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_9706]), ['final']). 6.97/7.26 cnf(c_0_15315, 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_9707])]), c_0_9708]), c_0_9708])]), ['final']). 6.97/7.26 cnf(c_0_15316, 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_9709]), ['final']). 6.97/7.26 cnf(c_0_15317, 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_9710, c_0_4881]), c_0_4881]), ['final']). 6.97/7.26 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_9711]), ['final']). 6.97/7.26 cnf(c_0_15319, 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))), inference(split_conjunct,[status(thm)],[c_0_9712]), ['final']). 6.97/7.26 cnf(c_0_15320, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X3),X4))=hAPP(c_Finite__Set_Ocard(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OSigma(X1,X3),X2),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X1),X4)))), inference(split_conjunct,[status(thm)],[c_0_9713]), ['final']). 6.97/7.26 cnf(c_0_15321, 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_9714]), ['final']). 6.97/7.26 cnf(c_0_15322, plain, (hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),X4)=c_Hilbert__Choice_OEps(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))), inference(split_conjunct,[status(thm)],[c_0_9715]), ['final']). 6.97/7.26 cnf(c_0_15323, 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_9716, c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15324, 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))), inference(split_conjunct,[status(thm)],[c_0_9717]), ['final']). 6.97/7.26 cnf(c_0_15325, 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_9718, c_0_4881]), ['final']). 6.97/7.26 cnf(c_0_15326, 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_9719]), ['final']). 6.97/7.26 cnf(c_0_15327, 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_9720]), ['final']). 6.97/7.26 cnf(c_0_15328, 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_9721]), ['final']). 6.97/7.26 cnf(c_0_15329, 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_9722]), ['final']). 6.97/7.26 cnf(c_0_15330, plain, (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))=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))), inference(split_conjunct,[status(thm)],[c_0_9723]), ['final']). 6.97/7.26 cnf(c_0_15331, plain, (hAPP(c_Relation_ORange(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(X2,tc_HOL_Obool)),hAPP(c_Relation_ORange(X1,X2),X3)),hAPP(c_Relation_ORange(X1,X2),X4))), inference(split_conjunct,[status(thm)],[c_0_9724]), ['final']). 6.97/7.26 cnf(c_0_15332, 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_9725, c_0_9726]), ['final']). 6.97/7.26 cnf(c_0_15333, 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_9727, c_0_9728]), ['final']). 6.97/7.26 cnf(c_0_15334, 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_9729]), ['final']). 6.97/7.26 cnf(c_0_15335, 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)), inference(split_conjunct,[status(thm)],[c_0_9730]), ['final']). 6.97/7.26 cnf(c_0_15336, 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_9731]), ['final']). 6.97/7.26 cnf(c_0_15337, 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_9732]), ['final']). 6.97/7.26 cnf(c_0_15338, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_Relation_ODomain(X1,X3),X4))=hAPP(c_Relation_ODomain(X1,X3),hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X2),X5)),X4))), inference(split_conjunct,[status(thm)],[c_0_9733]), ['final']). 6.97/7.26 cnf(c_0_15339, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_Relation_ORange(X3,X1),X4))=hAPP(c_Relation_ORange(X3,X1),hAPP(hAPP(c_Set_Oinsert(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),X5),X2)),X4))), inference(split_conjunct,[status(thm)],[c_0_9734]), ['final']). 6.97/7.26 cnf(c_0_15340, plain, (X1=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X2,tc_HOL_Obool)),X1),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))))), inference(split_conjunct,[status(thm)],[c_0_9735]), ['final']). 6.97/7.26 cnf(c_0_15341, 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_9736]), ['final']). 6.97/7.26 cnf(c_0_15342, 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_9737]), ['final']). 6.97/7.26 cnf(c_0_15343, plain, (hAPP(hAPP(X1,X2),X3)=c_Option_Ooption_Ooption__case(X4,tc_prod(X5,tc_Lazy__Sequence_Olazy__sequence(X5)),X6,hAPP(c_Product__Type_Oprod_Oprod__case(X5,tc_Lazy__Sequence_Olazy__sequence(X5),X4),X1),hAPP(c_Lazy__Sequence_Oyield(X5),c_Lazy__Sequence_Olazy__sequence_OInsert(X5,X2,X3)))), inference(rw,[status(thm)],[c_0_9738, c_0_9739]), ['final']). 6.97/7.26 cnf(c_0_15344, 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_9740, c_0_4467]), c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15345, 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_9741, c_0_5539]), ['final']). 6.97/7.26 cnf(c_0_15346, 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)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9742, c_0_5794]), c_0_5794]), ['final']). 6.97/7.26 cnf(c_0_15347, 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))), inference(split_conjunct,[status(thm)],[c_0_9743]), ['final']). 6.97/7.26 cnf(c_0_15348, 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_9744, c_0_6585]), ['final']). 6.97/7.26 cnf(c_0_15349, 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_9745, c_0_4645]), ['final']). 6.97/7.26 cnf(c_0_15350, 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_9746]), ['final']). 6.97/7.26 cnf(c_0_15351, 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_9747]), ['final']). 6.97/7.26 cnf(c_0_15352, 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))), inference(split_conjunct,[status(thm)],[c_0_9748]), ['final']). 6.97/7.26 cnf(c_0_15353, 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)), inference(split_conjunct,[status(thm)],[c_0_9749]), ['final']). 6.97/7.26 cnf(c_0_15354, 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_9750, c_0_4768]), ['final']). 6.97/7.26 cnf(c_0_15355, 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_9751, c_0_4881]), ['final']). 6.97/7.26 cnf(c_0_15356, 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_9752]), ['final']). 6.97/7.26 cnf(c_0_15357, 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_9753, c_0_5560]), ['final']). 6.97/7.26 cnf(c_0_15358, 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))), inference(split_conjunct,[status(thm)],[c_0_9754]), ['final']). 6.97/7.26 cnf(c_0_15359, 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))), inference(split_conjunct,[status(thm)],[c_0_9755]), ['final']). 6.97/7.26 cnf(c_0_15360, plain, (hAPP(hAPP(c_List_Otake(X1),X2),hAPP(hAPP(c_List_Odrop(X1),X3),X4))=hAPP(hAPP(c_List_Odrop(X1),X3),hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),X4))), inference(split_conjunct,[status(thm)],[c_0_9756]), ['final']). 6.97/7.26 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_9757]), ['final']). 6.97/7.26 cnf(c_0_15362, 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_9758, c_0_4881]), c_0_4881]), ['final']). 6.97/7.26 cnf(c_0_15363, 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_9759]), ['final']). 6.97/7.26 cnf(c_0_15364, 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)), inference(split_conjunct,[status(thm)],[c_0_9760]), ['final']). 6.97/7.26 cnf(c_0_15365, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_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_9761]), ['final']). 6.97/7.26 cnf(c_0_15366, 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_9762]), ['final']). 6.97/7.26 cnf(c_0_15367, 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_9763]), ['final']). 6.97/7.26 cnf(c_0_15368, 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))), inference(split_conjunct,[status(thm)],[c_0_9764]), ['final']). 6.97/7.26 cnf(c_0_15369, 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))), inference(split_conjunct,[status(thm)],[c_0_9765]), ['final']). 6.97/7.26 cnf(c_0_15370, 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_9766]), ['final']). 6.97/7.26 cnf(c_0_15371, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3))=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))), inference(split_conjunct,[status(thm)],[c_0_9767]), ['final']). 6.97/7.26 cnf(c_0_15372, 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_9768]), ['final']). 6.97/7.26 cnf(c_0_15373, 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))), inference(split_conjunct,[status(thm)],[c_0_9769]), ['final']). 6.97/7.26 cnf(c_0_15374, 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_9770, c_0_5539]), ['final']). 6.97/7.26 cnf(c_0_15375, 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(er,[status(thm)],[inference(rw,[status(thm)],[c_0_9771, c_0_4768])]), ['final']). 6.97/7.26 cnf(c_0_15376, 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_9772, c_0_5539]), c_0_9773]), ['final']). 6.97/7.26 cnf(c_0_15377, 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))), inference(split_conjunct,[status(thm)],[c_0_9774]), ['final']). 6.97/7.26 cnf(c_0_15378, 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_9775, c_0_4645]), ['final']). 6.97/7.26 cnf(c_0_15379, 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_9776]), ['final']). 6.97/7.26 cnf(c_0_15380, plain, (hAPP(c_Relation_OField(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__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OField(X1),X2)),hAPP(c_Relation_OField(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_9777]), ['final']). 6.97/7.26 cnf(c_0_15381, 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_9778]), ['final']). 6.97/7.26 cnf(c_0_15382, 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_9779]), ['final']). 6.97/7.26 cnf(c_0_15383, 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_9780, c_0_4978]), c_0_4978]), ['final']). 6.97/7.26 cnf(c_0_15384, 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_9781, c_0_6370]), c_0_6370]), ['final']). 6.97/7.26 cnf(c_0_15385, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),hAPP(X3,X4)),hAPP(X5,X6))=hAPP(c_Product__Type_Omap__pair(X7,X1,X8,X2,X3,X5),hAPP(hAPP(c_Product__Type_OPair(X7,X8),X4),X6))), inference(split_conjunct,[status(thm)],[c_0_9782]), ['final']). 6.97/7.26 cnf(c_0_15386, 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))), inference(split_conjunct,[status(thm)],[c_0_9783]), ['final']). 6.97/7.26 cnf(c_0_15387, 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), inference(rw,[status(thm)],[c_0_9784, c_0_4813]), ['final']). 6.97/7.26 cnf(c_0_15388, 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_9785]), ['final']). 6.97/7.26 cnf(c_0_15389, 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),X2),X3))=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)), inference(split_conjunct,[status(thm)],[c_0_9786]), ['final']). 6.97/7.26 cnf(c_0_15390, 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_9787, c_0_4977]), ['final']). 6.97/7.26 cnf(c_0_15391, 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_9788, c_0_4742]), c_0_6030]), ['final']). 6.97/7.26 cnf(c_0_15392, 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_9789, c_0_4471]), ['final']). 6.97/7.26 cnf(c_0_15393, 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_9790, c_0_4742]), c_0_6021]), c_0_6030]), ['final']). 6.97/7.26 cnf(c_0_15394, 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_9791, c_0_4881]), c_0_4881]), ['final']). 6.97/7.26 cnf(c_0_15395, 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_9792, c_0_5560]), ['final']). 6.97/7.26 cnf(c_0_15396, 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)), inference(rw,[status(thm)],[c_0_9793, c_0_5560]), ['final']). 6.97/7.26 cnf(c_0_15397, 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_9794]), ['final']). 6.97/7.26 cnf(c_0_15398, 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))), inference(split_conjunct,[status(thm)],[c_0_9795]), ['final']). 6.97/7.26 cnf(c_0_15399, plain, (hAPP(c_New__DSequence_Oneg__bind(X1,X2,X3,X4),X5)=c_Lazy__Sequence_Ohb__bind(X1,X2,hAPP(X3,X5),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2))),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_9796]), ['final']). 6.97/7.26 cnf(c_0_15400, 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_9797]), ['final']). 6.97/7.26 cnf(c_0_15401, 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), inference(split_conjunct,[status(thm)],[c_0_9798]), ['final']). 6.97/7.26 cnf(c_0_15402, 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_9799]), ['final']). 6.97/7.26 cnf(c_0_15403, plain, (c_List_Oreplicate(X1,X2,X3)=hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),hAPP(c_COMBK(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)),X2)))), inference(rw,[status(thm)],[c_0_9800, c_0_4471]), ['final']). 6.97/7.26 cnf(c_0_15404, 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_9801])])]), c_0_9802]), c_0_4742]), c_0_9803]), ['final']). 6.97/7.26 cnf(c_0_15405, 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_9804, c_0_9631]), ['final']). 6.97/7.26 cnf(c_0_15406, plain, (hAPP(c_List_Ofilter(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4))=hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Ofilter(X1,X2),X3)),hAPP(c_List_Ofilter(X1,X2),X4))), inference(split_conjunct,[status(thm)],[c_0_9805]), ['final']). 6.97/7.26 cnf(c_0_15407, 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_9806]), ['final']). 6.97/7.26 cnf(c_0_15408, 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_9807]), ['final']). 6.97/7.26 cnf(c_0_15409, 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_9808]), ['final']). 6.97/7.26 cnf(c_0_15410, 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_9809]), ['final']). 6.97/7.26 cnf(c_0_15411, 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))), inference(split_conjunct,[status(thm)],[c_0_9810]), ['final']). 6.97/7.26 cnf(c_0_15412, 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_9811]), ['final']). 6.97/7.26 cnf(c_0_15413, 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_9812]), ['final']). 6.97/7.26 cnf(c_0_15414, 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)), inference(split_conjunct,[status(thm)],[c_0_9813]), ['final']). 6.97/7.26 cnf(c_0_15415, 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)), inference(split_conjunct,[status(thm)],[c_0_9814]), ['final']). 6.97/7.26 cnf(c_0_15416, 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)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9815]), ['final']). 6.97/7.26 cnf(c_0_15417, 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_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_9816]), ['final']). 6.97/7.26 cnf(c_0_15418, 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_9817, c_0_5746]), ['final']). 6.97/7.26 cnf(c_0_15419, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Otake(X1),X3),X4))=hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_OSuc,X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_9818]), ['final']). 6.97/7.26 cnf(c_0_15420, 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_9819]), ['final']). 6.97/7.26 cnf(c_0_15421, 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_9820, c_0_4768]), ['final']). 6.97/7.26 cnf(c_0_15422, 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),X1)),c_Int_OMin))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)), inference(rw,[status(thm)],[c_0_9821, c_0_5815]), ['final']). 6.97/7.26 cnf(c_0_15423, plain, (c_List_Olex(X1,X2)=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))), inference(split_conjunct,[status(thm)],[c_0_9822]), ['final']). 6.97/7.26 cnf(c_0_15424, 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_9823, c_0_4768]), ['final']). 6.97/7.26 cnf(c_0_15425, 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_9824, c_0_4768]), ['final']). 6.97/7.26 cnf(c_0_15426, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_COMBI(X1))=X2), inference(rw,[status(thm)],[c_0_9825, c_0_4768]), ['final']). 6.97/7.26 cnf(c_0_15427, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_Fun_Oid(X1))=X2), inference(rw,[status(thm)],[c_0_9826, c_0_4768]), ['final']). 6.97/7.26 cnf(c_0_15428, 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_9827, c_0_4471]), c_0_4471]), ['final']). 6.97/7.26 cnf(c_0_15429, 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_9828]), ['final']). 6.97/7.26 cnf(c_0_15430, 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_9829]), ['final']). 6.97/7.26 cnf(c_0_15431, 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)), inference(split_conjunct,[status(thm)],[c_0_9830]), ['final']). 6.97/7.26 cnf(c_0_15432, 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_9831]), ['final']). 6.97/7.26 cnf(c_0_15433, 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_9832, c_0_4415]), c_0_5002]), c_0_4742]), ['final']). 6.97/7.26 cnf(c_0_15434, 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))), inference(er,[status(thm)],[c_0_9833]), ['final']). 6.97/7.26 cnf(c_0_15435, plain, (X1=c_Option_Ooption_Ooption__case(X2,tc_prod(X3,tc_Lazy__Sequence_Olazy__sequence(X3)),X1,hAPP(c_Product__Type_Oprod_Oprod__case(X3,tc_Lazy__Sequence_Olazy__sequence(X3),X2),X4),hAPP(c_Lazy__Sequence_Oyield(X3),c_Lazy__Sequence_Olazy__sequence_OEmpty(X3)))), inference(rw,[status(thm)],[c_0_9834, c_0_9739]), ['final']). 6.97/7.26 cnf(c_0_15436, plain, (hAPP(c_List_Orev(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_Olist_OCons(X1)),c_List_Olist_ONil(X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_9835]), ['final']). 6.97/7.26 cnf(c_0_15437, 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_9836, c_0_5815]), ['final']). 6.97/7.26 cnf(c_0_15438, 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))), inference(split_conjunct,[status(thm)],[c_0_9837]), ['final']). 6.97/7.26 cnf(c_0_15439, 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_9838]), ['final']). 6.97/7.26 cnf(c_0_15440, 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_9839]), ['final']). 6.97/7.26 cnf(c_0_15441, 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_9840, c_0_5560]), ['final']). 6.97/7.26 cnf(c_0_15442, 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_9841]), ['final']). 6.97/7.26 cnf(c_0_15443, plain, (c_Fun_Oinj__on(X1,tc_prod(X2,X1),esk420_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_9594]), ['final']). 6.97/7.26 cnf(c_0_15444, 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_9842]), ['final']). 6.97/7.26 cnf(c_0_15445, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(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_9843, c_0_5794]), ['final']). 6.97/7.26 cnf(c_0_15446, 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))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)), inference(rw,[status(thm)],[c_0_9844, c_0_5815]), ['final']). 6.97/7.26 cnf(c_0_15447, 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_9845, c_0_5002]), c_0_5002]), ['final']). 6.97/7.26 cnf(c_0_15448, 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_9846]), c_0_9847]), c_0_9847]), ['final']). 6.97/7.26 cnf(c_0_15449, 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_9848]), ['final']). 6.97/7.26 cnf(c_0_15450, 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_9849]), ['final']). 6.97/7.26 cnf(c_0_15451, 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_9850, c_0_5941]), c_0_9851]), c_0_4742]), c_0_5941]), c_0_5746]), ['final']). 6.97/7.26 cnf(c_0_15452, 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_9852, c_0_9853]), ['final']). 6.97/7.26 cnf(c_0_15453, 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_9854, c_0_6285]), ['final']). 6.97/7.26 cnf(c_0_15454, 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_9855]), ['final']). 6.97/7.26 cnf(c_0_15455, plain, (hAPP(c_Relation_OField(X1),X2)=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))), inference(split_conjunct,[status(thm)],[c_0_9856]), ['final']). 6.97/7.26 cnf(c_0_15456, 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_9857]), ['final']). 6.97/7.26 cnf(c_0_15457, 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_9858]), ['final']). 6.97/7.26 cnf(c_0_15458, 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_9859]), ['final']). 6.97/7.26 cnf(c_0_15459, 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_9860]), ['final']). 6.97/7.26 cnf(c_0_15460, 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_9861]), ['final']). 6.97/7.26 cnf(c_0_15461, 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_9862]), ['final']). 6.97/7.26 cnf(c_0_15462, 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_9863]), ['final']). 6.97/7.26 cnf(c_0_15463, 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_9864]), ['final']). 6.97/7.26 cnf(c_0_15464, 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_9865]), ['final']). 6.97/7.26 cnf(c_0_15465, 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_9866, c_0_4881]), ['final']). 6.97/7.26 cnf(c_0_15466, 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))), inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_9867])]), ['final']). 6.97/7.26 cnf(c_0_15467, 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_9868]), ['final']). 6.97/7.26 cnf(c_0_15468, 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_9869]), ['final']). 6.97/7.26 cnf(c_0_15469, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_9870]), ['final']). 6.97/7.26 cnf(c_0_15470, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_9871]), ['final']). 6.97/7.26 cnf(c_0_15471, 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_9872]), ['final']). 6.97/7.26 cnf(c_0_15472, 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_9873]), ['final']). 6.97/7.26 cnf(c_0_15473, plain, (c_List_Obutlast(X1,X2)=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)), inference(split_conjunct,[status(thm)],[c_0_9874]), ['final']). 6.97/7.26 cnf(c_0_15474, 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_9875]), ['final']). 6.97/7.26 cnf(c_0_15475, 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_9876]), ['final']). 6.97/7.26 cnf(c_0_15476, 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_9877]), ['final']). 6.97/7.26 cnf(c_0_15477, plain, (c_List_Oreplicate(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3),X4)=hAPP(hAPP(c_List_Oappend(X1),c_List_Oreplicate(X1,X2,X4)),c_List_Oreplicate(X1,X3,X4))), inference(split_conjunct,[status(thm)],[c_0_9878]), ['final']). 6.97/7.26 cnf(c_0_15478, 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)), inference(split_conjunct,[status(thm)],[c_0_9879]), ['final']). 6.97/7.26 cnf(c_0_15479, 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_9880]), ['final']). 6.97/7.26 cnf(c_0_15480, 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_9881, c_0_4742]), ['final']). 6.97/7.26 cnf(c_0_15481, 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_9882, c_0_5202]), c_0_4742]), c_0_6030]), ['final']). 6.97/7.26 cnf(c_0_15482, 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_9883]), ['final']). 6.97/7.26 cnf(c_0_15483, 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_9884]), ['final']). 6.97/7.26 cnf(c_0_15484, 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_9885]), ['final']). 6.97/7.26 cnf(c_0_15485, 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_9886]), ['final']). 6.97/7.26 cnf(c_0_15486, 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_9887]), ['final']). 6.97/7.26 cnf(c_0_15487, 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_9888]), ['final']). 6.97/7.26 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_9889, c_0_5794]), ['final']). 6.97/7.26 cnf(c_0_15489, 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_9890]), ['final']). 6.97/7.26 cnf(c_0_15490, 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)), inference(split_conjunct,[status(thm)],[c_0_9891]), ['final']). 6.97/7.26 cnf(c_0_15491, 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_9892]), ['final']). 6.97/7.26 cnf(c_0_15492, 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_9893]), ['final']). 6.97/7.26 cnf(c_0_15493, plain, (hAPP(c_List_Ofilter(X1,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X1,c_fNot),X2)),X3)=hAPP(c_Product__Type_Osnd(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Opartition(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_9894]), ['final']). 6.97/7.26 cnf(c_0_15494, 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_9895]), ['final']). 6.97/7.26 cnf(c_0_15495, 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_9896]), ['final']). 6.97/7.26 cnf(c_0_15496, 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)), inference(rw,[status(thm)],[c_0_9897, c_0_4645]), ['final']). 6.97/7.26 cnf(c_0_15497, 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_9898]), ['final']). 6.97/7.26 cnf(c_0_15498, 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_9899, c_0_5174]), ['final']). 6.97/7.26 cnf(c_0_15499, 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_9900, c_0_5174]), ['final']). 6.97/7.26 cnf(c_0_15500, 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_9901]), ['final']). 6.97/7.26 cnf(c_0_15501, 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_9902]), ['final']). 6.97/7.26 cnf(c_0_15502, 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_9903, c_0_5539]), ['final']). 6.97/7.26 cnf(c_0_15503, 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_9904, c_0_5560]), c_0_5560]), ['final']). 6.97/7.26 cnf(c_0_15504, 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_9905, c_0_5539]), ['final']). 6.97/7.26 cnf(c_0_15505, 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(rw,[status(thm)],[c_0_9906, c_0_9907]), ['final']). 6.97/7.26 cnf(c_0_15506, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(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),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9908]), ['final']). 6.97/7.26 cnf(c_0_15507, plain, (c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)=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)))), inference(split_conjunct,[status(thm)],[c_0_9909]), ['final']). 6.97/7.26 cnf(c_0_15508, plain, (c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)=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)))), inference(split_conjunct,[status(thm)],[c_0_9910]), ['final']). 6.97/7.26 cnf(c_0_15509, 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_9911, c_0_4467])]), ['final']). 6.97/7.26 cnf(c_0_15510, 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_9912]), ['final']). 6.97/7.26 cnf(c_0_15511, 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_9913, c_0_5538]), ['final']). 6.97/7.26 cnf(c_0_15512, 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_9914, c_0_5538]), ['final']). 6.97/7.26 cnf(c_0_15513, plain, (c_Predicate_Oconversep(X1,X2,c_Predicate_Opred__comp(X1,X3,X2,X4,X5))=c_Predicate_Opred__comp(X2,X3,X1,c_Predicate_Oconversep(X3,X2,X5),c_Predicate_Oconversep(X1,X3,X4))), inference(split_conjunct,[status(thm)],[c_0_9915]), ['final']). 6.97/7.26 cnf(c_0_15514, 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)), inference(split_conjunct,[status(thm)],[c_0_9916]), ['final']). 6.97/7.26 cnf(c_0_15515, 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_9917]), ['final']). 6.97/7.26 cnf(c_0_15516, 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_9918]), ['final']). 6.97/7.26 cnf(c_0_15517, 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_9919]), ['final']). 6.97/7.26 cnf(c_0_15518, 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_9920]), ['final']). 6.97/7.26 cnf(c_0_15519, 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_9921]), ['final']). 6.97/7.26 cnf(c_0_15520, plain, (hAPP(hAPP(c_List_Otake(X1),X2),hAPP(c_List_Otl(X1),X3))=hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_OSuc,X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_9922]), ['final']). 6.97/7.26 cnf(c_0_15521, 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_9923]), ['final']). 6.97/7.26 cnf(c_0_15522, 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)), inference(split_conjunct,[status(thm)],[c_0_9924]), ['final']). 6.97/7.26 cnf(c_0_15523, 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_9925]), ['final']). 6.97/7.26 cnf(c_0_15524, 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_9926, c_0_4742]), c_0_6030]), ['final']). 6.97/7.26 cnf(c_0_15525, 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))), inference(split_conjunct,[status(thm)],[c_0_9927]), ['final']). 6.97/7.26 cnf(c_0_15526, 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_9928, c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15527, 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_9929, c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15528, 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_9930]), ['final']). 6.97/7.26 cnf(c_0_15529, 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_9931]), ['final']). 6.97/7.26 cnf(c_0_15530, 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_9932]), ['final']). 6.97/7.26 cnf(c_0_15531, plain, (c_Relation_Osym(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(c_Relation_Oconverse(X1,X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_9933]), ['final']). 6.97/7.26 cnf(c_0_15532, plain, (c_Relation_Osym(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(c_Relation_Oconverse(X1,X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_9934]), ['final']). 6.97/7.26 cnf(c_0_15533, 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_9935]), ['final']). 6.97/7.26 cnf(c_0_15534, 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_9936]), ['final']). 6.97/7.26 cnf(c_0_15535, 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_9937]), ['final']). 6.97/7.26 cnf(c_0_15536, 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_9938]), ['final']). 6.97/7.26 cnf(c_0_15537, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Int_OMin))),c_Int_OMin))=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_9939, c_0_9940]), ['final']). 6.97/7.26 cnf(c_0_15538, 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_9941]), ['final']). 6.97/7.26 cnf(c_0_15539, 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_9942]), ['final']). 6.97/7.26 cnf(c_0_15540, 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_9943]), c_0_9944]), ['final']). 6.97/7.26 cnf(c_0_15541, 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_9945]), ['final']). 6.97/7.26 cnf(c_0_15542, 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_9946, c_0_5202]), ['final']). 6.97/7.26 cnf(c_0_15543, 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_9947, c_0_5202]), ['final']). 6.97/7.26 cnf(c_0_15544, 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_9948, c_0_5202]), ['final']). 6.97/7.26 cnf(c_0_15545, 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_9949, c_0_5202]), ['final']). 6.97/7.26 cnf(c_0_15546, 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_9950, c_0_5560]), ['final']). 6.97/7.26 cnf(c_0_15547, 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)), inference(split_conjunct,[status(thm)],[c_0_9951]), ['final']). 6.97/7.26 cnf(c_0_15548, plain, (X1=hAPP(hAPP(c_Relation_Orel__comp(X2,X3,X3),X1),c_Transitive__Closure_Ortrancl(X3,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_HOL_Obool))))), inference(rw,[status(thm)],[c_0_9952, c_0_5560]), ['final']). 6.97/7.26 cnf(c_0_15549, 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_9953]), ['final']). 6.97/7.26 cnf(c_0_15550, 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_9954]), ['final']). 6.97/7.26 cnf(c_0_15551, 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_9955])]), ['final']). 6.97/7.26 cnf(c_0_15552, 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_9956]), ['final']). 6.97/7.26 cnf(c_0_15553, 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_9957, c_0_6783]), ['final']). 6.97/7.26 cnf(c_0_15554, 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_9958]), ['final']). 6.97/7.26 cnf(c_0_15555, 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))), inference(split_conjunct,[status(thm)],[fact_INT__greaterThan__UNIV]), ['final']). 6.97/7.26 cnf(c_0_15556, 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))), inference(split_conjunct,[status(thm)],[fact_UN__atLeast__UNIV]), ['final']). 6.97/7.26 cnf(c_0_15557, 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']). 6.97/7.26 cnf(c_0_15558, 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_OatMost(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[fact_UN__atMost__UNIV]), ['final']). 6.97/7.26 cnf(c_0_15559, 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_9959]), ['final']). 6.97/7.26 cnf(c_0_15560, 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_9960]), ['final']). 6.97/7.26 cnf(c_0_15561, 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_9961, c_0_4413]), c_0_4413]), c_0_4456]), c_0_4740]), ['final']). 6.97/7.26 cnf(c_0_15562, 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_9962, c_0_5038]), c_0_7514]), ['final']). 6.97/7.26 cnf(c_0_15563, 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))), inference(split_conjunct,[status(thm)],[c_0_9963]), ['final']). 6.97/7.26 cnf(c_0_15564, 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_9964]), ['final']). 6.97/7.26 cnf(c_0_15565, 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_9965, c_0_4881]), c_0_4881]), ['final']). 6.97/7.26 cnf(c_0_15566, 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_9966, c_0_4978]), c_0_4978]), ['final']). 6.97/7.26 cnf(c_0_15567, 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_9967]), ['final']). 6.97/7.26 cnf(c_0_15568, 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_9968, c_0_5202]), c_0_5202]), c_0_5202]), ['final']). 6.97/7.26 cnf(c_0_15569, 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_9969, c_0_5202]), c_0_5202]), c_0_5202]), ['final']). 6.97/7.26 cnf(c_0_15570, 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_9970]), ['final']). 6.97/7.26 cnf(c_0_15571, 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_9971]), ['final']). 6.97/7.26 cnf(c_0_15572, 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))), inference(split_conjunct,[status(thm)],[c_0_9972]), ['final']). 6.97/7.26 cnf(c_0_15573, 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)), inference(split_conjunct,[status(thm)],[c_0_9973]), ['final']). 6.97/7.26 cnf(c_0_15574, 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_9974, c_0_4881]), ['final']). 6.97/7.26 cnf(c_0_15575, 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_9975]), ['final']). 6.97/7.26 cnf(c_0_15576, 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_9976]), ['final']). 6.97/7.26 cnf(c_0_15577, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=hAPP(c_List_Oset(X1),c_List_Oreplicate(X1,hAPP(c_Nat_OSuc,X3),X2))), inference(split_conjunct,[status(thm)],[c_0_9977]), ['final']). 6.97/7.26 cnf(c_0_15578, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)=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,X2),X1)))), inference(rw,[status(thm)],[c_0_9978, c_0_4471]), ['final']). 6.97/7.26 cnf(c_0_15579, 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_9979]), ['final']). 6.97/7.26 cnf(c_0_15580, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9980]), ['final']). 6.97/7.26 cnf(c_0_15581, 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_9981]), ['final']). 6.97/7.26 cnf(c_0_15582, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_9982]), ['final']). 6.97/7.26 cnf(c_0_15583, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)=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)))), inference(rw,[status(thm)],[c_0_9983, c_0_6164]), ['final']). 6.97/7.26 cnf(c_0_15584, 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_9984]), ['final']). 6.97/7.26 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_9985]), ['final']). 6.97/7.26 cnf(c_0_15586, 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_9986, c_0_6783]), c_0_6783]), ['final']). 6.97/7.26 cnf(c_0_15587, plain, (hAPP(hAPP(c_Product__Type_Ocurry(X1,X2,X3,X4),X5),X6)=hAPP(X4,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6))), inference(split_conjunct,[status(thm)],[c_0_9987]), ['final']). 6.97/7.26 cnf(c_0_15588, plain, (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,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X2)), inference(split_conjunct,[status(thm)],[c_0_9988]), ['final']). 6.97/7.26 cnf(c_0_15589, 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_9989, c_0_5746]), ['final']). 6.97/7.26 cnf(c_0_15590, 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_9990]), ['final']). 6.97/7.26 cnf(c_0_15591, 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))), inference(split_conjunct,[status(thm)],[c_0_9991]), ['final']). 6.97/7.26 cnf(c_0_15592, 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_9992]), ['final']). 6.97/7.26 cnf(c_0_15593, 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_9993, c_0_5202]), c_0_4742]), c_0_6030]), ['final']). 6.97/7.26 cnf(c_0_15594, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2))=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))), inference(split_conjunct,[status(thm)],[c_0_9994]), ['final']). 6.97/7.26 cnf(c_0_15595, 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_9995]), ['final']). 6.97/7.26 cnf(c_0_15596, plain, (c_Fun_Ofun__upd(X1,X2,c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X4,X6)=c_Fun_Ofun__upd(X1,X2,X3,X4,X6)), inference(split_conjunct,[status(thm)],[c_0_9996]), ['final']). 6.97/7.26 cnf(c_0_15597, 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_9997, c_0_4467]), ['final']). 6.97/7.26 cnf(c_0_15598, 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_9998]), ['final']). 6.97/7.26 cnf(c_0_15599, 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_9999]), ['final']). 6.97/7.26 cnf(c_0_15600, 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_10000]), ['final']). 6.97/7.26 cnf(c_0_15601, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin)))), inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_10001, c_0_4741])]), ['final']). 6.97/7.26 cnf(c_0_15602, 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_10002]), ['final']). 6.97/7.26 cnf(c_0_15603, 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_10003]), ['final']). 6.97/7.26 cnf(c_0_15604, 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)), inference(split_conjunct,[status(thm)],[c_0_10004]), ['final']). 6.97/7.26 cnf(c_0_15605, 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_10005]), ['final']). 6.97/7.26 cnf(c_0_15606, 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))), inference(split_conjunct,[status(thm)],[c_0_10006]), ['final']). 6.97/7.26 cnf(c_0_15607, 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_10007, c_0_10008]), c_0_5202]), c_0_5202]), c_0_5202]), ['final']). 6.97/7.26 cnf(c_0_15608, plain, (c_Transitive__Closure_Ortrancl(X1,X2)=c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))), inference(rw,[status(thm)],[c_0_10009, c_0_5174]), ['final']). 6.97/7.26 cnf(c_0_15609, 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_10010]), ['final']). 6.97/7.26 cnf(c_0_15610, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),c_List_Oreplicate(X1,X4,X5))=c_List_Oreplicate(X2,X4,hAPP(X3,X5))), inference(split_conjunct,[status(thm)],[c_0_10011]), ['final']). 6.97/7.26 cnf(c_0_15611, plain, (c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X1)=hAPP(c_fequal,X1)), inference(rw,[status(thm)],[c_0_10012, c_0_5539]), ['final']). 6.97/7.26 cnf(c_0_15612, 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))), inference(split_conjunct,[status(thm)],[c_0_10013]), ['final']). 6.97/7.26 cnf(c_0_15613, plain, (c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X1)=hAPP(c_fequal,X1)), inference(rw,[status(thm)],[c_0_10014, c_0_5539]), ['final']). 6.97/7.26 cnf(c_0_15614, 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_10015]), ['final']). 6.97/7.26 cnf(c_0_15615, 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), inference(rw,[status(thm)],[c_0_10016, c_0_5560]), ['final']). 6.97/7.26 cnf(c_0_15616, 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_10017]), ['final']). 6.97/7.26 cnf(c_0_15617, 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']). 6.97/7.26 cnf(c_0_15618, 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_10018, c_0_5202]), ['final']). 6.97/7.26 cnf(c_0_15619, 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))), inference(split_conjunct,[status(thm)],[c_0_10019]), ['final']). 6.97/7.26 cnf(c_0_15620, 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_10020]), ['final']). 6.97/7.26 cnf(c_0_15621, 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_10021]), ['final']). 6.97/7.26 cnf(c_0_15622, plain, (X1=hAPP(c_Finite__Set_Ofold1(X2,X3),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_10022]), ['final']). 6.97/7.26 cnf(c_0_15623, 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_10023]), ['final']). 6.97/7.26 cnf(c_0_15624, 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_10024]), ['final']). 6.97/7.26 cnf(c_0_15625, 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))), inference(split_conjunct,[status(thm)],[c_0_10025]), ['final']). 6.97/7.26 cnf(c_0_15626, 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_10026]), ['final']). 6.97/7.26 cnf(c_0_15627, 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_10027, c_0_6164]), ['final']). 6.97/7.26 cnf(c_0_15628, 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_10028]), ['final']). 6.97/7.26 cnf(c_0_15629, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Int_OMin))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2)), inference(rw,[status(thm)],[c_0_10029, c_0_4741]), ['final']). 6.97/7.26 cnf(c_0_15630, 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_10030]), ['final']). 6.97/7.26 cnf(c_0_15631, 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_10031]), ['final']). 6.97/7.26 cnf(c_0_15632, 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_10032]), ['final']). 6.97/7.26 cnf(c_0_15633, plain, (hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6)=hAPP(hAPP(X4,X6),X5)), inference(split_conjunct,[status(thm)],[c_0_10033]), ['final']). 6.97/7.26 cnf(c_0_15634, plain, (hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6)=hAPP(X4,hAPP(X5,X6))), inference(split_conjunct,[status(thm)],[c_0_10034]), ['final']). 6.97/7.26 cnf(c_0_15635, 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_10035]), ['final']). 6.97/7.26 cnf(c_0_15636, 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_10036, c_0_10037]), ['final']). 6.97/7.26 cnf(c_0_15637, 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_10038]), ['final']). 6.97/7.26 cnf(c_0_15638, 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_10039]), ['final']). 6.97/7.26 cnf(c_0_15639, plain, (hAPP(hAPP(X1,X2),X3)=c_Nitpick_Opair__box_Opair__box__case(X4,X5,X6,X1,c_Nitpick_Opair__box_OPairBox(X4,X5,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_10040]), ['final']). 6.97/7.26 cnf(c_0_15640, 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_10041]), ['final']). 6.97/7.26 cnf(c_0_15641, 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_10042]), ['final']). 6.97/7.26 cnf(c_0_15642, 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_10043, c_0_5002]), ['final']). 6.97/7.26 cnf(c_0_15643, 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)), inference(rw,[status(thm)],[c_0_10044, c_0_6164]), ['final']). 6.97/7.26 cnf(c_0_15644, 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_10045, c_0_5202]), ['final']). 6.97/7.26 cnf(c_0_15645, 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_10046]), ['final']). 6.97/7.26 cnf(c_0_15646, 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)), inference(split_conjunct,[status(thm)],[c_0_10047]), ['final']). 6.97/7.26 cnf(c_0_15647, 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))), inference(split_conjunct,[status(thm)],[c_0_10048]), ['final']). 6.97/7.26 cnf(c_0_15648, 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_10049, c_0_4821]), ['final']). 6.97/7.26 cnf(c_0_15649, 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_10050, c_0_5941]), c_0_5941]), c_0_5746]), ['final']). 6.97/7.26 cnf(c_0_15650, 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_10051]), ['final']). 6.97/7.26 cnf(c_0_15651, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),X5)=c_HOL_OThe(X2,c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5))), inference(split_conjunct,[status(thm)],[c_0_10052]), ['final']). 6.97/7.26 cnf(c_0_15652, 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_10053]), ['final']). 6.97/7.26 cnf(c_0_15653, 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_10054, c_0_5202]), ['final']). 6.97/7.26 cnf(c_0_15654, plain, (X1=hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X3)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_10055]), ['final']). 6.97/7.26 cnf(c_0_15655, 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))), inference(er,[status(thm)],[c_0_10056]), ['final']). 6.97/7.26 cnf(c_0_15656, 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_10057]), ['final']). 6.97/7.26 cnf(c_0_15657, 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_10058]), ['final']). 6.97/7.26 cnf(c_0_15658, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))=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)))), inference(split_conjunct,[status(thm)],[c_0_10059]), ['final']). 6.97/7.26 cnf(c_0_15659, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))=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)))), inference(split_conjunct,[status(thm)],[c_0_10060]), ['final']). 6.97/7.26 cnf(c_0_15660, 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_10061]), ['final']). 6.97/7.26 cnf(c_0_15661, 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))), inference(split_conjunct,[status(thm)],[c_0_10062]), ['final']). 6.97/7.26 cnf(c_0_15662, 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_10063]), ['final']). 6.97/7.26 cnf(c_0_15663, 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_10064, c_0_4742]), c_0_6030]), ['final']). 6.97/7.26 cnf(c_0_15664, 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_10065]), ['final']). 6.97/7.26 cnf(c_0_15665, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk17_1(X1)),c_Int_OInteg))), inference(split_conjunct,[status(thm)],[c_0_10066]), ['final']). 6.97/7.26 cnf(c_0_15666, plain, (c_Relation_Otrans(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))), inference(rw,[status(thm)],[c_0_10067, c_0_5174]), ['final']). 6.97/7.26 cnf(c_0_15667, 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_10068]), ['final']). 6.97/7.26 cnf(c_0_15668, 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_10069]), ['final']). 6.97/7.26 cnf(c_0_15669, 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_10070]), ['final']). 6.97/7.26 cnf(c_0_15670, 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_10071]), ['final']). 6.97/7.26 cnf(c_0_15671, 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_10072]), ['final']). 6.97/7.26 cnf(c_0_15672, 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_10073]), ['final']). 6.97/7.26 cnf(c_0_15673, 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_10074, c_0_6164]), ['final']). 6.97/7.26 cnf(c_0_15674, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_10075]), ['final']). 6.97/7.26 cnf(c_0_15675, 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_10076]), ['final']). 6.97/7.26 cnf(c_0_15676, 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_10077, c_0_10078]), ['final']). 6.97/7.26 cnf(c_0_15677, 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_10079]), ['final']). 6.97/7.26 cnf(c_0_15678, 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_10080]), ['final']). 6.97/7.26 cnf(c_0_15679, 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_10081]), ['final']). 6.97/7.26 cnf(c_0_15680, 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_10082]), ['final']). 6.97/7.26 cnf(c_0_15681, 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_10083]), ['final']). 6.97/7.26 cnf(c_0_15682, 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_10084]), ['final']). 6.97/7.26 cnf(c_0_15683, 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)), inference(split_conjunct,[status(thm)],[c_0_10085]), ['final']). 6.97/7.26 cnf(c_0_15684, plain, (hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X1),X2),X3),X4),X5)=c_New__DSequence_Opos__single(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_10086]), ['final']). 6.97/7.26 cnf(c_0_15685, 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_10087]), ['final']). 6.97/7.26 cnf(c_0_15686, 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(er,[status(thm)],[c_0_10088]), ['final']). 6.97/7.26 cnf(c_0_15687, plain, (c_List_Otranspose(X1,X2)=c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_10089]), ['final']). 6.97/7.26 cnf(c_0_15688, plain, (c_Lazy__Sequence_Oflat(X1,c_Lazy__Sequence_Omap(X2,tc_Lazy__Sequence_Olazy__sequence(X1),X3,X4))=hAPP(c_Lazy__Sequence_Obind(X2,X1,X4),X3)), inference(split_conjunct,[status(thm)],[c_0_10090]), ['final']). 6.97/7.26 cnf(c_0_15689, 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)), inference(split_conjunct,[status(thm)],[c_0_10091]), ['final']). 6.97/7.26 cnf(c_0_15690, 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_10092]), ['final']). 6.97/7.26 cnf(c_0_15691, plain, (c_Fun_Oid(tc_prod(X1,X2))=c_Product__Type_Omap__pair(X1,X1,X2,X2,c_COMBI(X1),c_COMBI(X2))), inference(split_conjunct,[status(thm)],[c_0_10093]), ['final']). 6.97/7.26 cnf(c_0_15692, 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_10094]), ['final']). 6.97/7.26 cnf(c_0_15693, 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_10095]), ['final']). 6.97/7.26 cnf(c_0_15694, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=X4), inference(split_conjunct,[status(thm)],[c_0_10096]), ['final']). 6.97/7.26 cnf(c_0_15695, 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_10097]), ['final']). 6.97/7.26 cnf(c_0_15696, plain, (X1=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2)), inference(split_conjunct,[status(thm)],[c_0_10098]), ['final']). 6.97/7.26 cnf(c_0_15697, plain, (X1=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_10099]), ['final']). 6.97/7.26 cnf(c_0_15698, 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_10100]), ['final']). 6.97/7.26 cnf(c_0_15699, 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_10101, c_0_4742])]), ['final']). 6.97/7.26 cnf(c_0_15700, 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), inference(split_conjunct,[status(thm)],[c_0_10102]), ['final']). 6.97/7.26 cnf(c_0_15701, plain, (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)=X1), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10103, c_0_4411]), c_0_4565]), ['final']). 6.97/7.26 cnf(c_0_15702, 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_10104]), ['final']). 6.97/7.26 cnf(c_0_15703, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(c_Relation_OImage(X2,X1,X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_10105]), ['final']). 6.97/7.26 cnf(c_0_15704, 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), inference(split_conjunct,[status(thm)],[c_0_10106]), ['final']). 6.97/7.26 cnf(c_0_15705, 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_10107]), ['final']). 6.97/7.26 cnf(c_0_15706, 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_10108]), ['final']). 6.97/7.26 cnf(c_0_15707, 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_10109]), ['final']). 6.97/7.26 cnf(c_0_15708, plain, (c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,c_Lazy__Sequence_Oappend(X1,X3,X4))=c_Lazy__Sequence_Oappend(X1,c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,X3),X4)), inference(split_conjunct,[status(thm)],[c_0_10110]), ['final']). 6.97/7.26 cnf(c_0_15709, 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_10111]), ['final']). 6.97/7.26 cnf(c_0_15710, 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))), inference(split_conjunct,[status(thm)],[c_0_10112]), ['final']). 6.97/7.26 cnf(c_0_15711, 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_10113]), ['final']). 6.97/7.26 cnf(c_0_15712, 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(er,[status(thm)],[c_0_10114]), ['final']). 6.97/7.26 cnf(c_0_15713, 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_10115, c_0_4415]), ['final']). 6.97/7.26 cnf(c_0_15714, 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_10116]), ['final']). 6.97/7.26 cnf(c_0_15715, 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_10117]), ['final']). 6.97/7.26 cnf(c_0_15716, 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_10118, c_0_4742]), c_0_4742])]), ['final']). 6.97/7.26 cnf(c_0_15717, 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)), inference(split_conjunct,[status(thm)],[c_0_10119]), ['final']). 6.97/7.26 cnf(c_0_15718, 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_10120, c_0_5560]), ['final']). 6.97/7.26 cnf(c_0_15719, 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_10121, c_0_4471]), ['final']). 6.97/7.26 cnf(c_0_15720, plain, (c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X1,X2)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin)),X2)), inference(rw,[status(thm)],[c_0_10122, c_0_4741]), ['final']). 6.97/7.26 cnf(c_0_15721, 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_10123]), ['final']). 6.97/7.26 cnf(c_0_15722, 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']). 6.97/7.26 cnf(c_0_15723, 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_10124]), ['final']). 6.97/7.26 cnf(c_0_15724, 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_10125]), ['final']). 6.97/7.26 cnf(c_0_15725, 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_10126]), ['final']). 6.97/7.26 cnf(c_0_15726, 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_10127]), ['final']). 6.97/7.26 cnf(c_0_15727, plain, (c_Lazy__Sequence_Oappend(X1,X2,c_Lazy__Sequence_Oflat(X1,X3))=c_Lazy__Sequence_Oflat(X1,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(X1),X2,X3))), inference(split_conjunct,[status(thm)],[c_0_10128]), ['final']). 6.97/7.26 cnf(c_0_15728, 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']). 6.97/7.26 cnf(c_0_15729, plain, (c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))=hAPP(c_Set_OPow(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_10129]), ['final']). 6.97/7.26 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_10130]), ['final']). 6.97/7.26 cnf(c_0_15731, 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_10131, c_0_5941]), ['final']). 6.97/7.26 cnf(c_0_15732, 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_10132]), ['final']). 6.97/7.26 cnf(c_0_15733, plain, (c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X2)=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin),X2)), inference(rw,[status(thm)],[c_0_5772, c_0_4741]), ['final']). 6.97/7.26 cnf(c_0_15734, plain, (X1=hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,X4),c_Product__Type_Ocurry(X2,X3,X4,X1))), inference(split_conjunct,[status(thm)],[c_0_10133]), ['final']). 6.97/7.26 cnf(c_0_15735, 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_10134]), ['final']). 6.97/7.26 cnf(c_0_15736, plain, (c_Product__Type_Ocurry(X1,X2,X3,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4))=X4), inference(split_conjunct,[status(thm)],[c_0_10135]), ['final']). 6.97/7.26 cnf(c_0_15737, 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), inference(rw,[status(thm)],[c_0_10136, c_0_5174]), ['final']). 6.97/7.26 cnf(c_0_15738, plain, (hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)=X2), inference(split_conjunct,[status(thm)],[c_0_10137]), ['final']). 6.97/7.26 cnf(c_0_15739, 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_10138]), ['final']). 6.97/7.26 cnf(c_0_15740, 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_10139]), ['final']). 6.97/7.26 cnf(c_0_15741, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),X3),c_List_Olist_ONil(X2))=c_List_Olist_ONil(tc_prod(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10140]), ['final']). 6.97/7.26 cnf(c_0_15742, plain, (hAPP(c_Relation_OField(X1),hAPP(c_Relation_Oconverse(X1,X1),X2))=hAPP(c_Relation_OField(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_10141]), ['final']). 6.97/7.26 cnf(c_0_15743, 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_10142, c_0_10143]), ['final']). 6.97/7.26 cnf(c_0_15744, 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_10144]), ['final']). 6.97/7.26 cnf(c_0_15745, 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_10145]), ['final']). 6.97/7.26 cnf(c_0_15746, 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_10146]), ['final']). 6.97/7.26 cnf(c_0_15747, 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_10147]), ['final']). 6.97/7.26 cnf(c_0_15748, 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_10148]), ['final']). 6.97/7.26 cnf(c_0_15749, 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']). 6.97/7.26 cnf(c_0_15750, 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_10149]), ['final']). 6.97/7.26 cnf(c_0_15751, plain, (c_Relation_Oantisym(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_10150, c_0_5560]), ['final']). 6.97/7.26 cnf(c_0_15752, plain, (c_Relation_Osym(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_10151, c_0_5560]), ['final']). 6.97/7.26 cnf(c_0_15753, plain, (hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2))), inference(er,[status(thm)],[c_0_10152]), ['final']). 6.97/7.26 cnf(c_0_15754, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2)))), inference(er,[status(thm)],[c_0_10153]), ['final']). 6.97/7.26 cnf(c_0_15755, plain, (c_Fun_Oid(X1)=c_Hilbert__Choice_Oinv__into(X1,X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Fun_Oid(X1))), inference(split_conjunct,[status(thm)],[c_0_10154]), ['final']). 6.97/7.26 cnf(c_0_15756, 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_10155]), ['final']). 6.97/7.26 cnf(c_0_15757, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))), inference(rw,[status(thm)],[c_0_10156, c_0_4742]), ['final']). 6.97/7.26 cnf(c_0_15758, plain, (hAPP(c_Code__Numeral_Onat__of,esk433_1(X1))=X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10157, c_0_8490])]), ['final']). 6.97/7.26 cnf(c_0_15759, 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_10158]), ['final']). 6.97/7.26 cnf(c_0_15760, 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_10159, c_0_5002]), ['final']). 6.97/7.26 cnf(c_0_15761, 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_10160]), ['final']). 6.97/7.26 cnf(c_0_15762, 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_10161]), ['final']). 6.97/7.26 cnf(c_0_15763, plain, (c_List_Oremdups(X1,c_List_Oinsert(X1,X2,X3))=c_List_Oinsert(X1,X2,c_List_Oremdups(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_10162]), ['final']). 6.97/7.26 cnf(c_0_15764, 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_10163]), ['final']). 6.97/7.26 cnf(c_0_15765, 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))), inference(split_conjunct,[status(thm)],[c_0_10164]), ['final']). 6.97/7.26 cnf(c_0_15766, plain, (c_Divides_OnegateSnd=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))), inference(rw,[status(thm)],[c_0_10165, c_0_4734]), ['final']). 6.97/7.26 cnf(c_0_15767, 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_10166]), ['final']). 6.97/7.26 cnf(c_0_15768, plain, (hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X2), inference(split_conjunct,[status(thm)],[c_0_10167]), ['final']). 6.97/7.26 cnf(c_0_15769, 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_10168]), ['final']). 6.97/7.26 cnf(c_0_15770, plain, (hAPP(c_List_Ohd(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=X2), inference(split_conjunct,[status(thm)],[c_0_10169]), ['final']). 6.97/7.26 cnf(c_0_15771, plain, (X1=hAPP(c_List_Otl(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1))), inference(split_conjunct,[status(thm)],[c_0_10170]), ['final']). 6.97/7.26 cnf(c_0_15772, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))=c_List_Oinsert(X1,X2,c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_10171]), ['final']). 6.97/7.26 cnf(c_0_15773, plain, (hAPP(c_Relation_Oconverse(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3))=X3), inference(split_conjunct,[status(thm)],[c_0_10172]), ['final']). 6.97/7.26 cnf(c_0_15774, 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_10173]), ['final']). 6.97/7.26 cnf(c_0_15775, 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), inference(split_conjunct,[status(thm)],[c_0_10174]), ['final']). 6.97/7.26 cnf(c_0_15776, plain, (hAPP(c_Relation_ODomain(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_10175]), ['final']). 6.97/7.26 cnf(c_0_15777, 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_10176]), ['final']). 6.97/7.26 cnf(c_0_15778, 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_10177]), ['final']). 6.97/7.26 cnf(c_0_15779, plain, (hAPP(c_List_Oset(X1),hAPP(c_List_Orev(X1),X2))=hAPP(c_List_Oset(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_10178]), ['final']). 6.97/7.26 cnf(c_0_15780, 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_10179, c_0_4742]), ['final']). 6.97/7.26 cnf(c_0_15781, 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_10180]), ['final']). 6.97/7.26 cnf(c_0_15782, 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_10181, c_0_5202]), ['final']). 6.97/7.26 cnf(c_0_15783, 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']). 6.97/7.26 cnf(c_0_15784, 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_10182]), ['final']). 6.97/7.26 cnf(c_0_15785, 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']). 6.97/7.26 cnf(c_0_15786, 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_10183]), ['final']). 6.97/7.26 cnf(c_0_15787, 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_10184]), ['final']). 6.97/7.26 cnf(c_0_15788, 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_10185, c_0_4471]), ['final']). 6.97/7.26 cnf(c_0_15789, plain, (hAPP(c_Finite__Set_Ofold1(X1,X2),X3)=c_HOL_OThe(X1,c_Finite__Set_Ofold1Set(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_10186]), ['final']). 6.97/7.26 cnf(c_0_15790, 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_10187, c_0_6758]), ['final']). 6.97/7.26 cnf(c_0_15791, 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_10188]), ['final']). 6.97/7.26 cnf(c_0_15792, 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_10189]), ['final']). 6.97/7.26 cnf(c_0_15793, plain, (hAPP(hAPP(c_List_Olist__update(X1,c_List_Olist_ONil(X1)),X2),X3)=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_10190]), ['final']). 6.97/7.26 cnf(c_0_15794, 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']). 6.97/7.26 cnf(c_0_15795, 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']). 6.97/7.26 cnf(c_0_15796, 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))), inference(split_conjunct,[status(thm)],[c_0_10191]), ['final']). 6.97/7.26 cnf(c_0_15797, 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_10192]), ['final']). 6.97/7.26 cnf(c_0_15798, plain, (c_Nat_Onat_Onat__case(X1,X2,X3,hAPP(c_Nat_OSuc,X4))=hAPP(X3,X4)), inference(split_conjunct,[status(thm)],[c_0_10193]), ['final']). 6.97/7.26 cnf(c_0_15799, 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_10194]), ['final']). 6.97/7.26 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_10195]), ['final']). 6.97/7.26 cnf(c_0_15801, plain, (hAPP(c_Relation_Oconverse(X1,X1),c_Relation_OId__on(X1,X2))=c_Relation_OId__on(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_10196]), ['final']). 6.97/7.26 cnf(c_0_15802, plain, (hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X4)=X5), inference(split_conjunct,[status(thm)],[c_0_10197]), ['final']). 6.97/7.26 cnf(c_0_15803, plain, (X1=hAPP(c_Fun_Ocomp(X2,X2,X3,c_Fun_Oid(X2)),X1)), inference(split_conjunct,[status(thm)],[c_0_10198]), ['final']). 6.97/7.26 cnf(c_0_15804, plain, (hAPP(c_Fun_Ocomp(X1,X2,X1,X3),c_Fun_Oid(X1))=X3), inference(split_conjunct,[status(thm)],[c_0_10199]), ['final']). 6.97/7.26 cnf(c_0_15805, plain, (X1=hAPP(c_List_Olist_Olist__case(X2,X3,X1,X4),c_List_Olist_ONil(X3))), inference(split_conjunct,[status(thm)],[c_0_10200]), ['final']). 6.97/7.26 cnf(c_0_15806, plain, (X1=hAPP(c_List_Ofoldl(X2,X3,X4,X1),c_List_Olist_ONil(X3))), inference(split_conjunct,[status(thm)],[c_0_10201]), ['final']). 6.97/7.26 cnf(c_0_15807, plain, (c_Code__Numeral_Oint__of=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)), inference(split_conjunct,[status(thm)],[fact_int__of__def]), ['final']). 6.97/7.26 cnf(c_0_15808, 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_10202]), ['final']). 6.97/7.26 cnf(c_0_15809, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X2)=X2), inference(split_conjunct,[status(thm)],[c_0_10203]), ['final']). 6.97/7.26 cnf(c_0_15810, 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_10204]), ['final']). 6.97/7.26 cnf(c_0_15811, plain, (X1=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_Oreplicate(X2,X1,X3))), inference(split_conjunct,[status(thm)],[c_0_10205]), ['final']). 6.97/7.26 cnf(c_0_15812, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2)=c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_10206]), ['final']). 6.97/7.26 cnf(c_0_15813, plain, (c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=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))), inference(split_conjunct,[status(thm)],[fact_code__numeral__zero__minus__one]), ['final']). 6.97/7.26 cnf(c_0_15814, hypothesis, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_G))), inference(split_conjunct,[status(thm)],[conj_0]), ['final']). 6.97/7.26 cnf(c_0_15815, hypothesis, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),v_Ga))), inference(split_conjunct,[status(thm)],[conj_1]), ['final']). 6.97/7.26 cnf(c_0_15816, plain, (c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_OPow(X1),X2))=X2), inference(split_conjunct,[status(thm)],[c_0_10207]), ['final']). 6.97/7.26 cnf(c_0_15817, plain, (hAPP(c_List_Oset(X1),X2)=hAPP(c_List_Oset(X1),c_List_Oremdups(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10208]), ['final']). 6.97/7.26 cnf(c_0_15818, plain, (c_Fun_Ofun__upd(X1,X2,X3,X4,hAPP(X3,X4))=X3), inference(er,[status(thm)],[c_0_10209]), ['final']). 6.97/7.26 cnf(c_0_15819, 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_10210, c_0_5002]), ['final']). 6.97/7.26 cnf(c_0_15820, 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_10211]), ['final']). 6.97/7.26 cnf(c_0_15821, plain, (c_List_Olist__all2(X1,X2,X3,c_List_Olist_ONil(X1),c_List_Olist_ONil(X2))), inference(er,[status(thm)],[c_0_10212]), ['final']). 6.97/7.26 cnf(c_0_15822, 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_10213, c_0_5202]), ['final']). 6.97/7.26 cnf(c_0_15823, 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_10214]), ['final']). 6.97/7.26 cnf(c_0_15824, 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_10215]), ['final']). 6.97/7.26 cnf(c_0_15825, 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_10216]), ['final']). 6.97/7.26 cnf(c_0_15826, 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_10217]), ['final']). 6.97/7.26 cnf(c_0_15827, 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_10218]), ['final']). 6.97/7.26 cnf(c_0_15828, 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_10219]), ['final']). 6.97/7.26 cnf(c_0_15829, plain, (c_List_Olist_ONil(X1)=c_List_Osublist(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_10220]), ['final']). 6.97/7.26 cnf(c_0_15830, 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_10221, c_0_4415]), ['final']). 6.97/7.26 cnf(c_0_15831, plain, (c_Relation_Oantisym(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_10222]), ['final']). 6.97/7.26 cnf(c_0_15832, 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_10223]), ['final']). 6.97/7.26 cnf(c_0_15833, 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_10224]), ['final']). 6.97/7.26 cnf(c_0_15834, 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_10225, c_0_4742]), ['final']). 6.97/7.26 cnf(c_0_15835, 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']). 6.97/7.26 cnf(c_0_15836, 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_10226]), ['final']). 6.97/7.26 cnf(c_0_15837, 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_10227]), ['final']). 6.97/7.26 cnf(c_0_15838, 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_10228]), ['final']). 6.97/7.26 cnf(c_0_15839, 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_10229, c_0_4881]), ['final']). 6.97/7.26 cnf(c_0_15840, 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)), inference(split_conjunct,[status(thm)],[c_0_10230]), ['final']). 6.97/7.26 cnf(c_0_15841, 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)), inference(split_conjunct,[status(thm)],[c_0_10231]), ['final']). 6.97/7.26 cnf(c_0_15842, 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_10232]), ['final']). 6.97/7.26 cnf(c_0_15843, 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_10233, c_0_4881]), ['final']). 6.97/7.26 cnf(c_0_15844, 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_10234]), ['final']). 6.97/7.26 cnf(c_0_15845, 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_10235]), ['final']). 6.97/7.26 cnf(c_0_15846, plain, (c_Fun_Oid(tc_List_Olist(X1))=hAPP(c_List_Omap(X1,X1),c_COMBI(X1))), inference(split_conjunct,[status(thm)],[c_0_10236]), ['final']). 6.97/7.26 cnf(c_0_15847, plain, (X1=c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X2,X3,X1,X4,c_Lazy__Sequence_Olazy__sequence_OEmpty(X3))), inference(split_conjunct,[status(thm)],[c_0_10237]), ['final']). 6.97/7.26 cnf(c_0_15848, plain, (c_Predicate_Oconversep(X1,X2,c_Predicate_Oconversep(X2,X1,X3))=X3), inference(split_conjunct,[status(thm)],[c_0_10238]), ['final']). 6.97/7.26 cnf(c_0_15849, plain, (hAPP(c_Set_Oimage(X1,X1,c_Fun_Oid(X1)),X2)=X2), inference(split_conjunct,[status(thm)],[c_0_10239]), ['final']). 6.97/7.26 cnf(c_0_15850, plain, (X1=hAPP(c_Set_Oimage(X2,X2,c_COMBI(X2)),X1)), inference(split_conjunct,[status(thm)],[c_0_10240]), ['final']). 6.97/7.26 cnf(c_0_15851, 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_10241]), ['final']). 6.97/7.26 cnf(c_0_15852, plain, (X1=hAPP(hAPP(c_COMBK(X2,X3),X1),X4)), inference(split_conjunct,[status(thm)],[c_0_10242]), ['final']). 6.97/7.26 cnf(c_0_15853, plain, (hAPP(c_Relation_ODomain(X1,X1),c_Relation_OId__on(X1,X2))=X2), inference(split_conjunct,[status(thm)],[c_0_10243]), ['final']). 6.97/7.26 cnf(c_0_15854, plain, (X1=hAPP(c_Relation_ORange(X2,X2),c_Relation_OId__on(X2,X1))), inference(split_conjunct,[status(thm)],[c_0_10244]), ['final']). 6.97/7.26 cnf(c_0_15855, plain, (hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)=X2), inference(split_conjunct,[status(thm)],[c_0_10245]), ['final']). 6.97/7.26 cnf(c_0_15856, plain, (hAPP(c_New__DSequence_Opos__single(X1,X2),X3)=hAPP(c_Lazy__Sequence_Osingle(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_10246]), ['final']). 6.97/7.26 cnf(c_0_15857, plain, (X1=hAPP(hAPP(c_List_Odrop(X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)), inference(split_conjunct,[status(thm)],[c_0_10247]), ['final']). 6.97/7.26 cnf(c_0_15858, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1))=X2), inference(split_conjunct,[status(thm)],[c_0_10248]), ['final']). 6.97/7.26 cnf(c_0_15859, 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_10249]), ['final']). 6.97/7.26 cnf(c_0_15860, 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_10250, c_0_4978]), ['final']). 6.97/7.26 cnf(c_0_15861, 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_10251]), ['final']). 6.97/7.26 cnf(c_0_15862, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)), inference(split_conjunct,[status(thm)],[c_0_10252]), ['final']). 6.97/7.26 cnf(c_0_15863, plain, (X1=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)), inference(split_conjunct,[status(thm)],[c_0_10253]), ['final']). 6.97/7.26 cnf(c_0_15864, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))=X1), inference(split_conjunct,[status(thm)],[c_0_10254]), ['final']). 6.97/7.26 cnf(c_0_15865, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1), inference(split_conjunct,[status(thm)],[c_0_10255]), ['final']). 6.97/7.26 cnf(c_0_15866, 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_10256, c_0_4978]), ['final']). 6.97/7.26 cnf(c_0_15867, plain, (X1=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_10257]), ['final']). 6.97/7.26 cnf(c_0_15868, 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_10258]), ['final']). 6.97/7.26 cnf(c_0_15869, 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']). 6.97/7.26 cnf(c_0_15870, 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_10259]), ['final']). 6.97/7.26 cnf(c_0_15871, plain, (c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_10260]), ['final']). 6.97/7.26 cnf(c_0_15872, plain, (c_Lazy__Sequence_Olazy__sequence_OEmpty(X1)=c_Lazy__Sequence_Omap(X2,X1,X3,c_Lazy__Sequence_Olazy__sequence_OEmpty(X2))), inference(split_conjunct,[status(thm)],[c_0_10261]), ['final']). 6.97/7.26 cnf(c_0_15873, plain, (c_List_Olist_ONil(X1)=c_List_Omaps(X2,X1,X3,c_List_Olist_ONil(X2))), inference(split_conjunct,[status(thm)],[c_0_10262]), ['final']). 6.97/7.26 cnf(c_0_15874, plain, (hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2))), inference(split_conjunct,[status(thm)],[c_0_10263]), ['final']). 6.97/7.26 cnf(c_0_15875, 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_10264]), ['final']). 6.97/7.26 cnf(c_0_15876, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X1))), inference(split_conjunct,[status(thm)],[c_0_10265]), ['final']). 6.97/7.26 cnf(c_0_15877, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X1))), inference(split_conjunct,[status(thm)],[c_0_10266]), ['final']). 6.97/7.26 cnf(c_0_15878, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1))), inference(split_conjunct,[status(thm)],[c_0_10267]), ['final']). 6.97/7.26 cnf(c_0_15879, plain, (c_Fun_Obij__betw(X1,X1,c_Fun_Oid(X1),X2,X2)), inference(split_conjunct,[status(thm)],[c_0_10268]), ['final']). 6.97/7.26 cnf(c_0_15880, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),c_List_Olist_ONil(X1)))), inference(split_conjunct,[status(thm)],[c_0_10269]), ['final']). 6.97/7.26 cnf(c_0_15881, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oremdups(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_10270]), ['final']). 6.97/7.26 cnf(c_0_15882, plain, (hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_10271]), ['final']). 6.97/7.26 cnf(c_0_15883, 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_10272, c_0_4413]), ['final']). 6.97/7.26 cnf(c_0_15884, 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_10273, c_0_4413]), ['final']). 6.97/7.26 cnf(c_0_15885, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OMin))), inference(rw,[status(thm)],[c_0_10274, c_0_4415]), ['final']). 6.97/7.26 cnf(c_0_15886, 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_10275]), ['final']). 6.97/7.26 cnf(c_0_15887, plain, (c_List_Olist__all2(X1,X1,c_fequal,X2,X2)), inference(er,[status(thm)],[c_0_10276]), ['final']). 6.97/7.26 cnf(c_0_15888, plain, (hBOOL(hAPP(hAPP(c_fequal,X1),X1))), inference(er,[status(thm)],[c_0_10277]), ['final']). 6.97/7.26 cnf(c_0_15889, plain, (hAPP(c_List_Ofilter(X1,X2),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_10278]), ['final']). 6.97/7.26 cnf(c_0_15890, 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_10279]), ['final']). 6.97/7.26 cnf(c_0_15891, plain, (hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2),c_Lazy__Sequence_Olazy__sequence_OEmpty(X1))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_10280]), ['final']). 6.97/7.26 cnf(c_0_15892, 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_10281]), ['final']). 6.97/7.26 cnf(c_0_15893, 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)), inference(split_conjunct,[status(thm)],[c_0_10282]), ['final']). 6.97/7.26 cnf(c_0_15894, plain, (hAPP(c_New__DSequence_Oneg__single(X1,X2),X3)=c_Lazy__Sequence_Ohb__single(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_10283]), ['final']). 6.97/7.26 cnf(c_0_15895, plain, (c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Ortrancl(X1,X2))=c_Transitive__Closure_Ortrancl(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_10284]), ['final']). 6.97/7.26 cnf(c_0_15896, plain, (c_List_Oremdups(X1,c_List_Oremdups(X1,X2))=c_List_Oremdups(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_10285]), ['final']). 6.97/7.26 cnf(c_0_15897, plain, (c_List_Otranspose(X1,c_List_Olist_ONil(tc_List_Olist(X1)))=c_List_Olist_ONil(tc_List_Olist(X1))), inference(split_conjunct,[status(thm)],[c_0_10286]), ['final']). 6.97/7.26 cnf(c_0_15898, 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_10287]), ['final']). 6.97/7.26 cnf(c_0_15899, 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_10288]), ['final']). 6.97/7.26 cnf(c_0_15900, plain, (X1=c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X2,X1,X3,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), inference(split_conjunct,[status(thm)],[c_0_10289]), ['final']). 6.97/7.26 cnf(c_0_15901, 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_10290, c_0_4413]), ['final']). 6.97/7.26 cnf(c_0_15902, 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_10291, c_0_4413]), c_0_4413]), ['final']). 6.97/7.26 cnf(c_0_15903, plain, (c_List_OtakeWhile(X1,X2,c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_10292]), ['final']). 6.97/7.26 cnf(c_0_15904, plain, (c_List_Olist_ONil(X1)=c_List_Osublist(X1,c_List_Olist_ONil(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_10293]), ['final']). 6.97/7.26 cnf(c_0_15905, plain, (c_List_Olist_ONil(X1)=c_List_Oremove1(X1,X2,c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_10294]), ['final']). 6.97/7.26 cnf(c_0_15906, 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_10295]), ['final']). 6.97/7.26 cnf(c_0_15907, plain, (c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_10296]), ['final']). 6.97/7.26 cnf(c_0_15908, plain, (c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_10297]), ['final']). 6.97/7.26 cnf(c_0_15909, plain, (c_Relation_Osingle__valued(X1,X1,c_Relation_OId__on(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10298]), ['final']). 6.97/7.26 cnf(c_0_15910, plain, (c_List_Oreplicate(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_10299]), ['final']). 6.97/7.26 cnf(c_0_15911, 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_10300]), ['final']). 6.97/7.26 cnf(c_0_15912, plain, (c_Relation_Orefl__on(X1,X2,c_Relation_OId__on(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10301]), ['final']). 6.97/7.26 cnf(c_0_15913, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olist_ONil(X1)))), inference(split_conjunct,[status(thm)],[c_0_10302]), ['final']). 6.97/7.26 cnf(c_0_15914, plain, (c_Relation_Otrans(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X1))), inference(split_conjunct,[status(thm)],[c_0_10303]), ['final']). 6.97/7.26 cnf(c_0_15915, plain, (c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X1))), inference(split_conjunct,[status(thm)],[c_0_10304]), ['final']). 6.97/7.26 cnf(c_0_15916, plain, (c_Lazy__Sequence_Olazy__sequence_OEmpty(X1)=c_Lazy__Sequence_Oflat(X1,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(X1)))), inference(split_conjunct,[status(thm)],[c_0_10305]), ['final']). 6.97/7.26 cnf(c_0_15917, plain, (hAPP(c_List_Otl(X1),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_10306]), ['final']). 6.97/7.26 cnf(c_0_15918, plain, (hAPP(c_List_Orotate1(X1),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_9409]), ['final']). 6.97/7.26 cnf(c_0_15919, plain, (c_List_Olist_ONil(X1)=hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_10307]), ['final']). 6.97/7.26 cnf(c_0_15920, plain, (c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than)=c_FunDef_Opair__less), inference(split_conjunct,[status(thm)],[fact_pair__less__def]), ['final']). 6.97/7.26 cnf(c_0_15921, plain, (c_Lazy__Sequence_Oappend(X1,c_Lazy__Sequence_Olazy__sequence_OEmpty(X1),X2)=X2), inference(split_conjunct,[status(thm)],[c_0_10308]), ['final']). 6.97/7.26 cnf(c_0_15922, plain, (c_List_Osplice(X1,X2,c_List_Olist_ONil(X1))=X2), inference(split_conjunct,[status(thm)],[c_0_10309]), ['final']). 6.97/7.26 cnf(c_0_15923, plain, (X1=c_List_Osplice(X2,c_List_Olist_ONil(X2),X1)), inference(split_conjunct,[status(thm)],[c_0_10310]), ['final']). 6.97/7.26 cnf(c_0_15924, plain, (X1=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[c_0_10232]), ['final']). 6.97/7.26 cnf(c_0_15925, plain, (c_HOL_OThe(X1,hAPP(c_fequal,X2))=X2), inference(split_conjunct,[status(thm)],[c_0_10311]), ['final']). 6.97/7.26 cnf(c_0_15926, plain, (X1=c_Hilbert__Choice_OEps(X2,hAPP(c_fequal,X1))), inference(split_conjunct,[status(thm)],[c_0_10312]), ['final']). 6.97/7.26 cnf(c_0_15927, 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_10313, c_0_5202]), ['final']). 6.97/7.26 cnf(c_0_15928, 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_transfer__int__nat__numerals_I2_J]), ['final']). 6.97/7.26 cnf(c_0_15929, 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_10314, c_0_5202]), ['final']). 6.97/7.26 cnf(c_0_15930, plain, (X1=hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X1))), inference(split_conjunct,[status(thm)],[c_0_10315]), ['final']). 6.97/7.26 cnf(c_0_15931, 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_transfer__int__nat__numerals_I1_J]), ['final']). 6.97/7.26 cnf(c_0_15932, plain, (c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)=c_FunDef_Omin__strict), inference(split_conjunct,[status(thm)],[fact_min__strict__def]), ['final']). 6.97/7.26 cnf(c_0_15933, 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']). 6.97/7.26 cnf(c_0_15934, 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']). 6.97/7.26 cnf(c_0_15935, 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_10316]), ['final']). 6.97/7.26 cnf(c_0_15936, 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_10317]), ['final']). 6.97/7.26 cnf(c_0_15937, plain, (c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1)), inference(split_conjunct,[status(thm)],[c_0_10318]), ['final']). 6.97/7.26 cnf(c_0_15938, plain, (c_List_Olist__all(X1,X2,c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_10319]), ['final']). 6.97/7.26 cnf(c_0_15939, 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']). 6.97/7.26 cnf(c_0_15940, plain, (c_Relation_Oantisym(X1,c_Relation_OId__on(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10320]), ['final']). 6.97/7.26 cnf(c_0_15941, plain, (c_Relation_Otrans(X1,c_Transitive__Closure_Ortrancl(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10321]), ['final']). 6.97/7.26 cnf(c_0_15942, 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_10322]), ['final']). 6.97/7.26 cnf(c_0_15943, plain, (c_Relation_Otrans(X1,c_Relation_OId__on(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10323]), ['final']). 6.97/7.26 cnf(c_0_15944, plain, (c_Relation_Osym(X1,c_Relation_OId__on(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10324]), ['final']). 6.97/7.26 cnf(c_0_15945, plain, (c_Wellfounded_Owf(X1,c_List_Omeasures(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10325]), ['final']). 6.97/7.26 cnf(c_0_15946, plain, (c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10326]), ['final']). 6.97/7.26 cnf(c_0_15947, 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_10327]), ['final']). 6.97/7.26 cnf(c_0_15948, 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']). 6.97/7.26 cnf(c_0_15949, plain, (c_Nitpick_Onat__gcd(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1), inference(er,[status(thm)],[c_0_10328]), ['final']). 6.97/7.26 cnf(c_0_15950, plain, (c_List_Obutlast(X1,c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_10329]), ['final']). 6.97/7.26 cnf(c_0_15951, plain, (c_List_Oremdups(X1,c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_10330]), ['final']). 6.97/7.26 cnf(c_0_15952, plain, (c_Lazy__Sequence_Oempty(X1)=hAPP(c_New__DSequence_Opos__empty(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_10331]), ['final']). 6.97/7.26 cnf(c_0_15953, plain, (c_Random_Oinc__shift(X1,X1)=c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), inference(er,[status(thm)],[c_0_10332]), ['final']). 6.97/7.26 cnf(c_0_15954, plain, (c_Quickcheck_Obeyond(X1,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[c_0_10333]), ['final']). 6.97/7.26 cnf(c_0_15955, 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']). 6.97/7.26 cnf(c_0_15956, 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_10334, c_0_4413]), ['final']). 6.97/7.26 cnf(c_0_15957, 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']). 6.97/7.26 cnf(c_0_15958, 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_10335, c_0_5202]), ['final']). 6.97/7.26 cnf(c_0_15959, plain, (c_Predicate_Oconversep(X1,X1,c_fequal)=c_fequal), inference(split_conjunct,[status(thm)],[c_0_10336]), ['final']). 6.97/7.26 cnf(c_0_15960, plain, (X1=hAPP(c_COMBI(X2),X1)), inference(split_conjunct,[status(thm)],[c_0_10337]), ['final']). 6.97/7.26 cnf(c_0_15961, plain, (X1=hAPP(c_Fun_Oid(X2),X1)), inference(split_conjunct,[status(thm)],[c_0_10338]), ['final']). 6.97/7.26 cnf(c_0_15962, plain, (X1=hAPP(c_Int_OAbs__Integ,esk17_1(X1))), inference(split_conjunct,[status(thm)],[c_0_10066]), ['final']). 6.97/7.26 cnf(c_0_15963, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),esk571_1(X1))=X1), inference(rw,[status(thm)],[c_0_10339, c_0_5202]), ['final']). 6.97/7.26 cnf(c_0_15964, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X1)=X1), inference(split_conjunct,[status(thm)],[c_0_10340]), ['final']). 6.97/7.26 cnf(c_0_15965, plain, (c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc)), inference(split_conjunct,[status(thm)],[fact_mono__Suc]), ['final']). 6.97/7.26 cnf(c_0_15966, plain, (class_Nat_Osize(tc_Nitpick_Opair__box(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10341]), ['final']). 6.97/7.26 cnf(c_0_15967, plain, (class_Nat_Osize(tc_sum(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10342]), ['final']). 6.97/7.26 cnf(c_0_15968, plain, (class_Nat_Osize(tc_prod(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10343]), ['final']). 6.97/7.26 cnf(c_0_15969, plain, (c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X1))), inference(split_conjunct,[status(thm)],[c_0_10344]), ['final']). 6.97/7.26 cnf(c_0_15970, plain, (c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X1))), inference(split_conjunct,[status(thm)],[c_0_10345]), ['final']). 6.97/7.26 cnf(c_0_15971, 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']). 6.97/7.26 cnf(c_0_15972, plain, (c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than)), inference(split_conjunct,[status(thm)],[fact_trans__less__than]), ['final']). 6.97/7.26 cnf(c_0_15973, plain, (c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than)), inference(split_conjunct,[status(thm)],[fact_wf__less__than]), ['final']). 6.97/7.26 cnf(c_0_15974, plain, (c_Equiv__Relations_Oequivp(X1,c_fequal)), inference(split_conjunct,[status(thm)],[c_0_10346]), ['final']). 6.97/7.26 cnf(c_0_15975, plain, (c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat)), inference(split_conjunct,[status(thm)],[fact_wf__pred__nat]), ['final']). 6.97/7.26 cnf(c_0_15976, 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']). 6.97/7.26 cnf(c_0_15977, plain, (class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X1))), inference(split_conjunct,[status(thm)],[c_0_10347]), ['final']). 6.97/7.26 cnf(c_0_15978, plain, (class_Nat_Osize(tc_List_Olist(X1))), inference(split_conjunct,[status(thm)],[c_0_10348]), ['final']). 6.97/7.26 cnf(c_0_15979, plain, (class_Nat_Osize(tc_Option_Ooption(X1))), inference(split_conjunct,[status(thm)],[c_0_10349]), ['final']). 6.97/7.26 cnf(c_0_15980, plain, (class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X1))), inference(split_conjunct,[status(thm)],[c_0_10350]), ['final']). 6.97/7.26 cnf(c_0_15981, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_HOL_Obool_Obool__size(c_fFalse)), inference(split_conjunct,[status(thm)],[fact_bool_Osize_I2_J]), ['final']). 6.97/7.26 cnf(c_0_15982, 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']). 6.97/7.26 cnf(c_0_15983, 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']). 6.97/7.26 cnf(c_0_15984, 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']). 6.97/7.26 cnf(c_0_15985, 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']). 6.97/7.26 cnf(c_0_15986, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Orderings_Obot__class_Obot(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[fact_bot__nat__def]), ['final']). 6.97/7.26 cnf(c_0_15987, plain, (class_Orderings_Owellorder(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Owellorder]), ['final']). 6.97/7.26 cnf(c_0_15988, plain, (class_Rings_Ocomm__ring__1(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring__1]), ['final']). 6.97/7.26 cnf(c_0_15989, plain, (class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocancel__ab__semigroup__add]), ['final']). 6.97/7.26 cnf(c_0_15990, 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']). 6.97/7.26 cnf(c_0_15991, plain, (class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add]), ['final']). 6.97/7.26 cnf(c_0_15992, plain, (class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1__strict]), ['final']). 6.97/7.26 cnf(c_0_15993, plain, (class_Groups_Oone(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oone]), ['final']). 6.97/7.26 cnf(c_0_15994, plain, (class_Groups_Oone(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oone]), ['final']). 6.97/7.26 cnf(c_0_15995, plain, (class_Groups_Oone(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]), ['final']). 6.97/7.26 cnf(c_0_15996, plain, (class_Rings_Ocomm__semiring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]), ['final']). 6.97/7.26 cnf(c_0_15997, plain, (class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring]), ['final']). 6.97/7.26 cnf(c_0_15998, plain, (class_Rings_Ocomm__semiring(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]), ['final']). 6.97/7.26 cnf(c_0_15999, 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']). 6.97/7.26 cnf(c_0_16000, 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']). 6.97/7.26 cnf(c_0_16001, plain, (class_Orderings_Otop(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Otop]), ['final']). 6.97/7.26 cnf(c_0_16002, plain, (class_Groups_Oabs__if(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oabs__if]), ['final']). 6.97/7.26 cnf(c_0_16003, plain, (class_Rings_Olinordered__semiring__1(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1]), ['final']). 6.97/7.26 cnf(c_0_16004, plain, (class_Groups_Osgn__if(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Osgn__if]), ['final']). 6.97/7.26 cnf(c_0_16005, plain, (class_Rings_Olinordered__semiring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]), ['final']). 6.97/7.26 cnf(c_0_16006, plain, (class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring]), ['final']). 6.97/7.26 cnf(c_0_16007, plain, (class_Rings_Olinordered__semiring(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]), ['final']). 6.97/7.26 cnf(c_0_16008, plain, (class_Rings_Osemiring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring]), ['final']). 6.97/7.26 cnf(c_0_16009, plain, (class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring]), ['final']). 6.97/7.26 cnf(c_0_16010, plain, (class_Rings_Osemiring(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]), ['final']). 6.97/7.26 cnf(c_0_16011, plain, (class_Groups_Olinordered__ab__group__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Olinordered__ab__group__add]), ['final']). 6.97/7.26 cnf(c_0_16012, plain, (class_Lattices_Obounded__lattice__bot(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice__bot]), ['final']). 6.97/7.26 cnf(c_0_16013, plain, (class_Groups_Omonoid__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]), ['final']). 6.97/7.26 cnf(c_0_16014, plain, (class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add]), ['final']). 6.97/7.26 cnf(c_0_16015, plain, (class_Groups_Omonoid__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]), ['final']). 6.97/7.26 cnf(c_0_16016, plain, (class_Rings_Ozero__neq__one(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ozero__neq__one]), ['final']). 6.97/7.26 cnf(c_0_16017, 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']). 6.97/7.26 cnf(c_0_16018, plain, (class_Rings_Ozero__neq__one(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ozero__neq__one]), ['final']). 6.97/7.26 cnf(c_0_16019, 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']). 6.97/7.26 cnf(c_0_16020, plain, (class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__comm__semiring__strict]), ['final']). 6.97/7.26 cnf(c_0_16021, 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']). 6.97/7.26 cnf(c_0_16022, plain, (class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict]), ['final']). 6.97/7.26 cnf(c_0_16023, plain, (class_Groups_Ocancel__semigroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocancel__semigroup__add]), ['final']). 6.97/7.26 cnf(c_0_16024, 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']). 6.97/7.26 cnf(c_0_16025, plain, (class_Groups_Ocancel__semigroup__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__semigroup__add]), ['final']). 6.97/7.26 cnf(c_0_16026, plain, (class_Rings_Olinordered__ring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]), ['final']). 6.97/7.26 cnf(c_0_16027, plain, (class_Rings_Oordered__comm__semiring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__comm__semiring]), ['final']). 6.97/7.26 cnf(c_0_16028, 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']). 6.97/7.26 cnf(c_0_16029, plain, (class_Rings_Oordered__comm__semiring(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__comm__semiring]), ['final']). 6.97/7.26 cnf(c_0_16030, plain, (class_Divides_Oring__div(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Oring__div]), ['final']). 6.97/7.26 cnf(c_0_16031, plain, (class_Rings_Ono__zero__divisors(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ono__zero__divisors]), ['final']). 6.97/7.26 cnf(c_0_16032, 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']). 6.97/7.26 cnf(c_0_16033, plain, (class_Rings_Ono__zero__divisors(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ono__zero__divisors]), ['final']). 6.97/7.26 cnf(c_0_16034, plain, (class_Rings_Ocomm__ring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring]), ['final']). 6.97/7.26 cnf(c_0_16035, plain, (class_Rings_Oidom(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oidom]), ['final']). 6.97/7.26 cnf(c_0_16036, plain, (class_Rings_Oordered__cancel__semiring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__cancel__semiring]), ['final']). 6.97/7.26 cnf(c_0_16037, 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']). 6.97/7.26 cnf(c_0_16038, plain, (class_Rings_Oordered__cancel__semiring(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__cancel__semiring]), ['final']). 6.97/7.26 cnf(c_0_16039, plain, (class_Rings_Oordered__ring__abs(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring__abs]), ['final']). 6.97/7.26 cnf(c_0_16040, plain, (class_Rings_Olinordered__ring__strict(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring__strict]), ['final']). 6.97/7.26 cnf(c_0_16041, plain, (class_Groups_Omonoid__mult(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]), ['final']). 6.97/7.26 cnf(c_0_16042, plain, (class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult]), ['final']). 6.97/7.26 cnf(c_0_16043, plain, (class_Groups_Omonoid__mult(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]), ['final']). 6.97/7.26 cnf(c_0_16044, plain, (class_Rings_Oordered__ring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]), ['final']). 6.97/7.26 cnf(c_0_16045, plain, (class_Groups_Ominus(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ominus]), ['final']). 6.97/7.26 cnf(c_0_16046, plain, (class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ominus]), ['final']). 6.97/7.26 cnf(c_0_16047, plain, (class_Groups_Ominus(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ominus]), ['final']). 6.97/7.26 cnf(c_0_16048, plain, (class_Groups_Ominus(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ominus]), ['final']). 6.97/7.26 cnf(c_0_16049, plain, (class_Rings_Osemiring__0(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]), ['final']). 6.97/7.26 cnf(c_0_16050, plain, (class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0]), ['final']). 6.97/7.26 cnf(c_0_16051, plain, (class_Rings_Osemiring__0(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]), ['final']). 6.97/7.26 cnf(c_0_16052, plain, (class_Groups_Ouminus(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ouminus]), ['final']). 6.97/7.26 cnf(c_0_16053, plain, (class_Groups_Ouminus(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ouminus]), ['final']). 6.97/7.26 cnf(c_0_16054, plain, (class_Rings_Oordered__semiring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]), ['final']). 6.97/7.26 cnf(c_0_16055, plain, (class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring]), ['final']). 6.97/7.26 cnf(c_0_16056, plain, (class_Rings_Oordered__semiring(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]), ['final']). 6.97/7.26 cnf(c_0_16057, plain, (class_Rings_Oring__no__zero__divisors(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__no__zero__divisors]), ['final']). 6.97/7.26 cnf(c_0_16058, plain, (class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit)), inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy]), ['final']). 6.97/7.26 cnf(c_0_16059, plain, (class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lazy__Sequence_Osmall__lazy]), ['final']). 6.97/7.26 cnf(c_0_16060, plain, (class_Groups_Ogroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]), ['final']). 6.97/7.26 cnf(c_0_16061, plain, (class_Rings_Oring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring]), ['final']). 6.97/7.26 cnf(c_0_16062, plain, (class_Groups_Osemigroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Osemigroup__add]), ['final']). 6.97/7.26 cnf(c_0_16063, plain, (class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add]), ['final']). 6.97/7.26 cnf(c_0_16064, plain, (class_Groups_Osemigroup__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Osemigroup__add]), ['final']). 6.97/7.26 cnf(c_0_16065, plain, (class_Nat_Osemiring__char__0(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Nat_Osemiring__char__0]), ['final']). 6.97/7.26 cnf(c_0_16066, 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']). 6.97/7.26 cnf(c_0_16067, plain, (class_Nat_Osemiring__char__0(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Nat_Osemiring__char__0]), ['final']). 6.97/7.26 cnf(c_0_16068, plain, (class_Groups_Oab__semigroup__mult(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__mult]), ['final']). 6.97/7.26 cnf(c_0_16069, 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']). 6.97/7.26 cnf(c_0_16070, plain, (class_Groups_Oab__semigroup__mult(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__mult]), ['final']). 6.97/7.26 cnf(c_0_16071, plain, (class_Lattices_Obounded__lattice(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice]), ['final']). 6.97/7.26 cnf(c_0_16072, plain, (class_Rings_Omult__zero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]), ['final']). 6.97/7.26 cnf(c_0_16073, plain, (class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero]), ['final']). 6.97/7.26 cnf(c_0_16074, plain, (class_Rings_Omult__zero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]), ['final']). 6.97/7.26 cnf(c_0_16075, plain, (class_Groups_Oab__semigroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__add]), ['final']). 6.97/7.26 cnf(c_0_16076, 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']). 6.97/7.26 cnf(c_0_16077, plain, (class_Groups_Oab__semigroup__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__add]), ['final']). 6.97/7.26 cnf(c_0_16078, plain, (class_Orderings_Obot(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Obot]), ['final']). 6.97/7.26 cnf(c_0_16079, plain, (class_Orderings_Obot(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Obot]), ['final']). 6.97/7.26 cnf(c_0_16080, plain, (class_Finite__Set_Ofinite(tc_Product__Type_Ounit)), inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Finite__Set_Ofinite]), ['final']). 6.97/7.26 cnf(c_0_16081, plain, (class_Finite__Set_Ofinite(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Finite__Set_Ofinite]), ['final']). 6.97/7.26 cnf(c_0_16082, plain, (class_Rings_Odvd(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Odvd]), ['final']). 6.97/7.26 cnf(c_0_16083, plain, (class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Odvd]), ['final']). 6.97/7.26 cnf(c_0_16084, plain, (class_Rings_Odvd(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Odvd]), ['final']). 6.97/7.26 cnf(c_0_16085, plain, (class_Enum_Oenum(tc_Product__Type_Ounit)), inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Enum_Oenum]), ['final']). 6.97/7.26 cnf(c_0_16086, plain, (class_Enum_Oenum(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Enum_Oenum]), ['final']). 6.97/7.26 cnf(c_0_16087, plain, (class_Lattices_Oboolean__algebra(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]), ['final']). 6.97/7.26 cnf(c_0_16088, plain, (class_Groups_Oordered__ab__group__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add]), ['final']). 6.97/7.26 cnf(c_0_16089, plain, (class_Rings_Olinordered__semidom(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]), ['final']). 6.97/7.26 cnf(c_0_16090, plain, (class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom]), ['final']). 6.97/7.26 cnf(c_0_16091, plain, (class_Rings_Olinordered__semidom(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]), ['final']). 6.97/7.26 cnf(c_0_16092, plain, (class_Orderings_Oord(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oord]), ['final']). 6.97/7.26 cnf(c_0_16093, plain, (class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Oord]), ['final']). 6.97/7.26 cnf(c_0_16094, plain, (class_Orderings_Oord(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]), ['final']). 6.97/7.26 cnf(c_0_16095, plain, (class_Orderings_Oord(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]), ['final']). 6.97/7.26 cnf(c_0_16096, plain, (class_Lattices_Obounded__lattice__top(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice__top]), ['final']). 6.97/7.26 cnf(c_0_16097, 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']). 6.97/7.26 cnf(c_0_16098, 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']). 6.97/7.26 cnf(c_0_16099, 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']). 6.97/7.26 cnf(c_0_16100, plain, (class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add]), ['final']). 6.97/7.26 cnf(c_0_16101, 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']). 6.97/7.26 cnf(c_0_16102, plain, (class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add]), ['final']). 6.97/7.26 cnf(c_0_16103, plain, (class_Lattices_Osemilattice__inf(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Osemilattice__inf]), ['final']). 6.97/7.26 cnf(c_0_16104, plain, (class_Lattices_Osemilattice__inf(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__inf]), ['final']). 6.97/7.26 cnf(c_0_16105, plain, (class_Lattices_Osemilattice__inf(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__inf]), ['final']). 6.97/7.26 cnf(c_0_16106, plain, (class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice]), ['final']). 6.97/7.26 cnf(c_0_16107, 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']). 6.97/7.26 cnf(c_0_16108, 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']). 6.97/7.26 cnf(c_0_16109, 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']). 6.97/7.26 cnf(c_0_16110, 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']). 6.97/7.26 cnf(c_0_16111, plain, (class_Lattices_Osemilattice__sup(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Osemilattice__sup]), ['final']). 6.97/7.26 cnf(c_0_16112, plain, (class_Lattices_Osemilattice__sup(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__sup]), ['final']). 6.97/7.26 cnf(c_0_16113, plain, (class_Lattices_Osemilattice__sup(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__sup]), ['final']). 6.97/7.26 cnf(c_0_16114, plain, (class_Power_Opower(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Power_Opower]), ['final']). 6.97/7.26 cnf(c_0_16115, plain, (class_Power_Opower(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Power_Opower]), ['final']). 6.97/7.26 cnf(c_0_16116, plain, (class_Power_Opower(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Power_Opower]), ['final']). 6.97/7.26 cnf(c_0_16117, plain, (class_Groups_Oordered__comm__monoid__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__comm__monoid__add]), ['final']). 6.97/7.26 cnf(c_0_16118, 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']). 6.97/7.26 cnf(c_0_16119, plain, (class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__comm__monoid__add]), ['final']). 6.97/7.26 cnf(c_0_16120, plain, (class_Int_Oring__char__0(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Oring__char__0]), ['final']). 6.97/7.26 cnf(c_0_16121, plain, (class_Divides_Osemiring__div(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Osemiring__div]), ['final']). 6.97/7.26 cnf(c_0_16122, plain, (class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div]), ['final']). 6.97/7.26 cnf(c_0_16123, plain, (class_Divides_Osemiring__div(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Divides_Osemiring__div]), ['final']). 6.97/7.26 cnf(c_0_16124, plain, (class_Int_Onumber__ring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber__ring]), ['final']). 6.97/7.26 cnf(c_0_16125, plain, (class_Groups_Ocomm__monoid__mult(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__mult]), ['final']). 6.97/7.26 cnf(c_0_16126, 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']). 6.97/7.26 cnf(c_0_16127, plain, (class_Groups_Ocomm__monoid__mult(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__mult]), ['final']). 6.97/7.26 cnf(c_0_16128, plain, (class_Rings_Ocomm__semiring__1(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__1]), ['final']). 6.97/7.26 cnf(c_0_16129, 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']). 6.97/7.26 cnf(c_0_16130, plain, (class_Rings_Ocomm__semiring__1(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__1]), ['final']). 6.97/7.26 cnf(c_0_16131, plain, (class_Groups_Oab__group__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__group__add]), ['final']). 6.97/7.26 cnf(c_0_16132, plain, (class_Orderings_Opreorder(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]), ['final']). 6.97/7.26 cnf(c_0_16133, plain, (class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder]), ['final']). 6.97/7.26 cnf(c_0_16134, plain, (class_Orderings_Opreorder(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]), ['final']). 6.97/7.26 cnf(c_0_16135, plain, (class_Orderings_Opreorder(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]), ['final']). 6.97/7.26 cnf(c_0_16136, plain, (class_Orderings_Oorder(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oorder]), ['final']). 6.97/7.26 cnf(c_0_16137, plain, (class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Oorder]), ['final']). 6.97/7.26 cnf(c_0_16138, plain, (class_Orderings_Oorder(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]), ['final']). 6.97/7.26 cnf(c_0_16139, plain, (class_Orderings_Oorder(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]), ['final']). 6.97/7.26 cnf(c_0_16140, plain, (class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Olinordered__ab__semigroup__add]), ['final']). 6.97/7.26 cnf(c_0_16141, 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']). 6.97/7.26 cnf(c_0_16142, plain, (class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add]), ['final']). 6.97/7.26 cnf(c_0_16143, plain, (class_Groups_Ocomm__monoid__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__add]), ['final']). 6.97/7.26 cnf(c_0_16144, 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']). 6.97/7.26 cnf(c_0_16145, plain, (class_Groups_Ocomm__monoid__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__add]), ['final']). 6.97/7.26 cnf(c_0_16146, plain, (class_Lattices_Odistrib__lattice(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Odistrib__lattice]), ['final']). 6.97/7.26 cnf(c_0_16147, plain, (class_Lattices_Odistrib__lattice(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Odistrib__lattice]), ['final']). 6.97/7.26 cnf(c_0_16148, plain, (class_Lattices_Odistrib__lattice(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Odistrib__lattice]), ['final']). 6.97/7.26 cnf(c_0_16149, plain, (class_Orderings_Olinorder(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]), ['final']). 6.97/7.26 cnf(c_0_16150, plain, (class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder]), ['final']). 6.97/7.26 cnf(c_0_16151, plain, (class_Orderings_Olinorder(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]), ['final']). 6.97/7.26 cnf(c_0_16152, plain, (class_Rings_Olinordered__semiring__strict(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__strict]), ['final']). 6.97/7.26 cnf(c_0_16153, 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']). 6.97/7.26 cnf(c_0_16154, plain, (class_Rings_Olinordered__semiring__strict(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring__strict]), ['final']). 6.97/7.26 cnf(c_0_16155, plain, (class_Rings_Olinordered__idom(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]), ['final']). 6.97/7.26 cnf(c_0_16156, plain, (class_Rings_Oring__1(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__1]), ['final']). 6.97/7.26 cnf(c_0_16157, plain, (class_Nat_Osize(tc_Code__Evaluation_Oterm)), inference(split_conjunct,[status(thm)],[arity_Code____Evaluation__Oterm__Nat_Osize]), ['final']). 6.97/7.26 cnf(c_0_16158, plain, (class_Nat_Osize(tc_Product__Type_Ounit)), inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Nat_Osize]), ['final']). 6.97/7.26 cnf(c_0_16159, plain, (class_Nat_Osize(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Nat_Osize]), ['final']). 6.97/7.26 cnf(c_0_16160, plain, (class_Nat_Osize(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Nat_Osize]), ['final']). 6.97/7.26 cnf(c_0_16161, plain, (class_Nat_Osize(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Nat_Osize]), ['final']). 6.97/7.26 cnf(c_0_16162, plain, (class_Groups_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ozero]), ['final']). 6.97/7.26 cnf(c_0_16163, plain, (class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ozero]), ['final']). 6.97/7.26 cnf(c_0_16164, plain, (class_Groups_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]), ['final']). 6.97/7.26 cnf(c_0_16165, plain, (class_Rings_Osemiring__1(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__1]), ['final']). 6.97/7.26 cnf(c_0_16166, plain, (class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1]), ['final']). 6.97/7.26 cnf(c_0_16167, plain, (class_Rings_Osemiring__1(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__1]), ['final']). 6.97/7.26 cnf(c_0_16168, plain, (class_Int_Onumber(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber]), ['final']). 6.97/7.26 cnf(c_0_16169, plain, (class_Int_Onumber(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Int_Onumber]), ['final']). 6.97/7.26 cnf(c_0_16170, plain, (class_Int_Onumber(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Int_Onumber]), ['final']). 6.97/7.26 cnf(c_0_16171, plain, (class_Lattices_Olattice(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Olattice]), ['final']). 6.97/7.26 cnf(c_0_16172, plain, (class_Lattices_Olattice(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Olattice]), ['final']). 6.97/7.26 cnf(c_0_16173, plain, (class_Lattices_Olattice(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Olattice]), ['final']). 6.97/7.26 cnf(c_0_16174, plain, (hBOOL(c_fTrue)), inference(split_conjunct,[status(thm)],[help_c__fTrue__1]), ['final']). 6.97/7.26 6.97/7.26 # End clausification derivation 6.97/7.26 # Begin listing active clauses obtained from FOF to CNF conversion 6.97/7.26 cnf(i_0_2970, plain, (hBOOL(c_fTrue))). 6.97/7.26 cnf(i_0_2984, plain, (c_Int_OPls=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 6.97/7.26 cnf(i_0_6451, plain, (c_Code__Numeral_Oof__nat=c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_4465, plain, (c_Code__Numeral_Osubtract__code__numeral=c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_2775, plain, (class_Lattices_Olattice(tc_HOL_Obool))). 6.97/7.26 cnf(i_0_6833, plain, (class_Lattices_Olattice(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_4168, plain, (class_Lattices_Olattice(tc_Int_Oint))). 6.97/7.26 cnf(i_0_4796, plain, (class_Int_Onumber(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_2294, plain, (class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_2807, plain, (class_Int_Onumber(tc_Int_Oint))). 6.97/7.26 cnf(i_0_1156, plain, (class_Rings_Osemiring__1(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_3136, plain, (class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_5703, plain, (class_Rings_Osemiring__1(tc_Int_Oint))). 6.97/7.26 cnf(i_0_21, plain, (class_Groups_Ozero(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_1336, plain, (class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_7507, plain, (class_Groups_Ozero(tc_Int_Oint))). 6.97/7.26 cnf(i_0_7464, plain, (class_Nat_Osize(tc_HOL_Obool))). 6.97/7.26 cnf(i_0_5257, plain, (class_Nat_Osize(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_3657, plain, (class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_5305, plain, (class_Nat_Osize(tc_Product__Type_Ounit))). 6.97/7.26 cnf(i_0_7223, plain, (class_Nat_Osize(tc_Code__Evaluation_Oterm))). 6.97/7.26 cnf(i_0_3495, plain, (class_Rings_Oring__1(tc_Int_Oint))). 6.97/7.26 cnf(i_0_691, plain, (class_Rings_Olinordered__idom(tc_Int_Oint))). 6.97/7.26 cnf(i_0_447, plain, (class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_3219, plain, (class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_369, plain, (class_Rings_Olinordered__semiring__strict(tc_Int_Oint))). 6.97/7.26 cnf(i_0_279, plain, (class_Orderings_Olinorder(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_4318, plain, (class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_3887, plain, (class_Orderings_Olinorder(tc_Int_Oint))). 6.97/7.26 cnf(i_0_5037, plain, (class_Lattices_Odistrib__lattice(tc_HOL_Obool))). 6.97/7.26 cnf(i_0_2904, plain, (class_Lattices_Odistrib__lattice(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_55, plain, (class_Lattices_Odistrib__lattice(tc_Int_Oint))). 6.97/7.26 cnf(i_0_5420, plain, (class_Groups_Ocomm__monoid__add(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_3819, plain, (class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_2729, plain, (class_Groups_Ocomm__monoid__add(tc_Int_Oint))). 6.97/7.26 cnf(i_0_78, plain, (class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_2770, plain, (class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_5535, plain, (class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))). 6.97/7.26 cnf(i_0_3220, plain, (class_Orderings_Oorder(tc_HOL_Obool))). 6.97/7.26 cnf(i_0_211, plain, (class_Orderings_Oorder(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_6809, plain, (class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_5077, plain, (class_Orderings_Oorder(tc_Int_Oint))). 6.97/7.26 cnf(i_0_2247, plain, (class_Orderings_Opreorder(tc_HOL_Obool))). 6.97/7.26 cnf(i_0_4729, plain, (class_Orderings_Opreorder(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_2035, plain, (class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_2823, plain, (class_Orderings_Opreorder(tc_Int_Oint))). 6.97/7.26 cnf(i_0_1137, plain, (class_Groups_Oab__group__add(tc_Int_Oint))). 6.97/7.26 cnf(i_0_6216, plain, (class_Rings_Ocomm__semiring__1(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_5241, plain, (class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_3529, plain, (class_Rings_Ocomm__semiring__1(tc_Int_Oint))). 6.97/7.26 cnf(i_0_200, plain, (class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_389, plain, (class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_2210, plain, (class_Groups_Ocomm__monoid__mult(tc_Int_Oint))). 6.97/7.26 cnf(i_0_99, plain, (class_Int_Onumber__ring(tc_Int_Oint))). 6.97/7.26 cnf(i_0_714, plain, (class_Divides_Osemiring__div(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_3259, plain, (class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_7124, plain, (class_Divides_Osemiring__div(tc_Int_Oint))). 6.97/7.26 cnf(i_0_4071, plain, (class_Int_Oring__char__0(tc_Int_Oint))). 6.97/7.26 cnf(i_0_1110, plain, (class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_3079, plain, (class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_2974, plain, (class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))). 6.97/7.26 cnf(i_0_818, plain, (class_Power_Opower(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_826, plain, (class_Power_Opower(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_446, plain, (class_Power_Opower(tc_Int_Oint))). 6.97/7.26 cnf(i_0_7144, plain, (class_Lattices_Osemilattice__sup(tc_HOL_Obool))). 6.97/7.26 cnf(i_0_1667, plain, (class_Lattices_Osemilattice__sup(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_5472, plain, (class_Lattices_Osemilattice__sup(tc_Int_Oint))). 6.97/7.26 cnf(i_0_4221, plain, (class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))). 6.97/7.26 cnf(i_0_6975, plain, (class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_209, plain, (class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_3726, plain, (class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))). 6.97/7.26 cnf(i_0_7267, plain, (class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))). 6.97/7.26 cnf(i_0_5952, plain, (class_Lattices_Osemilattice__inf(tc_HOL_Obool))). 6.97/7.26 cnf(i_0_3771, plain, (class_Lattices_Osemilattice__inf(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_1415, plain, (class_Lattices_Osemilattice__inf(tc_Int_Oint))). 6.97/7.26 cnf(i_0_2922, plain, (class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_5787, plain, (class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_3057, plain, (class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))). 6.97/7.26 cnf(i_0_6000, plain, (class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_3415, plain, (class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_5938, plain, (class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))). 6.97/7.26 cnf(i_0_310, plain, (class_Lattices_Obounded__lattice__top(tc_HOL_Obool))). 6.97/7.26 cnf(i_0_1296, plain, (class_Orderings_Oord(tc_HOL_Obool))). 6.97/7.26 cnf(i_0_6219, plain, (class_Orderings_Oord(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_7404, plain, (class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_6552, plain, (class_Orderings_Oord(tc_Int_Oint))). 6.97/7.26 cnf(i_0_3166, plain, (class_Rings_Olinordered__semidom(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_3672, plain, (class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_6910, plain, (class_Rings_Olinordered__semidom(tc_Int_Oint))). 6.97/7.26 cnf(i_0_6114, plain, (class_Groups_Oordered__ab__group__add(tc_Int_Oint))). 6.97/7.26 cnf(i_0_6289, plain, (class_Lattices_Oboolean__algebra(tc_HOL_Obool))). 6.97/7.26 cnf(i_0_6246, plain, (class_Enum_Oenum(tc_HOL_Obool))). 6.97/7.26 cnf(i_0_5065, plain, (class_Enum_Oenum(tc_Product__Type_Ounit))). 6.97/7.26 cnf(i_0_4217, plain, (class_Rings_Odvd(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_1160, plain, (class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_484, plain, (class_Rings_Odvd(tc_Int_Oint))). 6.97/7.26 cnf(i_0_2078, plain, (class_Finite__Set_Ofinite(tc_HOL_Obool))). 6.97/7.26 cnf(i_0_6712, plain, (class_Finite__Set_Ofinite(tc_Product__Type_Ounit))). 6.97/7.26 cnf(i_0_5525, plain, (class_Orderings_Obot(tc_HOL_Obool))). 6.97/7.26 cnf(i_0_2690, plain, (class_Orderings_Obot(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_3673, plain, (class_Groups_Oab__semigroup__add(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_3420, plain, (class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_7035, plain, (class_Groups_Oab__semigroup__add(tc_Int_Oint))). 6.97/7.26 cnf(i_0_7004, plain, (class_Rings_Omult__zero(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_2516, plain, (class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_1128, plain, (class_Rings_Omult__zero(tc_Int_Oint))). 6.97/7.26 cnf(i_0_1782, plain, (class_Lattices_Obounded__lattice(tc_HOL_Obool))). 6.97/7.26 cnf(i_0_1527, plain, (class_Groups_Oab__semigroup__mult(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_1353, plain, (class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_6116, plain, (class_Groups_Oab__semigroup__mult(tc_Int_Oint))). 6.97/7.26 cnf(i_0_4647, plain, (class_Nat_Osemiring__char__0(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_5902, plain, (class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_4529, plain, (class_Nat_Osemiring__char__0(tc_Int_Oint))). 6.97/7.26 cnf(i_0_4725, plain, (class_Groups_Osemigroup__add(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_806, plain, (class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_2525, plain, (class_Groups_Osemigroup__add(tc_Int_Oint))). 6.97/7.26 cnf(i_0_3052, plain, (class_Rings_Oring(tc_Int_Oint))). 6.97/7.26 cnf(i_0_4059, plain, (class_Groups_Ogroup__add(tc_Int_Oint))). 6.97/7.26 cnf(i_0_4920, plain, (class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))). 6.97/7.26 cnf(i_0_6167, plain, (class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))). 6.97/7.26 cnf(i_0_2203, plain, (class_Rings_Oring__no__zero__divisors(tc_Int_Oint))). 6.97/7.26 cnf(i_0_5541, plain, (class_Rings_Oordered__semiring(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_4283, plain, (class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_3741, plain, (class_Rings_Oordered__semiring(tc_Int_Oint))). 6.97/7.26 cnf(i_0_890, plain, (class_Groups_Ouminus(tc_HOL_Obool))). 6.97/7.26 cnf(i_0_3032, plain, (class_Groups_Ouminus(tc_Int_Oint))). 6.97/7.26 cnf(i_0_2026, plain, (class_Rings_Osemiring__0(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_4020, plain, (class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_1871, plain, (class_Rings_Osemiring__0(tc_Int_Oint))). 6.97/7.26 cnf(i_0_7524, plain, (class_Groups_Ominus(tc_HOL_Obool))). 6.97/7.26 cnf(i_0_1525, plain, (class_Groups_Ominus(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_6035, plain, (class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_1000, plain, (class_Groups_Ominus(tc_Int_Oint))). 6.97/7.26 cnf(i_0_7358, plain, (class_Rings_Oordered__ring(tc_Int_Oint))). 6.97/7.26 cnf(i_0_1070, plain, (class_Groups_Omonoid__mult(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_3418, plain, (class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_1321, plain, (class_Groups_Omonoid__mult(tc_Int_Oint))). 6.97/7.26 cnf(i_0_6461, plain, (class_Rings_Olinordered__ring__strict(tc_Int_Oint))). 6.97/7.26 cnf(i_0_7142, plain, (class_Rings_Oordered__ring__abs(tc_Int_Oint))). 6.97/7.26 cnf(i_0_1435, plain, (class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_1395, plain, (class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_5358, plain, (class_Rings_Oordered__cancel__semiring(tc_Int_Oint))). 6.97/7.26 cnf(i_0_1747, plain, (class_Rings_Oidom(tc_Int_Oint))). 6.97/7.26 cnf(i_0_1551, plain, (class_Rings_Ocomm__ring(tc_Int_Oint))). 6.97/7.26 cnf(i_0_3076, plain, (class_Rings_Ono__zero__divisors(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_1560, plain, (class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_2838, plain, (class_Rings_Ono__zero__divisors(tc_Int_Oint))). 6.97/7.26 cnf(i_0_2938, plain, (class_Divides_Oring__div(tc_Int_Oint))). 6.97/7.26 cnf(i_0_6072, plain, (class_Rings_Oordered__comm__semiring(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_2290, plain, (class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_1630, plain, (class_Rings_Oordered__comm__semiring(tc_Int_Oint))). 6.97/7.26 cnf(i_0_6174, plain, (class_Rings_Olinordered__ring(tc_Int_Oint))). 6.97/7.26 cnf(i_0_5418, plain, (class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_6556, plain, (class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_1873, plain, (class_Groups_Ocancel__semigroup__add(tc_Int_Oint))). 6.97/7.26 cnf(i_0_4320, plain, (class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_4182, plain, (class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_6286, plain, (class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))). 6.97/7.26 cnf(i_0_3309, plain, (class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))). 6.97/7.26 cnf(i_0_1995, plain, (class_Rings_Ozero__neq__one(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_7096, plain, (class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_3464, plain, (class_Rings_Ozero__neq__one(tc_Int_Oint))). 6.97/7.26 cnf(i_0_2653, plain, (class_Groups_Omonoid__add(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_5363, plain, (class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_4470, plain, (class_Groups_Omonoid__add(tc_Int_Oint))). 6.97/7.26 cnf(i_0_2592, plain, (class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))). 6.97/7.26 cnf(i_0_4961, plain, (class_Groups_Olinordered__ab__group__add(tc_Int_Oint))). 6.97/7.26 cnf(i_0_7081, plain, (class_Rings_Osemiring(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_2181, plain, (class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_4303, plain, (class_Rings_Osemiring(tc_Int_Oint))). 6.97/7.26 cnf(i_0_5384, plain, (class_Rings_Olinordered__semiring(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_4716, plain, (class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_2208, plain, (class_Rings_Olinordered__semiring(tc_Int_Oint))). 6.97/7.26 cnf(i_0_5171, plain, (class_Groups_Osgn__if(tc_Int_Oint))). 6.97/7.26 cnf(i_0_2520, plain, (class_Rings_Olinordered__semiring__1(tc_Int_Oint))). 6.97/7.26 cnf(i_0_2537, plain, (class_Groups_Oabs__if(tc_Int_Oint))). 6.97/7.26 cnf(i_0_3893, plain, (class_Orderings_Otop(tc_HOL_Obool))). 6.97/7.26 cnf(i_0_4309, plain, (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_2945, plain, (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))). 6.97/7.26 cnf(i_0_3049, plain, (class_Rings_Ocomm__semiring(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_4353, plain, (class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_5878, plain, (class_Rings_Ocomm__semiring(tc_Int_Oint))). 6.97/7.26 cnf(i_0_6168, plain, (class_Groups_Oone(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_3176, plain, (class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_3322, plain, (class_Groups_Oone(tc_Int_Oint))). 6.97/7.26 cnf(i_0_3264, plain, (class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))). 6.97/7.26 cnf(i_0_4811, plain, (class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_6745, plain, (class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_4266, plain, (class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))). 6.97/7.26 cnf(i_0_4241, plain, (class_Rings_Ocomm__ring__1(tc_Int_Oint))). 6.97/7.26 cnf(i_0_6008, plain, (class_Orderings_Owellorder(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_6813, plain, (c_Orderings_Obot__class_Obot(tc_Nat_Onat)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_6119, plain, (c_Orderings_Oord__class_Omin(tc_Nat_Onat)=c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_5236, plain, (c_Int_Oring__1__class_Oof__int(tc_Int_Oint)=c_Fun_Oid(tc_Int_Oint))). 6.97/7.26 cnf(i_0_6452, plain, (c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). 6.97/7.26 cnf(i_0_2628, plain, (c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))). 6.97/7.26 cnf(i_0_3294, plain, (c_Orderings_Oord__class_Omax(tc_Nat_Onat)=c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_5808, plain, (c_HOL_Obool_Obool__size(c_fTrue)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_5170, plain, (c_HOL_Obool_Obool__size(c_fFalse)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_22, plain, (class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)))). 6.97/7.26 cnf(i_0_1066, plain, (class_Nat_Osize(tc_Option_Ooption(X1)))). 6.97/7.26 cnf(i_0_4774, plain, (class_Nat_Osize(tc_List_Olist(X1)))). 6.97/7.26 cnf(i_0_5190, plain, (class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X1)))). 6.97/7.26 cnf(i_0_1844, plain, (c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_4422, plain, (c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat))). 6.97/7.26 cnf(i_0_271, plain, (c_Equiv__Relations_Oequivp(X1,c_fequal))). 6.97/7.26 cnf(i_0_436, plain, (c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than))). 6.97/7.26 cnf(i_0_4818, plain, (c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than))). 6.97/7.26 cnf(i_0_3134, 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))). 6.97/7.26 cnf(i_0_2895, plain, (c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X1)))). 6.97/7.26 cnf(i_0_5042, plain, (c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X1)))). 6.97/7.26 cnf(i_0_2828, plain, (class_Nat_Osize(tc_prod(X1,X2)))). 6.97/7.26 cnf(i_0_5514, plain, (class_Nat_Osize(tc_sum(X1,X2)))). 6.97/7.26 cnf(i_0_3976, plain, (class_Nat_Osize(tc_Nitpick_Opair__box(X1,X2)))). 6.97/7.26 cnf(i_0_4174, plain, (c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc))). 6.97/7.26 cnf(i_0_27, 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))). 6.97/7.26 cnf(i_0_314, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)=X1)). 6.97/7.26 cnf(i_0_613, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X1)=X1)). 6.97/7.26 cnf(i_0_4142, 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))). 6.97/7.26 cnf(i_0_7307, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),esk571_1(X1))=X1)). 6.97/7.26 cnf(i_0_220, plain, (hAPP(c_Int_OAbs__Integ,esk17_1(X1))=X1)). 6.97/7.26 cnf(i_0_6091, plain, (hAPP(c_Set_OCollect(X1),X2)=X2)). 6.97/7.26 cnf(i_0_5292, plain, (hAPP(c_Fun_Oid(X1),X2)=X2)). 6.97/7.26 cnf(i_0_7256, plain, (hAPP(c_COMBI(X1),X2)=X2)). 6.97/7.26 cnf(i_0_1343, plain, (c_Predicate_Oconversep(X1,X1,c_fequal)=c_fequal)). 6.97/7.26 cnf(i_0_4116, 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))). 6.97/7.26 cnf(i_0_6221, 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))). 6.97/7.26 cnf(i_0_170, plain, (hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_6962, plain, (hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_6793, 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))). 6.97/7.26 cnf(i_0_2740, plain, (hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_7342, plain, (c_Quickcheck_Obeyond(X1,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_4747, plain, (c_Random_Oinc__shift(X1,X1)=c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))). 6.97/7.26 cnf(i_0_3487, plain, (hAPP(c_New__DSequence_Opos__empty(X1),X2)=c_Lazy__Sequence_Oempty(X1))). 6.97/7.26 cnf(i_0_6421, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Int_OMin)). 6.97/7.26 cnf(i_0_1410, plain, (c_List_Oremdups(X1,c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 6.97/7.26 cnf(i_0_2944, plain, (c_List_Obutlast(X1,c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 6.97/7.26 cnf(i_0_2754, plain, (c_Nitpick_Onat__gcd(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1)). 6.97/7.26 cnf(i_0_1436, plain, (c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less))). 6.97/7.26 cnf(i_0_6591, plain, (c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))). 6.97/7.26 cnf(i_0_768, plain, (c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X2)))). 6.97/7.26 cnf(i_0_2547, plain, (c_Wellfounded_Owf(X1,c_List_Omeasures(X1,X2)))). 6.97/7.26 cnf(i_0_6284, plain, (c_Relation_Osym(X1,c_Relation_OId__on(X1,X2)))). 6.97/7.26 cnf(i_0_1114, plain, (c_Relation_Otrans(X1,c_Relation_OId__on(X1,X2)))). 6.97/7.26 cnf(i_0_6798, 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))). 6.97/7.26 cnf(i_0_4189, plain, (c_Relation_Otrans(X1,c_Transitive__Closure_Ortrancl(X1,X2)))). 6.97/7.26 cnf(i_0_2105, plain, (c_Relation_Oantisym(X1,c_Relation_OId__on(X1,X2)))). 6.97/7.26 cnf(i_0_2371, plain, (c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))))). 6.97/7.26 cnf(i_0_6901, plain, (c_List_Olist__all(X1,X2,c_List_Olist_ONil(X1)))). 6.97/7.26 cnf(i_0_5340, plain, (c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1))). 6.97/7.26 cnf(i_0_4109, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 6.97/7.26 cnf(i_0_1123, 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))). 6.97/7.26 cnf(i_0_4583, 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))). 6.97/7.26 cnf(i_0_6614, plain, (c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)=c_FunDef_Omax__strict)). 6.97/7.26 cnf(i_0_3205, plain, (c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)=c_FunDef_Omin__strict)). 6.97/7.26 cnf(i_0_1111, 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))). 6.97/7.26 cnf(i_0_6998, plain, (hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X1))=X1)). 6.97/7.26 cnf(i_0_4673, plain, (hAPP(c_Code__Numeral_Onat__of,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X1))=X1)). 6.97/7.26 cnf(i_0_2262, 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))). 6.97/7.26 cnf(i_0_5693, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Onat__of,X1))=X1)). 6.97/7.26 cnf(i_0_6846, plain, (c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X2))=X2)). 6.97/7.26 cnf(i_0_7002, plain, (c_HOL_OThe(X1,hAPP(c_fequal,X2))=X2)). 6.97/7.26 cnf(i_0_4034, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=X1)). 6.97/7.26 cnf(i_0_2781, plain, (c_List_Osplice(X1,c_List_Olist_ONil(X1),X2)=X2)). 6.97/7.26 cnf(i_0_4899, plain, (c_List_Osplice(X1,X2,c_List_Olist_ONil(X1))=X2)). 6.97/7.26 cnf(i_0_7469, plain, (c_Lazy__Sequence_Oappend(X1,c_Lazy__Sequence_Olazy__sequence_OEmpty(X1),X2)=X2)). 6.97/7.26 cnf(i_0_3274, plain, (c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than)=c_FunDef_Opair__less)). 6.97/7.26 cnf(i_0_4525, plain, (hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 6.97/7.26 cnf(i_0_2108, plain, (hAPP(c_List_Orotate1(X1),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 6.97/7.26 cnf(i_0_5924, plain, (hAPP(c_List_Otl(X1),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 6.97/7.26 cnf(i_0_7340, plain, (c_Lazy__Sequence_Oflat(X1,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(X1)))=c_Lazy__Sequence_Olazy__sequence_OEmpty(X1))). 6.97/7.26 cnf(i_0_4892, plain, (c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X1)))). 6.97/7.26 cnf(i_0_4605, plain, (c_Relation_Otrans(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X1)))). 6.97/7.26 cnf(i_0_3953, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olist_ONil(X1))))). 6.97/7.26 cnf(i_0_7315, plain, (c_Relation_Orefl__on(X1,X2,c_Relation_OId__on(X1,X2)))). 6.97/7.26 cnf(i_0_3156, 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))). 6.97/7.26 cnf(i_0_4717, plain, (c_List_Oreplicate(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)=c_List_Olist_ONil(X1))). 6.97/7.26 cnf(i_0_4745, plain, (c_Relation_Osingle__valued(X1,X1,c_Relation_OId__on(X1,X2)))). 6.97/7.26 cnf(i_0_2151, plain, (c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X2))). 6.97/7.26 cnf(i_0_2420, plain, (c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2))). 6.97/7.26 cnf(i_0_6817, plain, (c_List_Olist_Olist__size(X1,X2,c_List_Olist_ONil(X1))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_6366, plain, (c_List_Oremove1(X1,X2,c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 6.97/7.26 cnf(i_0_1319, plain, (c_List_Osublist(X1,c_List_Olist_ONil(X1),X2)=c_List_Olist_ONil(X1))). 6.97/7.26 cnf(i_0_388, plain, (c_List_OtakeWhile(X1,X2,c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 6.97/7.26 cnf(i_0_675, 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))). 6.97/7.26 cnf(i_0_2256, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)=X1)). 6.97/7.26 cnf(i_0_1368, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=X1)). 6.97/7.26 cnf(i_0_5443, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=X1)). 6.97/7.26 cnf(i_0_764, plain, (c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X1,X2,X3,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=X2)). 6.97/7.26 cnf(i_0_7574, plain, (c_Nat_Onat_Onat__case(X1,X2,X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X2)). 6.97/7.26 cnf(i_0_1956, plain, (c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X1,X2,X3,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=X2)). 6.97/7.26 cnf(i_0_5155, plain, (c_List_Otranspose(X1,c_List_Olist_ONil(tc_List_Olist(X1)))=c_List_Olist_ONil(tc_List_Olist(X1)))). 6.97/7.26 cnf(i_0_6184, plain, (c_List_Oremdups(X1,c_List_Oremdups(X1,X2))=c_List_Oremdups(X1,X2))). 6.97/7.26 cnf(i_0_1880, plain, (c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Ortrancl(X1,X2))=c_Transitive__Closure_Ortrancl(X1,X2))). 6.97/7.26 cnf(i_0_4054, plain, (hAPP(c_New__DSequence_Oneg__single(X1,X2),X3)=c_Lazy__Sequence_Ohb__single(X1,X2))). 6.97/7.26 cnf(i_0_5748, 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))). 6.97/7.26 cnf(i_0_2046, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Olist_ONil(X1))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_2662, plain, (hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2),c_Lazy__Sequence_Olazy__sequence_OEmpty(X1))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_1224, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 6.97/7.26 cnf(i_0_2611, plain, (hAPP(c_List_Ofilter(X1,X2),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 6.97/7.26 cnf(i_0_3405, plain, (hBOOL(hAPP(hAPP(c_fequal,X1),X1)))). 6.97/7.26 cnf(i_0_2048, plain, (c_List_Olist__all2(X1,X1,c_fequal,X2,X2))). 6.97/7.26 cnf(i_0_6714, 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))). 6.97/7.26 cnf(i_0_2251, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1)))). 6.97/7.26 cnf(i_0_1518, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OMin)))). 6.97/7.26 cnf(i_0_348, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 6.97/7.26 cnf(i_0_7486, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 6.97/7.26 cnf(i_0_4302, plain, (hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X1,X2))))). 6.97/7.26 cnf(i_0_3303, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oremdups(X1,X2))))). 6.97/7.26 cnf(i_0_466, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),c_List_Olist_ONil(X1))))). 6.97/7.26 cnf(i_0_6865, plain, (c_Fun_Obij__betw(X1,X1,c_Fun_Oid(X1),X2,X2))). 6.97/7.26 cnf(i_0_1261, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1)))). 6.97/7.26 cnf(i_0_2721, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X1)))). 6.97/7.26 cnf(i_0_5064, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X1)))). 6.97/7.26 cnf(i_0_2497, plain, (c_Relation_Ototal__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2))). 6.97/7.26 cnf(i_0_1757, plain, (hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)))). 6.97/7.26 cnf(i_0_1622, plain, (c_List_Omaps(X1,X2,X3,c_List_Olist_ONil(X1))=c_List_Olist_ONil(X2))). 6.97/7.26 cnf(i_0_7012, plain, (c_Lazy__Sequence_Omap(X1,X2,X3,c_Lazy__Sequence_Olazy__sequence_OEmpty(X1))=c_Lazy__Sequence_Olazy__sequence_OEmpty(X2))). 6.97/7.26 cnf(i_0_5312, plain, (c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)))). 6.97/7.26 cnf(i_0_719, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))). 6.97/7.26 cnf(i_0_1419, 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)))). 6.97/7.26 cnf(i_0_2955, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))=X1)). 6.97/7.26 cnf(i_0_6916, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1)). 6.97/7.26 cnf(i_0_7199, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1)). 6.97/7.26 cnf(i_0_5282, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1)). 6.97/7.26 cnf(i_0_3756, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1)). 6.97/7.26 cnf(i_0_4968, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))=X1)). 6.97/7.26 cnf(i_0_4058, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)=X1)). 6.97/7.26 cnf(i_0_2272, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=X1)). 6.97/7.26 cnf(i_0_3239, 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))). 6.97/7.26 cnf(i_0_7274, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)=X1)). 6.97/7.26 cnf(i_0_7485, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=X1)). 6.97/7.26 cnf(i_0_1136, plain, (hAPP(c_List_Oset(X1),c_List_Olist_ONil(X1))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 6.97/7.26 cnf(i_0_4131, plain, (hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2))=X2)). 6.97/7.26 cnf(i_0_5742, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1))=X2)). 6.97/7.27 cnf(i_0_702, plain, (hAPP(hAPP(c_List_Odrop(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)=X2)). 6.97/7.27 cnf(i_0_2678, plain, (hAPP(c_New__DSequence_Opos__single(X1,X2),X3)=hAPP(c_Lazy__Sequence_Osingle(X1),X2))). 6.97/7.27 cnf(i_0_3033, plain, (hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)=X2)). 6.97/7.27 cnf(i_0_1216, plain, (hAPP(c_Relation_ORange(X1,X1),c_Relation_OId__on(X1,X2))=X2)). 6.97/7.27 cnf(i_0_6487, plain, (hAPP(c_Relation_ODomain(X1,X1),c_Relation_OId__on(X1,X2))=X2)). 6.97/7.27 cnf(i_0_1569, plain, (hAPP(hAPP(c_COMBK(X1,X2),X3),X4)=X3)). 6.97/7.27 cnf(i_0_5450, plain, (hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X2)). 6.97/7.27 cnf(i_0_4881, plain, (hAPP(c_Set_Oimage(X1,X1,c_COMBI(X1)),X2)=X2)). 6.97/7.27 cnf(i_0_3542, plain, (hAPP(c_Set_Oimage(X1,X1,c_Fun_Oid(X1)),X2)=X2)). 6.97/7.27 cnf(i_0_1430, plain, (c_Predicate_Oconversep(X1,X2,c_Predicate_Oconversep(X2,X1,X3))=X3)). 6.97/7.27 cnf(i_0_4091, plain, (c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X1,X2,X3,X4,c_Lazy__Sequence_Olazy__sequence_OEmpty(X2))=X3)). 6.97/7.27 cnf(i_0_2229, plain, (hAPP(c_List_Omap(X1,X1),c_COMBI(X1))=c_Fun_Oid(tc_List_Olist(X1)))). 6.97/7.27 cnf(i_0_3199, plain, (hAPP(c_List_Omap(X1,X1),c_Fun_Oid(X1))=c_Fun_Oid(tc_List_Olist(X1)))). 6.97/7.27 cnf(i_0_1554, 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))). 6.97/7.27 cnf(i_0_106, 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))). 6.97/7.27 cnf(i_0_2396, 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))). 6.97/7.27 cnf(i_0_6021, 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))). 6.97/7.27 cnf(i_0_3109, 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))). 6.97/7.27 cnf(i_0_4035, 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))). 6.97/7.27 cnf(i_0_2557, 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))). 6.97/7.27 cnf(i_0_7288, 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))). 6.97/7.27 cnf(i_0_3302, 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))). 6.97/7.27 cnf(i_0_1258, 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))). 6.97/7.27 cnf(i_0_6779, plain, (hAPP(hAPP(c_List_Otake(X1),X2),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 6.97/7.27 cnf(i_0_1135, plain, (hAPP(hAPP(c_List_Odrop(X1),X2),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 6.97/7.27 cnf(i_0_162, plain, (hAPP(hAPP(c_List_Otake(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)=c_List_Olist_ONil(X1))). 6.97/7.27 cnf(i_0_4164, 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))). 6.97/7.27 cnf(i_0_1540, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 6.97/7.27 cnf(i_0_1429, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X2))))). 6.97/7.27 cnf(i_0_3790, 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))). 6.97/7.27 cnf(i_0_1964, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))). 6.97/7.27 cnf(i_0_142, plain, (c_Wellfounded_Owf(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))). 6.97/7.27 cnf(i_0_584, plain, (c_Relation_Oantisym(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))). 6.97/7.27 cnf(i_0_6248, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_OMin)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 6.97/7.27 cnf(i_0_956, plain, (c_List_Osublist(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))=c_List_Olist_ONil(X1))). 6.97/7.27 cnf(i_0_4728, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))))). 6.97/7.27 cnf(i_0_4519, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2))))). 6.97/7.27 cnf(i_0_4402, 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)))). 6.97/7.27 cnf(i_0_3738, plain, (c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Orev(X1),X2))). 6.97/7.27 cnf(i_0_5232, plain, (c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))). 6.97/7.27 cnf(i_0_518, 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))). 6.97/7.27 cnf(i_0_3791, 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))). 6.97/7.27 cnf(i_0_986, plain, (c_List_Olist__all2(X1,X2,X3,c_List_Olist_ONil(X1),c_List_Olist_ONil(X2)))). 6.97/7.27 cnf(i_0_6071, 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))). 6.97/7.27 cnf(i_0_5031, plain, (hAPP(c_Product__Type_Osnd(X1,X2),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4))=X4)). 6.97/7.27 cnf(i_0_3439, 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))). 6.97/7.27 cnf(i_0_5222, 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))). 6.97/7.27 cnf(i_0_7090, plain, (hAPP(c_Product__Type_Ofst(X1,X2),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4))=X3)). 6.97/7.27 cnf(i_0_6839, 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))). 6.97/7.27 cnf(i_0_2178, plain, (hAPP(c_Int_Onat,X1)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))). 6.97/7.27 cnf(i_0_2616, 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))). 6.97/7.27 cnf(i_0_3412, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))=X1)). 6.97/7.27 cnf(i_0_7407, plain, (c_Fun_Ofun__upd(X1,X2,X3,X4,hAPP(X3,X4))=X3)). 6.97/7.27 cnf(i_0_4671, 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)))). 6.97/7.27 cnf(i_0_7356, plain, (hAPP(c_List_Oset(X1),c_List_Oremdups(X1,X2))=hAPP(c_List_Oset(X1),X2))). 6.97/7.27 cnf(i_0_6558, plain, (c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_OPow(X1),X2))=X2)). 6.97/7.27 cnf(i_0_490, hypothesis, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),v_Ga)))). 6.97/7.27 cnf(i_0_7110, hypothesis, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_G)))). 6.97/7.27 cnf(i_0_398, plain, (hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X1,X2))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2))). 6.97/7.27 cnf(i_0_7316, 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))). 6.97/7.27 cnf(i_0_6376, 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))). 6.97/7.27 cnf(i_0_5119, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oreplicate(X1,X2,X3))=X2)). 6.97/7.27 cnf(i_0_1282, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X2)=X2)). 6.97/7.27 cnf(i_0_4804, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X2)=X2)). 6.97/7.27 cnf(i_0_2346, plain, (c_Enum_Oproduct(X1,X2,c_List_Olist_ONil(X1),X3)=c_List_Olist_ONil(tc_prod(X1,X2)))). 6.97/7.27 cnf(i_0_330, 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)). 6.97/7.27 cnf(i_0_7553, plain, (hAPP(c_List_Ofoldl(X1,X2,X3,X4),c_List_Olist_ONil(X2))=X4)). 6.97/7.27 cnf(i_0_1614, plain, (hAPP(c_List_Olist_Olist__case(X1,X2,X3,X4),c_List_Olist_ONil(X2))=X3)). 6.97/7.27 cnf(i_0_4123, plain, (hAPP(c_Fun_Ocomp(X1,X2,X1,X3),c_Fun_Oid(X1))=X3)). 6.97/7.27 cnf(i_0_2806, plain, (hAPP(c_Fun_Ocomp(X1,X1,X2,c_Fun_Oid(X1)),X3)=X3)). 6.97/7.27 cnf(i_0_1748, plain, (hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X4)=X5)). 6.97/7.27 cnf(i_0_6055, 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))). 6.97/7.27 cnf(i_0_4910, 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))). 6.97/7.27 cnf(i_0_7099, plain, (hAPP(c_Relation_Oconverse(X1,X1),c_Relation_OId__on(X1,X2))=c_Relation_OId__on(X1,X2))). 6.97/7.27 cnf(i_0_3409, plain, (c_List_Olistrel(X1,c_Transitive__Closure_Ortrancl(X1,X2))=c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X2)))). 6.97/7.27 cnf(i_0_6711, plain, (c_Nitpick_OAbs__Frac(X1,c_Nitpick_Onorm__frac(X2,X3))=hAPP(hAPP(c_Nitpick_Ofrac(X1),X2),X3))). 6.97/7.27 cnf(i_0_873, plain, (c_Nat_Onat_Onat__case(X1,X2,X3,hAPP(c_Nat_OSuc,X4))=hAPP(X3,X4))). 6.97/7.27 cnf(i_0_5623, 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))). 6.97/7.27 cnf(i_0_2747, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X2))). 6.97/7.27 cnf(i_0_5946, plain, (hAPP(hAPP(c_Nat_Ocompow(X1,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)=c_Fun_Oid(X1))). 6.97/7.27 cnf(i_0_1831, 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)))). 6.97/7.27 cnf(i_0_1423, 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))))). 6.97/7.27 cnf(i_0_5296, 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))))). 6.97/7.27 cnf(i_0_5529, plain, (hAPP(hAPP(c_List_Olist__update(X1,c_List_Olist_ONil(X1)),X2),X3)=c_List_Olist_ONil(X1))). 6.97/7.27 cnf(i_0_1797, plain, (c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)))). 6.97/7.27 cnf(i_0_7170, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))))). 6.97/7.27 cnf(i_0_3714, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X1),c_Wellfounded_Oless__than),X2)))). 6.97/7.27 cnf(i_0_4909, plain, (c_HOL_OThe(X1,c_Finite__Set_Ofold1Set(X1,X2,X3))=hAPP(c_Finite__Set_Ofold1(X1,X2),X3))). 6.97/7.27 cnf(i_0_4877, 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))))). 6.97/7.27 cnf(i_0_188, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))))). 6.97/7.27 cnf(i_0_5326, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X2))))). 6.97/7.27 cnf(i_0_3674, 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))))). 6.97/7.27 cnf(i_0_4775, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X2)))). 6.97/7.27 cnf(i_0_6179, 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))))). 6.97/7.27 cnf(i_0_6115, 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))))). 6.97/7.27 cnf(i_0_1647, 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))). 6.97/7.27 cnf(i_0_5454, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1)). 6.97/7.27 cnf(i_0_2264, plain, (hAPP(c_List_Oset(X1),hAPP(c_List_Orev(X1),X2))=hAPP(c_List_Oset(X1),X2))). 6.97/7.27 cnf(i_0_7093, plain, (hAPP(c_List_Oset(X1),hAPP(c_List_Orotate1(X1),X2))=hAPP(c_List_Oset(X1),X2))). 6.97/7.27 cnf(i_0_7532, plain, (hAPP(c_Relation_ORange(X1,X1),c_Transitive__Closure_Ortrancl(X1,X2))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))). 6.97/7.27 cnf(i_0_1753, plain, (hAPP(c_Relation_ODomain(X1,X1),c_Transitive__Closure_Ortrancl(X1,X2))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))). 6.97/7.27 cnf(i_0_6424, 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)). 6.97/7.27 cnf(i_0_3781, 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))). 6.97/7.27 cnf(i_0_1813, 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))). 6.97/7.27 cnf(i_0_4491, plain, (hAPP(c_Relation_Oconverse(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3))=X3)). 6.97/7.27 cnf(i_0_5359, plain, (c_List_Oinsert(X1,X2,c_List_Olist_ONil(X1))=hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))). 6.97/7.27 cnf(i_0_5584, plain, (hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=X3)). 6.97/7.27 cnf(i_0_4127, plain, (hAPP(c_List_Ohd(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=X2)). 6.97/7.27 cnf(i_0_5400, plain, (hAPP(c_List_Orev(X1),c_List_Oreplicate(X1,X2,X3))=c_List_Oreplicate(X1,X2,X3))). 6.97/7.27 cnf(i_0_2111, plain, (hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X2)). 6.97/7.27 cnf(i_0_5254, plain, (c_Fun_Ooverride__on(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=X3)). 6.97/7.27 cnf(i_0_3923, 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)). 6.97/7.27 cnf(i_0_1316, 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)))). 6.97/7.27 cnf(i_0_283, 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)))). 6.97/7.27 cnf(i_0_2576, plain, (c_List_Oinsert(X1,X2,c_List_Oremdups(X1,X3))=c_List_Oremdups(X1,c_List_Oinsert(X1,X2,X3)))). 6.97/7.27 cnf(i_0_3883, 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))). 6.97/7.27 cnf(i_0_2636, 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))). 6.97/7.27 cnf(i_0_7183, 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))). 6.97/7.27 cnf(i_0_4179, 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))))). 6.97/7.27 cnf(i_0_3252, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))). 6.97/7.27 cnf(i_0_5685, plain, (hAPP(c_Code__Numeral_Onat__of,esk433_1(X1))=X1)). 6.97/7.27 cnf(i_0_1755, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)))). 6.97/7.27 cnf(i_0_4524, 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))). 6.97/7.27 cnf(i_0_6411, plain, (c_Hilbert__Choice_Oinv__into(X1,X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Fun_Oid(X1))=c_Fun_Oid(X1))). 6.97/7.27 cnf(i_0_1712, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))))). 6.97/7.27 cnf(i_0_6896, plain, (hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2)))). 6.97/7.27 cnf(i_0_155, plain, (c_Relation_Osym(X1,c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))). 6.97/7.27 cnf(i_0_395, plain, (c_Relation_Oantisym(X1,c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))). 6.97/7.27 cnf(i_0_4024, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),X1)))). 6.97/7.27 cnf(i_0_560, 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))). 6.97/7.27 cnf(i_0_3194, plain, (c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X4))). 6.97/7.27 cnf(i_0_1499, 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)). 6.97/7.27 cnf(i_0_2234, plain, (c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))=X2)). 6.97/7.27 cnf(i_0_1328, 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))). 6.97/7.27 cnf(i_0_3823, 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))). 6.97/7.27 cnf(i_0_4364, plain, (hAPP(c_COMBK(tc_HOL_Obool,X1),c_fTrue)=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))). 6.97/7.27 cnf(i_0_5047, plain, (hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 6.97/7.27 cnf(i_0_819, 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))))). 6.97/7.27 cnf(i_0_1494, plain, (hAPP(c_Relation_OField(X1),hAPP(c_Relation_Oconverse(X1,X1),X2))=hAPP(c_Relation_OField(X1),X2))). 6.97/7.27 cnf(i_0_6134, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),X3),c_List_Olist_ONil(X2))=c_List_Olist_ONil(tc_prod(X1,X2)))). 6.97/7.27 cnf(i_0_5098, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),c_List_Olist_ONil(X1)),X3)=c_List_Olist_ONil(tc_prod(X1,X2)))). 6.97/7.27 cnf(i_0_6679, 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)))). 6.97/7.27 cnf(i_0_2524, plain, (hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)=X2)). 6.97/7.27 cnf(i_0_1204, 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)). 6.97/7.27 cnf(i_0_5473, plain, (c_Product__Type_Ocurry(X1,X2,X3,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4))=X4)). 6.97/7.27 cnf(i_0_1007, 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)))). 6.97/7.27 cnf(i_0_2186, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),c_Product__Type_Ocurry(X1,X2,X3,X4))=X4)). 6.97/7.27 cnf(i_0_3566, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin))). 6.97/7.27 cnf(i_0_6819, plain, (c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X2)=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin),X2))). 6.97/7.27 cnf(i_0_519, 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))). 6.97/7.27 cnf(i_0_6159, 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))). 6.97/7.27 cnf(i_0_1889, 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))). 6.97/7.27 cnf(i_0_6917, plain, (c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=X3)). 6.97/7.27 cnf(i_0_5802, 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)))). 6.97/7.27 cnf(i_0_2581, 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))))). 6.97/7.27 cnf(i_0_2212, plain, (c_Lazy__Sequence_Oflat(X1,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(X1),X2,X3))=c_Lazy__Sequence_Oappend(X1,X2,c_Lazy__Sequence_Oflat(X1,X3)))). 6.97/7.27 cnf(i_0_5638, 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))). 6.97/7.27 cnf(i_0_168, 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))). 6.97/7.27 cnf(i_0_2003, plain, (c_List_Obutlast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))=c_List_Olist_ONil(X1))). 6.97/7.27 cnf(i_0_1692, 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))))). 6.97/7.27 cnf(i_0_1651, 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))). 6.97/7.27 cnf(i_0_3188, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olists(X1,X2))))). 6.97/7.27 cnf(i_0_3417, plain, (c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X1,X2)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin)),X2))). 6.97/7.27 cnf(i_0_6792, 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)))))). 6.97/7.27 cnf(i_0_4918, 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)))))). 6.97/7.27 cnf(i_0_1389, 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))). 6.97/7.27 cnf(i_0_5025, 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))). 6.97/7.27 cnf(i_0_302, 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)))). 6.97/7.27 cnf(i_0_1795, 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)))). 6.97/7.27 cnf(i_0_2068, 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))). 6.97/7.27 cnf(i_0_3958, 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)))). 6.97/7.27 cnf(i_0_7298, 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)))). 6.97/7.27 cnf(i_0_3949, 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)))). 6.97/7.27 cnf(i_0_5050, 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)))). 6.97/7.27 cnf(i_0_1550, plain, (c_List_Oremdups(X1,hAPP(c_List_Ofilter(X1,X2),X3))=hAPP(c_List_Ofilter(X1,X2),c_List_Oremdups(X1,X3)))). 6.97/7.27 cnf(i_0_863, 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)))). 6.97/7.27 cnf(i_0_6977, 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)))). 6.97/7.27 cnf(i_0_3885, 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)). 6.97/7.27 cnf(i_0_5652, 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)). 6.97/7.27 cnf(i_0_4244, 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)). 6.97/7.27 cnf(i_0_958, 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)). 6.97/7.27 cnf(i_0_6283, 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)))). 6.97/7.27 cnf(i_0_6850, 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)))). 6.97/7.27 cnf(i_0_5256, plain, (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)=X1)). 6.97/7.27 cnf(i_0_6337, 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)). 6.97/7.27 cnf(i_0_3550, 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))))). 6.97/7.27 cnf(i_0_4846, 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))). 6.97/7.27 cnf(i_0_2350, 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)). 6.97/7.27 cnf(i_0_7544, 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)). 6.97/7.27 cnf(i_0_1394, 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)). 6.97/7.27 cnf(i_0_6681, 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)). 6.97/7.27 cnf(i_0_5543, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=X4)). 6.97/7.27 cnf(i_0_5255, plain, (c_Predicate_Opred__comp(X1,X1,X1,c_fequal,c_Predicate_Opred__comp(X1,X1,X1,X2,c_fequal))=X2)). 6.97/7.27 cnf(i_0_7543, 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)))). 6.97/7.27 cnf(i_0_6588, plain, (c_Product__Type_Omap__pair(X1,X1,X2,X2,c_COMBI(X1),c_COMBI(X2))=c_Fun_Oid(tc_prod(X1,X2)))). 6.97/7.27 cnf(i_0_2372, 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)))). 6.97/7.27 cnf(i_0_2364, 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))). 6.97/7.27 cnf(i_0_411, plain, (c_Lazy__Sequence_Oflat(X1,c_Lazy__Sequence_Omap(X2,tc_Lazy__Sequence_Olazy__sequence(X1),X3,X4))=hAPP(c_Lazy__Sequence_Obind(X2,X1,X4),X3))). 6.97/7.27 cnf(i_0_3942, 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))). 6.97/7.27 cnf(i_0_1380, 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))))). 6.97/7.27 cnf(i_0_136, plain, (hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(X1),X2),X3),X4),X5)=c_New__DSequence_Oneg__single(X1,X2))). 6.97/7.27 cnf(i_0_1509, plain, (hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X1),X2),X3),X4),X5)=c_New__DSequence_Opos__single(X1,X2))). 6.97/7.27 cnf(i_0_4136, 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))). 6.97/7.27 cnf(i_0_2158, plain, (hAPP(c_Relation_ODomain(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3))=hAPP(c_Relation_ORange(X2,X1),X3))). 6.97/7.27 cnf(i_0_6374, plain, (hAPP(c_Relation_ORange(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3))=hAPP(c_Relation_ODomain(X2,X1),X3))). 6.97/7.27 cnf(i_0_6211, 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)). 6.97/7.27 cnf(i_0_6210, 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)). 6.97/7.27 cnf(i_0_2508, 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))). 6.97/7.27 cnf(i_0_2951, 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))))). 6.97/7.27 cnf(i_0_3094, 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))))). 6.97/7.27 cnf(i_0_4187, 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))). 6.97/7.27 cnf(i_0_816, 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))))). 6.97/7.27 cnf(i_0_3190, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))))). 6.97/7.27 cnf(i_0_6245, 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)))))). 6.97/7.27 cnf(i_0_5983, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X2))))). 6.97/7.27 cnf(i_0_6188, 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)))))). 6.97/7.27 cnf(i_0_5712, 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))))))). 6.97/7.27 cnf(i_0_494, 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)))). 6.97/7.27 cnf(i_0_7023, 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)))). 6.97/7.27 cnf(i_0_6024, 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)))). 6.97/7.27 cnf(i_0_2228, plain, (c_Relation_Otrans(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))))). 6.97/7.27 cnf(i_0_219, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk17_1(X1)),c_Int_OInteg)))). 6.97/7.27 cnf(i_0_7143, plain, (hAPP(hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5),X6)=hAPP(X4,hAPP(X5,X6)))). 6.97/7.27 cnf(i_0_2275, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X4)))). 6.97/7.27 cnf(i_0_5609, plain, (c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X1))=hAPP(c_Nat_OSuc,c_Nat_Onat_Onat__size(X1)))). 6.97/7.27 cnf(i_0_1863, 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)). 6.97/7.27 cnf(i_0_6582, 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)))). 6.97/7.27 cnf(i_0_5311, plain, (hAPP(hAPP(c_List_Olist__update(X1,X2),X3),hAPP(hAPP(c_List_Onth(X1),X2),X3))=X2)). 6.97/7.27 cnf(i_0_7444, 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)))). 6.97/7.27 cnf(i_0_3321, 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)))). 6.97/7.27 cnf(i_0_651, 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)))). 6.97/7.27 cnf(i_0_5561, 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)))). 6.97/7.27 cnf(i_0_5124, 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)))). 6.97/7.27 cnf(i_0_1682, 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)). 6.97/7.27 cnf(i_0_674, 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))). 6.97/7.27 cnf(i_0_3229, 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))). 6.97/7.27 cnf(i_0_5974, 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))). 6.97/7.27 cnf(i_0_5914, 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))))). 6.97/7.27 cnf(i_0_1901, 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))). 6.97/7.27 cnf(i_0_4939, 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))). 6.97/7.27 cnf(i_0_7189, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 6.97/7.27 cnf(i_0_6513, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)=c_Groups_Oone__class_Oone(tc_Int_Oint))). 6.97/7.27 cnf(i_0_2376, 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)))). 6.97/7.27 cnf(i_0_761, 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))). 6.97/7.27 cnf(i_0_4445, 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))). 6.97/7.27 cnf(i_0_4163, 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))). 6.97/7.27 cnf(i_0_2786, 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))). 6.97/7.27 cnf(i_0_5577, 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)))). 6.97/7.27 cnf(i_0_101, 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)))). 6.97/7.27 cnf(i_0_2300, 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)))). 6.97/7.27 cnf(i_0_5950, 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))). 6.97/7.27 cnf(i_0_4386, 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))). 6.97/7.27 cnf(i_0_2029, 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))). 6.97/7.27 cnf(i_0_3884, 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))). 6.97/7.27 cnf(i_0_6355, plain, (hAPP(c_Set_Oimage(tc_prod(X1,X2),X2,c_Product__Type_Osnd(X1,X2)),X3)=hAPP(c_Relation_ORange(X1,X2),X3))). 6.97/7.27 cnf(i_0_5175, plain, (hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),X3)=hAPP(c_Relation_ODomain(X1,X2),X3))). 6.97/7.27 cnf(i_0_4975, 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)))). 6.97/7.27 cnf(i_0_7292, 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))). 6.97/7.27 cnf(i_0_1971, 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)))))). 6.97/7.27 cnf(i_0_2240, 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))). 6.97/7.27 cnf(i_0_6559, plain, (hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6)=hAPP(X4,hAPP(X5,X6)))). 6.97/7.27 cnf(i_0_7027, plain, (hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6)=hAPP(hAPP(X4,X6),X5))). 6.97/7.27 cnf(i_0_4596, 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)))). 6.97/7.27 cnf(i_0_2241, 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))). 6.97/7.27 cnf(i_0_1648, 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)))). 6.97/7.27 cnf(i_0_4378, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Int_OMin))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2))). 6.97/7.27 cnf(i_0_6888, 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)))). 6.97/7.27 cnf(i_0_6265, 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))). 6.97/7.27 cnf(i_0_2692, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Int_OMin)=c_Groups_Oone__class_Oone(tc_Int_Oint))). 6.97/7.27 cnf(i_0_3972, 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)))))). 6.97/7.27 cnf(i_0_6666, 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)))). 6.97/7.27 cnf(i_0_2027, 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)))). 6.97/7.27 cnf(i_0_1937, 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)))). 6.97/7.27 cnf(i_0_81, 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)). 6.97/7.27 cnf(i_0_7127, 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)))). 6.97/7.27 cnf(i_0_685, 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)))). 6.97/7.27 cnf(i_0_3597, 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)))). 6.97/7.27 cnf(i_0_6014, 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)). 6.97/7.27 cnf(i_0_3975, 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)). 6.97/7.27 cnf(i_0_5997, 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)). 6.97/7.27 cnf(i_0_5129, 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)). 6.97/7.27 cnf(i_0_6526, plain, (hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X3,tc_prod(X2,X3)),X4),c_Product__Type_OPair(X2,X3))=X4)). 6.97/7.27 cnf(i_0_5059, plain, (c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X1)=hAPP(c_fequal,X1))). 6.97/7.27 cnf(i_0_5901, 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)))). 6.97/7.27 cnf(i_0_5877, plain, (c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X1)=hAPP(c_fequal,X1))). 6.97/7.27 cnf(i_0_6854, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),c_List_Oreplicate(X1,X4,X5))=c_List_Oreplicate(X2,X4,hAPP(X3,X5)))). 6.97/7.27 cnf(i_0_963, 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))). 6.97/7.27 cnf(i_0_3834, 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))). 6.97/7.27 cnf(i_0_5985, 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))). 6.97/7.27 cnf(i_0_6004, 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)))). 6.97/7.27 cnf(i_0_6458, 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)))). 6.97/7.27 cnf(i_0_3584, 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)))))). 6.97/7.27 cnf(i_0_5218, 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))). 6.97/7.27 cnf(i_0_1130, 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))). 6.97/7.27 cnf(i_0_3775, 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)))). 6.97/7.27 cnf(i_0_602, 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))))). 6.97/7.27 cnf(i_0_53, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin))))). 6.97/7.27 cnf(i_0_6269, 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))))). 6.97/7.27 cnf(i_0_2660, 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)))))). 6.97/7.27 cnf(i_0_7272, 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))))). 6.97/7.27 cnf(i_0_1620, 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))))). 6.97/7.27 cnf(i_0_3833, plain, (c_Fun_Ofun__upd(X1,X2,c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X4,X6)=c_Fun_Ofun__upd(X1,X2,X3,X4,X6))). 6.97/7.27 cnf(i_0_54, 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)))). 6.97/7.27 cnf(i_0_1312, 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)))). 6.97/7.27 cnf(i_0_5794, 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)))). 6.97/7.27 cnf(i_0_2943, 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))). 6.97/7.27 cnf(i_0_2313, 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)))). 6.97/7.27 cnf(i_0_1798, 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)))). 6.97/7.27 cnf(i_0_740, 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))). 6.97/7.27 cnf(i_0_1012, 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))). 6.97/7.27 cnf(i_0_228, plain, (hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)=X2)). 6.97/7.27 cnf(i_0_4047, plain, (hAPP(hAPP(c_Product__Type_Ocurry(X1,X2,X3,X4),X5),X6)=hAPP(X4,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)))). 6.97/7.27 cnf(i_0_1568, 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)))). 6.97/7.27 cnf(i_0_5275, 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)))). 6.97/7.27 cnf(i_0_5885, 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)))). 6.97/7.27 cnf(i_0_530, 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))). 6.97/7.27 cnf(i_0_7512, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))). 6.97/7.27 cnf(i_0_6273, 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)))). 6.97/7.27 cnf(i_0_4036, 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)))). 6.97/7.27 cnf(i_0_3982, 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))). 6.97/7.27 cnf(i_0_5364, 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))). 6.97/7.27 cnf(i_0_790, 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))). 6.97/7.27 cnf(i_0_6886, 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))))). 6.97/7.27 cnf(i_0_7266, 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))). 6.97/7.27 cnf(i_0_5001, 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))). 6.97/7.27 cnf(i_0_1386, 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))). 6.97/7.27 cnf(i_0_2246, 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))). 6.97/7.27 cnf(i_0_5007, 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)))). 6.97/7.27 cnf(i_0_3921, plain, (hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X1,X3),hAPP(c_Product__Type_OPair(X2,X1),X4)),X5)=hAPP(X5,X4))). 6.97/7.27 cnf(i_0_5690, 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)))). 6.97/7.27 cnf(i_0_4520, 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)))). 6.97/7.27 cnf(i_0_3974, 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)))). 6.97/7.27 cnf(i_0_80, 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))))))). 6.97/7.27 cnf(i_0_2779, 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)))). 6.97/7.27 cnf(i_0_7573, 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)))). 6.97/7.27 cnf(i_0_2122, 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))))). 6.97/7.27 cnf(i_0_7441, 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)))). 6.97/7.27 cnf(i_0_103, 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))). 6.97/7.27 cnf(i_0_6204, 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))). 6.97/7.27 cnf(i_0_5226, 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))). 6.97/7.27 cnf(i_0_3325, 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))). 6.97/7.27 cnf(i_0_4643, 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)))). 6.97/7.27 cnf(i_0_5633, 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)))). 6.97/7.27 cnf(i_0_208, 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)))). 6.97/7.27 cnf(i_0_1210, 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)))). 6.97/7.27 cnf(i_0_4262, 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)))). 6.97/7.27 cnf(i_0_5899, 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)))). 6.97/7.27 cnf(i_0_2233, 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))). 6.97/7.27 cnf(i_0_2450, 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)). 6.97/7.27 cnf(i_0_3536, 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)))). 6.97/7.27 cnf(i_0_1855, 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)). 6.97/7.27 cnf(i_0_1571, 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))). 6.97/7.27 cnf(i_0_5480, 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)). 6.97/7.27 cnf(i_0_7065, 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))). 6.97/7.27 cnf(i_0_4273, 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)). 6.97/7.27 cnf(i_0_94, 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))). 6.97/7.27 cnf(i_0_2071, 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))). 6.97/7.27 cnf(i_0_4312, 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))). 6.97/7.27 cnf(i_0_6226, 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))). 6.97/7.27 cnf(i_0_1854, 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)). 6.97/7.27 cnf(i_0_4317, 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)))). 6.97/7.27 cnf(i_0_2620, 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))). 6.97/7.27 cnf(i_0_979, 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))). 6.97/7.27 cnf(i_0_3818, 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))))). 6.97/7.27 cnf(i_0_86, 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))))). 6.97/7.27 cnf(i_0_5433, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)),c_Int_OMin)))). 6.97/7.27 cnf(i_0_2467, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Int_OMin))),c_Int_OMin))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)))). 6.97/7.27 cnf(i_0_191, 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))))). 6.97/7.27 cnf(i_0_765, 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))))). 6.97/7.27 cnf(i_0_6166, 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))))). 6.97/7.27 cnf(i_0_3019, 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)))). 6.97/7.27 cnf(i_0_2802, plain, (c_Relation_Osym(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(c_Relation_Oconverse(X1,X1),X2))))). 6.97/7.27 cnf(i_0_5770, plain, (c_Relation_Osym(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(c_Relation_Oconverse(X1,X1),X2))))). 6.97/7.27 cnf(i_0_1093, 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)))). 6.97/7.27 cnf(i_0_6887, 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)))). 6.97/7.27 cnf(i_0_3308, 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)))). 6.97/7.27 cnf(i_0_3315, 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))))). 6.97/7.27 cnf(i_0_5057, 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))))). 6.97/7.27 cnf(i_0_3305, 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)))). 6.97/7.27 cnf(i_0_3716, 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)))). 6.97/7.27 cnf(i_0_4426, 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)))). 6.97/7.27 cnf(i_0_3265, 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))). 6.97/7.27 cnf(i_0_7003, 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))). 6.97/7.27 cnf(i_0_2422, 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)))). 6.97/7.27 cnf(i_0_2464, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)),hAPP(hAPP(c_List_Odrop(X1),X2),X3))=X3)). 6.97/7.27 cnf(i_0_361, 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))). 6.97/7.27 cnf(i_0_4755, 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))). 6.97/7.27 cnf(i_0_4808, 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))). 6.97/7.27 cnf(i_0_3212, 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)))). 6.97/7.27 cnf(i_0_1317, 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))). 6.97/7.27 cnf(i_0_5458, 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))). 6.97/7.27 cnf(i_0_5354, 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))). 6.97/7.27 cnf(i_0_258, 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)))). 6.97/7.27 cnf(i_0_6844, 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)))). 6.97/7.27 cnf(i_0_469, 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))). 6.97/7.27 cnf(i_0_3719, 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)))). 6.97/7.27 cnf(i_0_5096, 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))). 6.97/7.27 cnf(i_0_1376, 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))))). 6.97/7.27 cnf(i_0_3301, plain, (c_HOL_OThe(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2)). 6.97/7.27 cnf(i_0_1890, 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)). 6.97/7.27 cnf(i_0_1637, 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)))). 6.97/7.27 cnf(i_0_3894, 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))). 6.97/7.27 cnf(i_0_3897, 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)))))). 6.97/7.27 cnf(i_0_1450, 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))). 6.97/7.27 cnf(i_0_703, 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))). 6.97/7.27 cnf(i_0_1520, 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)))). 6.97/7.27 cnf(i_0_413, 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))). 6.97/7.27 cnf(i_0_5041, plain, (c_List_Olists(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=hAPP(c_fequal,c_List_Olist_ONil(X1)))). 6.97/7.27 cnf(i_0_3312, 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))))). 6.97/7.27 cnf(i_0_1975, plain, (c_List_Olistset(X1,c_List_Olist_ONil(tc_fun(X1,tc_HOL_Obool)))=hAPP(c_fequal,c_List_Olist_ONil(X1)))). 6.97/7.27 cnf(i_0_5980, 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)))))). 6.97/7.27 cnf(i_0_5325, 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)))). 6.97/7.27 cnf(i_0_1344, 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))). 6.97/7.27 cnf(i_0_5910, 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))). 6.97/7.27 cnf(i_0_6005, 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))))). 6.97/7.27 cnf(i_0_5431, 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))). 6.97/7.27 cnf(i_0_1947, 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)))))). 6.97/7.27 cnf(i_0_622, 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))))))). 6.97/7.27 cnf(i_0_6414, 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))))). 6.97/7.27 cnf(i_0_2323, 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))). 6.97/7.27 cnf(i_0_1758, 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)))). 6.97/7.27 cnf(i_0_2039, 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)))). 6.97/7.27 cnf(i_0_926, 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))). 6.97/7.27 cnf(i_0_491, 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)))). 6.97/7.27 cnf(i_0_7229, 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))). 6.97/7.27 cnf(i_0_805, 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))). 6.97/7.27 cnf(i_0_4471, 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)))). 6.97/7.27 cnf(i_0_6722, 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)))))). 6.97/7.27 cnf(i_0_1234, 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)))). 6.97/7.27 cnf(i_0_2913, 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)))). 6.97/7.27 cnf(i_0_4812, 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)))). 6.97/7.27 cnf(i_0_2217, 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)))). 6.97/7.27 cnf(i_0_6034, 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)))). 6.97/7.27 cnf(i_0_7239, 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)))). 6.97/7.27 cnf(i_0_2967, 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))). 6.97/7.27 cnf(i_0_5513, 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))). 6.97/7.27 cnf(i_0_4759, 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))). 6.97/7.27 cnf(i_0_7391, 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))). 6.97/7.27 cnf(i_0_3106, 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))). 6.97/7.27 cnf(i_0_908, 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))). 6.97/7.27 cnf(i_0_4497, 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))). 6.97/7.27 cnf(i_0_3254, 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))). 6.97/7.27 cnf(i_0_6674, 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))))))). 6.97/7.27 cnf(i_0_4080, 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)))). 6.97/7.27 cnf(i_0_5432, 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)))). 6.97/7.27 cnf(i_0_6217, 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)))). 6.97/7.27 cnf(i_0_5846, 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)))). 6.97/7.27 cnf(i_0_7029, 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)))). 6.97/7.27 cnf(i_0_824, 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)))). 6.97/7.27 cnf(i_0_7017, 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)))). 6.97/7.27 cnf(i_0_5125, 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)))). 6.97/7.27 cnf(i_0_2859, 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)))). 6.97/7.27 cnf(i_0_6489, 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))). 6.97/7.27 cnf(i_0_4387, 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))). 6.97/7.27 cnf(i_0_5631, 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)))). 6.97/7.27 cnf(i_0_6823, 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))))). 6.97/7.27 cnf(i_0_2633, 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)))))). 6.97/7.27 cnf(i_0_529, 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))))). 6.97/7.27 cnf(i_0_2453, 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))))). 6.97/7.27 cnf(i_0_4083, 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))). 6.97/7.27 cnf(i_0_6129, 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))). 6.97/7.27 cnf(i_0_1363, 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))))). 6.97/7.27 cnf(i_0_5586, 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))). 6.97/7.27 cnf(i_0_6201, 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))). 6.97/7.27 cnf(i_0_4330, 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))). 6.97/7.27 cnf(i_0_1761, 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))). 6.97/7.27 cnf(i_0_4954, 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))). 6.97/7.27 cnf(i_0_5314, 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))). 6.97/7.27 cnf(i_0_558, 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))). 6.97/7.27 cnf(i_0_3857, 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))). 6.97/7.27 cnf(i_0_2449, 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))). 6.97/7.27 cnf(i_0_2224, 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))). 6.97/7.27 cnf(i_0_5766, 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))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))). 6.97/7.27 cnf(i_0_2082, 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))). 6.97/7.27 cnf(i_0_3316, 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))))). 6.97/7.27 cnf(i_0_5515, plain, (c_Fun_Oinj__on(X1,tc_prod(X2,X1),esk420_4(X3,X4,X2,X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X4),X3)))). 6.97/7.27 cnf(i_0_1874, 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)). 6.97/7.27 cnf(i_0_6449, 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))))))). 6.97/7.27 cnf(i_0_1821, 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)). 6.97/7.27 cnf(i_0_7011, 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)). 6.97/7.27 cnf(i_0_3712, 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)))). 6.97/7.27 cnf(i_0_3861, 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)). 6.97/7.27 cnf(i_0_3208, 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))). 6.97/7.27 cnf(i_0_6310, plain, (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),c_Lazy__Sequence_Olazy__sequence_OEmpty(X2)))=X3)). 6.97/7.27 cnf(i_0_1287, 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)))). 6.97/7.27 cnf(i_0_5414, 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)))). 6.97/7.27 cnf(i_0_61, 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))). 6.97/7.27 cnf(i_0_1333, 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))). 6.97/7.27 cnf(i_0_5396, 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)))). 6.97/7.27 cnf(i_0_306, 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)))). 6.97/7.27 cnf(i_0_7373, 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))). 6.97/7.27 cnf(i_0_3014, 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)))). 6.97/7.27 cnf(i_0_5769, 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)))). 6.97/7.27 cnf(i_0_7207, 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)))). 6.97/7.27 cnf(i_0_1113, plain, (hAPP(c_Set_Ovimage(X1,X2,X3),X4)=hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3))). 6.97/7.27 cnf(i_0_4565, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_Fun_Oid(X1))=X2)). 6.97/7.27 cnf(i_0_420, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_COMBI(X1))=X2)). 6.97/7.27 cnf(i_0_1459, 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)))). 6.97/7.27 cnf(i_0_5641, 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)))). 6.97/7.27 cnf(i_0_6403, 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))). 6.97/7.27 cnf(i_0_6063, 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),X1)),c_Int_OMin))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))). 6.97/7.27 cnf(i_0_1804, 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)))). 6.97/7.27 cnf(i_0_2050, 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))). 6.97/7.27 cnf(i_0_5066, 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)))). 6.97/7.27 cnf(i_0_2101, 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)))). 6.97/7.27 cnf(i_0_6810, 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))). 6.97/7.27 cnf(i_0_4126, 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))). 6.97/7.27 cnf(i_0_5856, 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))). 6.97/7.27 cnf(i_0_1756, 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))). 6.97/7.27 cnf(i_0_583, 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))))). 6.97/7.27 cnf(i_0_7228, 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))))). 6.97/7.27 cnf(i_0_4452, 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)))). 6.97/7.27 cnf(i_0_6493, 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)))))). 6.97/7.27 cnf(i_0_2383, 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)))))). 6.97/7.27 cnf(i_0_5343, 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)))). 6.97/7.27 cnf(i_0_5355, 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)))). 6.97/7.27 cnf(i_0_1498, 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)))). 6.97/7.27 cnf(i_0_426, 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)))). 6.97/7.27 cnf(i_0_6043, 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)))). 6.97/7.27 cnf(i_0_933, 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))). 6.97/7.27 cnf(i_0_4501, 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))). 6.97/7.27 cnf(i_0_4672, 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)))). 6.97/7.27 cnf(i_0_1532, 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)). 6.97/7.27 cnf(i_0_7231, 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))). 6.97/7.27 cnf(i_0_6492, 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))). 6.97/7.27 cnf(i_0_5598, 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)))). 6.97/7.27 cnf(i_0_1800, 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)))). 6.97/7.27 cnf(i_0_7083, 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))). 6.97/7.27 cnf(i_0_6125, 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))). 6.97/7.27 cnf(i_0_3295, 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))). 6.97/7.27 cnf(i_0_4858, 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))). 6.97/7.27 cnf(i_0_2543, 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))). 6.97/7.27 cnf(i_0_2502, 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))). 6.97/7.27 cnf(i_0_6771, 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))))). 6.97/7.27 cnf(i_0_5334, 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)). 6.97/7.27 cnf(i_0_507, 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)))). 6.97/7.27 cnf(i_0_1309, 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)))). 6.97/7.27 cnf(i_0_5504, 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)))). 6.97/7.27 cnf(i_0_525, 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))). 6.97/7.27 cnf(i_0_573, 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)))). 6.97/7.27 cnf(i_0_4916, 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)))). 6.97/7.27 cnf(i_0_3096, 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)). 6.97/7.27 cnf(i_0_5389, 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)))). 6.97/7.27 cnf(i_0_1780, 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)))). 6.97/7.27 cnf(i_0_1891, 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)))). 6.97/7.27 cnf(i_0_2259, 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))). 6.97/7.27 cnf(i_0_3214, 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)))). 6.97/7.27 cnf(i_0_4914, 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)))))). 6.97/7.27 cnf(i_0_2542, 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)))). 6.97/7.27 cnf(i_0_6525, 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)). 6.97/7.27 cnf(i_0_235, 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))). 6.97/7.27 cnf(i_0_6549, 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)))). 6.97/7.27 cnf(i_0_1786, 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))). 6.97/7.27 cnf(i_0_3767, 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))))). 6.97/7.27 cnf(i_0_110, 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))))). 6.97/7.27 cnf(i_0_4531, 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)))). 6.97/7.27 cnf(i_0_6697, 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))))). 6.97/7.27 cnf(i_0_2329, 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)))). 6.97/7.27 cnf(i_0_7527, 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)))). 6.97/7.27 cnf(i_0_2442, 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)))). 6.97/7.27 cnf(i_0_5092, 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)))). 6.97/7.27 cnf(i_0_3813, 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)))). 6.97/7.27 cnf(i_0_4707, 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)))). 6.97/7.27 cnf(i_0_177, 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))))). 6.97/7.27 cnf(i_0_1424, 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))). 6.97/7.27 cnf(i_0_5571, 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))). 6.97/7.27 cnf(i_0_4957, 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))). 6.97/7.27 cnf(i_0_4259, 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))). 6.97/7.27 cnf(i_0_2614, 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))). 6.97/7.27 cnf(i_0_351, 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))))). 6.97/7.27 cnf(i_0_1936, 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)))). 6.97/7.27 cnf(i_0_4636, 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)))). 6.97/7.27 cnf(i_0_1452, 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)))). 6.97/7.27 cnf(i_0_2769, 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))). 6.97/7.27 cnf(i_0_33, 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))))))). 6.97/7.27 cnf(i_0_6363, 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))))). 6.97/7.27 cnf(i_0_5613, 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)))). 6.97/7.27 cnf(i_0_1091, 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))). 6.97/7.27 cnf(i_0_2391, 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))). 6.97/7.27 cnf(i_0_6710, 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)))). 6.97/7.27 cnf(i_0_5987, 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)))). 6.97/7.27 cnf(i_0_3889, 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)))). 6.97/7.27 cnf(i_0_4543, 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)))). 6.97/7.27 cnf(i_0_1017, 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)). 6.97/7.27 cnf(i_0_763, 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)))). 6.97/7.27 cnf(i_0_2830, 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))). 6.97/7.27 cnf(i_0_6635, 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)))). 6.97/7.27 cnf(i_0_7263, 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))). 6.97/7.27 cnf(i_0_3158, plain, (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),c_Lazy__Sequence_Olazy__sequence_OInsert(X2,X5,X6)))=hAPP(hAPP(X4,X5),X6))). 6.97/7.27 cnf(i_0_4106, 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))))). 6.97/7.27 cnf(i_0_4188, 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)))). 6.97/7.27 cnf(i_0_7021, 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)). 6.97/7.27 cnf(i_0_514, 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)))). 6.97/7.27 cnf(i_0_6767, 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)))). 6.97/7.27 cnf(i_0_5661, 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)))). 6.97/7.27 cnf(i_0_6506, 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)))). 6.97/7.27 cnf(i_0_4190, 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))). 6.97/7.27 cnf(i_0_4546, 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)))). 6.97/7.27 cnf(i_0_3082, 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)))). 6.97/7.27 cnf(i_0_3202, 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)))). 6.97/7.27 cnf(i_0_2760, 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)))). 6.97/7.27 cnf(i_0_6703, 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)))). 6.97/7.27 cnf(i_0_4354, 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)))). 6.97/7.27 cnf(i_0_1409, 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)))). 6.97/7.27 cnf(i_0_3438, 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)))). 6.97/7.27 cnf(i_0_6701, 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))))). 6.97/7.27 cnf(i_0_2080, 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))). 6.97/7.27 cnf(i_0_4093, 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)))). 6.97/7.27 cnf(i_0_2670, 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)))))). 6.97/7.27 cnf(i_0_5112, 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)))). 6.97/7.27 cnf(i_0_2927, 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)))). 6.97/7.27 cnf(i_0_100, 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)). 6.97/7.27 cnf(i_0_4658, plain, (c_Hilbert__Choice_OEps(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))=hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),X4))). 6.97/7.27 cnf(i_0_6504, 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))). 6.97/7.27 cnf(i_0_4432, 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)))). 6.97/7.27 cnf(i_0_1454, 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)))). 6.97/7.27 cnf(i_0_7108, 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)))). 6.97/7.27 cnf(i_0_6181, 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)))). 6.97/7.27 cnf(i_0_6561, 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))). 6.97/7.27 cnf(i_0_2774, 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)))). 6.97/7.27 cnf(i_0_318, 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)))))). 6.97/7.27 cnf(i_0_409, 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)). 6.97/7.27 cnf(i_0_1439, 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))). 6.97/7.27 cnf(i_0_1857, plain, (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),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))). 6.97/7.27 cnf(i_0_3047, 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)))). 6.97/7.27 cnf(i_0_6569, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(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),X1)),c_Int_OMin))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))). 6.97/7.27 cnf(i_0_7435, 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))). 6.97/7.27 cnf(i_0_1895, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Int_OMin)=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),c_Int_OMin),c_Int_OMin)))). 6.97/7.27 cnf(i_0_2558, 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))). 6.97/7.27 cnf(i_0_6862, 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))). 6.97/7.27 cnf(i_0_5152, 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))). 6.97/7.27 cnf(i_0_1543, 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)))). 6.97/7.27 cnf(i_0_4981, 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)))). 6.97/7.27 cnf(i_0_4570, 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))). 6.97/7.27 cnf(i_0_4760, 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))). 6.97/7.27 cnf(i_0_2325, 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))). 6.97/7.27 cnf(i_0_6965, 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)))). 6.97/7.27 cnf(i_0_3806, 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)))). 6.97/7.27 cnf(i_0_4853, 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))). 6.97/7.27 cnf(i_0_7060, 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)))). 6.97/7.27 cnf(i_0_24, 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))). 6.97/7.27 cnf(i_0_7426, 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))))). 6.97/7.27 cnf(i_0_6647, 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_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__less)=c_FunDef_Opair__leq)). 6.97/7.27 cnf(i_0_5341, 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))). 6.97/7.27 cnf(i_0_3137, 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)))). 6.97/7.27 cnf(i_0_3403, 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))). 6.97/7.27 cnf(i_0_6439, 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))). 6.97/7.27 cnf(i_0_6315, 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)))). 6.97/7.27 cnf(i_0_3941, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))),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)))). 6.97/7.27 cnf(i_0_1524, 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)))). 6.97/7.27 cnf(i_0_4656, 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)))). 6.97/7.27 cnf(i_0_2727, 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)))). 6.97/7.27 cnf(i_0_2213, 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)))). 6.97/7.27 cnf(i_0_4873, 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))). 6.97/7.27 cnf(i_0_1600, 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)). 6.97/7.27 cnf(i_0_4379, 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))). 6.97/7.27 cnf(i_0_4245, 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))). 6.97/7.27 cnf(i_0_5751, 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))). 6.97/7.27 cnf(i_0_4104, 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))). 6.97/7.27 cnf(i_0_3485, 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))). 6.97/7.27 cnf(i_0_837, 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))). 6.97/7.27 cnf(i_0_5634, 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)))). 6.97/7.27 cnf(i_0_4097, 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))). 6.97/7.27 cnf(i_0_6151, 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))). 6.97/7.27 cnf(i_0_1809, 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))). 6.97/7.27 cnf(i_0_6243, 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))). 6.97/7.27 cnf(i_0_5219, 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))). 6.97/7.27 cnf(i_0_4038, 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)))). 6.97/7.27 cnf(i_0_5648, 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))). 6.97/7.27 cnf(i_0_3748, plain, (c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))). 6.97/7.27 cnf(i_0_778, 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))). 6.97/7.27 cnf(i_0_32, 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))). 6.97/7.27 cnf(i_0_2826, 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))). 6.97/7.27 cnf(i_0_1808, 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))). 6.97/7.27 cnf(i_0_715, 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))))). 6.97/7.27 cnf(i_0_6076, 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))). 6.97/7.27 cnf(i_0_4382, 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))). 6.97/7.27 cnf(i_0_3133, 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))). 6.97/7.27 cnf(i_0_939, 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))). 6.97/7.27 cnf(i_0_91, 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)))). 6.97/7.27 cnf(i_0_7014, 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))). 6.97/7.27 cnf(i_0_1841, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),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)))). 6.97/7.27 cnf(i_0_4051, 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)))). 6.97/7.27 cnf(i_0_5307, 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)))). 6.97/7.27 cnf(i_0_5079, 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)))). 6.97/7.27 cnf(i_0_5318, 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)))). 6.97/7.27 cnf(i_0_7172, 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)))). 6.97/7.27 cnf(i_0_5972, 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))). 6.97/7.27 cnf(i_0_2898, 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))). 6.97/7.27 cnf(i_0_2099, 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))). 6.97/7.27 cnf(i_0_6936, 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)))). 6.97/7.27 cnf(i_0_3314, 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)))). 6.97/7.27 cnf(i_0_6949, 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)))). 6.97/7.27 cnf(i_0_6075, 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)))))). 6.97/7.27 cnf(i_0_5000, 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)))). 6.97/7.27 cnf(i_0_3778, 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)))). 6.97/7.27 cnf(i_0_829, 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)))). 6.97/7.27 cnf(i_0_5520, 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)))). 6.97/7.27 cnf(i_0_5510, 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)))). 6.97/7.27 cnf(i_0_4815, 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)))). 6.97/7.27 cnf(i_0_6790, 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))). 6.97/7.27 cnf(i_0_410, 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)))). 6.97/7.27 cnf(i_0_2199, 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))). 6.97/7.27 cnf(i_0_3100, 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))). 6.97/7.27 cnf(i_0_7259, 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),esk566_1(X1)),esk567_1(X1)))))=X1)). 6.97/7.27 cnf(i_0_1190, 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)))). 6.97/7.27 cnf(i_0_1253, 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)))). 6.97/7.27 cnf(i_0_276, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))=hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))). 6.97/7.27 cnf(i_0_3730, 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))). 6.97/7.27 cnf(i_0_1654, 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)))). 6.97/7.27 cnf(i_0_256, plain, (c_Random__Sequence_Obind(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_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X2)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),X1,c_Random__Sequence_Osingle(X2)),X4))=c_Random__Sequence_Omap(X1,X2,X4,X3))). 6.97/7.27 cnf(i_0_311, 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)))). 6.97/7.27 cnf(i_0_3165, 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))). 6.97/7.27 cnf(i_0_3780, 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)))). 6.97/7.27 cnf(i_0_4679, 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))). 6.97/7.27 cnf(i_0_4454, 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))). 6.97/7.27 cnf(i_0_4415, 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))). 6.97/7.27 cnf(i_0_7091, 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))). 6.97/7.27 cnf(i_0_7064, 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),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),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))))). 6.97/7.27 cnf(i_0_4089, 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))). 6.97/7.27 cnf(i_0_384, 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))). 6.97/7.27 cnf(i_0_667, 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)))). 6.97/7.27 cnf(i_0_4293, 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))). 6.97/7.27 cnf(i_0_2131, 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))))). 6.97/7.27 cnf(i_0_1403, 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)))). 6.97/7.27 cnf(i_0_7488, 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))). 6.97/7.27 cnf(i_0_4966, 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)))))). 6.97/7.27 cnf(i_0_838, plain, (c_Nat__Transfer_Ois__nat(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)),c_Int_OMin)),c_Int_OMin)))). 6.97/7.27 cnf(i_0_5416, 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)))). 6.97/7.27 cnf(i_0_2798, 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)))). 6.97/7.27 cnf(i_0_4095, 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)))). 6.97/7.27 cnf(i_0_3297, 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)))). 6.97/7.27 cnf(i_0_7467, 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)))). 6.97/7.27 cnf(i_0_6017, 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)))). 6.97/7.27 cnf(i_0_5761, 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))). 6.97/7.27 cnf(i_0_1872, 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))). 6.97/7.27 cnf(i_0_5845, 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)))))). 6.97/7.27 cnf(i_0_443, 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)))). 6.97/7.27 cnf(i_0_1228, 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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))). 6.97/7.27 cnf(i_0_5516, 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),esk420_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))))). 6.97/7.27 cnf(i_0_6978, 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))). 6.97/7.27 cnf(i_0_1535, 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))). 6.97/7.27 cnf(i_0_3886, 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)))). 6.97/7.27 cnf(i_0_4103, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),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)))). 6.97/7.27 cnf(i_0_2801, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),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),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))). 6.97/7.27 cnf(i_0_7423, 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))))). 6.97/7.27 cnf(i_0_1652, 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)))))). 6.97/7.27 cnf(i_0_7242, 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))). 6.97/7.27 cnf(i_0_1593, 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)))). 6.97/7.27 cnf(i_0_2824, 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)))))). 6.97/7.27 cnf(i_0_1506, 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)))))). 6.97/7.27 cnf(i_0_4056, 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)))))). 6.97/7.27 cnf(i_0_7238, 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)))). 6.97/7.27 cnf(i_0_6651, 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)))))). 6.97/7.27 cnf(i_0_4231, 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)))))). 6.97/7.27 cnf(i_0_2089, 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)))))). 6.97/7.27 cnf(i_0_1967, 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)))). 6.97/7.27 cnf(i_0_5526, 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)))). 6.97/7.27 cnf(i_0_6234, 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)))). 6.97/7.27 cnf(i_0_1519, 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)))). 6.97/7.27 cnf(i_0_5875, 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))). 6.97/7.27 cnf(i_0_595, 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))). 6.97/7.27 cnf(i_0_6316, 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))))))). 6.97/7.27 cnf(i_0_2060, 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)))))). 6.97/7.27 cnf(i_0_645, 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)))))). 6.97/7.27 cnf(i_0_4157, 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)))))). 6.97/7.27 cnf(i_0_4876, 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))). 6.97/7.27 cnf(i_0_224, 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))). 6.97/7.27 cnf(i_0_5069, 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))). 6.97/7.27 cnf(i_0_6980, 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))). 6.97/7.27 cnf(i_0_5149, 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)). 6.97/7.27 cnf(i_0_2409, 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)))). 6.97/7.27 cnf(i_0_7360, 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))). 6.97/7.27 cnf(i_0_7079, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),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)),c_Int_OMin)),c_Int_OMin))=hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 6.97/7.27 cnf(i_0_4226, 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)). 6.97/7.27 cnf(i_0_1249, 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))). 6.97/7.27 cnf(i_0_201, 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))). 6.97/7.27 cnf(i_0_4592, 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))). 6.97/7.27 cnf(i_0_2894, 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))). 6.97/7.27 cnf(i_0_3874, 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)))). 6.97/7.27 cnf(i_0_3811, 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))). 6.97/7.27 cnf(i_0_4033, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),c_Int_OMin))))). 6.97/7.27 cnf(i_0_1247, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))=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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))))). 6.97/7.27 cnf(i_0_5044, 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)))). 6.97/7.27 cnf(i_0_6683, 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)))). 6.97/7.27 cnf(i_0_6127, 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)))). 6.97/7.27 cnf(i_0_7405, 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)))). 6.97/7.27 cnf(i_0_4508, 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))). 6.97/7.27 cnf(i_0_5534, 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))). 6.97/7.27 cnf(i_0_6459, 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)))). 6.97/7.27 cnf(i_0_4507, 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))). 6.97/7.27 cnf(i_0_1693, 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))). 6.97/7.27 cnf(i_0_6748, 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)))))). 6.97/7.27 cnf(i_0_7428, 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))). 6.97/7.27 cnf(i_0_3058, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),c_Int_OMin))),X2)))=hAPP(c_New__DSequence_Opos__not__seq(X1),X2))). 6.97/7.27 cnf(i_0_439, 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))). 6.97/7.27 cnf(i_0_3213, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),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),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)))). 6.97/7.27 cnf(i_0_1946, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),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),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)))))). 6.97/7.27 cnf(i_0_214, 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))). 6.97/7.27 cnf(i_0_2731, 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)))). 6.97/7.27 cnf(i_0_2799, 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)))). 6.97/7.27 cnf(i_0_1826, 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)))))). 6.97/7.27 cnf(i_0_5939, 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))))). 6.97/7.27 cnf(i_0_275, 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))). 6.97/7.27 cnf(i_0_4105, 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))). 6.97/7.27 cnf(i_0_2505, 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))). 6.97/7.27 cnf(i_0_414, plain, (c_Hilbert__Choice_OEps(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_Hilbert__Choice_Oinv__into(X1,X3,X2,X4),X5))). 6.97/7.27 cnf(i_0_2377, 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))). 6.97/7.27 cnf(i_0_3689, 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))). 6.97/7.27 cnf(i_0_5662, 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))))))). 6.97/7.27 cnf(i_0_1885, 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)))). 6.97/7.27 cnf(i_0_4990, 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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))). 6.97/7.27 cnf(i_0_5058, plain, (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))=hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),X2))). 6.97/7.27 cnf(i_0_2293, 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)))))). 6.97/7.27 cnf(i_0_2058, 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))). 6.97/7.27 cnf(i_0_3596, 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))). 6.97/7.27 cnf(i_0_1953, 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))). 6.97/7.27 cnf(i_0_2599, 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))). 6.97/7.27 cnf(i_0_4844, 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))). 6.97/7.27 cnf(i_0_1157, 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))). 6.97/7.27 cnf(i_0_6373, 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))). 6.97/7.27 cnf(i_0_111, 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))). 6.97/7.27 cnf(i_0_994, 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)))). 6.97/7.27 cnf(i_0_1634, 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))). 6.97/7.27 cnf(i_0_5701, 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))))). 6.97/7.27 cnf(i_0_7429, 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))))). 6.97/7.27 cnf(i_0_3595, 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)))). 6.97/7.27 cnf(i_0_3306, 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))). 6.97/7.27 cnf(i_0_7380, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),c_Int_OMin))). 6.97/7.27 cnf(i_0_5269, 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))). 6.97/7.27 cnf(i_0_1284, 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))))). 6.97/7.27 cnf(i_0_3507, 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))). 6.97/7.27 cnf(i_0_3961, 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))). 6.97/7.27 cnf(i_0_4294, 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)))). 6.97/7.27 cnf(i_0_415, 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))). 6.97/7.27 cnf(i_0_4776, 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))). 6.97/7.27 cnf(i_0_1384, 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))). 6.97/7.27 cnf(i_0_722, 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))). 6.97/7.27 cnf(i_0_6938, 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))). 6.97/7.27 cnf(i_0_3546, 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)))))). 6.97/7.27 cnf(i_0_7129, 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)))). 6.97/7.27 cnf(i_0_1425, 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)))). 6.97/7.27 cnf(i_0_4787, 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))). 6.97/7.27 cnf(i_0_5600, 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))))). 6.97/7.27 cnf(i_0_4549, 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))). 6.97/7.27 cnf(i_0_3018, 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)))). 6.97/7.27 cnf(i_0_5835, plain, (hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OEx(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_fconj),X3))),hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X4)))=hAPP(c_Relation_OImage(X1,X2,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X4)),X3))). 6.97/7.27 cnf(i_0_478, 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))). 6.97/7.27 cnf(i_0_717, 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))). 6.97/7.27 cnf(i_0_3107, 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)))). 6.97/7.27 cnf(i_0_2510, 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)))). 6.97/7.27 cnf(i_0_1580, 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))). 6.97/7.27 cnf(i_0_1968, 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)))). 6.97/7.27 cnf(i_0_4081, 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))). 6.97/7.27 cnf(i_0_4144, plain, (hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(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_fconj),X2))),c_member(X1)))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))). 6.97/7.27 cnf(i_0_3414, 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)). 6.97/7.27 cnf(i_0_4730, 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)). 6.97/7.27 cnf(i_0_6587, 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)))). 6.97/7.27 cnf(i_0_1805, 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)))). 6.97/7.27 cnf(i_0_6200, 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))))))). 6.97/7.27 cnf(i_0_1252, 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))))). 6.97/7.27 cnf(i_0_3805, 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)))). 6.97/7.27 cnf(i_0_2916, 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))). 6.97/7.27 cnf(i_0_7243, 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)))). 6.97/7.27 cnf(i_0_618, 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)))). 6.97/7.27 cnf(i_0_3772, 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)))). 6.97/7.27 cnf(i_0_4247, 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)))). 6.97/7.27 cnf(i_0_2757, 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)))). 6.97/7.27 cnf(i_0_7284, 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))))). 6.97/7.27 cnf(i_0_733, 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)). 6.97/7.27 cnf(i_0_1169, 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))). 6.97/7.27 cnf(i_0_6744, 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))). 6.97/7.27 cnf(i_0_7080, 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))). 6.97/7.27 cnf(i_0_3706, 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))). 6.97/7.27 cnf(i_0_1920, 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))). 6.97/7.27 cnf(i_0_4502, 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))). 6.97/7.27 cnf(i_0_5607, plain, (c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),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))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2)),c_fequal)),X4))))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4))). 6.97/7.27 cnf(i_0_227, plain, (c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),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))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2)),c_fequal)),X4))))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4))). 6.97/7.27 cnf(i_0_1244, 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)))). 6.97/7.27 cnf(i_0_4326, 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)))). 6.97/7.27 cnf(i_0_4509, 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))). 6.97/7.27 cnf(i_0_4726, 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))))). 6.97/7.27 cnf(i_0_877, 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)))). 6.97/7.27 cnf(i_0_2170, 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))))). 6.97/7.27 cnf(i_0_6352, 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)))). 6.97/7.27 cnf(i_0_4833, plain, (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))). 6.97/7.27 cnf(i_0_1914, 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)))). 6.97/7.27 cnf(i_0_6889, 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))). 6.97/7.27 cnf(i_0_1067, 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)))). 6.97/7.27 cnf(i_0_7492, 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))). 6.97/7.27 cnf(i_0_7402, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),X3)),c_Int_OMin)))),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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),X3)),X1)))=hAPP(c_Divides_Oadjust(X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X1)))). 6.97/7.27 cnf(i_0_3440, 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))). 6.97/7.27 cnf(i_0_5724, 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))). 6.97/7.27 cnf(i_0_1324, 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)))). 6.97/7.27 cnf(i_0_6187, 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)))). 6.97/7.27 cnf(i_0_3989, 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)))). 6.97/7.27 cnf(i_0_1369, 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)))). 6.97/7.27 cnf(i_0_64, 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))). 6.97/7.27 cnf(i_0_7470, 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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),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(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))=c_Divides_Oadjust(X1))). 6.97/7.27 cnf(i_0_4870, 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))). 6.97/7.27 cnf(i_0_7036, 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))). 6.97/7.27 cnf(i_0_2803, 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))). 6.97/7.27 cnf(i_0_6491, 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))). 6.97/7.27 cnf(i_0_3167, 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))). 6.97/7.27 cnf(i_0_1617, 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))). 6.97/7.27 cnf(i_0_6064, 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))). 6.97/7.27 cnf(i_0_4684, 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))). 6.97/7.27 cnf(i_0_713, 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)))). 6.97/7.27 cnf(i_0_5745, 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_Osublists(X1,c_List_Olist_ONil(X1)))). 6.97/7.27 cnf(i_0_2688, 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)))). 6.97/7.27 cnf(i_0_147, plain, (hAPP(c_New__DSequence_Opos__union(X1,X2,X3),X4)=c_Lazy__Sequence_Oappend(X1,hAPP(X2,X4),hAPP(X3,X4)))). 6.97/7.27 cnf(i_0_4494, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X1,X2)),c_Product__Type_OPair(X1,X2))=c_Fun_Oid(tc_prod(X1,X2)))). 6.97/7.27 cnf(i_0_845, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=hAPP(c_fequal,X2))). 6.97/7.27 cnf(i_0_3599, plain, (c_List_Oremove1(X1,X2,c_List_Oremove1(X1,X3,X4))=c_List_Oremove1(X1,X3,c_List_Oremove1(X1,X2,X4)))). 6.97/7.27 cnf(i_0_3488, plain, (c_Enum_On__lists(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)=hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olist_ONil(tc_List_Olist(X1))))). 6.97/7.27 cnf(i_0_1325, plain, (hAPP(c_List_Orev(X1),hAPP(c_List_Ofilter(X1,X2),X3))=hAPP(c_List_Ofilter(X1,X2),hAPP(c_List_Orev(X1),X3)))). 6.97/7.27 cnf(i_0_4195, plain, (c_List_Opartition(X1,X2,c_List_Olist_ONil(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)))). 6.97/7.27 cnf(i_0_4991, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))). 6.97/7.27 cnf(i_0_3268, 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))). 6.97/7.27 cnf(i_0_1235, 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))). 6.97/7.27 cnf(i_0_4532, plain, (hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),X4),X5),X6)=hAPP(hAPP(X4,X6),hAPP(X5,X6)))). 6.97/7.27 cnf(i_0_6170, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))). 6.97/7.27 cnf(i_0_5773, 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)))). 6.97/7.27 cnf(i_0_7068, 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))). 6.97/7.27 cnf(i_0_250, 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)))). 6.97/7.27 cnf(i_0_2650, 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)))). 6.97/7.27 cnf(i_0_7285, plain, (c_Random__Sequence_Oempty(X1,X2,X3)=hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X1)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X1)))). 6.97/7.27 cnf(i_0_3798, plain, (c_Lazy__Sequence_Omap(X1,X2,X3,c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X4,X5))=c_Lazy__Sequence_Olazy__sequence_OInsert(X2,hAPP(X3,X4),c_Lazy__Sequence_Omap(X1,X2,X3,X5)))). 6.97/7.27 cnf(i_0_5694, 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)))). 6.97/7.27 cnf(i_0_7375, 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)))). 6.97/7.27 cnf(i_0_2570, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_List_Oset(X1),X4))=hAPP(c_List_Oset(X2),hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)))). 6.97/7.27 cnf(i_0_1762, 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))). 6.97/7.27 cnf(i_0_3903, plain, (hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X4)=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),X1),c_List_Olist_ONil(X2)),X4))). 6.97/7.27 cnf(i_0_775, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)))). 6.97/7.27 cnf(i_0_6542, 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)))). 6.97/7.27 cnf(i_0_4447, plain, (hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))=hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(c_List_Orev(X2),X4)))). 6.97/7.27 cnf(i_0_4001, plain, (hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))=hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(c_List_Otl(X2),X4)))). 6.97/7.27 cnf(i_0_2109, 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))))). 6.97/7.27 cnf(i_0_7145, plain, (c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(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(hAPP(X3,X4),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X1,X2,X3,X4)))). 6.97/7.27 cnf(i_0_5328, plain, (c_List_Olist_Olist__size(X1,X2,hAPP(hAPP(c_List_Omap(X3,X1),X4),X5))=c_List_Olist_Olist__size(X3,hAPP(c_Fun_Ocomp(X1,tc_Nat_Onat,X3,X2),X4),X5))). 6.97/7.27 cnf(i_0_5669, 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)))). 6.97/7.27 cnf(i_0_1980, 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)))). 6.97/7.27 cnf(i_0_3660, plain, (hAPP(hAPP(hAPP(X1,X2),X3),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X4,X5,X6,X1,X3))=c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X4,X5,X6,X1,c_Lazy__Sequence_Olazy__sequence_OInsert(X5,X2,X3)))). 6.97/7.27 cnf(i_0_4790, 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)))))). 6.97/7.27 cnf(i_0_4882, plain, (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))=c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2)))). 6.97/7.27 cnf(i_0_4733, 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))). 6.97/7.27 cnf(i_0_1721, 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))). 6.97/7.27 cnf(i_0_1487, 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)))). 6.97/7.27 cnf(i_0_7525, 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)))). 6.97/7.27 cnf(i_0_1650, 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))). 6.97/7.27 cnf(i_0_6551, 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))). 6.97/7.27 cnf(i_0_2216, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Oimage(X4,X1,X5),X6))=hAPP(c_Set_Oimage(X4,X2,hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5)),X6))). 6.97/7.27 cnf(i_0_2263, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),hAPP(hAPP(c_COMBB(X3,tc_HOL_Obool,X1),X4),X5)),X6)=hAPP(hAPP(c_COMBB(X3,tc_HOL_Obool,X2),X4),hAPP(c_Fun_Ocomp(X1,X3,X2,X5),X6)))). 6.97/7.27 cnf(i_0_559, plain, (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))). 6.97/7.27 cnf(i_0_1763, plain, (hAPP(hAPP(c_List_Otake(X1),X2),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5))=hAPP(hAPP(c_List_Omap(X3,X1),X4),hAPP(hAPP(c_List_Otake(X3),X2),X5)))). 6.97/7.27 cnf(i_0_186, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(hAPP(c_List_Odrop(X1),X4),X5))=hAPP(hAPP(c_List_Odrop(X2),X4),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)))). 6.97/7.27 cnf(i_0_159, 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)))). 6.97/7.27 cnf(i_0_3696, plain, (hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X1)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(X1),X2))=hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(X1),X2),X3),X4))). 6.97/7.27 cnf(i_0_5207, 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),hAPP(hAPP(c_Set_Oinsert(X4),X3),X5)))). 6.97/7.27 cnf(i_0_6416, plain, (hAPP(c_Set_Oimage(X1,X2,X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X4))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X4),c_Set_Oimage(X1,X2,X3)))). 6.97/7.27 cnf(i_0_1025, 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)))). 6.97/7.27 cnf(i_0_2245, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Oimage(X4,X1,X5),X6))=hAPP(c_Set_Oimage(X4,X2,hAPP(hAPP(c_COMBB(X1,X2,X4),X3),X5)),X6))). 6.97/7.27 cnf(i_0_6868, 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)))). 6.97/7.27 cnf(i_0_2168, plain, (hAPP(c_Relation_ORange(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(X2,tc_HOL_Obool)),X3),c_Relation_ORange(X1,X2)))). 6.97/7.27 cnf(i_0_5803, 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)))). 6.97/7.27 cnf(i_0_7009, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),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)),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)))). 6.97/7.27 cnf(i_0_6879, plain, (hAPP(hAPP(c_List_Omap(X1,X2),hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5)),X6)=hAPP(hAPP(c_List_Omap(X3,X2),X4),hAPP(hAPP(c_List_Omap(X1,X3),X5),X6)))). 6.97/7.27 cnf(i_0_2030, 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)))). 6.97/7.27 cnf(i_0_375, 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)))). 6.97/7.27 cnf(i_0_3471, plain, (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),c_Fun_Ofun__upd(X1,X3,X5,X6,X7)))). 6.97/7.27 cnf(i_0_1900, 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)))). 6.97/7.27 cnf(i_0_1214, 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)))). 6.97/7.27 cnf(i_0_3683, 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))))). 6.97/7.27 cnf(i_0_5071, 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))))). 6.97/7.27 cnf(i_0_7539, 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)))). 6.97/7.27 cnf(i_0_2941, plain, (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))=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)))). 6.97/7.27 cnf(i_0_3909, 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))). 6.97/7.27 cnf(i_0_5347, 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)))). 6.97/7.27 cnf(i_0_1537, 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)))). 6.97/7.27 cnf(i_0_903, 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)))). 6.97/7.27 cnf(i_0_5075, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),hAPP(hAPP(c_Relation_Orel__comp(X1,X4,X2),X5),X6)),X7)=hAPP(hAPP(c_Relation_Orel__comp(X1,X4,X3),X5),hAPP(hAPP(c_Relation_Orel__comp(X4,X2,X3),X6),X7)))). 6.97/7.27 cnf(i_0_3428, 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)))). 6.97/7.27 cnf(i_0_3915, 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)))). 6.97/7.27 cnf(i_0_7337, plain, (hAPP(c_Fun_Ocomp(tc_prod(X1,X2),X1,tc_prod(X3,X4),c_Product__Type_Ofst(X1,X2)),c_Product__Type_Omap__pair(X3,X1,X4,X2,X5,X6))=hAPP(c_Fun_Ocomp(X3,X1,tc_prod(X3,X4),X5),c_Product__Type_Ofst(X3,X4)))). 6.97/7.27 cnf(i_0_2621, 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)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,X3))=c_SetInterval_Oord__class_OatLeastAtMost(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)))). 6.97/7.27 cnf(i_0_6543, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X3,X1,X4),X5)),X6)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X2,tc_HOL_Obool)),X5),hAPP(c_Fun_Ocomp(X1,tc_fun(X2,tc_HOL_Obool),X3,X6),X4)))). 6.97/7.27 cnf(i_0_6950, 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)))). 6.97/7.27 cnf(i_0_1391, 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)),hAPP(hAPP(c_Set_Oinsert(X4),X3),X5)),X2))). 6.97/7.27 cnf(i_0_2865, 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)),hAPP(hAPP(c_Set_Oinsert(X4),X3),X5)),X2))). 6.97/7.27 cnf(i_0_975, 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))). 6.97/7.27 cnf(i_0_3557, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(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_OINFI(X4,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X4,X6),X3)),X5))). 6.97/7.27 cnf(i_0_1241, 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)))). 6.97/7.27 cnf(i_0_6563, 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))))). 6.97/7.27 cnf(i_0_1285, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)),hAPP(hAPP(c_List_Olist_OCons(X2),X5),X6))=hAPP(hAPP(c_List_Olist_OCons(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X5)),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X6)))). 6.97/7.27 cnf(i_0_5921, 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))))). 6.97/7.27 cnf(i_0_4871, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),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))),c_Int_OMin)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))). 6.97/7.27 cnf(i_0_5225, 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)))). 6.97/7.27 cnf(i_0_2435, 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))). 6.97/7.27 cnf(i_0_3978, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X4),c_List_Orotate1(X1)),X5))=hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X2),tc_List_Olist(X2)),X4),c_List_Orotate1(X2)),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)))). 6.97/7.27 cnf(i_0_3950, plain, (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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)),X1))). 6.97/7.27 cnf(i_0_4933, plain, (hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X4,X5,X6),hAPP(c_Product__Type_Omap__pair(X7,X1,X8,X3,X9,X10),X11))=hAPP(c_Product__Type_Omap__pair(X7,X2,X8,X4,hAPP(c_Fun_Ocomp(X1,X2,X7,X5),X9),hAPP(c_Fun_Ocomp(X3,X4,X8,X6),X10)),X11))). 6.97/7.27 cnf(i_0_1856, 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)))). 6.97/7.27 cnf(i_0_7013, 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(c_Product__Type_Omap__pair(X5,X1,X3,X3,X6,c_Fun_Oid(X3)),hAPP(c_Product__Type_Omap__pair(X5,X5,X2,X3,c_Fun_Oid(X5),X4),X7)))). 6.97/7.27 cnf(i_0_925, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),hAPP(X3,hAPP(c_Product__Type_Ofst(X4,X5),X6))),hAPP(X7,hAPP(c_Product__Type_Osnd(X4,X5),X6)))=hAPP(c_Product__Type_Omap__pair(X4,X1,X2,X2,X3,c_Fun_Oid(X2)),hAPP(c_Product__Type_Omap__pair(X4,X4,X5,X2,c_Fun_Oid(X4),X7),X6)))). 6.97/7.27 cnf(i_0_5339, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),hAPP(X3,hAPP(c_Product__Type_Ofst(X4,X5),X6))),hAPP(X7,hAPP(c_Product__Type_Osnd(X4,X5),X6)))=hAPP(c_Product__Type_Omap__pair(X1,X1,X5,X2,c_Fun_Oid(X1),X7),hAPP(c_Product__Type_Omap__pair(X4,X1,X5,X5,X3,c_Fun_Oid(X5)),X6)))). 6.97/7.27 cnf(i_0_7531, plain, (hAPP(c_List_Ofoldl(X1,X2,hAPP(c_COMBC(X2,X1,X1),X3),X4),hAPP(c_List_Orev(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X5),X6)))=hAPP(hAPP(X3,X5),hAPP(c_List_Ofoldl(X1,X2,hAPP(c_COMBC(X2,X1,X1),X3),X4),hAPP(c_List_Orev(X2),X6))))). 6.97/7.27 cnf(i_0_2596, 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)))). 6.97/7.27 cnf(i_0_2595, 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))))). 6.97/7.27 cnf(i_0_4852, 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))). 6.97/7.27 cnf(i_0_3125, 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))))). 6.97/7.27 cnf(i_0_4010, 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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,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)),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,X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4))),X3))). 6.97/7.27 cnf(i_0_5280, 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)))))). 6.97/7.27 cnf(i_0_3222, 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)))). 6.97/7.27 cnf(i_0_1306, 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))))). 6.97/7.27 cnf(i_0_3677, 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)))). 6.97/7.27 cnf(i_0_3754, 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)))). 6.97/7.27 cnf(i_0_4813, 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),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__sup__class_Osup(tc_fun(X2,tc_HOL_Obool))),X4)),X5)))). 6.97/7.27 cnf(i_0_2018, 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__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool))),X4)),X5))=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)))). 6.97/7.27 cnf(i_0_5618, 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)))). 6.97/7.27 cnf(i_0_2971, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),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(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)))). 6.97/7.27 cnf(i_0_548, plain, (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),X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),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_Nat_Onat),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),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),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)))))). 6.97/7.27 cnf(i_0_20, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),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))=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)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)))). 6.97/7.27 cnf(i_0_5151, plain, (hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X3,X4),hAPP(hAPP(c_Product__Type_Oscomp(X1,X5,X6,tc_prod(X2,X3)),X7),X8)),X9)=hAPP(hAPP(c_Product__Type_Oscomp(X1,X5,X6,X4),X7),hAPP(hAPP(c_COMBC(X5,tc_fun(X2,tc_fun(X3,X4)),tc_fun(X6,X4)),hAPP(hAPP(c_COMBB(tc_fun(X6,tc_prod(X2,X3)),tc_fun(tc_fun(X2,tc_fun(X3,X4)),tc_fun(X6,X4)),X5),c_Product__Type_Oscomp(X6,X2,X3,X4)),X8)),X9)))). 6.97/7.27 cnf(i_0_66, plain, (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))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))). 6.97/7.27 cnf(i_0_84, 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),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)))=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)))))). 6.97/7.27 cnf(i_0_5991, 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))). 6.97/7.27 cnf(i_0_5405, 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))),X4))=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))))). 6.97/7.27 cnf(i_0_7303, 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))). 6.97/7.27 cnf(i_0_3985, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),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_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)))))). 6.97/7.27 cnf(i_0_3215, plain, (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),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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),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),X2),X3)))))))). 6.97/7.27 cnf(i_0_2613, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(c_Set_Oimage(X3,X1,X4),X5)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_Oimage(X3,X2,X6)),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__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),c_Set_Ovimage(X3,X1,X4)),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)))))),X5)))=hAPP(c_Set_Oimage(X3,tc_prod(X1,X2),hAPP(hAPP(c_COMBS(X3,X2,tc_prod(X1,X2)),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_prod(X1,X2)),X3),c_Product__Type_OPair(X1,X2)),X4)),X6)),X5))). 6.97/7.27 cnf(i_0_3304, plain, (hAPP(X1,hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X3),tc_HOL_Obool),tc_HOL_Obool,X3),c_HOL_OEx(tc_fun(X2,X3))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X3),tc_HOL_Obool),tc_fun(tc_fun(X2,X3),tc_HOL_Obool),X3),hAPP(c_COMBS(tc_fun(X2,X3),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X2,X3)),c_fconj),X4))),hAPP(hAPP(c_COMBC(X3,tc_fun(tc_fun(X2,X3),X3),tc_fun(tc_fun(X2,X3),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X2,X3),X3),tc_fun(tc_fun(X2,X3),tc_HOL_Obool)),X3),c_COMBB(X3,tc_HOL_Obool,tc_fun(X2,X3))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X2,X3),X2,X3),c_COMBI(tc_fun(X2,X3))),X5)))))=c_Partial__Function_Ofun__lub(X3,X6,X2,X1,X4,X5))). 6.97/7.27 cnf(i_0_5989, 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)))))))). 6.97/7.27 cnf(i_0_4973, 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))))). 6.97/7.27 cnf(i_0_540, negated_conjecture, (~c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts))). 6.97/7.27 cnf(i_0_4478, plain, (~hBOOL(c_fFalse))). 6.97/7.27 cnf(i_0_5605, plain, (c_Int_OMin!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 6.97/7.27 cnf(i_0_5233, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 6.97/7.27 cnf(i_0_1227, plain, (hAPP(c_Nat_OSuc,X1)!=X1)). 6.97/7.27 cnf(i_0_4628, plain, (hAPP(c_Nat_OSuc,X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 6.97/7.27 cnf(i_0_2733, plain, (~c_List_Olist__ex(X1,X2,c_List_Olist_ONil(X1)))). 6.97/7.27 cnf(i_0_7468, plain, (~c_List_Olist__ex1(X1,X2,c_List_Olist_ONil(X1)))). 6.97/7.27 cnf(i_0_98, plain, (~hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 6.97/7.27 cnf(i_0_154, plain, (~hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))))). 6.97/7.27 cnf(i_0_1201, plain, (c_Lazy__Sequence_Olazy__sequence_OEmpty(X1)!=c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,X3))). 6.97/7.27 cnf(i_0_6233, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)!=X3)). 6.97/7.27 cnf(i_0_6325, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 6.97/7.27 cnf(i_0_3979, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)!=c_List_Olist_ONil(X1))). 6.97/7.27 cnf(i_0_207, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)))). 6.97/7.27 cnf(i_0_3724, plain, (c_Int_OMin!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))). 6.97/7.27 cnf(i_0_2351, plain, (~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))))). 6.97/7.27 cnf(i_0_3135, plain, (hAPP(c_Set_OPow(X1),X2)!=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))). 6.97/7.27 cnf(i_0_2568, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Int_OMin)))). 6.97/7.27 cnf(i_0_671, 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))))). 6.97/7.27 cnf(i_0_4184, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Int_OMin)))). 6.97/7.27 cnf(i_0_853, plain, (~c_Wellfounded_Omax__extp(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))). 6.97/7.27 cnf(i_0_1248, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)))). 6.97/7.27 cnf(i_0_978, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 6.97/7.27 cnf(i_0_5161, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X1)))). 6.97/7.27 cnf(i_0_1124, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 6.97/7.27 cnf(i_0_172, plain, (~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))). 6.97/7.27 cnf(i_0_3228, plain, (~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))). 6.97/7.27 cnf(i_0_1627, 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))). 6.97/7.27 cnf(i_0_2793, plain, (~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X3)))). 6.97/7.27 cnf(i_0_914, plain, (~hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2)))). 6.97/7.27 cnf(i_0_2902, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))). 6.97/7.27 cnf(i_0_2735, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X2)))). 6.97/7.27 cnf(i_0_3782, 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)))))). 6.97/7.27 cnf(i_0_992, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4)))). 6.97/7.27 cnf(i_0_2362, plain, (hAPP(c_Set_OPow(X1),X2)!=hAPP(c_Set_Oimage(X1,tc_fun(X1,tc_HOL_Obool),X3),X2))). 6.97/7.27 cnf(i_0_1116, 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))))). 6.97/7.27 cnf(i_0_4777, 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)))))). 6.97/7.27 cnf(i_0_189, 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)))). 6.97/7.27 cnf(i_0_1817, 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)))). 6.97/7.27 cnf(i_0_843, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 6.97/7.27 cnf(i_0_1134, 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))))). 6.97/7.27 cnf(i_0_6212, 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))). 6.97/7.27 cnf(i_0_6954, 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)))))). 6.97/7.27 cnf(i_0_4778, 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))))))). 6.97/7.27 cnf(i_0_3169, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))). 6.97/7.27 cnf(i_0_3788, 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))))))). 6.97/7.27 cnf(i_0_4547, 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))))). 6.97/7.27 cnf(i_0_2577, 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))))). 6.97/7.27 cnf(i_0_526, 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))))). 6.97/7.27 cnf(i_0_498, 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))))). 6.97/7.27 cnf(i_0_1183, 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))))). 6.97/7.27 cnf(i_0_1838, 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)))). 6.97/7.27 cnf(i_0_918, 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))))). 6.97/7.27 cnf(i_0_5599, plain, (c_Groups_Oone__class_Oone(X1)!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Ozero__neq__one(X1))). 6.97/7.27 cnf(i_0_4298, plain, (~c_Int_Oiszero(X1,c_Groups_Oone__class_Oone(X1))|~class_Rings_Osemiring__1(X1))). 6.97/7.27 cnf(i_0_5278, plain, (~hBOOL(hAPP(c_fNot,X1))|~hBOOL(X1))). 6.97/7.27 cnf(i_0_4904, plain, (c_Wellfounded_Oacyclic(X1,X2)|~c_Nitpick_Owf_H(X1,X2))). 6.97/7.27 cnf(i_0_3496, plain, (class_Enum_Oenum(tc_Option_Ooption(X1))|~class_Enum_Oenum(X1))). 6.97/7.27 cnf(i_0_3419, plain, (class_Finite__Set_Ofinite(tc_Option_Ooption(X1))|~class_Finite__Set_Ofinite(X1))). 6.97/7.27 cnf(i_0_857, plain, (class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X1))|~class_Lazy__Sequence_Osmall__lazy(X1))). 6.97/7.27 cnf(i_0_3287, plain, (c_Wellfounded_Oacyclic(X1,X2)|~c_Wellfounded_Owf(X1,X2))). 6.97/7.27 cnf(i_0_811, plain, (c_Predicate_Oreflp(X1,X2)|~c_Equiv__Relations_Oequivp(X1,X2))). 6.97/7.27 cnf(i_0_810, plain, (c_Predicate_Osymp(X1,X2)|~c_Equiv__Relations_Oequivp(X1,X2))). 6.97/7.27 cnf(i_0_2118, plain, (c_Predicate_Osymp(X1,X2)|~c_Equiv__Relations_Opart__equivp(X1,X2))). 6.97/7.27 cnf(i_0_809, plain, (c_Predicate_Otransp(X1,X2)|~c_Equiv__Relations_Oequivp(X1,X2))). 6.97/7.27 cnf(i_0_2119, plain, (c_Predicate_Otransp(X1,X2)|~c_Equiv__Relations_Opart__equivp(X1,X2))). 6.97/7.27 cnf(i_0_6667, plain, (c_Equiv__Relations_Opart__equivp(X1,X2)|~c_Equiv__Relations_Oequivp(X1,X2))). 6.97/7.27 cnf(i_0_3430, plain, (c_Orderings_Oord__class_Omin(X1)=c_Lattices_Osemilattice__inf__class_Oinf(X1)|~class_Lattices_Osemilattice__inf(X1)|~class_Orderings_Olinorder(X1))). 6.97/7.27 cnf(i_0_6238, plain, (c_Orderings_Oord__class_Omax(X1)=c_Lattices_Osemilattice__sup__class_Osup(X1)|~class_Lattices_Osemilattice__sup(X1)|~class_Orderings_Olinorder(X1))). 6.97/7.27 cnf(i_0_7089, plain, (~class_Int_Onumber__ring(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)))). 6.97/7.27 cnf(i_0_669, plain, (c_List_Onat__list(X1)|~c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X1)))). 6.97/7.27 cnf(i_0_5723, plain, (X1=c_List_Olist_ONil(X2)|c_List_Oremdups(X2,X1)!=c_List_Olist_ONil(X2))). 6.97/7.27 cnf(i_0_2273, 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))). 6.97/7.27 cnf(i_0_1212, plain, (~c_Partial__Function_Omk__less(X1,X2,X3,X4)|~hBOOL(hAPP(hAPP(X2,X4),X3)))). 6.97/7.27 cnf(i_0_7520, plain, (c_Relation_Oantisym(X1,X2)|esk597_2(X2,X1)!=esk596_2(X2,X1))). 6.97/7.27 cnf(i_0_2049, plain, (X1=X2|~c_List_Olist__all2(X3,X3,c_fequal,X1,X2))). 6.97/7.27 cnf(i_0_19, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|~c_Int_Oiszero(X1,X2)|~class_Rings_Osemiring__1(X1))). 6.97/7.27 cnf(i_0_3119, plain, (c_Int_Oiszero(X1,c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Osemiring__1(X1))). 6.97/7.27 cnf(i_0_5594, plain, (c_List_Olinorder__class_Osorted(X1,c_List_Olist_ONil(X1))|~class_Orderings_Olinorder(X1))). 6.97/7.27 cnf(i_0_5189, plain, (class_Lattices_Olattice(tc_fun(X1,X2))|~class_Lattices_Olattice(X2))). 6.97/7.27 cnf(i_0_6912, plain, (hBOOL(X1)|~hBOOL(hAPP(hAPP(c_fconj,X2),X1)))). 6.97/7.27 cnf(i_0_3127, plain, (hBOOL(X1)|~hBOOL(hAPP(hAPP(c_fconj,X1),X2)))). 6.97/7.27 cnf(i_0_6706, plain, (class_Lattices_Odistrib__lattice(tc_fun(X1,X2))|~class_Lattices_Odistrib__lattice(X2))). 6.97/7.27 cnf(i_0_5570, plain, (class_Orderings_Oorder(tc_fun(X1,X2))|~class_Orderings_Oorder(X2))). 6.97/7.27 cnf(i_0_898, plain, (class_Orderings_Opreorder(tc_fun(X1,X2))|~class_Orderings_Opreorder(X2))). 6.97/7.27 cnf(i_0_6937, plain, (class_Lattices_Osemilattice__sup(tc_fun(X1,X2))|~class_Lattices_Olattice(X2))). 6.97/7.27 cnf(i_0_6191, plain, (class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,X2))|~class_Complete__Lattice_Ocomplete__lattice(X2))). 6.97/7.27 cnf(i_0_2501, plain, (class_Lattices_Osemilattice__inf(tc_fun(X1,X2))|~class_Lattices_Olattice(X2))). 6.97/7.27 cnf(i_0_5990, plain, (class_Lattices_Obounded__lattice__top(tc_fun(X1,X2))|~class_Lattices_Obounded__lattice(X2))). 6.97/7.27 cnf(i_0_5601, plain, (class_Orderings_Oord(tc_fun(X1,X2))|~class_Orderings_Oord(X2))). 6.97/7.27 cnf(i_0_6576, plain, (class_Lattices_Oboolean__algebra(tc_fun(X1,X2))|~class_Lattices_Oboolean__algebra(X2))). 6.97/7.27 cnf(i_0_4869, plain, (class_Orderings_Obot(tc_fun(X1,X2))|~class_Orderings_Obot(X2))). 6.97/7.27 cnf(i_0_630, plain, (class_Lattices_Obounded__lattice(tc_fun(X1,X2))|~class_Lattices_Obounded__lattice(X2))). 6.97/7.27 cnf(i_0_4062, plain, (class_Groups_Ouminus(tc_fun(X1,X2))|~class_Groups_Ouminus(X2))). 6.97/7.27 cnf(i_0_3318, plain, (class_Groups_Ominus(tc_fun(X1,X2))|~class_Groups_Ominus(X2))). 6.97/7.27 cnf(i_0_3587, plain, (class_Lattices_Obounded__lattice__bot(tc_fun(X1,X2))|~class_Lattices_Obounded__lattice(X2))). 6.97/7.27 cnf(i_0_4162, plain, (class_Orderings_Otop(tc_fun(X1,X2))|~class_Orderings_Otop(X2))). 6.97/7.27 cnf(i_0_1032, plain, (c_Relation_Osym(X1,X2)|~c_Equiv__Relations_Oequiv(X1,X3,X2))). 6.97/7.27 cnf(i_0_1031, plain, (c_Relation_Otrans(X1,X2)|~c_Equiv__Relations_Oequiv(X1,X3,X2))). 6.97/7.27 cnf(i_0_5085, 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))). 6.97/7.27 cnf(i_0_1776, plain, (~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)))). 6.97/7.27 cnf(i_0_6482, plain, (c_Wellfounded_Owf(X1,X2)|esk506_2(X2,X1)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 6.97/7.27 cnf(i_0_1334, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_fequal,X2),X1)))). 6.97/7.27 cnf(i_0_3801, plain, (X1=X2|hAPP(c_Int_ORep__Integ,X1)!=hAPP(c_Int_ORep__Integ,X2))). 6.97/7.27 cnf(i_0_4550, plain, (X1=X2|hAPP(c_Nat_OSuc,X1)!=hAPP(c_Nat_OSuc,X2))). 6.97/7.27 cnf(i_0_1811, plain, (X1=X2|hAPP(c_Code__Numeral_Onat__of,X1)!=hAPP(c_Code__Numeral_Onat__of,X2))). 6.97/7.27 cnf(i_0_6431, plain, (X1=X2|~c_Fun_Obij__betw(X3,X3,c_Fun_Oid(X3),X1,X2))). 6.97/7.27 cnf(i_0_1030, plain, (c_Relation_Orefl__on(X1,X2,X3)|~c_Equiv__Relations_Oequiv(X1,X2,X3))). 6.97/7.27 cnf(i_0_822, plain, (hBOOL(hAPP(c_fNot,X1))|hBOOL(X1))). 6.97/7.27 cnf(i_0_4902, plain, (c_Nitpick_Owf_H(X1,X2)|~c_Nitpick_Ounknown(tc_HOL_Obool)|~c_Wellfounded_Oacyclic(X1,X2))). 6.97/7.27 cnf(i_0_2682, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 6.97/7.27 cnf(i_0_4536, plain, (X1=c_List_Olist_ONil(X2)|hAPP(c_List_Orev(X2),X1)!=c_List_Olist_ONil(X2))). 6.97/7.27 cnf(i_0_1906, plain, (c_List_Olist_ONil(X1)=X2|hAPP(c_List_Orotate1(X1),X2)!=c_List_Olist_ONil(X1))). 6.97/7.27 cnf(i_0_4564, 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)))). 6.97/7.27 cnf(i_0_982, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Groups_Osgn__class_Osgn(X1,X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__idom(X1))). 6.97/7.27 cnf(i_0_3078, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_List_Oreplicate(X2,X1,X3)!=c_List_Olist_ONil(X2))). 6.97/7.27 cnf(i_0_7034, 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))). 6.97/7.27 cnf(i_0_3731, 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))). 6.97/7.27 cnf(i_0_3753, plain, (c_Equiv__Relations_Oequivp(X1,X2)|~c_Predicate_Otransp(X1,X2)|~c_Predicate_Osymp(X1,X2)|~c_Predicate_Oreflp(X1,X2))). 6.97/7.27 cnf(i_0_5637, plain, (hBOOL(X1)|~hBOOL(hAPP(hAPP(c_fimplies,X2),X1))|~hBOOL(X2))). 6.97/7.27 cnf(i_0_1511, 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))). 6.97/7.27 cnf(i_0_1108, plain, (c_Relation_Osym(X1,X2)|~c_Relation_Osym(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)))). 6.97/7.27 cnf(i_0_1708, plain, (c_Relation_Otrans(X1,X2)|~c_Relation_Otrans(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)))). 6.97/7.27 cnf(i_0_2655, plain, (c_Relation_Oantisym(X1,X2)|~c_Relation_Oantisym(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)))). 6.97/7.27 cnf(i_0_3073, plain, (c_Wellfounded_Oacyclic(X1,X2)|~c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)))). 6.97/7.27 cnf(i_0_5581, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|esk425_1(X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 6.97/7.27 cnf(i_0_6354, 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)))). 6.97/7.27 cnf(i_0_1329, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),X5)!=c_List_Olist_ONil(X1)|~class_Orderings_Olinorder(X2))). 6.97/7.27 cnf(i_0_6765, plain, (class_Enum_Oenum(tc_fun(X1,X2))|~class_Enum_Oenum(X2)|~class_Enum_Oenum(X1))). 6.97/7.27 cnf(i_0_6780, plain, (class_Enum_Oenum(tc_prod(X1,X2))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2))). 6.97/7.27 cnf(i_0_5246, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 6.97/7.27 cnf(i_0_3684, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|c_List_Oremdups(X1,X2)!=X2)). 6.97/7.27 cnf(i_0_7314, plain, (class_Enum_Oenum(tc_sum(X1,X2))|~class_Enum_Oenum(X2)|~class_Enum_Oenum(X1))). 6.97/7.27 cnf(i_0_493, plain, (class_Finite__Set_Ofinite(tc_fun(X1,X2))|~class_Finite__Set_Ofinite(X2)|~class_Finite__Set_Ofinite(X1))). 6.97/7.27 cnf(i_0_6255, plain, (class_Finite__Set_Ofinite(tc_prod(X1,X2))|~class_Finite__Set_Ofinite(X1)|~class_Finite__Set_Ofinite(X2))). 6.97/7.27 cnf(i_0_3773, plain, (class_Finite__Set_Ofinite(tc_sum(X1,X2))|~class_Finite__Set_Ofinite(X1)|~class_Finite__Set_Ofinite(X2))). 6.97/7.27 cnf(i_0_3065, plain, (c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X1,X2))|~c_Nat__Transfer_Ois__nat(X2)|~c_Nat__Transfer_Ois__nat(X1))). 6.97/7.27 cnf(i_0_6385, plain, (class_Lazy__Sequence_Osmall__lazy(tc_prod(X1,X2))|~class_Lazy__Sequence_Osmall__lazy(X2)|~class_Lazy__Sequence_Osmall__lazy(X1))). 6.97/7.27 cnf(i_0_3685, plain, (c_List_Oremdups(X1,X2)=X2|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 6.97/7.27 cnf(i_0_670, plain, (c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X1))|~c_List_Onat__list(X1))). 6.97/7.27 cnf(i_0_1206, plain, (~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)))). 6.97/7.27 cnf(i_0_1069, plain, (c_Finite__Set_Ofun__left__comm(X1,X1,c_Groups_Otimes__class_Otimes(X1))|~class_Groups_Oab__semigroup__mult(X1))). 6.97/7.27 cnf(i_0_2919, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1))|~class_Lattices_Osemilattice__sup(X1))). 6.97/7.27 cnf(i_0_780, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Groups_Otimes__class_Otimes(X1))|~class_Lattices_Oab__semigroup__idem__mult(X1))). 6.97/7.27 cnf(i_0_5371, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1))|~class_Lattices_Osemilattice__inf(X1))). 6.97/7.27 cnf(i_0_5029, plain, (c_Orderings_Oord_Omax(X1,c_Orderings_Oord__class_Oless__eq(X1))=c_Orderings_Oord__class_Omax(X1)|~class_Orderings_Oord(X1))). 6.97/7.27 cnf(i_0_1710, plain, (~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)))). 6.97/7.27 cnf(i_0_5019, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Orderings_Oord__class_Omin(X1))|~class_Orderings_Olinorder(X1))). 6.97/7.27 cnf(i_0_2360, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Orderings_Oord__class_Omax(X1))|~class_Orderings_Olinorder(X1))). 6.97/7.27 cnf(i_0_3555, plain, (c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2))|~c_Nat__Transfer_Ois__nat(X1))). 6.97/7.27 cnf(i_0_6507, plain, (c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Osgn__if(X1))). 6.97/7.27 cnf(i_0_5196, plain, (c_List_Otranspose(X1,X2)=c_List_Olist_ONil(tc_List_Olist(X1))|esk402_2(X2,X1)!=c_List_Olist_ONil(X1))). 6.97/7.27 cnf(i_0_3059, plain, (c_Orderings_Oord_Omin(X1,c_Orderings_Oord__class_Oless__eq(X1))=c_Orderings_Oord__class_Omin(X1)|~class_Orderings_Oord(X1))). 6.97/7.27 cnf(i_0_4277, plain, (c_List_Olist_ONil(X1)=X2|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 6.97/7.27 cnf(i_0_5039, plain, (c_Relation_Osym(X1,c_Transitive__Closure_Ortrancl(X1,X2))|~c_Relation_Osym(X1,X2))). 6.97/7.27 cnf(i_0_2023, plain, (X1=X2|c_List_Oreplicate(X3,X1,X4)!=c_List_Oreplicate(X3,X2,X5))). 6.97/7.27 cnf(i_0_1598, plain, (X1=X2|c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X4,X1)!=c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X5,X2))). 6.97/7.27 cnf(i_0_1597, plain, (X1=X2|c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X1,X4)!=c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X2,X5))). 6.97/7.27 cnf(i_0_3867, plain, (c_Relation_Oantisym(X1,c_Transitive__Closure_Ortrancl(X1,X2))|~c_Wellfounded_Oacyclic(X1,X2))). 6.97/7.27 cnf(i_0_3814, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Finite__Set_Ofinite(X1))). 6.97/7.27 cnf(i_0_4825, plain, (c_List_Oall__interval__int(X1,X2,X3)|~c_List_Olist__all(tc_Int_Oint,X1,c_List_Oupto(X2,X3)))). 6.97/7.27 cnf(i_0_6655, plain, (c_Relation_Osingle__valued(X1,X2,X3)|esk521_3(X3,X2,X1)!=esk520_3(X3,X2,X1))). 6.97/7.27 cnf(i_0_5590, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)!=X2)). 6.97/7.27 cnf(i_0_6532, plain, (X1=c_List_Olist_ONil(X2)|hAPP(c_List_Oset(X2),X1)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 6.97/7.27 cnf(i_0_1523, plain, (X1=c_List_Olist_ONil(X2)|hAPP(hAPP(c_List_Oappend(X2),X1),X3)!=X3)). 6.97/7.27 cnf(i_0_1149, plain, (c_Relation_Ototal__on(X1,X2,X3)|esk92_3(X3,X2,X1)!=esk91_3(X3,X2,X1))). 6.97/7.27 cnf(i_0_985, plain, (c_List_Olist_ONil(X1)=X2|~c_List_Olist__all2(X1,X3,X4,X2,c_List_Olist_ONil(X3)))). 6.97/7.27 cnf(i_0_4251, plain, (c_List_Olist_ONil(X1)=X2|hAPP(hAPP(c_List_Oappend(X1),X3),X2)!=X3)). 6.97/7.27 cnf(i_0_2652, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)!=X2|~class_Groups_Olinordered__ab__group__add(X1))). 6.97/7.27 cnf(i_0_577, plain, (c_List_Olist_ONil(X1)=X2|~c_List_Olist__all2(X3,X1,X4,c_List_Olist_ONil(X3),X2))). 6.97/7.27 cnf(i_0_5869, plain, (c_Orderings_Oorder__class_Omono(X1,X2,X3)|~c_Orderings_Oorder__class_Ostrict__mono(X1,X2,X3)|~class_Orderings_Oorder(X1)|~class_Orderings_Oorder(X2))). 6.97/7.27 cnf(i_0_981, plain, (c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__idom(X1))). 6.97/7.27 cnf(i_0_996, plain, (c_Fun_Oinj__on(X1,X2,X3,X4)|~c_Fun_Obij__betw(X1,X2,X3,X4,X5))). 6.97/7.27 cnf(i_0_850, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~c_Wellfounded_Omax__extp(X1,X3,X4,X2))). 6.97/7.27 cnf(i_0_3954, 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))). 6.97/7.27 cnf(i_0_6637, 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))). 6.97/7.27 cnf(i_0_854, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~c_Wellfounded_Omax__extp(X1,X3,X2,X4))). 6.97/7.27 cnf(i_0_4408, plain, (c_Relation_Osym(X1,X2)|hAPP(c_Relation_Oconverse(X1,X1),X2)!=X2)). 6.97/7.27 cnf(i_0_6189, plain, (X1=X2|hAPP(c_List_Orev(X3),X1)!=hAPP(c_List_Orev(X3),X2))). 6.97/7.27 cnf(i_0_2421, plain, (c_Divides_Odiv__class_Omod(X1,X2,X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 6.97/7.27 cnf(i_0_6278, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|esk491_2(X2,X1)!=esk492_2(X2,X1))). 6.97/7.27 cnf(i_0_6942, plain, (c_List_Olist__ex(X1,X2,X3)|~c_List_Olist__ex(X1,X2,hAPP(c_List_Orev(X1),X3)))). 6.97/7.27 cnf(i_0_150, plain, (c_List_Olist__all(X1,X2,X3)|~c_List_Olist__all(X1,X2,hAPP(c_List_Orev(X1),X3)))). 6.97/7.27 cnf(i_0_6729, 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))))). 6.97/7.27 cnf(i_0_2451, 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))))). 6.97/7.27 cnf(i_0_4563, 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))). 6.97/7.27 cnf(i_0_2867, plain, (hBOOL(X1)|hBOOL(X2)|~hBOOL(hAPP(hAPP(c_fdisj,X1),X2)))). 6.97/7.27 cnf(i_0_3013, plain, (c_Quickcheck_Obeyond(X1,X2)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2)))). 6.97/7.27 cnf(i_0_4412, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 6.97/7.27 cnf(i_0_4603, plain, (c_List_Oall__interval__int(X1,X2,X3)|~hBOOL(hAPP(X1,esk352_3(X3,X2,X1))))). 6.97/7.27 cnf(i_0_5549, plain, (c_List_Olist__all(X1,X2,X3)|~hBOOL(hAPP(X2,esk423_3(X3,X2,X1))))). 6.97/7.27 cnf(i_0_5935, plain, (c_List_Olist__all(X1,X2,X3)|~hBOOL(hAPP(X2,esk461_3(X3,X2,X1))))). 6.97/7.27 cnf(i_0_6566, plain, (c_List_Olist__all(X1,X2,X3)|~hBOOL(hAPP(X2,esk513_3(X2,X3,X1))))). 6.97/7.27 cnf(i_0_4413, 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))). 6.97/7.27 cnf(i_0_6318, plain, (X1=c_List_Olist_ONil(X2)|hAPP(hAPP(c_List_Oappend(X2),X3),X1)!=c_List_Olist_ONil(X2))). 6.97/7.27 cnf(i_0_6858, plain, (X1=c_List_Olist_ONil(X2)|hAPP(hAPP(c_List_Oappend(X2),X1),X3)!=c_List_Olist_ONil(X2))). 6.97/7.27 cnf(i_0_2651, 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))). 6.97/7.27 cnf(i_0_3146, plain, (c_List_Oall__interval__nat(X1,X2,X3)|~hBOOL(hAPP(X1,esk239_3(X3,X2,X1))))). 6.97/7.27 cnf(i_0_5251, plain, (c_Wellfounded_OwfP(X1,X2)|~hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk407_2(X2,X1))))). 6.97/7.27 cnf(i_0_7408, plain, (X1=hAPP(X2,X3)|c_Fun_Ofun__upd(X4,X5,X2,X3,X1)!=X2)). 6.97/7.27 cnf(i_0_773, 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))). 6.97/7.27 cnf(i_0_4118, 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))). 6.97/7.27 cnf(i_0_2443, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1))). 6.97/7.27 cnf(i_0_3256, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(c_Groups_Oabs__class_Oabs(X1),X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Oordered__ab__group__add__abs(X1))). 6.97/7.27 cnf(i_0_5786, plain, (X1=X2|c_Nitpick_Opair__box_OPairBox(X3,X4,X5,X2)!=c_Nitpick_Opair__box_OPairBox(X3,X4,X6,X1))). 6.97/7.27 cnf(i_0_5785, plain, (X1=X2|c_Nitpick_Opair__box_OPairBox(X3,X4,X1,X5)!=c_Nitpick_Opair__box_OPairBox(X3,X4,X2,X6))). 6.97/7.27 cnf(i_0_505, plain, (c_Relation_Orefl__on(X1,X2,X3)|~c_Relation_Orefl__on(X1,X2,hAPP(c_Relation_Oconverse(X1,X1),X3)))). 6.97/7.27 cnf(i_0_5905, plain, (c_Relation_Ototal__on(X1,X2,X3)|~c_Relation_Ototal__on(X1,X2,hAPP(c_Relation_Oconverse(X1,X1),X3)))). 6.97/7.27 cnf(i_0_1211, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~c_Partial__Function_Omk__less(X4,X1,X2,X3))). 6.97/7.27 cnf(i_0_586, 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))). 6.97/7.27 cnf(i_0_4997, plain, (hBOOL(hAPP(hAPP(c_fdisj,X1),X2))|~hBOOL(X2))). 6.97/7.27 cnf(i_0_571, plain, (hBOOL(hAPP(hAPP(c_fdisj,X1),X2))|~hBOOL(X1))). 6.97/7.27 cnf(i_0_5011, plain, (hBOOL(hAPP(hAPP(c_fimplies,X1),X2))|~hBOOL(X2))). 6.97/7.27 cnf(i_0_4117, 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))). 6.97/7.27 cnf(i_0_7098, 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))). 6.97/7.27 cnf(i_0_1331, plain, (X1=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),X1),X2)!=c_Groups_Ozero__class_Ozero(X3)|~class_Groups_Ogroup__add(X3))). 6.97/7.27 cnf(i_0_45, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),X1)))). 6.97/7.27 cnf(i_0_1713, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_fequal,X2))))). 6.97/7.27 cnf(i_0_3948, plain, (c_Divides_Odiv__class_Omod(X1,X2,c_Groups_Ozero__class_Ozero(X1))=X2|~class_Divides_Osemiring__div(X1))). 6.97/7.27 cnf(i_0_1223, 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)))). 6.97/7.27 cnf(i_0_2513, plain, (c_List_Olinorder__class_Osorted(X1,c_List_Oremdups(X1,X2))|~c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1))). 6.97/7.27 cnf(i_0_4644, plain, (X1=X2|hAPP(c_SetInterval_Oord__class_OatMost(X3),X1)!=hAPP(c_SetInterval_Oord__class_OatMost(X3),X2)|~class_Orderings_Olinorder(X3))). 6.97/7.27 cnf(i_0_6730, plain, (X1=X2|hAPP(c_SetInterval_Oord__class_OatLeast(X3),X1)!=hAPP(c_SetInterval_Oord__class_OatLeast(X3),X2)|~class_Orderings_Olinorder(X3))). 6.97/7.27 cnf(i_0_7260, 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))). 6.97/7.27 cnf(i_0_5380, plain, (X1=X2|hAPP(c_SetInterval_Oord__class_OlessThan(X3),X1)!=hAPP(c_SetInterval_Oord__class_OlessThan(X3),X2)|~class_Orderings_Olinorder(X3))). 6.97/7.27 cnf(i_0_2284, plain, (X1=X2|hAPP(c_SetInterval_Oord__class_OgreaterThan(X3),X1)!=hAPP(c_SetInterval_Oord__class_OgreaterThan(X3),X2)|~class_Orderings_Olinorder(X3))). 6.97/7.27 cnf(i_0_6499, plain, (X1=c_List_Olist_ONil(X2)|hAPP(hAPP(c_List_Omap(X2,X3),X4),X1)!=c_List_Olist_ONil(X3))). 6.97/7.27 cnf(i_0_2589, 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))). 6.97/7.27 cnf(i_0_2668, plain, (c_List_Olist_ONil(X1)=X2|hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4)!=c_List_Olist_ONil(X1))). 6.97/7.27 cnf(i_0_5214, plain, (c_List_OtakeWhile(X1,X2,X3)=X3|~hBOOL(hAPP(X2,esk405_3(X3,X2,X1))))). 6.97/7.27 cnf(i_0_4841, 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))). 6.97/7.27 cnf(i_0_5807, 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))). 6.97/7.27 cnf(i_0_381, plain, (X1=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)!=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 6.97/7.27 cnf(i_0_1833, 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))). 6.97/7.27 cnf(i_0_1023, 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))))). 6.97/7.27 cnf(i_0_5234, 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))). 6.97/7.27 cnf(i_0_6058, 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))). 6.97/7.27 cnf(i_0_1649, plain, (c_Wellfounded_Owf(X1,c_Wellfounded_Omlex__prod(X1,X2,X3))|~c_Wellfounded_Owf(X1,X3))). 6.97/7.27 cnf(i_0_4723, plain, (c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X2))|~c_Wellfounded_Owf(X1,X2))). 6.97/7.27 cnf(i_0_1029, plain, (c_Equiv__Relations_Oequiv(X1,X2,X3)|~c_Relation_Otrans(X1,X3)|~c_Relation_Osym(X1,X3)|~c_Relation_Orefl__on(X1,X2,X3))). 6.97/7.27 cnf(i_0_70, 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)),esk6_1(X1))))). 6.97/7.27 cnf(i_0_6636, plain, (c_Wellfounded_Owf(tc_List_Olist(X1),c_List_Olex(X1,X2))|~c_Wellfounded_Owf(X1,X2))). 6.97/7.27 cnf(i_0_3871, plain, (c_Wellfounded_Owf(tc_List_Olist(X1),c_List_Olenlex(X1,X2))|~c_Wellfounded_Owf(X1,X2))). 6.97/7.27 cnf(i_0_2167, plain, (c_Relation_Osym(tc_List_Olist(X1),c_List_Olistrel(X1,X2))|~c_Relation_Osym(X1,X2))). 6.97/7.27 cnf(i_0_454, 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))). 6.97/7.27 cnf(i_0_1658, 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))). 6.97/7.27 cnf(i_0_694, 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))). 6.97/7.27 cnf(i_0_692, 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))). 6.97/7.27 cnf(i_0_253, plain, (c_Relation_Otrans(tc_List_Olist(X1),c_List_Olexord(X1,X2))|~c_Relation_Otrans(X1,X2))). 6.97/7.27 cnf(i_0_4657, plain, (c_Relation_Otrans(tc_List_Olist(X1),c_List_Olistrel(X1,X2))|~c_Relation_Otrans(X1,X2))). 6.97/7.27 cnf(i_0_2780, plain, (hBOOL(hAPP(hAPP(c_fimplies,X1),X2))|hBOOL(X1))). 6.97/7.27 cnf(i_0_1933, plain, (c_Fun_Oinj__on(X1,X1,c_Groups_Ouminus__class_Ouminus(X1),X2)|~class_Groups_Oordered__ab__group__add(X1))). 6.97/7.27 cnf(i_0_1695, plain, (c_Fun_Oinj__on(X1,X2,X3,X4)|esk143_4(X4,X3,X2,X1)!=esk144_4(X4,X3,X2,X1))). 6.97/7.27 cnf(i_0_3293, plain, (X1=X2|hAPP(X1,esk253_2(X2,X1))!=hAPP(X2,esk253_2(X2,X1)))). 6.97/7.27 cnf(i_0_2820, 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)))). 6.97/7.27 cnf(i_0_2900, 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)))). 6.97/7.27 cnf(i_0_6578, 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)))). 6.97/7.27 cnf(i_0_5403, plain, (~class_Orderings_Owellorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Orderings_Oord__class_OLeast(X1,X3)))|~hBOOL(hAPP(X3,X2)))). 6.97/7.27 cnf(i_0_3654, 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))). 6.97/7.27 cnf(i_0_475, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X2)=X2|~class_Orderings_Olinorder(X1))). 6.97/7.27 cnf(i_0_661, plain, (c_Wellfounded_Owf(X1,X2)|~c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2)))). 6.97/7.27 cnf(i_0_6020, plain, (X1=X2|hAPP(c_Groups_Ouminus__class_Ouminus(X3),X1)!=hAPP(c_Groups_Ouminus__class_Ouminus(X3),X2)|~class_Lattices_Oboolean__algebra(X3))). 6.97/7.27 cnf(i_0_2597, plain, (X1=X2|hAPP(c_Groups_Ouminus__class_Ouminus(X3),X1)!=hAPP(c_Groups_Ouminus__class_Ouminus(X3),X2)|~class_Groups_Ogroup__add(X3))). 6.97/7.27 cnf(i_0_4948, 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))). 6.97/7.27 cnf(i_0_668, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X2)=X2|~class_Orderings_Olinorder(X1))). 6.97/7.27 cnf(i_0_6553, 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))). 6.97/7.27 cnf(i_0_5603, 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))))). 6.97/7.27 cnf(i_0_5971, 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))). 6.97/7.27 cnf(i_0_6368, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2)!=X3|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1))). 6.97/7.27 cnf(i_0_2487, plain, (c_Nat__Transfer_Ois__nat(X1)|~c_Nat__Transfer_Onat__set(X2)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X2)))). 6.97/7.27 cnf(i_0_867, plain, (c_List_Olist__all(X1,X2,X3)|~c_List_Olist__all(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3)))). 6.97/7.27 cnf(i_0_1140, plain, (c_List_Olist__all(X1,X2,X3)|~c_List_Olist__all(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X4),X3)))). 6.97/7.27 cnf(i_0_1139, plain, (c_List_Olist__all(X1,X2,X3)|~c_List_Olist__all(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4)))). 6.97/7.27 cnf(i_0_5596, 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))))). 6.97/7.27 cnf(i_0_5395, 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))))). 6.97/7.27 cnf(i_0_2009, plain, (c_Wellfounded_Owf(X1,X2)|~c_Wellfounded_Oacyclic(X1,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2)))). 6.97/7.27 cnf(i_0_6252, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),esk488_2(X2,X1)))))). 6.97/7.27 cnf(i_0_7442, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(c_Int_OAbs__Integ,esk591_2(X2,X1)))))). 6.97/7.27 cnf(i_0_1927, 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)))). 6.97/7.27 cnf(i_0_6401, plain, (c_Nitpick_Ocard_H(X1,X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 6.97/7.27 cnf(i_0_4409, plain, (hAPP(c_Relation_Oconverse(X1,X1),X2)=X2|~c_Relation_Osym(X1,X2))). 6.97/7.27 cnf(i_0_6016, 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))). 6.97/7.27 cnf(i_0_4404, 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))). 6.97/7.27 cnf(i_0_3839, 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)))). 6.97/7.27 cnf(i_0_3456, 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)))). 6.97/7.27 cnf(i_0_6440, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3)!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Oring__1__no__zero__divisors(X2))). 6.97/7.27 cnf(i_0_2093, 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))). 6.97/7.27 cnf(i_0_4826, plain, (c_List_Olist__all(tc_Int_Oint,X1,c_List_Oupto(X2,X3))|~c_List_Oall__interval__int(X1,X2,X3))). 6.97/7.27 cnf(i_0_1719, plain, (hBOOL(hAPP(hAPP(c_fconj,X1),X2))|~hBOOL(X2)|~hBOOL(X1))). 6.97/7.27 cnf(i_0_4911, 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))). 6.97/7.27 cnf(i_0_6764, 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))). 6.97/7.27 cnf(i_0_2094, 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))). 6.97/7.27 cnf(i_0_868, plain, (hBOOL(hAPP(X1,X2))|~c_List_Olist__all(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)))). 6.97/7.27 cnf(i_0_1636, 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))))). 6.97/7.27 cnf(i_0_2901, 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))))). 6.97/7.27 cnf(i_0_666, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X2))|~class_Enum_Oenum(X1)|~hBOOL(hAPP(X2,esk54_2(X2,X1))))). 6.97/7.27 cnf(i_0_6861, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X2))|~class_Enum_Oenum(X1)|~hBOOL(hAPP(X2,esk538_2(X2,X1))))). 6.97/7.27 cnf(i_0_2858, plain, (X1=X2|hAPP(X3,X1)!=hAPP(X3,X2)|~c_Typedef_Otype__definition(X4,X5,X3,X6,X7))). 6.97/7.27 cnf(i_0_3326, plain, (c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2))|~c_Nat__Transfer_Ois__nat(X1))). 6.97/7.27 cnf(i_0_5003, 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)))). 6.97/7.27 cnf(i_0_5979, plain, (c_List_Olinorder__class_Osorted(X1,esk469_2(X2,X1))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 6.97/7.27 cnf(i_0_50, plain, (c_List_Olinorder__class_Osorted(X1,c_List_OtakeWhile(X1,X2,X3))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 6.97/7.27 cnf(i_0_1894, plain, (c_List_Olinorder__class_Osorted(X1,c_List_Oremove1(X1,X2,X3))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 6.97/7.27 cnf(i_0_3221, plain, (c_Equiv__Relations_Opart__equivp(X1,X2)|~c_Predicate_Otransp(X1,X2)|~c_Predicate_Osymp(X1,X2)|~hBOOL(hAPP(hAPP(X2,X3),X3)))). 6.97/7.27 cnf(i_0_336, 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)))). 6.97/7.27 cnf(i_0_4701, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X2)=X2|~class_Lattices_Osemilattice__sup(X1))). 6.97/7.27 cnf(i_0_4009, 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))). 6.97/7.27 cnf(i_0_665, plain, (hBOOL(hAPP(X1,X2))|~class_Enum_Oenum(X3)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X3),X1)))). 6.97/7.27 cnf(i_0_7347, plain, (hAPP(c_List_Ofilter(X1,X2),X3)=X3|~hBOOL(hAPP(X2,esk578_3(X3,X2,X1))))). 6.97/7.27 cnf(i_0_995, plain, (hAPP(c_Set_Oimage(X1,X2,X3),X4)=X5|~c_Fun_Obij__betw(X1,X2,X3,X4,X5))). 6.97/7.27 cnf(i_0_4660, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)=X2|~class_Lattices_Oab__semigroup__idem__mult(X1))). 6.97/7.27 cnf(i_0_249, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X2)=X2|~class_Lattices_Osemilattice__inf(X1))). 6.97/7.27 cnf(i_0_6244, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X2)=X2|~class_Lattices_Olattice(X1))). 6.97/7.27 cnf(i_0_4903, plain, (c_Nitpick_Owf_H(X1,X2)|~c_Wellfounded_Oacyclic(X1,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2)))). 6.97/7.27 cnf(i_0_1297, plain, (hBOOL(hAPP(hAPP(X1,X2),X2))|~c_Equiv__Relations_Oequivp(X3,X1))). 6.97/7.27 cnf(i_0_5996, plain, (hBOOL(hAPP(hAPP(X1,X2),X2))|~c_Predicate_Oreflp(X3,X1))). 6.97/7.27 cnf(i_0_6613, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X2)=X2|~class_Lattices_Olattice(X1))). 6.97/7.27 cnf(i_0_7534, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X1)=c_Groups_Oone__class_Oone(tc_Int_Oint)|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 6.97/7.27 cnf(i_0_3511, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))|~c_Wellfounded_OwfP(X1,X2))). 6.97/7.27 cnf(i_0_3432, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(X2,esk259_3(X3,X2,X1))))). 6.97/7.27 cnf(i_0_1632, plain, (hBOOL(hAPP(c_Predicate_OPowp(X1,X2),X3))|~hBOOL(hAPP(X2,esk134_3(X3,X2,X1))))). 6.97/7.27 cnf(i_0_89, plain, (~c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),X1),X2,X3)|~c_List_Olist__ex(tc_Int_Oint,X1,c_List_Oupto(X2,X3)))). 6.97/7.27 cnf(i_0_771, 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))). 6.97/7.27 cnf(i_0_3907, plain, (c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_member(X1),esk294_2(X2,X1)),c_Wellfounded_Oacc(X1,X2))))). 6.97/7.27 cnf(i_0_672, plain, (c_Wellfounded_Owf(X1,X2)|~c_Wellfounded_Owf(X1,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2)))). 6.97/7.27 cnf(i_0_5356, 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)))). 6.97/7.27 cnf(i_0_1447, plain, (c_Fun_Oinj__on(X1,X2,X3,X4)|~c_Orderings_Oorder__class_Ostrict__mono(X1,X2,X3)|~class_Orderings_Oorder(X2)|~class_Orderings_Olinorder(X1))). 6.97/7.27 cnf(i_0_1482, 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)))). 6.97/7.27 cnf(i_0_4692, 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)))))). 6.97/7.27 cnf(i_0_5604, 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)))). 6.97/7.27 cnf(i_0_5429, 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))). 6.97/7.27 cnf(i_0_5428, plain, (c_Orderings_Otop__class_Otop(X1)=X2|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)!=c_Orderings_Otop__class_Otop(X1)|~class_Lattices_Obounded__lattice__top(X1))). 6.97/7.27 cnf(i_0_911, plain, (c_Lazy__Sequence_Oempty(tc_Int_Oint)=c_Lazy__Sequence_Osmall__lazy_H(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 6.97/7.27 cnf(i_0_5863, 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))). 6.97/7.27 cnf(i_0_4252, 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))). 6.97/7.27 cnf(i_0_6668, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Otl(X1),X2))|~c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1))). 6.97/7.27 cnf(i_0_6989, plain, (hAPP(hAPP(X1,X2),X2)=X2|~c_Finite__Set_Ofolding__one__idem(X3,X1,X4))). 6.97/7.27 cnf(i_0_3987, 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)))). 6.97/7.27 cnf(i_0_4022, 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))). 6.97/7.27 cnf(i_0_7140, 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))). 6.97/7.27 cnf(i_0_970, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orev(X1),X2))))). 6.97/7.27 cnf(i_0_6642, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orotate1(X1),X2))))). 6.97/7.27 cnf(i_0_291, 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))). 6.97/7.27 cnf(i_0_7460, 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))). 6.97/7.27 cnf(i_0_192, 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))). 6.97/7.27 cnf(i_0_6123, plain, (hAPP(c_Nat_OSuc,esk483_1(X1))=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 6.97/7.27 cnf(i_0_7039, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X3,X4,X5,X2),X6)))). 6.97/7.27 cnf(i_0_4522, plain, (X1=X2|hAPP(X3,X1)!=hAPP(X3,X2)|~c_Orderings_Oorder__class_Ostrict__mono(X4,X5,X3)|~class_Orderings_Oorder(X5)|~class_Orderings_Olinorder(X4))). 6.97/7.27 cnf(i_0_7148, 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)))). 6.97/7.27 cnf(i_0_4601, plain, (c_List_Olinorder__class_Osort__key(X1,X2,X3,c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1)|~class_Orderings_Olinorder(X2))). 6.97/7.27 cnf(i_0_1109, plain, (c_Relation_Osym(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))|~c_Relation_Osym(X1,X2))). 6.97/7.27 cnf(i_0_1707, plain, (c_Relation_Otrans(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))|~c_Relation_Otrans(X1,X2))). 6.97/7.27 cnf(i_0_2654, plain, (c_Relation_Oantisym(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))|~c_Relation_Oantisym(X1,X2))). 6.97/7.27 cnf(i_0_2347, 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))). 6.97/7.27 cnf(i_0_3103, 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))))). 6.97/7.27 cnf(i_0_3072, plain, (c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))|~c_Wellfounded_Oacyclic(X1,X2))). 6.97/7.27 cnf(i_0_5555, plain, (c_Fun_Oinj__on(X1,X2,X3,X4)|~c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)))). 6.97/7.27 cnf(i_0_399, plain, (X1=X2|hAPP(hAPP(c_List_Oappend(X3),X4),X1)!=hAPP(hAPP(c_List_Oappend(X3),X4),X2))). 6.97/7.27 cnf(i_0_294, plain, (X1=X2|hAPP(hAPP(c_List_Oappend(X3),X1),X4)!=hAPP(hAPP(c_List_Oappend(X3),X2),X4))). 6.97/7.27 cnf(i_0_5537, plain, (X1=X2|hAPP(hAPP(c_List_Olist_OCons(X3),X4),X1)!=hAPP(hAPP(c_List_Olist_OCons(X3),X5),X2))). 6.97/7.27 cnf(i_0_7277, plain, (c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omax__ext(X1,X2))|~c_Wellfounded_Owf(X1,X2))). 6.97/7.27 cnf(i_0_4134, plain, (c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omin__ext(X1,X2))|~c_Wellfounded_Owf(X1,X2))). 6.97/7.27 cnf(i_0_5505, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2))|~class_Orderings_Opreorder(X1))). 6.97/7.27 cnf(i_0_3413, plain, (c_Inductive_Ocomplete__lattice__class_Olfp(X1,hAPP(c_COMBK(X1,X1),X2))=X2|~class_Complete__Lattice_Ocomplete__lattice(X1))). 6.97/7.27 cnf(i_0_5538, plain, (X1=X2|hAPP(hAPP(c_List_Olist_OCons(X3),X1),X4)!=hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5))). 6.97/7.27 cnf(i_0_4712, plain, (c_FunDef_OTHE__default(X1,X2,X3)=c_HOL_OThe(X1,X3)|esk365_4(X2,X1,X3,X4)!=X4|~hBOOL(hAPP(X3,X4)))). 6.97/7.27 cnf(i_0_232, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),esk18_1(X1)))))). 6.97/7.27 cnf(i_0_1784, plain, (c_List_Oall__interval__nat(X1,X2,X3)|~c_List_Olist__all(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))))). 6.97/7.27 cnf(i_0_1310, plain, (c_List_Olast(X1,c_List_Oreplicate(X1,X2,X3))=X3|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 6.97/7.27 cnf(i_0_137, 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)))). 6.97/7.27 cnf(i_0_2209, 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)))). 6.97/7.27 cnf(i_0_1842, 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))))). 6.97/7.27 cnf(i_0_2403, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~c_Fun_Obij__betw(X1,X3,X4,X2,X5)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X5)))). 6.97/7.27 cnf(i_0_2402, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~c_Fun_Obij__betw(X3,X1,X4,X5,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X5)))). 6.97/7.27 cnf(i_0_2022, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X2=X3|c_List_Oreplicate(X4,X1,X2)!=c_List_Oreplicate(X4,X5,X3))). 6.97/7.27 cnf(i_0_3084, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X2))|~class_Enum_Oenum(X1)|~hBOOL(hAPP(X2,X3)))). 6.97/7.27 cnf(i_0_976, plain, (hAPP(c_Finite__Set_Ocard(X1),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 6.97/7.27 cnf(i_0_7216, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1))). 6.97/7.27 cnf(i_0_3387, plain, (hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,X2)),X3)=c_Orderings_Otop__class_Otop(X2)|~class_Orderings_Otop(X2))). 6.97/7.27 cnf(i_0_501, plain, (hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,X2)),X3)=c_Orderings_Obot__class_Obot(X2)|~class_Orderings_Obot(X2))). 6.97/7.27 cnf(i_0_3588, 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)))))). 6.97/7.27 cnf(i_0_5733, 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))). 6.97/7.27 cnf(i_0_2387, 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))). 6.97/7.27 cnf(i_0_3549, 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))))). 6.97/7.27 cnf(i_0_1803, 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))). 6.97/7.27 cnf(i_0_6257, plain, (hBOOL(hAPP(X1,esk489_2(X2,X1)))|~hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X2,X1))))). 6.97/7.27 cnf(i_0_1326, plain, (hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X2,X1)))|~hBOOL(hAPP(X1,X3)))). 6.97/7.27 cnf(i_0_4746, 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))|X1=X2)). 6.97/7.27 cnf(i_0_7392, plain, (hBOOL(hAPP(X1,esk587_2(X1,X2)))|~hBOOL(hAPP(X1,X3)))). 6.97/7.27 cnf(i_0_46, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(X3,X2)))). 6.97/7.27 cnf(i_0_6941, plain, (c_List_Olist__ex(X1,X2,hAPP(c_List_Orev(X1),X3))|~c_List_Olist__ex(X1,X2,X3))). 6.97/7.27 cnf(i_0_149, plain, (c_List_Olist__all(X1,X2,hAPP(c_List_Orev(X1),X3))|~c_List_Olist__all(X1,X2,X3))). 6.97/7.27 cnf(i_0_3996, plain, (c_Enum_On__lists(X1,X2,c_List_Olist_ONil(X1))=c_List_Olist_ONil(tc_List_Olist(X1))|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 6.97/7.27 cnf(i_0_847, plain, (hBOOL(hAPP(X1,esk66_3(X2,X1,X3)))|~c_List_Olist__ex(X3,X1,X2))). 6.97/7.27 cnf(i_0_2302, plain, (hBOOL(hAPP(X1,esk181_3(X2,X1,X3)))|~c_List_Olist__ex(X3,X1,X2))). 6.97/7.27 cnf(i_0_3163, plain, (hBOOL(hAPP(X1,esk241_3(X2,X1,X3)))|~c_List_Olist__ex1(X3,X1,X2))). 6.97/7.27 cnf(i_0_4443, plain, (hBOOL(hAPP(X1,esk335_3(X1,X2,X3)))|~c_List_Olist__ex(X3,X1,X2))). 6.97/7.27 cnf(i_0_6737, plain, (hBOOL(hAPP(X1,esk528_3(X2,X1,X3)))|~c_List_Olist__ex1(X3,X1,X2))). 6.97/7.27 cnf(i_0_5616, 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))). 6.97/7.27 cnf(i_0_2815, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_List_Olist_ONil(X2)=X3|hAPP(hAPP(c_List_Otake(X2),X1),X3)!=c_List_Olist_ONil(X2))). 6.97/7.27 cnf(i_0_1193, 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))). 6.97/7.27 cnf(i_0_3835, plain, (c_Equiv__Relations_Ocongruent(X1,X2,X3,X4)|hAPP(X4,esk286_4(X2,X4,X3,X1))!=hAPP(X4,esk285_4(X2,X4,X3,X1)))). 6.97/7.27 cnf(i_0_3846, 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))). 6.97/7.27 cnf(i_0_4958, 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))). 6.97/7.27 cnf(i_0_7141, plain, (c_List_Olinorder__class_Osorted(X1,c_List_Olinorder__class_Osort__key(X1,X1,c_COMBI(X1),X2))|~class_Orderings_Olinorder(X1))). 6.97/7.27 cnf(i_0_1466, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))=X2|~class_Groups_Ogroup__add(X1))). 6.97/7.27 cnf(i_0_4598, 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_Rings_Ozero__neq__one(X1)|~class_Rings_Ono__zero__divisors(X1)|~class_Rings_Omult__zero(X1)|~class_Power_Opower(X1))). 6.97/7.27 cnf(i_0_3959, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(c_Set_Oimage(X1,X3,X4),X2)!=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))). 6.97/7.27 cnf(i_0_3243, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_List_Oset(X3),c_List_Oreplicate(X3,X4,X2)))))). 6.97/7.27 cnf(i_0_1724, 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)))). 6.97/7.27 cnf(i_0_4338, plain, (c_Quotient_OBabs(X1,X2,c_Quotient_ORespects(X1,X3),X4)=X4|~c_Equiv__Relations_Oequivp(X1,X3))). 6.97/7.27 cnf(i_0_6837, 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))). 6.97/7.27 cnf(i_0_1428, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X2|~class_Groups_Omonoid__mult(X1))). 6.97/7.27 cnf(i_0_2837, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1))=X2|~class_Lattices_Obounded__lattice__bot(X1))). 6.97/7.27 cnf(i_0_5093, 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)))). 6.97/7.27 cnf(i_0_3012, plain, (c_Quickcheck_Obeyond(X1,X2)=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2)))). 6.97/7.27 cnf(i_0_3278, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),c_Groups_Oone__class_Oone(X1))=X2|~class_Rings_Odivision__ring(X1))). 6.97/7.27 cnf(i_0_1977, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1))=X2|~class_Groups_Ocomm__monoid__mult(X1))). 6.97/7.27 cnf(i_0_1521, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Orderings_Otop__class_Otop(X1))=X2|~class_Lattices_Obounded__lattice__top(X1))). 6.97/7.27 cnf(i_0_2411, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1))=X2|~class_Groups_Ocomm__monoid__add(X1))). 6.97/7.27 cnf(i_0_1656, 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))). 6.97/7.27 cnf(i_0_43, 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))). 6.97/7.27 cnf(i_0_3920, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1))=X2|~class_Rings_Ocomm__semiring__1(X1))). 6.97/7.27 cnf(i_0_2605, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1))=X2|~class_Groups_Omonoid__add(X1))). 6.97/7.27 cnf(i_0_834, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),c_Groups_Ozero__class_Ozero(X1))=X2|~class_Groups_Ogroup__add(X1))). 6.97/7.27 cnf(i_0_4074, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))=X2|~class_Lattices_Oboolean__algebra(X1))). 6.97/7.27 cnf(i_0_2161, 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))). 6.97/7.27 cnf(i_0_1925, 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))). 6.97/7.27 cnf(i_0_2897, 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))). 6.97/7.27 cnf(i_0_732, plain, (X1=X2|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X4),X2))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X4),X1)))). 6.97/7.27 cnf(i_0_4016, 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)))). 6.97/7.27 cnf(i_0_957, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1))=X2|~class_Rings_Ocomm__semiring__1(X1))). 6.97/7.27 cnf(i_0_7568, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1))=X2|~class_Groups_Omonoid__mult(X1))). 6.97/7.27 cnf(i_0_4891, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),c_Groups_Oone__class_Oone(X1))=X2|~class_Divides_Osemiring__div(X1))). 6.97/7.27 cnf(i_0_3218, 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)))). 6.97/7.27 cnf(i_0_85, 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)))). 6.97/7.27 cnf(i_0_3768, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2)=X2|~class_Rings_Ocomm__semiring__1(X1))). 6.97/7.27 cnf(i_0_6425, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2)=X2|~class_Lattices_Obounded__lattice__bot(X1))). 6.97/7.27 cnf(i_0_7497, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2)=X2|~class_Groups_Ocomm__monoid__mult(X1))). 6.97/7.27 cnf(i_0_6807, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2)=X2|~class_Groups_Omonoid__mult(X1))). 6.97/7.27 cnf(i_0_2324, plain, (X1=hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))|~c_Finite__Set_Ofolding__image__simple(X4,X3,X5,X1,X6,X2))). 6.97/7.27 cnf(i_0_1018, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(c_List_Olistsp(X3,X1),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))))). 6.97/7.27 cnf(i_0_1818, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~c_Fun_Obij__betw(X3,X2,X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)),X1))). 6.97/7.27 cnf(i_0_4269, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Otop__class_Otop(X1)),X2)=X2|~class_Lattices_Obounded__lattice__top(X1))). 6.97/7.27 cnf(i_0_7188, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=X2|~class_Groups_Ocomm__monoid__add(X1))). 6.97/7.27 cnf(i_0_5097, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=X2|~class_Rings_Ocomm__semiring__1(X1))). 6.97/7.27 cnf(i_0_7355, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=X2|~class_Groups_Omonoid__add(X1))). 6.97/7.27 cnf(i_0_2248, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|~c_Fun_Obij__betw(X1,X3,X4,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))). 6.97/7.27 cnf(i_0_1311, plain, (hAPP(c_Finite__Set_Ocard(X1),X2)=hAPP(c_Finite__Set_Ocard(X3),X4)|~c_Fun_Obij__betw(X1,X3,X5,X2,X4))). 6.97/7.27 cnf(i_0_6443, 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))). 6.97/7.27 cnf(i_0_1623, plain, (hAPP(X1,c_Inductive_Ocomplete__lattice__class_Ogfp(X2,X1))=c_Inductive_Ocomplete__lattice__class_Ogfp(X2,X1)|~class_Complete__Lattice_Ocomplete__lattice(X2)|~c_Orderings_Oorder__class_Omono(X2,X2,X1))). 6.97/7.27 cnf(i_0_3083, plain, (hBOOL(hAPP(X1,esk234_2(X1,X2)))|~class_Enum_Oenum(X2)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X2),X1)))). 6.97/7.27 cnf(i_0_6652, plain, (hBOOL(hAPP(X1,esk518_2(X1,X2)))|~class_Enum_Oenum(X2)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X2),X1)))). 6.97/7.27 cnf(i_0_5099, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))|~hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk396_3(X3,X2,X1))))). 6.97/7.27 cnf(i_0_6820, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))|~hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk532_3(X3,X2,X1))))). 6.97/7.27 cnf(i_0_2153, plain, (hAPP(X1,c_Inductive_Ocomplete__lattice__class_Olfp(X2,X1))=c_Inductive_Ocomplete__lattice__class_Olfp(X2,X1)|~class_Complete__Lattice_Ocomplete__lattice(X2)|~c_Orderings_Oorder__class_Omono(X2,X2,X1))). 6.97/7.27 cnf(i_0_171, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X4,X5,X1),X3),X2)))). 6.97/7.27 cnf(i_0_5010, plain, (X1=c_Int_OMin|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)!=c_Int_OMin)). 6.97/7.27 cnf(i_0_3237, 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)))). 6.97/7.27 cnf(i_0_3722, 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)))). 6.97/7.27 cnf(i_0_7296, plain, (c_List_Olist__all(X1,X2,X3)|~hBOOL(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),esk569_3(X3,X2,X1)))))). 6.97/7.27 cnf(i_0_5707, plain, (hAPP(X1,hAPP(X2,X3))=X3|~c_Typedef_Otype__definition(X4,X5,X2,X1,X6))). 6.97/7.27 cnf(i_0_5790, 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)))). 6.97/7.27 cnf(i_0_6708, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),X1),X2)))). 6.97/7.27 cnf(i_0_7111, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk549_1(X1))=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 6.97/7.27 cnf(i_0_460, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|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))). 6.97/7.27 cnf(i_0_3662, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X1),X4),X2)))). 6.97/7.27 cnf(i_0_950, plain, (c_Predicate_Osymp(X1,X2)|~c_Relation_Osym(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))). 6.97/7.27 cnf(i_0_461, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(c_Groups_Ouminus__class_Ouminus(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))). 6.97/7.27 cnf(i_0_3943, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2))|~class_Orderings_Oorder(X1))). 6.97/7.27 cnf(i_0_7180, plain, (c_Predicate_Otransp(X1,X2)|~c_Relation_Otrans(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))). 6.97/7.27 cnf(i_0_2204, plain, (c_Wellfounded_OwfP(X1,X2)|~c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))). 6.97/7.27 cnf(i_0_6023, 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)))). 6.97/7.27 cnf(i_0_2135, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|X3=X1|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X3),X1)!=c_Groups_Oone__class_Oone(X2)|~class_Rings_Odivision__ring(X2))). 6.97/7.27 cnf(i_0_3860, 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))). 6.97/7.27 cnf(i_0_5653, plain, (hAPP(X1,X2)=hAPP(X1,X3)|~c_Equiv__Relations_Oequivp(X4,X1)|~hBOOL(hAPP(hAPP(X1,X2),X3)))). 6.97/7.27 cnf(i_0_5777, plain, (hAPP(X1,X2)=hAPP(X1,X3)|~c_Equiv__Relations_Opart__equivp(X4,X1)|~hBOOL(hAPP(hAPP(X1,X2),X3)))). 6.97/7.27 cnf(i_0_5017, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk391_2(X1,X2)),X2)))). 6.97/7.27 cnf(i_0_30, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk2_2(X1,X2)),X2)))). 6.97/7.27 cnf(i_0_5843, plain, (X1=c_List_Olist_ONil(X2)|c_List_Olinorder__class_Osorted(X2,esk452_2(X1,X2))|~c_List_Olinorder__class_Osorted(X2,X1)|~class_Orderings_Olinorder(X2))). 6.97/7.27 cnf(i_0_6990, 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))). 6.97/7.27 cnf(i_0_6367, 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))). 6.97/7.27 cnf(i_0_401, 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))). 6.97/7.27 cnf(i_0_842, 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))))). 6.97/7.27 cnf(i_0_5628, plain, (X1=X2|hAPP(hAPP(c_Product__Type_OPair(X3,X4),X5),X2)!=hAPP(hAPP(c_Product__Type_OPair(X3,X4),X6),X1))). 6.97/7.27 cnf(i_0_161, plain, (X1=X2|hAPP(hAPP(c_Product__Type_OPair(X3,X4),X1),X5)!=hAPP(hAPP(c_Product__Type_OPair(X3,X4),X2),X6))). 6.97/7.27 cnf(i_0_4484, 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)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 6.97/7.27 cnf(i_0_5913, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|~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))))). 6.97/7.27 cnf(i_0_800, 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)))). 6.97/7.27 cnf(i_0_5855, 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))))). 6.97/7.27 cnf(i_0_7097, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Oab__group__add(X1))). 6.97/7.27 cnf(i_0_4687, 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))). 6.97/7.27 cnf(i_0_770, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))))). 6.97/7.27 cnf(i_0_7251, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))))). 6.97/7.27 cnf(i_0_5160, 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)))). 6.97/7.27 cnf(i_0_2465, plain, (c_Wellfounded_Owf(tc_List_Olist(X1),hAPP(c_List_Olexn(X1,X2),X3))|~c_Wellfounded_Owf(X1,X2))). 6.97/7.27 cnf(i_0_4648, plain, (hAPP(c_List_Ohd(X1),c_List_Oreplicate(X1,X2,X3))=X3|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2)). 6.97/7.27 cnf(i_0_5728, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Oappend(X1),X3),X2))))). 6.97/7.27 cnf(i_0_5729, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3))))). 6.97/7.27 cnf(i_0_7252, 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))))). 6.97/7.27 cnf(i_0_2694, 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)))). 6.97/7.27 cnf(i_0_5301, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=X1|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)!=X2)). 6.97/7.27 cnf(i_0_71, plain, (c_Nat__Transfer_Onat__set(X1)|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk6_1(X1)),X1)))). 6.97/7.27 cnf(i_0_2847, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Orderings_Otop__class_Otop(X1)))|~class_Orderings_Otop(X1))). 6.97/7.27 cnf(i_0_1144, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Ocomm__semiring__1(X1))). 6.97/7.27 cnf(i_0_5832, 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(X1))). 6.97/7.27 cnf(i_0_6897, plain, (X1=X2|hBOOL(hAPP(X3,X2))|~hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X4),X1),X3),X2)))). 6.97/7.27 cnf(i_0_1917, 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))). 6.97/7.27 cnf(i_0_3291, 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))). 6.97/7.27 cnf(i_0_6353, 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)))). 6.97/7.27 cnf(i_0_1974, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Orderings_Obot__class_Obot(X1)),X2))|~class_Orderings_Obot(X1))). 6.97/7.27 cnf(i_0_948, 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))). 6.97/7.27 cnf(i_0_3728, 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))). 6.97/7.27 cnf(i_0_1239, plain, (X1=X2|hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X1),X3)!=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X4)))). 6.97/7.27 cnf(i_0_504, plain, (c_Relation_Orefl__on(X1,X2,hAPP(c_Relation_Oconverse(X1,X1),X3))|~c_Relation_Orefl__on(X1,X2,X3))). 6.97/7.27 cnf(i_0_807, plain, (hAPP(c_Int_ORep__Integ,esk64_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)))). 6.97/7.27 cnf(i_0_5028, 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))). 6.97/7.27 cnf(i_0_2874, 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)))). 6.97/7.27 cnf(i_0_2753, plain, (c_Nitpick_Onat__gcd(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1))=c_Nitpick_Onat__gcd(X2,X1)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1)). 6.97/7.27 cnf(i_0_5906, plain, (c_Relation_Ototal__on(X1,X2,hAPP(c_Relation_Oconverse(X1,X1),X3))|~c_Relation_Ototal__on(X1,X2,X3))). 6.97/7.27 cnf(i_0_5544, 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)))). 6.97/7.27 cnf(i_0_4934, 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)))). 6.97/7.27 cnf(i_0_5992, 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))). 6.97/7.27 cnf(i_0_7007, plain, (hAPP(hAPP(X1,X2),X2)=X2|~c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X1,X5,X6,X7))). 6.97/7.27 cnf(i_0_5123, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X1),X3)!=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool)))). 6.97/7.27 cnf(i_0_2579, 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))))). 6.97/7.27 cnf(i_0_6864, 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))))). 6.97/7.27 cnf(i_0_2594, 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)))). 6.97/7.27 cnf(i_0_4237, 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))))). 6.97/7.27 cnf(i_0_727, 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))))). 6.97/7.27 cnf(i_0_2211, 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))). 6.97/7.27 cnf(i_0_4329, 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))). 6.97/7.27 cnf(i_0_4584, 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))). 6.97/7.27 cnf(i_0_2041, 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))). 6.97/7.27 cnf(i_0_601, 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))). 6.97/7.27 cnf(i_0_7558, 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)))). 6.97/7.27 cnf(i_0_7556, 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)))). 6.97/7.27 cnf(i_0_5511, 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))). 6.97/7.27 cnf(i_0_1393, 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))). 6.97/7.27 cnf(i_0_4703, 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))). 6.97/7.27 cnf(i_0_6816, 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))). 6.97/7.27 cnf(i_0_6061, 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))). 6.97/7.27 cnf(i_0_1129, 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))). 6.97/7.27 cnf(i_0_4235, 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))))). 6.97/7.27 cnf(i_0_5920, plain, (hBOOL(hAPP(X1,c_Orderings_Oord__class_OLeast(X2,X1)))|~class_Orderings_Owellorder(X2)|~hBOOL(hAPP(X1,X3)))). 6.97/7.27 cnf(i_0_303, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_HOL_Obool))|hAPP(c_Relation_ORange(X2,X3),X1)!=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))). 6.97/7.27 cnf(i_0_1796, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))=X3|hAPP(c_Relation_ODomain(X1,X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 6.97/7.27 cnf(i_0_5471, 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))). 6.97/7.27 cnf(i_0_2669, 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))). 6.97/7.27 cnf(i_0_6634, 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))). 6.97/7.27 cnf(i_0_7072, 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))). 6.97/7.27 cnf(i_0_886, 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))). 6.97/7.27 cnf(i_0_2485, plain, (hBOOL(hAPP(X1,esk201_1(X1)))|~hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))))). 6.97/7.27 cnf(i_0_3490, plain, (hBOOL(hAPP(hAPP(X1,X2),X2))|~hBOOL(hAPP(c_Quotient_ORespects(X3,X1),X2)))). 6.97/7.27 cnf(i_0_3491, plain, (hBOOL(hAPP(c_Quotient_ORespects(X1,X2),X3))|~hBOOL(hAPP(hAPP(X2,X3),X3)))). 6.97/7.27 cnf(i_0_112, 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)))). 6.97/7.27 cnf(i_0_678, plain, (hBOOL(hAPP(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),esk55_1(X1))))|~hBOOL(hAPP(X1,X2)))). 6.97/7.27 cnf(i_0_7255, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)=X3|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3)))). 6.97/7.27 cnf(i_0_3030, 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)))). 6.97/7.27 cnf(i_0_4290, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OatLeast(X4,X1,X2))))). 6.97/7.27 cnf(i_0_5579, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OgreaterThan(X4,X1,X2))))). 6.97/7.27 cnf(i_0_2632, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OlessThan(X4,X1,X3))))). 6.97/7.27 cnf(i_0_6392, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OatMost(X4,X1,X3))))). 6.97/7.27 cnf(i_0_887, 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))). 6.97/7.27 cnf(i_0_5002, 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)))). 6.97/7.27 cnf(i_0_5976, plain, (hAPP(c_List_Oset(X1),esk469_2(X2,X1))=X2|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 6.97/7.27 cnf(i_0_1121, 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)))). 6.97/7.27 cnf(i_0_937, plain, (hAPP(c_Finite__Set_Ocard(X1),X2)!=hAPP(c_Nat_OSuc,X3)|~hBOOL(hAPP(hAPP(c_member(X1),esk80_3(X3,X2,X1)),esk81_3(X3,X2,X1))))). 6.97/7.27 cnf(i_0_5422, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(X2,X3))|~hBOOL(hAPP(X2,esk414_4(X2,X3,X1,X4))))). 6.97/7.27 cnf(i_0_4170, 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)))). 6.97/7.27 cnf(i_0_6763, 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))). 6.97/7.27 cnf(i_0_5379, 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)))). 6.97/7.27 cnf(i_0_5640, plain, (~c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),X1),X2,X3)|~c_List_Olist__ex(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))))). 6.97/7.27 cnf(i_0_4599, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3)!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Ozero__neq__one(X2)|~class_Rings_Ono__zero__divisors(X2)|~class_Rings_Omult__zero(X2)|~class_Power_Opower(X2))). 6.97/7.27 cnf(i_0_997, plain, (c_Fun_Obij__betw(X1,X2,X3,X4,hAPP(c_Set_Oimage(X1,X2,X3),X4))|~c_Fun_Oinj__on(X1,X2,X3,X4))). 6.97/7.27 cnf(i_0_5412, 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)))). 6.97/7.27 cnf(i_0_3037, 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)))). 6.97/7.27 cnf(i_0_6801, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Oordered__ab__group__add__abs(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Groups_Oabs__class_Oabs(X2),X1)),c_Groups_Ozero__class_Ozero(X2))))). 6.97/7.27 cnf(i_0_6797, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X3),hAPP(hAPP(c_List_Omap(X1,X3),X4),X2))))). 6.97/7.27 cnf(i_0_2583, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))|~class_Orderings_Olinorder(X1))). 6.97/7.27 cnf(i_0_1725, 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)))). 6.97/7.27 cnf(i_0_1462, 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,esk116_2(X2,X1))))). 6.97/7.27 cnf(i_0_5656, plain, (c_Equiv__Relations_Oequivp(X1,X2)|hAPP(X2,esk431_1(X2))!=hAPP(X2,esk432_1(X2))|~hBOOL(hAPP(hAPP(X2,esk431_1(X2)),esk432_1(X2))))). 6.97/7.27 cnf(i_0_4301, 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))). 6.97/7.27 cnf(i_0_720, 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))). 6.97/7.27 cnf(i_0_7387, 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))). 6.97/7.27 cnf(i_0_5279, 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))). 6.97/7.27 cnf(i_0_1992, 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))). 6.97/7.27 cnf(i_0_551, 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)))). 6.97/7.27 cnf(i_0_6018, 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))). 6.97/7.27 cnf(i_0_3298, 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)))). 6.97/7.27 cnf(i_0_5365, 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))). 6.97/7.27 cnf(i_0_7220, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),c_List_OtakeWhile(X3,X1,X4)))))). 6.97/7.27 cnf(i_0_4714, plain, (c_FunDef_OTHE__default(X1,X2,X3)=X2|hBOOL(hAPP(X3,esk364_3(X2,X1,X3))))). 6.97/7.27 cnf(i_0_1541, plain, (c_List_Olast(X1,hAPP(c_List_Orev(X1),X2))=hAPP(c_List_Ohd(X1),X2)|X2=c_List_Olist_ONil(X1))). 6.97/7.27 cnf(i_0_3020, 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)))). 6.97/7.27 cnf(i_0_4088, 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)))). 6.97/7.27 cnf(i_0_2742, 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))). 6.97/7.27 cnf(i_0_2433, 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))). 6.97/7.27 cnf(i_0_1125, plain, (hAPP(c_List_Ohd(X1),X2)=hAPP(hAPP(c_List_Onth(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|X2=c_List_Olist_ONil(X1))). 6.97/7.27 cnf(i_0_6003, 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))))). 6.97/7.27 cnf(i_0_885, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|X3=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Oring__no__zero__divisors(X1))). 6.97/7.27 cnf(i_0_4527, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|X3=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Ono__zero__divisors(X1))). 6.97/7.27 cnf(i_0_4793, plain, (X1=X2|hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))!=c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X1)|~class_Orderings_Oorder(X3))). 6.97/7.27 cnf(i_0_5775, plain, (hBOOL(hAPP(hAPP(X1,esk450_1(X1)),esk450_1(X1)))|~c_Equiv__Relations_Opart__equivp(X2,X1))). 6.97/7.27 cnf(i_0_4792, plain, (X1=X2|hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))!=c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)|~class_Orderings_Oorder(X3))). 6.97/7.27 cnf(i_0_3944, 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)))). 6.97/7.27 cnf(i_0_3455, 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)))). 6.97/7.27 cnf(i_0_2817, 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_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1))). 6.97/7.27 cnf(i_0_5168, 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)))). 6.97/7.27 cnf(i_0_2554, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OgreaterThanLessThan(X4,X1,X2,X5))))). 6.97/7.27 cnf(i_0_4696, 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)))). 6.97/7.27 cnf(i_0_5004, 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)))). 6.97/7.27 cnf(i_0_5978, plain, (hBOOL(hAPP(c_List_Odistinct(X1),esk469_2(X2,X1)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 6.97/7.27 cnf(i_0_6863, 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))))). 6.97/7.27 cnf(i_0_6890, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OatLeastAtMost(X4,X1,X2,X5))))). 6.97/7.27 cnf(i_0_2555, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OgreaterThanLessThan(X4,X1,X5,X3))))). 6.97/7.27 cnf(i_0_6891, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OatLeastAtMost(X4,X1,X5,X3))))). 6.97/7.27 cnf(i_0_5654, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|hAPP(X1,X3)!=hAPP(X1,X2)|~c_Equiv__Relations_Oequivp(X4,X1))). 6.97/7.27 cnf(i_0_4743, 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)))). 6.97/7.27 cnf(i_0_4677, 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)))). 6.97/7.27 cnf(i_0_3386, 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)). 6.97/7.27 cnf(i_0_3260, 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)))). 6.97/7.27 cnf(i_0_5049, 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)))). 6.97/7.27 cnf(i_0_1868, 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)),X3),X1)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 6.97/7.27 cnf(i_0_1867, 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)),X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 6.97/7.27 cnf(i_0_971, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orev(X1),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 6.97/7.27 cnf(i_0_6641, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orotate1(X1),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 6.97/7.27 cnf(i_0_6423, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Otl(X1),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 6.97/7.27 cnf(i_0_3898, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_OtakeWhile(X1,X2,X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 6.97/7.27 cnf(i_0_182, 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)))). 6.97/7.27 cnf(i_0_2141, 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)))). 6.97/7.27 cnf(i_0_3489, 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))))))). 6.97/7.27 cnf(i_0_6707, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oinsert(X1,X2,X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 6.97/7.27 cnf(i_0_1704, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oremove1(X1,X2,X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 6.97/7.27 cnf(i_0_4090, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Osublist(X1,X2,X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 6.97/7.27 cnf(i_0_1119, plain, (X1=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),X4),X4)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),X1),X2)|~class_Groups_Oab__group__add(X3))). 6.97/7.27 cnf(i_0_3509, 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))). 6.97/7.27 cnf(i_0_3998, 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))). 6.97/7.27 cnf(i_0_5804, 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))). 6.97/7.27 cnf(i_0_4693, plain, (hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3)))|~hBOOL(hAPP(X1,esk361_3(X3,X2,X1)))|~hBOOL(hAPP(X1,X2)))). 6.97/7.27 cnf(i_0_3534, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|c_Sum__Type_OPlus(X3,X2,X4,X1)!=c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X3,X2),tc_HOL_Obool)))). 6.97/7.27 cnf(i_0_3535, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Sum__Type_OPlus(X1,X3,X2,X4)!=c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X1,X3),tc_HOL_Obool)))). 6.97/7.27 cnf(i_0_1019, 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))))). 6.97/7.27 cnf(i_0_1595, plain, (hAPP(c_List_Ohd(X1),hAPP(c_List_Orev(X1),X2))=c_List_Olast(X1,X2)|c_List_Olist_ONil(X1)=X2)). 6.97/7.27 cnf(i_0_2674, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))|~c_Wellfounded_Owf(X1,X3))). 6.97/7.27 cnf(i_0_5713, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Oinv__image(X2,X1),X3),X4))|~c_Wellfounded_Owf(X2,X3))). 6.97/7.27 cnf(i_0_814, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(c_List_Olistsp(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X4),X3))))). 6.97/7.27 cnf(i_0_813, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(c_List_Olistsp(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4))))). 6.97/7.27 cnf(i_0_6079, 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))). 6.97/7.27 cnf(i_0_4197, 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)))). 6.97/7.27 cnf(i_0_3267, plain, (c_Relation_Osym(X1,hAPP(hAPP(c_Relation_Oinv__image(X2,X1),X3),X4))|~c_Relation_Osym(X2,X3))). 6.97/7.27 cnf(i_0_7202, plain, (c_Relation_Otrans(X1,hAPP(hAPP(c_Relation_Oinv__image(X2,X1),X3),X4))|~c_Relation_Otrans(X2,X3))). 6.97/7.27 cnf(i_0_2144, plain, (c_FunDef_Oreduction__pair(X1,hAPP(hAPP(c_FunDef_Orp__inv__image(X2,X1),X3),X4))|~c_FunDef_Oreduction__pair(X2,X3))). 6.97/7.27 cnf(i_0_4809, 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))))). 6.97/7.27 cnf(i_0_2663, 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)))). 6.97/7.27 cnf(i_0_1534, 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))). 6.97/7.27 cnf(i_0_6592, 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))). 6.97/7.27 cnf(i_0_2280, plain, (hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))|~hBOOL(hAPP(X1,esk178_1(X1))))). 6.97/7.27 cnf(i_0_4742, 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))). 6.97/7.27 cnf(i_0_864, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))=hAPP(c_Set_Oimage(X2,X1,X3),X4)|~c_Typedef_Otype__definition(X1,X2,X5,X3,X4))). 6.97/7.27 cnf(i_0_1081, plain, (hBOOL(hAPP(X1,X2))|hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)!=hAPP(c_List_Ofilter(X3,X1),X5))). 6.97/7.27 cnf(i_0_690, 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))). 6.97/7.27 cnf(i_0_5864, 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)|esk457_2(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 6.97/7.27 cnf(i_0_7135, 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)))). 6.97/7.27 cnf(i_0_3919, plain, (hBOOL(hAPP(X1,esk297_3(X1,X2,X3)))|~c_Equiv__Relations_Oequivp(X3,X2)|~hBOOL(hAPP(X1,X4)))). 6.97/7.27 cnf(i_0_5027, 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)))). 6.97/7.27 cnf(i_0_7491, 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))). 6.97/7.27 cnf(i_0_6378, 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))))). 6.97/7.27 cnf(i_0_3466, 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))). 6.97/7.27 cnf(i_0_4838, 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))). 6.97/7.27 cnf(i_0_412, 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)))). 6.97/7.27 cnf(i_0_1653, 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))). 6.97/7.27 cnf(i_0_6031, 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))). 6.97/7.27 cnf(i_0_4781, 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))). 6.97/7.27 cnf(i_0_2289, 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))). 6.97/7.27 cnf(i_0_4569, plain, (c_List_Oinsert(X1,X2,X3)=X3|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 6.97/7.27 cnf(i_0_3519, 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)))))). 6.97/7.27 cnf(i_0_1733, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))). 6.97/7.27 cnf(i_0_2999, plain, (hBOOL(hAPP(c_Predicate_ODomainP(X1,X2,X3),X4))|~hBOOL(hAPP(hAPP(X3,X4),X5)))). 6.97/7.27 cnf(i_0_4065, plain, (hBOOL(hAPP(c_Predicate_ORangeP(X1,X2,X3),X4))|~hBOOL(hAPP(hAPP(X3,X5),X4)))). 6.97/7.27 cnf(i_0_298, 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))). 6.97/7.27 cnf(i_0_6160, plain, (c_Orderings_Oord__class_OLeast(X1,X2)=X3|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),esk486_3(X3,X2,X1)))|~hBOOL(hAPP(X2,X3)))). 6.97/7.27 cnf(i_0_2541, 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)))). 6.97/7.27 cnf(i_0_1221, 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))). 6.97/7.27 cnf(i_0_6042, 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))). 6.97/7.27 cnf(i_0_6547, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OatLeastLessThan(X4,X1,X5,X2,X6))))). 6.97/7.27 cnf(i_0_5720, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OgreaterThanAtMost(X4,X5,X1,X2,X6))))). 6.97/7.27 cnf(i_0_6546, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OatLeastLessThan(X4,X5,X1,X6,X3))))). 6.97/7.27 cnf(i_0_5719, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OgreaterThanAtMost(X4,X1,X5,X6,X3))))). 6.97/7.27 cnf(i_0_5130, 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)))). 6.97/7.27 cnf(i_0_547, 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)))). 6.97/7.27 cnf(i_0_2322, 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))). 6.97/7.27 cnf(i_0_684, 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))))). 6.97/7.27 cnf(i_0_2954, 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))))). 6.97/7.27 cnf(i_0_2953, 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))))). 6.97/7.27 cnf(i_0_1888, 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)))). 6.97/7.27 cnf(i_0_1392, 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)))). 6.97/7.27 cnf(i_0_6149, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|~class_Rings_Osemiring__0(X1)|~class_Power_Opower(X1))). 6.97/7.27 cnf(i_0_3400, 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)))). 6.97/7.27 cnf(i_0_5559, 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)))). 6.97/7.27 cnf(i_0_4393, 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))))). 6.97/7.27 cnf(i_0_2989, 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)))). 6.97/7.27 cnf(i_0_4101, 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))))). 6.97/7.27 cnf(i_0_3721, plain, (X1=X2|hAPP(c_Product__Type_Ofst(X3,X4),X1)!=hAPP(c_Product__Type_Ofst(X3,X4),X2)|hAPP(c_Product__Type_Osnd(X3,X4),X1)!=hAPP(c_Product__Type_Osnd(X3,X4),X2))). 6.97/7.27 cnf(i_0_6308, 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))). 6.97/7.27 cnf(i_0_5764, 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))). 6.97/7.27 cnf(i_0_6192, 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)))). 6.97/7.27 cnf(i_0_183, plain, (c_List_Olist__ex(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))|~c_List_Olist__ex(X1,X2,X4))). 6.97/7.27 cnf(i_0_552, plain, (c_List_Olist__ex(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4))|~c_List_Olist__ex(X1,X2,X4))). 6.97/7.27 cnf(i_0_553, plain, (c_List_Olist__ex(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4))|~c_List_Olist__ex(X1,X2,X3))). 6.97/7.27 cnf(i_0_1460, 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))))). 6.97/7.27 cnf(i_0_6909, plain, (hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X6)=hAPP(X3,X6)|X6=X4)). 6.97/7.27 cnf(i_0_3397, 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))))). 6.97/7.27 cnf(i_0_935, plain, (hAPP(c_Finite__Set_Ocard(X1),esk81_3(X2,X3,X1))=X2|hAPP(c_Finite__Set_Ocard(X1),X3)!=hAPP(c_Nat_OSuc,X2))). 6.97/7.27 cnf(i_0_5413, 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))))). 6.97/7.27 cnf(i_0_3656, 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)))). 6.97/7.27 cnf(i_0_4715, plain, (c_FunDef_OTHE__default(X1,X2,X3)=X2|X4=esk364_3(X2,X1,X3)|~hBOOL(hAPP(X3,X4)))). 6.97/7.27 cnf(i_0_184, plain, (c_List_Olist__ex(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))|~hBOOL(hAPP(X2,X3)))). 6.97/7.27 cnf(i_0_6895, plain, (hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4))|~hBOOL(hAPP(X3,X4)))). 6.97/7.27 cnf(i_0_495, plain, (hAPP(c_List_Ofilter(X1,X2),X3)=c_List_Olist_ONil(X1)|hBOOL(hAPP(X2,esk40_3(X3,X2,X1))))). 6.97/7.27 cnf(i_0_4768, 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)))). 6.97/7.27 cnf(i_0_4542, plain, (c_Relation_Oantisym(X1,X2)|~c_Relation_Oantisym(X1,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))). 6.97/7.27 cnf(i_0_3743, 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)))). 6.97/7.27 cnf(i_0_4814, 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))). 6.97/7.27 cnf(i_0_4942, 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))). 6.97/7.27 cnf(i_0_1267, 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))). 6.97/7.27 cnf(i_0_2640, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk210_3(X3,X2,X1))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 6.97/7.27 cnf(i_0_5625, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk429_3(X3,X2,X1))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 6.97/7.27 cnf(i_0_6688, 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))))). 6.97/7.27 cnf(i_0_4894, 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))). 6.97/7.27 cnf(i_0_6462, 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)))). 6.97/7.27 cnf(i_0_151, plain, (~class_Int_Oring__char__0(X1)|~class_Int_Onumber__ring(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))))). 6.97/7.27 cnf(i_0_5574, 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))))). 6.97/7.27 cnf(i_0_5575, 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))))). 6.97/7.27 cnf(i_0_7224, 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))))). 6.97/7.27 cnf(i_0_1327, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk103_2(X1,X2))=X2|c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 6.97/7.27 cnf(i_0_3822, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk284_2(X1,X2))=X2|c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 6.97/7.27 cnf(i_0_1836, 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))). 6.97/7.27 cnf(i_0_2687, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)=X3|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1))). 6.97/7.27 cnf(i_0_1096, 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))). 6.97/7.27 cnf(i_0_6849, 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))). 6.97/7.27 cnf(i_0_5023, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=X1|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 6.97/7.27 cnf(i_0_936, plain, (esk81_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))). 6.97/7.27 cnf(i_0_4930, 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)))). 6.97/7.27 cnf(i_0_6010, 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)))). 6.97/7.27 cnf(i_0_3789, 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))). 6.97/7.27 cnf(i_0_5767, 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)))). 6.97/7.27 cnf(i_0_6037, 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)))). 6.97/7.27 cnf(i_0_4167, 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)))). 6.97/7.27 cnf(i_0_1592, 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)))). 6.97/7.27 cnf(i_0_915, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(X1,esk77_1(X1))))). 6.97/7.27 cnf(i_0_881, plain, (c_Relation_Otrans(tc_prod(X1,X2),c_Wellfounded_Olex__prod(X1,X2,X3,X4))|~c_Relation_Otrans(X2,X4)|~c_Relation_Otrans(X1,X3))). 6.97/7.27 cnf(i_0_1265, 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)))). 6.97/7.27 cnf(i_0_4816, 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)))). 6.97/7.27 cnf(i_0_4905, plain, (c_Nitpick_Ounknown(tc_HOL_Obool)|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))|~c_Nitpick_Owf_H(X1,X2))). 6.97/7.27 cnf(i_0_4912, 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)))). 6.97/7.27 cnf(i_0_2741, 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)))). 6.97/7.27 cnf(i_0_4061, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(X1,esk307_1(X1))))). 6.97/7.27 cnf(i_0_776, 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)))). 6.97/7.27 cnf(i_0_2201, 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)))). 6.97/7.27 cnf(i_0_2761, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~c_Equiv__Relations_Oequivp(X4,X1)|~hBOOL(hAPP(hAPP(X1,X3),X2)))). 6.97/7.27 cnf(i_0_6999, 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)))). 6.97/7.27 cnf(i_0_3503, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~c_Predicate_Osymp(X4,X1)|~hBOOL(hAPP(hAPP(X1,X3),X2)))). 6.97/7.27 cnf(i_0_7500, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~c_Equiv__Relations_Opart__equivp(X4,X1)|~hBOOL(hAPP(hAPP(X1,X3),X2)))). 6.97/7.27 cnf(i_0_5778, plain, (hBOOL(hAPP(hAPP(X1,X2),X2))|~c_Equiv__Relations_Opart__equivp(X3,X1)|~hBOOL(hAPP(hAPP(X1,X4),X2)))). 6.97/7.27 cnf(i_0_5776, plain, (hBOOL(hAPP(hAPP(X1,X2),X2))|~c_Equiv__Relations_Opart__equivp(X3,X1)|~hBOOL(hAPP(hAPP(X1,X2),X4)))). 6.97/7.27 cnf(i_0_296, 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))). 6.97/7.27 cnf(i_0_2812, 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))). 6.97/7.27 cnf(i_0_4622, 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))). 6.97/7.27 cnf(i_0_497, 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)))). 6.97/7.27 cnf(i_0_1213, plain, (c_Partial__Function_Omk__less(X1,X2,X3,X4)|hBOOL(hAPP(hAPP(X2,X4),X3))|~hBOOL(hAPP(hAPP(X2,X3),X4)))). 6.97/7.27 cnf(i_0_1897, 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))))). 6.97/7.27 cnf(i_0_2412, plain, (X1=c_List_Olist_ONil(X2)|hBOOL(hAPP(c_List_Odistinct(X2),c_List_Obutlast(X2,X1)))|~hBOOL(hAPP(c_List_Odistinct(X2),X1)))). 6.97/7.27 cnf(i_0_1705, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Ofilter(X1,X2),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 6.97/7.27 cnf(i_0_5527, plain, (hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),c_Enum_On__lists(X1,X2,X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 6.97/7.27 cnf(i_0_2340, 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)))))). 6.97/7.27 cnf(i_0_1852, 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)))). 6.97/7.27 cnf(i_0_660, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2))|~c_Wellfounded_Owf(X1,X2))). 6.97/7.27 cnf(i_0_4146, 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))). 6.97/7.27 cnf(i_0_4064, plain, (c_Fun_Obij__betw(X1,X2,c_Hilbert__Choice_Oinv__into(X2,X1,X3,X4),X5,X3)|~c_Fun_Obij__betw(X2,X1,X4,X3,X5))). 6.97/7.27 cnf(i_0_2787, plain, (c_Fun_Obij__betw(X1,X2,c_Fun_Othe__inv__into(X2,X1,X3,X4),X5,X3)|~c_Fun_Obij__betw(X2,X1,X4,X3,X5))). 6.97/7.27 cnf(i_0_606, 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))). 6.97/7.27 cnf(i_0_4988, 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))). 6.97/7.27 cnf(i_0_3144, 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))). 6.97/7.27 cnf(i_0_6545, 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)))). 6.97/7.27 cnf(i_0_1631, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),X4))|~hBOOL(hAPP(c_Predicate_OPowp(X3,X1),X4)))). 6.97/7.27 cnf(i_0_5383, plain, (hBOOL(hAPP(hAPP(X1,X2),X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),c_Quotient_ORespects(X3,X1))))). 6.97/7.27 cnf(i_0_6834, 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)))). 6.97/7.27 cnf(i_0_3879, 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))))). 6.97/7.27 cnf(i_0_7077, 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))))). 6.97/7.27 cnf(i_0_3009, 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))))). 6.97/7.27 cnf(i_0_4193, 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))))). 6.97/7.27 cnf(i_0_4697, 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,esk361_3(X1,X3,X2))))). 6.97/7.27 cnf(i_0_2117, plain, (hBOOL(hAPP(hAPP(X1,esk167_2(X1,X2)),esk167_2(X1,X2)))|~c_Equiv__Relations_Opart__equivp(X2,X1))). 6.97/7.27 cnf(i_0_3928, plain, (hBOOL(hAPP(hAPP(X1,esk299_2(X1,X2)),esk299_2(X1,X2)))|~c_Equiv__Relations_Opart__equivp(X2,X1))). 6.97/7.27 cnf(i_0_7028, 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))). 6.97/7.27 cnf(i_0_3679, 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)))). 6.97/7.27 cnf(i_0_255, 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)))). 6.97/7.27 cnf(i_0_7312, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(c_Code__Numeral_Onat__of,esk573_2(X1,X2)))))). 6.97/7.27 cnf(i_0_2184, 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)))). 6.97/7.27 cnf(i_0_1495, 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)))). 6.97/7.27 cnf(i_0_3468, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Big__Operators_Olattice__class_OInf__fin(X1,X2)=c_Complete__Lattice_OInf__class_OInf(X1,X2)|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 6.97/7.27 cnf(i_0_4634, 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)))). 6.97/7.27 cnf(i_0_404, 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)))). 6.97/7.27 cnf(i_0_193, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(X1,esk14_2(X1,X3))))). 6.97/7.27 cnf(i_0_4848, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(X1,esk374_2(X1,X3))))). 6.97/7.27 cnf(i_0_1143, plain, (X1=X2|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),X1),X2)))). 6.97/7.27 cnf(i_0_5162, 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)))). 6.97/7.27 cnf(i_0_4444, 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)))). 6.97/7.27 cnf(i_0_832, 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)))). 6.97/7.27 cnf(i_0_943, 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))). 6.97/7.27 cnf(i_0_6505, 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))). 6.97/7.27 cnf(i_0_5144, 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)))). 6.97/7.27 cnf(i_0_5456, 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))))). 6.97/7.27 cnf(i_0_528, plain, (hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5))|~hBOOL(hAPP(hAPP(X3,X5),X4)))). 6.97/7.27 cnf(i_0_2990, 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)))). 6.97/7.27 cnf(i_0_1006, 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))). 6.97/7.27 cnf(i_0_7092, plain, (hAPP(c_Quotient_OBabs(X1,X2,X3,X4),X5)=hAPP(X4,X5)|~hBOOL(hAPP(hAPP(c_member(X1),X5),X3)))). 6.97/7.27 cnf(i_0_3888, 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)))). 6.97/7.27 cnf(i_0_5186, 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))))). 6.97/7.27 cnf(i_0_2239, 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_Int_Oring__char__0(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1))))). 6.97/7.27 cnf(i_0_5815, 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)))). 6.97/7.27 cnf(i_0_1307, 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)))). 6.97/7.27 cnf(i_0_3434, 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))). 6.97/7.27 cnf(i_0_5847, plain, (hAPP(c_Nat_OSuc,esk455_2(X1,X2))=X2|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))))). 6.97/7.27 cnf(i_0_4635, 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))). 6.97/7.27 cnf(i_0_2720, 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))). 6.97/7.27 cnf(i_0_5812, 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))). 6.97/7.27 cnf(i_0_5551, 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))))). 6.97/7.27 cnf(i_0_4031, 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)))). 6.97/7.27 cnf(i_0_7280, plain, (c_List_Olast(X1,hAPP(hAPP(c_List_Oappend(X1),X2),X3))=c_List_Olast(X1,X3)|X3=c_List_Olist_ONil(X1))). 6.97/7.27 cnf(i_0_4756, 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))). 6.97/7.27 cnf(i_0_1120, 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))). 6.97/7.27 cnf(i_0_3704, 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))). 6.97/7.27 cnf(i_0_6590, 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))). 6.97/7.27 cnf(i_0_2373, 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)). 6.97/7.27 cnf(i_0_1300, 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)))). 6.97/7.27 cnf(i_0_4801, plain, (c_Predicate_Oinv__imagep(X1,X2,X3,X4,X5,X6)|~hBOOL(hAPP(hAPP(X3,hAPP(X4,X5)),hAPP(X4,X6))))). 6.97/7.27 cnf(i_0_6721, 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))). 6.97/7.27 cnf(i_0_2202, 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))). 6.97/7.27 cnf(i_0_3713, 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))). 6.97/7.27 cnf(i_0_1851, 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))))). 6.97/7.27 cnf(i_0_5108, 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)))). 6.97/7.27 cnf(i_0_679, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk55_1(X1)))|~hBOOL(hAPP(X1,X2)))). 6.97/7.27 cnf(i_0_7043, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Orderings_Oord__class_OLeast(X1,X2)),X3))|~class_Orderings_Owellorder(X1)|~hBOOL(hAPP(X2,X3)))). 6.97/7.27 cnf(i_0_1381, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk109_2(X2,X1))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 6.97/7.27 cnf(i_0_6699, 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)). 6.97/7.27 cnf(i_0_58, 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)))). 6.97/7.27 cnf(i_0_2446, plain, (hAPP(c_List_Ofilter(X1,X2),c_List_Oreplicate(X1,X3,X4))=c_List_Olist_ONil(X1)|hBOOL(hAPP(X2,X4)))). 6.97/7.27 cnf(i_0_7433, 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))). 6.97/7.27 cnf(i_0_1789, 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))). 6.97/7.27 cnf(i_0_423, plain, (c_List_OtakeWhile(X1,X2,X3)=hAPP(c_List_Ofilter(X1,X2),X3)|hBOOL(hAPP(X2,esk36_3(X3,X2,X1))))). 6.97/7.27 cnf(i_0_4779, 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)))). 6.97/7.28 cnf(i_0_1783, plain, (c_List_Olist__all(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_Oall__interval__nat(X1,X2,X3))). 6.97/7.28 cnf(i_0_954, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X2,esk82_4(X2,X3,X1,X4)))|~hBOOL(hAPP(X2,X3)))). 6.97/7.28 cnf(i_0_157, 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))). 6.97/7.28 cnf(i_0_2963, 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))). 6.97/7.28 cnf(i_0_4395, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Oring__char__0(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),X2))))). 6.97/7.28 cnf(i_0_1484, 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)))). 6.97/7.28 cnf(i_0_2590, 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,esk208_2(X1,X2)))))). 6.97/7.28 cnf(i_0_5195, 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))))). 6.97/7.28 cnf(i_0_4319, 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))). 6.97/7.28 cnf(i_0_5032, 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))). 6.97/7.28 cnf(i_0_1731, plain, (X1=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1))). 6.97/7.28 cnf(i_0_2930, 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),X1),X2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 6.97/7.28 cnf(i_0_1138, 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))). 6.97/7.28 cnf(i_0_3128, 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),esk238_2(X3,X1)))|~hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(X1,X2)))). 6.97/7.28 cnf(i_0_4602, plain, (hBOOL(hAPP(X1,X2))|~c_List_Oall__interval__int(X1,X3,X4)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X3,X4))))). 6.97/7.28 cnf(i_0_2736, 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)))). 6.97/7.28 cnf(i_0_5147, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))=X2|~c_Relation_Otrans(X1,X2))). 6.97/7.28 cnf(i_0_5117, 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)))). 6.97/7.28 cnf(i_0_841, 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)))). 6.97/7.28 cnf(i_0_4986, 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)))). 6.97/7.28 cnf(i_0_2427, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|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))))). 6.97/7.28 cnf(i_0_1884, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=X1|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X2,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X3))))). 6.97/7.28 cnf(i_0_6062, plain, (X1=hAPP(hAPP(c_List_Onth(X2),X3),X4)|hAPP(hAPP(c_List_Odrop(X2),X4),X3)!=hAPP(hAPP(c_List_Olist_OCons(X2),X1),X5))). 6.97/7.28 cnf(i_0_5580, 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))))). 6.97/7.28 cnf(i_0_6665, 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))))). 6.97/7.28 cnf(i_0_6511, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=X1|X2=c_Int_OMin|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)!=c_Groups_Oone__class_Oone(tc_Int_Oint))). 6.97/7.28 cnf(i_0_7066, 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))))). 6.97/7.28 cnf(i_0_2777, 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))))). 6.97/7.28 cnf(i_0_56, 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))))). 6.97/7.28 cnf(i_0_6510, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=X1|X1=c_Int_OMin|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)!=c_Groups_Oone__class_Oone(tc_Int_Oint))). 6.97/7.28 cnf(i_0_4107, 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))))). 6.97/7.28 cnf(i_0_4862, 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))))). 6.97/7.28 cnf(i_0_1179, 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)))). 6.97/7.28 cnf(i_0_2445, plain, (hAPP(c_List_Ofilter(X1,X2),c_List_Oreplicate(X1,X3,X4))=c_List_Oreplicate(X1,X3,X4)|~hBOOL(hAPP(X2,X4)))). 6.97/7.28 cnf(i_0_290, 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))))). 6.97/7.28 cnf(i_0_6508, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=X1|c_Int_OMin=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)!=c_Groups_Oone__class_Oone(tc_Int_Oint))). 6.97/7.28 cnf(i_0_869, 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)))). 6.97/7.28 cnf(i_0_1938, 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),esk157_3(X3,X1,X2))))). 6.97/7.28 cnf(i_0_7554, 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))))). 6.97/7.28 cnf(i_0_1013, 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))))). 6.97/7.28 cnf(i_0_5839, 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),esk454_4(hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),X1,X3,X2))))). 6.97/7.28 cnf(i_0_5438, 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))))). 6.97/7.28 cnf(i_0_3000, plain, (hBOOL(hAPP(hAPP(X1,X2),esk228_2(X2,X1)))|~hBOOL(hAPP(c_Predicate_ODomainP(X3,X4,X1),X2)))). 6.97/7.28 cnf(i_0_7087, plain, (hBOOL(hAPP(hAPP(X1,esk548_2(X2,X1)),X2))|~hBOOL(hAPP(c_Predicate_ORangeP(X3,X4,X1),X2)))). 6.97/7.28 cnf(i_0_1486, 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)))))). 6.97/7.28 cnf(i_0_3216, 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)))). 6.97/7.28 cnf(i_0_2149, 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)))). 6.97/7.28 cnf(i_0_6509, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=X1|c_Int_OMin=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)!=c_Groups_Oone__class_Oone(tc_Int_Oint))). 6.97/7.28 cnf(i_0_1266, 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)))). 6.97/7.28 cnf(i_0_3971, 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)))). 6.97/7.28 cnf(i_0_4632, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),esk356_3(X3,X2,X1)),X3)))). 6.97/7.28 cnf(i_0_3075, 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)))). 6.97/7.28 cnf(i_0_4102, 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)))). 6.97/7.28 cnf(i_0_3275, 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)))). 6.97/7.28 cnf(i_0_6828, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,esk533_4(X1,X3,X4,X5)))|~hBOOL(hAPP(hAPP(c_member(X5),X2),X4)))). 6.97/7.28 cnf(i_0_6829, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,esk533_4(X1,X3,X4,X5)))|~hBOOL(hAPP(hAPP(c_member(X5),X2),X3)))). 6.97/7.28 cnf(i_0_4926, 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,esk379_3(X2,X3,X1))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 6.97/7.28 cnf(i_0_6250, 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,esk487_3(X2,X3,X1))!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 6.97/7.28 cnf(i_0_2912, 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)))). 6.97/7.28 cnf(i_0_677, plain, (hBOOL(hAPP(X1,esk56_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))))). 6.97/7.28 cnf(i_0_2544, 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))))). 6.97/7.28 cnf(i_0_1314, 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))))). 6.97/7.28 cnf(i_0_7025, plain, (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)),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),X1))))). 6.97/7.28 cnf(i_0_1036, 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)))). 6.97/7.28 cnf(i_0_349, 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))). 6.97/7.28 cnf(i_0_4597, 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_Rings_Ozero__neq__one(X1)|~class_Rings_Ono__zero__divisors(X1)|~class_Rings_Omult__zero(X1)|~class_Power_Opower(X1))). 6.97/7.28 cnf(i_0_4139, plain, (c_Relation_Osym(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk313_2(X2,X1)),esk312_2(X2,X1))),X2)))). 6.97/7.28 cnf(i_0_7234, plain, (c_Relation_Otrans(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk562_2(X2,X1)),esk564_2(X2,X1))),X2)))). 6.97/7.28 cnf(i_0_2236, plain, (c_Nitpick_Orefl_H(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk172_2(X2,X1)),esk172_2(X2,X1))),X2)))). 6.97/7.28 cnf(i_0_6203, 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)))). 6.97/7.28 cnf(i_0_1497, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|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))). 6.97/7.28 cnf(i_0_5183, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X2),esk401_2(X1,X2)),X1)))). 6.97/7.28 cnf(i_0_5213, 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))))). 6.97/7.28 cnf(i_0_6413, 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))))). 6.97/7.28 cnf(i_0_262, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_member(X1),esk24_2(X2,X1)),X2)))). 6.97/7.28 cnf(i_0_7471, 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))). 6.97/7.28 cnf(i_0_1222, 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))). 6.97/7.28 cnf(i_0_2580, 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)))). 6.97/7.28 cnf(i_0_6161, plain, (c_Orderings_Oord__class_OLeast(X1,X2)=X3|hBOOL(hAPP(X2,esk486_3(X3,X2,X1)))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(X2,X3)))). 6.97/7.28 cnf(i_0_5441, plain, (X1=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3)|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X3),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X4))))). 6.97/7.28 cnf(i_0_1972, 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)))). 6.97/7.28 cnf(i_0_769, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 6.97/7.28 cnf(i_0_1102, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 6.97/7.28 cnf(i_0_7177, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 6.97/7.28 cnf(i_0_797, plain, (hAPP(c_Fun_Ooverride__on(X1,X2,X3,X4,X5),X6)=hAPP(X4,X6)|~hBOOL(hAPP(hAPP(c_member(X1),X6),X5)))). 6.97/7.28 cnf(i_0_4448, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_Oimage(X2,X1,X3),X4)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 6.97/7.28 cnf(i_0_6311, 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)))). 6.97/7.28 cnf(i_0_6736, 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)))). 6.97/7.28 cnf(i_0_1701, 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))). 6.97/7.28 cnf(i_0_5973, 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))). 6.97/7.28 cnf(i_0_31, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk2_2(X1,X2)),X1))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1)))). 6.97/7.28 cnf(i_0_5018, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk391_2(X1,X2)),X1))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1)))). 6.97/7.28 cnf(i_0_5691, plain, (X1=hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2))|hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2))!=hAPP(c_List_Orev(X2),X1))). 6.97/7.28 cnf(i_0_3159, plain, (c_List_Olist__ex1(X1,X2,X3)|esk242_4(X3,X2,X1,X4)!=X4|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X2,X4)))). 6.97/7.28 cnf(i_0_6740, plain, (c_List_Olist__ex1(X1,X2,X3)|esk527_4(X3,X2,X1,X4)!=X4|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X2,X4)))). 6.97/7.28 cnf(i_0_5882, 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))). 6.97/7.28 cnf(i_0_4767, 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))). 6.97/7.28 cnf(i_0_4008, 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))))). 6.97/7.28 cnf(i_0_4007, 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))))). 6.97/7.28 cnf(i_0_2121, 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))). 6.97/7.28 cnf(i_0_4045, 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))). 6.97/7.28 cnf(i_0_1990, 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))). 6.97/7.28 cnf(i_0_3036, 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))))). 6.97/7.28 cnf(i_0_3035, 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))))). 6.97/7.28 cnf(i_0_5104, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(X1,esk397_3(X3,X2,X1)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 6.97/7.28 cnf(i_0_6958, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(X1,esk545_3(X3,X2,X1)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 6.97/7.28 cnf(i_0_6218, 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))). 6.97/7.28 cnf(i_0_7323, 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)))). 6.97/7.28 cnf(i_0_223, 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))). 6.97/7.28 cnf(i_0_2569, 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))). 6.97/7.28 cnf(i_0_4041, 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_Rings_Osemiring__0(X1)|~class_Power_Opower(X1))). 6.97/7.28 cnf(i_0_3520, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(X1,esk269_3(X3,X2,X1)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 6.97/7.28 cnf(i_0_3749, 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)))). 6.97/7.28 cnf(i_0_2169, 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)))). 6.97/7.28 cnf(i_0_6761, 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))). 6.97/7.28 cnf(i_0_884, 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))). 6.97/7.28 cnf(i_0_5647, 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))). 6.97/7.28 cnf(i_0_3682, 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))). 6.97/7.28 cnf(i_0_3701, 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))). 6.97/7.28 cnf(i_0_6673, 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)))). 6.97/7.28 cnf(i_0_6194, 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)))). 6.97/7.28 cnf(i_0_5238, 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))). 6.97/7.28 cnf(i_0_2032, 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))). 6.97/7.28 cnf(i_0_4013, 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))). 6.97/7.28 cnf(i_0_5999, 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)))). 6.97/7.28 cnf(i_0_6193, 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)))). 6.97/7.28 cnf(i_0_3931, 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)))). 6.97/7.28 cnf(i_0_3930, 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)))). 6.97/7.28 cnf(i_0_3523, 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))))). 6.97/7.28 cnf(i_0_1993, 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))). 6.97/7.28 cnf(i_0_1034, 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)))). 6.97/7.28 cnf(i_0_3248, 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))))). 6.97/7.28 cnf(i_0_156, plain, (hAPP(X1,X2)=hAPP(c_Finite__Set_Ofold1(X3,X4),X2)|~c_Big__Operators_Osemilattice__big(X3,X4,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)))). 6.97/7.28 cnf(i_0_47, plain, (c_List_OtakeWhile(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=c_List_Olist_ONil(X1)|hBOOL(hAPP(X2,X3)))). 6.97/7.28 cnf(i_0_7112, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk549_1(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 6.97/7.28 cnf(i_0_4057, 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)))). 6.97/7.28 cnf(i_0_3320, 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)))). 6.97/7.28 cnf(i_0_4655, 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)))). 6.97/7.28 cnf(i_0_723, 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))). 6.97/7.28 cnf(i_0_5789, 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)))). 6.97/7.28 cnf(i_0_6678, plain, (hAPP(X1,X2)=hAPP(c_Finite__Set_Ofold1(X3,X4),X2)|~c_Finite__Set_Ofolding__one(X3,X4,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)))). 6.97/7.28 cnf(i_0_5830, 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)))))). 6.97/7.28 cnf(i_0_5829, 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),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))))). 6.97/7.28 cnf(i_0_2693, 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)))). 6.97/7.28 cnf(i_0_1151, plain, (c_Relation_Ototal__on(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk91_3(X3,X2,X1)),X2)))). 6.97/7.28 cnf(i_0_2538, 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)))). 6.97/7.28 cnf(i_0_4156, 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))). 6.97/7.28 cnf(i_0_1352, 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))). 6.97/7.28 cnf(i_0_1150, plain, (c_Relation_Ototal__on(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk92_3(X3,X2,X1)),X2)))). 6.97/7.28 cnf(i_0_7119, 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))))). 6.97/7.28 cnf(i_0_1899, 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))))). 6.97/7.28 cnf(i_0_6876, 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))))). 6.97/7.28 cnf(i_0_3174, plain, (hBOOL(hAPP(X1,esk243_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))|~hBOOL(hAPP(X1,X3)))). 6.97/7.28 cnf(i_0_1133, plain, (c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X1|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)))). 6.97/7.28 cnf(i_0_2415, plain, (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),X2),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 6.97/7.28 cnf(i_0_2414, plain, (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)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 6.97/7.28 cnf(i_0_2819, 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))). 6.97/7.28 cnf(i_0_4590, plain, (hBOOL(hAPP(X1,esk350_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))|~hBOOL(hAPP(X1,X3)))). 6.97/7.28 cnf(i_0_4449, 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))))). 6.97/7.28 cnf(i_0_2418, 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))))). 6.97/7.28 cnf(i_0_3145, plain, (hBOOL(hAPP(X1,X2))|~c_List_Oall__interval__nat(X1,X3,X4)|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))))). 6.97/7.28 cnf(i_0_1348, 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))))). 6.97/7.28 cnf(i_0_5740, 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))))). 6.97/7.28 cnf(i_0_4863, 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))))). 6.97/7.28 cnf(i_0_3817, 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))))). 6.97/7.28 cnf(i_0_6410, 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))). 6.97/7.28 cnf(i_0_6704, 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)))). 6.97/7.28 cnf(i_0_5145, 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)))). 6.97/7.28 cnf(i_0_549, 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),esk42_3(X2,X3,X1))))). 6.97/7.28 cnf(i_0_879, 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),esk72_3(X3,X2,X1))))). 6.97/7.28 cnf(i_0_646, 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))))). 6.97/7.28 cnf(i_0_360, 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))))). 6.97/7.28 cnf(i_0_4868, 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))))). 6.97/7.28 cnf(i_0_3524, 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,esk269_3(X1,X3,X2))))). 6.97/7.28 cnf(i_0_6130, 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))). 6.97/7.28 cnf(i_0_3330, plain, (hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))|~hBOOL(hAPP(X1,esk255_3(X3,X2,X1)))|~hBOOL(hAPP(X1,esk257_3(X3,X2,X1)))|~hBOOL(hAPP(X1,X2)))). 6.97/7.28 cnf(i_0_2305, 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),esk182_3(X3,X2,X1)),X3)))). 6.97/7.28 cnf(i_0_5749, 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),esk443_3(X3,X2,X1)),X3)))). 6.97/7.28 cnf(i_0_6145, 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)))). 6.97/7.28 cnf(i_0_4749, 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))))). 6.97/7.28 cnf(i_0_4493, 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))))). 6.97/7.28 cnf(i_0_4983, 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)))). 6.97/7.28 cnf(i_0_1616, 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))). 6.97/7.28 cnf(i_0_3774, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),X4))|~c_Typedef_Otype__definition(X5,X1,X2,X6,X4))). 6.97/7.28 cnf(i_0_987, 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)))). 6.97/7.28 cnf(i_0_6972, 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))))). 6.97/7.28 cnf(i_0_4291, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OatLeast(X1,X3,X4)))|~hBOOL(hAPP(hAPP(X3,X4),X2)))). 6.97/7.28 cnf(i_0_5578, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OgreaterThan(X1,X3,X4)))|~hBOOL(hAPP(hAPP(X3,X4),X2)))). 6.97/7.28 cnf(i_0_1178, 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)))). 6.97/7.28 cnf(i_0_7377, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X3,X4),esk584_3(X4,X3,X1)),esk585_3(X4,X3,X1)))))). 6.97/7.28 cnf(i_0_4568, 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)))). 6.97/7.28 cnf(i_0_1209, 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)))). 6.97/7.28 cnf(i_0_2631, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OlessThan(X1,X3,X4)))|~hBOOL(hAPP(hAPP(X3,X2),X4)))). 6.97/7.28 cnf(i_0_6391, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OatMost(X1,X3,X4)))|~hBOOL(hAPP(hAPP(X3,X2),X4)))). 6.97/7.28 cnf(i_0_2685, 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)))). 6.97/7.28 cnf(i_0_1441, plain, (hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3),X4))|~hBOOL(hAPP(X3,X4)))). 6.97/7.28 cnf(i_0_185, 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))). 6.97/7.28 cnf(i_0_7103, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),c_Groups_Ozero__class_Ozero(X1))!=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber(X1))). 6.97/7.28 cnf(i_0_1440, plain, (hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3),X4))|~hBOOL(hAPP(X2,X4)))). 6.97/7.28 cnf(i_0_716, 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))). 6.97/7.28 cnf(i_0_2406, plain, (c_Groups_Osgn__class_Osgn(X1,X2)=c_Groups_Oone__class_Oone(X1)|X2=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Osgn__if(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 6.97/7.28 cnf(i_0_2410, 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)))). 6.97/7.28 cnf(i_0_3742, 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)))). 6.97/7.28 cnf(i_0_492, 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))). 6.97/7.28 cnf(i_0_3279, 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))). 6.97/7.28 cnf(i_0_5313, 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))))). 6.97/7.28 cnf(i_0_345, 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)))). 6.97/7.28 cnf(i_0_6050, 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)))). 6.97/7.28 cnf(i_0_1603, 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)))). 6.97/7.28 cnf(i_0_5436, 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))). 6.97/7.28 cnf(i_0_959, 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))))). 6.97/7.28 cnf(i_0_4242, plain, (c_Relation_Oantisym(X1,X2)|~c_Relation_Oantisym(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))))))). 6.97/7.28 cnf(i_0_4246, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Rings_Odvd(X1))). 6.97/7.28 cnf(i_0_5088, 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)))). 6.97/7.28 cnf(i_0_1660, 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),esk139_3(X3,X2,X1))))). 6.97/7.28 cnf(i_0_4462, 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),esk340_3(X2,X3,X1))))). 6.97/7.28 cnf(i_0_2378, 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))). 6.97/7.28 cnf(i_0_6047, plain, (c_Wellfounded_Owf(X1,X2)|hBOOL(hAPP(hAPP(c_member(X1),esk474_2(X2,X1)),esk473_2(X2,X1))))). 6.97/7.28 cnf(i_0_6884, 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),esk540_3(X3,X2,X1))))). 6.97/7.28 cnf(i_0_4026, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),esk306_3(X3,X2,X1)),X3)))). 6.97/7.28 cnf(i_0_2964, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))|~hBOOL(hAPP(hAPP(X2,X3),X4))|~hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X4)))). 6.97/7.28 cnf(i_0_5100, plain, (hBOOL(hAPP(hAPP(X1,esk396_3(X2,X1,X3)),X2))|hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2)))). 6.97/7.28 cnf(i_0_1464, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk116_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))))). 6.97/7.28 cnf(i_0_5026, 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))). 6.97/7.28 cnf(i_0_3968, 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))). 6.97/7.28 cnf(i_0_6821, plain, (hBOOL(hAPP(hAPP(X1,esk532_3(X2,X1,X3)),X2))|hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2)))). 6.97/7.28 cnf(i_0_2618, 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))))). 6.97/7.28 cnf(i_0_2619, 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))))). 6.97/7.28 cnf(i_0_7070, 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))). 6.97/7.28 cnf(i_0_5788, 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))). 6.97/7.28 cnf(i_0_2606, 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))). 6.97/7.28 cnf(i_0_4255, 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))). 6.97/7.28 cnf(i_0_2522, 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)))). 6.97/7.28 cnf(i_0_2521, 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)))). 6.97/7.28 cnf(i_0_233, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk18_1(X1)))|hBOOL(hAPP(X1,X2)))). 6.97/7.28 cnf(i_0_231, 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,esk19_1(X1))))). 6.97/7.28 cnf(i_0_1337, 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))). 6.97/7.28 cnf(i_0_3501, 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))). 6.97/7.28 cnf(i_0_6270, 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))). 6.97/7.28 cnf(i_0_4411, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))|~class_Rings_Ocomm__semiring__1(X1)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),X3)))). 6.97/7.28 cnf(i_0_6778, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))|~class_Rings_Ocomm__semiring__1(X1)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3)))). 6.97/7.28 cnf(i_0_6375, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|~c_Wellfounded_Owf(X1,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Relation_OImage(X1,X1,X3),X2))))). 6.97/7.28 cnf(i_0_7529, 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))). 6.97/7.28 cnf(i_0_6453, 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))). 6.97/7.28 cnf(i_0_5692, 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))). 6.97/7.28 cnf(i_0_4734, 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))). 6.97/7.28 cnf(i_0_4495, plain, (hAPP(X1,hAPP(X2,X3))=X3|~c_Typedef_Otype__definition(X4,X5,X1,X2,X6)|~hBOOL(hAPP(hAPP(c_member(X5),X3),X6)))). 6.97/7.28 cnf(i_0_6746, 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)))). 6.97/7.28 cnf(i_0_2789, 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)))). 6.97/7.28 cnf(i_0_432, plain, (~hBOOL(hAPP(hAPP(c_member(X1),esk38_5(X2,X3,X4,X5,X1)),esk39_5(X2,X3,X4,X5,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X5,hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)),X2)))). 6.97/7.28 cnf(i_0_450, plain, (~class_Int_Onumber__ring(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Oone__class_Oone(tc_Int_Oint))))). 6.97/7.28 cnf(i_0_5300, 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))). 6.97/7.28 cnf(i_0_7560, 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))). 6.97/7.28 cnf(i_0_5211, plain, (~hBOOL(hAPP(hAPP(c_member(X1),esk403_5(X2,X3,X4,X5,X1)),esk404_5(X2,X3,X4,X5,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X5,hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)),X2)))). 6.97/7.28 cnf(i_0_581, 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)))). 6.97/7.28 cnf(i_0_6976, 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)))). 6.97/7.28 cnf(i_0_96, 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))). 6.97/7.28 cnf(i_0_3390, 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))). 6.97/7.28 cnf(i_0_7349, 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))))). 6.97/7.28 cnf(i_0_6624, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X2,esk516_3(X1,X3,X2)))|~hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1))))). 6.97/7.28 cnf(i_0_3217, 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)))). 6.97/7.28 cnf(i_0_1994, 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_Groups_Otimes__class_Otimes(X2),X1),X1)!=c_Groups_Oone__class_Oone(X2)|~class_Rings_Oring__1__no__zero__divisors(X2))). 6.97/7.28 cnf(i_0_3463, plain, (hAPP(X1,esk262_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)))). 6.97/7.28 cnf(i_0_554, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),esk43_3(X3,X2,X1)),c_Wellfounded_Oacc(X1,X3))))). 6.97/7.28 cnf(i_0_2560, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),esk203_3(X3,X2,X1)),c_Wellfounded_Oacc(X1,X3))))). 6.97/7.28 cnf(i_0_6583, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),esk515_3(X3,X2,X1)),c_Wellfounded_Oacc(X1,X3))))). 6.97/7.28 cnf(i_0_5382, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Quotient_ORespects(X1,X3)))|~hBOOL(hAPP(hAPP(X3,X2),X2)))). 6.97/7.28 cnf(i_0_225, 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)))). 6.97/7.28 cnf(i_0_1699, 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)))). 6.97/7.28 cnf(i_0_1566, 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))). 6.97/7.28 cnf(i_0_1732, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=X1|X2=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))). 6.97/7.28 cnf(i_0_212, plain, (c_Orderings_Oorder__class_Omono(tc_Nat_Onat,X1,X2)|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,esk16_2(X2,X1))),hAPP(X2,hAPP(c_Nat_OSuc,esk16_2(X2,X1))))))). 6.97/7.28 cnf(i_0_3431, 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)))). 6.97/7.28 cnf(i_0_2717, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Onumber__ring(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))). 6.97/7.28 cnf(i_0_2037, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Onumber__ring(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))). 6.97/7.28 cnf(i_0_1026, 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))))). 6.97/7.28 cnf(i_0_1843, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)=X3|~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)))))). 6.97/7.28 cnf(i_0_382, 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))))). 6.97/7.28 cnf(i_0_1456, 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))))). 6.97/7.28 cnf(i_0_3583, 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)))). 6.97/7.28 cnf(i_0_2260, 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))). 6.97/7.28 cnf(i_0_7105, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),c_Groups_Ozero__class_Ozero(X1))=hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)|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))). 6.97/7.28 cnf(i_0_234, 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))))). 6.97/7.28 cnf(i_0_5734, 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))). 6.97/7.28 cnf(i_0_2790, 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))). 6.97/7.28 cnf(i_0_1240, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X3),X4)!=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)))). 6.97/7.28 cnf(i_0_3445, 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)))). 6.97/7.28 cnf(i_0_2564, plain, (X1=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))!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__ring__strict(X2))). 6.97/7.28 cnf(i_0_2565, 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))). 6.97/7.28 cnf(i_0_1642, 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))|esk137_3(X3,X2,X1)=esk138_3(X3,X2,X1))). 6.97/7.28 cnf(i_0_7030, plain, (X1=c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)|X3=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X2,X3),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4),X1))))). 6.97/7.28 cnf(i_0_2957, 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))))). 6.97/7.28 cnf(i_0_4115, 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))))). 6.97/7.28 cnf(i_0_1122, 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)))). 6.97/7.28 cnf(i_0_4446, 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)))))). 6.97/7.28 cnf(i_0_6929, 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)))))). 6.97/7.28 cnf(i_0_6930, 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)))))). 6.97/7.28 cnf(i_0_5344, 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))))). 6.97/7.28 cnf(i_0_3407, 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_Ominus__class_Ominus(tc_Int_Oint),X2),c_Int_OMin))))). 6.97/7.28 cnf(i_0_1769, 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))))). 6.97/7.28 cnf(i_0_6222, 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))))). 6.97/7.28 cnf(i_0_2805, 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))))). 6.97/7.28 cnf(i_0_7339, 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))))). 6.97/7.28 cnf(i_0_6758, 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))))). 6.97/7.28 cnf(i_0_6340, 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))))). 6.97/7.28 cnf(i_0_7309, 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)))). 6.97/7.28 cnf(i_0_2033, 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))))). 6.97/7.28 cnf(i_0_1397, 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))). 6.97/7.28 cnf(i_0_689, 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)))). 6.97/7.28 cnf(i_0_5977, plain, (esk469_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)))). 6.97/7.28 cnf(i_0_3675, 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))))). 6.97/7.28 cnf(i_0_2385, 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_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin)),X2)))). 6.97/7.28 cnf(i_0_206, 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))). 6.97/7.28 cnf(i_0_4609, 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))))). 6.97/7.28 cnf(i_0_5083, plain, (X1=X2|c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2,X1)!=hAPP(c_fequal,X3))). 6.97/7.28 cnf(i_0_5082, plain, (X1=X2|c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3,X1)!=hAPP(c_fequal,X2))). 6.97/7.28 cnf(i_0_4288, plain, (c_Relation_Osym(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))|~c_Relation_Osym(X1,X2))). 6.97/7.28 cnf(i_0_6875, 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))). 6.97/7.28 cnf(i_0_4984, 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),esk386_2(X2,X1))))). 6.97/7.28 cnf(i_0_2207, 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))))). 6.97/7.28 cnf(i_0_36, 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))))). 6.97/7.28 cnf(i_0_2012, 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))))). 6.97/7.28 cnf(i_0_4616, 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)))). 6.97/7.28 cnf(i_0_63, 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))). 6.97/7.28 cnf(i_0_197, 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))). 6.97/7.28 cnf(i_0_2, 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))). 6.97/7.28 cnf(i_0_6013, 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))). 6.97/7.28 cnf(i_0_3081, 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))))). 6.97/7.28 cnf(i_0_6348, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X3),X4),esk499_4(X2,X1,X4,X3))))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X4))))). 6.97/7.28 cnf(i_0_1586, 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),esk130_5(X5,X4,X3,X2,X1))))|~hBOOL(hAPP(X4,X6)))). 6.97/7.28 cnf(i_0_3877, 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))). 6.97/7.28 cnf(i_0_4562, 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))). 6.97/7.28 cnf(i_0_3132, 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))). 6.97/7.28 cnf(i_0_95, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))|~class_Rings_Ocomm__semiring__1(X1))). 6.97/7.28 cnf(i_0_899, 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))). 6.97/7.28 cnf(i_0_557, plain, (hAPP(c_List_Ofilter(X1,X2),c_List_Oremove1(X1,X3,X4))=hAPP(c_List_Ofilter(X1,X2),X4)|hBOOL(hAPP(X2,X3)))). 6.97/7.28 cnf(i_0_1082, 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),esk87_5(X3,X2,X5,X4,X1))))|~hBOOL(hAPP(X4,X6)))). 6.97/7.28 cnf(i_0_4063, 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))))). 6.97/7.28 cnf(i_0_7394, plain, (hBOOL(hAPP(X1,esk586_1(X1)))|~hBOOL(hAPP(X1,X2)))). 6.97/7.28 cnf(i_0_1483, 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)))). 6.97/7.28 cnf(i_0_5752, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Rings_Ocomm__semiring__1(X1))). 7.00/7.28 cnf(i_0_26, 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))). 7.00/7.28 cnf(i_0_3868, 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))). 7.00/7.28 cnf(i_0_802, 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))). 7.00/7.28 cnf(i_0_3296, 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))). 7.00/7.28 cnf(i_0_3986, 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)))). 7.00/7.28 cnf(i_0_6236, 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))))). 7.00/7.28 cnf(i_0_990, 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))))). 7.00/7.28 cnf(i_0_2292, 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))))). 7.00/7.28 cnf(i_0_6420, 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))))). 7.00/7.28 cnf(i_0_2584, 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))). 7.00/7.28 cnf(i_0_5016, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk392_1(X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X2)))). 7.00/7.28 cnf(i_0_29, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),esk3_1(X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X2)))). 7.00/7.28 cnf(i_0_1463, 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,esk116_2(X1,X2))))). 7.00/7.28 cnf(i_0_3727, 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))). 7.00/7.28 cnf(i_0_2413, 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))). 7.00/7.28 cnf(i_0_6521, 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)))). 7.00/7.28 cnf(i_0_1045, 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))))). 7.00/7.28 cnf(i_0_5739, 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)))). 7.00/7.28 cnf(i_0_2137, 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))). 7.00/7.28 cnf(i_0_1014, 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)))). 7.00/7.28 cnf(i_0_1485, 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)))))). 7.00/7.28 cnf(i_0_7005, 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))). 7.00/7.28 cnf(i_0_4487, 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))))). 7.00/7.28 cnf(i_0_3567, 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))))). 7.00/7.28 cnf(i_0_4664, plain, (X1=c_Big__Operators_Olinorder__class_OMin(X2,X3)|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),esk359_3(X1,X3,X2)))|~hBOOL(hAPP(hAPP(c_member(X2),X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 7.00/7.28 cnf(i_0_1878, 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))))). 7.00/7.28 cnf(i_0_1322, 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))))). 7.00/7.28 cnf(i_0_4857, 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)))). 7.00/7.28 cnf(i_0_6474, 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)))). 7.00/7.28 cnf(i_0_7495, 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))))). 7.00/7.28 cnf(i_0_5424, 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)))). 7.00/7.28 cnf(i_0_952, 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)))). 7.00/7.28 cnf(i_0_2317, 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,esk184_4(X4,X3,X2,X1))!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 7.00/7.28 cnf(i_0_5617, 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)))). 7.00/7.28 cnf(i_0_5327, 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)))). 7.00/7.28 cnf(i_0_2164, 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))). 7.00/7.28 cnf(i_0_3900, plain, (c_List_Olist_ONil(X1)=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(X1)),X2))))). 7.00/7.28 cnf(i_0_510, 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,esk41_4(X4,X3,X1,X2))!=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))). 7.00/7.28 cnf(i_0_5228, 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,esk406_4(X4,X3,X2,X1))!=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))). 7.00/7.28 cnf(i_0_1715, 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,esk145_4(X4,X3,X1,X2))!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 7.00/7.28 cnf(i_0_7389, 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))))). 7.00/7.28 cnf(i_0_7537, 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))). 7.00/7.28 cnf(i_0_335, 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))). 7.00/7.28 cnf(i_0_2484, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk201_1(X1)))|~hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))))). 7.00/7.28 cnf(i_0_2087, plain, (c_Big__Operators_Olinorder__class_OMax(X1,X2)=X3|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk162_3(X3,X2,X1)),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 7.00/7.28 cnf(i_0_1245, plain, (c_Wellfounded_Owf(tc_prod(X1,X2),c_Recdef_Osame__fst(X1,X2,X3,X4))|~c_Wellfounded_Owf(X2,hAPP(X4,esk101_4(X1,X4,X2,X3))))). 7.00/7.28 cnf(i_0_2393, 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))). 7.00/7.28 cnf(i_0_2392, 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)))). 7.00/7.28 cnf(i_0_6802, 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))). 7.00/7.28 cnf(i_0_1043, 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)))). 7.00/7.28 cnf(i_0_3973, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk301_2(X2,X1)))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 7.00/7.28 cnf(i_0_6361, 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)))). 7.00/7.28 cnf(i_0_1618, plain, (X1=c_List_Olist_ONil(X2)|hBOOL(hAPP(hAPP(c_member(X2),c_List_Olast(X2,X1)),hAPP(c_List_Oset(X2),X1))))). 7.00/7.28 cnf(i_0_4713, plain, (c_FunDef_OTHE__default(X1,X2,X3)=c_HOL_OThe(X1,X3)|hBOOL(hAPP(X3,esk365_4(X2,X1,X3,X4)))|~hBOOL(hAPP(X3,X4)))). 7.00/7.28 cnf(i_0_1350, 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)))). 7.00/7.28 cnf(i_0_1591, 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))). 7.00/7.28 cnf(i_0_1028, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk84_3(X3,X1,X2))))|~c_List_Olist__ex(X2,X1,X3))). 7.00/7.28 cnf(i_0_3837, 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))). 7.00/7.28 cnf(i_0_7575, 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))). 7.00/7.28 cnf(i_0_7074, 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))). 7.00/7.28 cnf(i_0_5114, 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))). 7.00/7.28 cnf(i_0_6735, 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)))). 7.00/7.28 cnf(i_0_901, plain, (hBOOL(hAPP(X1,esk73_3(X2,X1,X3)))|~class_Rings_Osemiring__0(X3)|~class_Rings_Odvd(X3)|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X4))))). 7.00/7.28 cnf(i_0_5030, 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))). 7.00/7.28 cnf(i_0_5817, 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)))). 7.00/7.28 cnf(i_0_4928, 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),esk380_3(X2,X3,X1))))). 7.00/7.28 cnf(i_0_5265, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))|~class_Enum_Oenum(X1)|~class_Orderings_Oorder(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X3),X4)))). 7.00/7.28 cnf(i_0_3323, 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)))). 7.00/7.28 cnf(i_0_7168, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~class_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(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))))). 7.00/7.28 cnf(i_0_3056, 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))). 7.00/7.28 cnf(i_0_69, plain, (c_List_Olinorder__class_Osorted(X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk4_2(X2,X1)),esk5_2(X2,X1)))|~class_Orderings_Olinorder(X1))). 7.00/7.28 cnf(i_0_5926, plain, (c_List_Olinorder__class_Osorted(X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk460_2(X2,X1)),esk459_2(X2,X1)))|~class_Orderings_Olinorder(X1))). 7.00/7.28 cnf(i_0_5353, 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))). 7.00/7.28 cnf(i_0_1823, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~class_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(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))))). 7.00/7.28 cnf(i_0_4552, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(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))))). 7.00/7.28 cnf(i_0_1003, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(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))))). 7.00/7.28 cnf(i_0_4005, 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))). 7.00/7.28 cnf(i_0_6724, 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))))). 7.00/7.28 cnf(i_0_1512, 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))))). 7.00/7.28 cnf(i_0_1887, plain, (c_Fun_Oinj__on(X1,X2,c_Hilbert__Choice_Oinv__into(X2,X1,X3,X4),X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(c_Set_Oimage(X2,X1,X4),X3))))). 7.00/7.28 cnf(i_0_1544, 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)))))). 7.00/7.28 cnf(i_0_365, plain, (X1=hAPP(c_Set_Oimage(X2,X3,X4),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))|~c_Typedef_Otype__definition(X2,X3,X4,X5,X1))). 7.00/7.28 cnf(i_0_6920, 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)))). 7.00/7.28 cnf(i_0_3385, 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)). 7.00/7.28 cnf(i_0_7490, 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))))))). 7.00/7.28 cnf(i_0_1148, 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),esk91_3(X3,X2,X1)),esk92_3(X3,X2,X1))),X3)))). 7.00/7.28 cnf(i_0_1147, 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),esk92_3(X3,X2,X1)),esk91_3(X3,X2,X1))),X3)))). 7.00/7.28 cnf(i_0_5919, 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)))). 7.00/7.28 cnf(i_0_2155, 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)))). 7.00/7.28 cnf(i_0_4593, 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))))). 7.00/7.28 cnf(i_0_4594, 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))))). 7.00/7.28 cnf(i_0_1633, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk134_3(X2,X3,X1)),X2))|hBOOL(hAPP(c_Predicate_OPowp(X1,X3),X2)))). 7.00/7.28 cnf(i_0_2342, 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))))). 7.00/7.28 cnf(i_0_6996, 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)))). 7.00/7.28 cnf(i_0_6327, 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))))))). 7.00/7.28 cnf(i_0_2935, plain, (X1=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))|hAPP(c_Finite__Set_Ocard(X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))!=hAPP(c_Finite__Set_Ocard(X2),X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))). 7.00/7.28 cnf(i_0_88, plain, (c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),X1),X2,X3)|c_List_Olist__ex(tc_Int_Oint,X1,c_List_Oupto(X2,X3)))). 7.00/7.28 cnf(i_0_3878, 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)))). 7.00/7.28 cnf(i_0_3010, 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)))). 7.00/7.28 cnf(i_0_7076, 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)))). 7.00/7.28 cnf(i_0_5466, 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))). 7.00/7.28 cnf(i_0_4847, 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)))). 7.00/7.28 cnf(i_0_362, 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))))). 7.00/7.28 cnf(i_0_2311, plain, (c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|hAPP(c_Fun_Ocomp(X2,X1,X1,c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3)),X3)!=c_Fun_Oid(X1))). 7.00/7.28 cnf(i_0_4554, 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)))))). 7.00/7.28 cnf(i_0_3699, 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)))). 7.00/7.28 cnf(i_0_4327, 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)))). 7.00/7.28 cnf(i_0_4194, 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)))). 7.00/7.28 cnf(i_0_6947, plain, (hAPP(hAPP(c_List_Onth(X1),X2),esk544_3(X2,X3,X1))=X3|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2))))). 7.00/7.28 cnf(i_0_72, 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)))). 7.00/7.28 cnf(i_0_2282, 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),esk177_1(X1)))))). 7.00/7.28 cnf(i_0_3355, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1)))|~hBOOL(hAPP(X2,esk255_3(X1,X3,X2)))|~hBOOL(hAPP(X2,esk257_3(X1,X3,X2))))). 7.00/7.28 cnf(i_0_7067, 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)))). 7.00/7.28 cnf(i_0_6664, 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)))). 7.00/7.28 cnf(i_0_5449, 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))))). 7.00/7.28 cnf(i_0_4802, plain, (hBOOL(hAPP(hAPP(X1,hAPP(X2,X3)),hAPP(X2,X4)))|~c_Predicate_Oinv__imagep(X5,X6,X1,X2,X3,X4))). 7.00/7.28 cnf(i_0_6471, 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),esk505_3(X3,X2,X1)))))). 7.00/7.28 cnf(i_0_476, 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)))). 7.00/7.28 cnf(i_0_4108, 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)))). 7.00/7.28 cnf(i_0_57, 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)))). 7.00/7.28 cnf(i_0_980, 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)). 7.00/7.28 cnf(i_0_1745, 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))))). 7.00/7.28 cnf(i_0_1218, plain, (hBOOL(hAPP(X1,esk99_4(X1,X2,X3,X4)))|~c_Equiv__Relations_Oequivp(X4,X3)|~hBOOL(hAPP(X1,esk98_4(X1,X2,X3,X4)))|~hBOOL(hAPP(X2,X5)))). 7.00/7.28 cnf(i_0_5459, 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),esk416_3(X3,X2,X1)),X2)),X3)))). 7.00/7.28 cnf(i_0_2079, 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)))))). 7.00/7.28 cnf(i_0_1896, 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)))). 7.00/7.28 cnf(i_0_464, 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))). 7.00/7.28 cnf(i_0_2811, 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))). 7.00/7.28 cnf(i_0_5700, 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,esk435_1(X1))))=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.00/7.28 cnf(i_0_4030, 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)))). 7.00/7.28 cnf(i_0_1301, 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)))). 7.00/7.28 cnf(i_0_2748, 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))))). 7.00/7.28 cnf(i_0_3130, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk238_2(X1,X2)),X1))|hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X2,X1)))). 7.00/7.28 cnf(i_0_3821, 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))). 7.00/7.28 cnf(i_0_2514, 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))). 7.00/7.28 cnf(i_0_5943, 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)|esk462_2(X2,X1)!=c_List_Olist_ONil(X1))). 7.00/7.28 cnf(i_0_5486, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X3)=X2|c_Groups_Ozero__class_Ozero(X1)=X3|~class_Rings_Odivision__ring(X1))). 7.00/7.28 cnf(i_0_1696, plain, (hAPP(X1,esk143_4(X2,X1,X3,X4))=hAPP(X1,esk144_4(X2,X1,X3,X4))|c_Fun_Oinj__on(X4,X3,X1,X2))). 7.00/7.28 cnf(i_0_4850, 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,esk373_2(X1,X3))))). 7.00/7.28 cnf(i_0_6796, 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))))). 7.00/7.28 cnf(i_0_7436, 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)|esk590_2(X2,X1)!=c_List_Olist_ONil(X1))). 7.00/7.28 cnf(i_0_3126, 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))))). 7.00/7.28 cnf(i_0_7211, plain, (hBOOL(hAPP(X1,esk560_4(X1,X2,X3,X4)))|~hBOOL(hAPP(hAPP(c_member(X4),X5),X3))|~hBOOL(hAPP(X1,X5)))). 7.00/7.28 cnf(i_0_7209, plain, (hBOOL(hAPP(X1,esk560_4(X1,X2,X3,X4)))|~hBOOL(hAPP(hAPP(c_member(X4),X5),X2))|~hBOOL(hAPP(X1,X5)))). 7.00/7.28 cnf(i_0_1048, plain, (c_Fun_Obij__betw(X1,X2,X3,X4,X5)|~c_Fun_Obij__betw(X6,X2,hAPP(c_Fun_Ocomp(X1,X2,X6,X3),X7),X8,X5)|~c_Fun_Obij__betw(X6,X1,X7,X8,X4))). 7.00/7.28 cnf(i_0_3121, 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))). 7.00/7.28 cnf(i_0_2250, 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)))). 7.00/7.28 cnf(i_0_2249, 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)))). 7.00/7.28 cnf(i_0_2637, 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)))). 7.00/7.28 cnf(i_0_7551, 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)))). 7.00/7.28 cnf(i_0_346, 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)))). 7.00/7.28 cnf(i_0_4686, 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))). 7.00/7.28 cnf(i_0_6550, plain, (c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X2)=hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))|~class_Orderings_Oorder(X1))). 7.00/7.28 cnf(i_0_1335, 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))). 7.00/7.28 cnf(i_0_2162, 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))). 7.00/7.28 cnf(i_0_169, plain, (hAPP(c_Hilbert__Choice_Oinv__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)))). 7.00/7.28 cnf(i_0_4437, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),esk333_3(X1,X2,X3)),esk334_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)))). 7.00/7.28 cnf(i_0_67, 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),esk4_2(X2,X1))),hAPP(hAPP(c_List_Onth(X1),X2),esk5_2(X2,X1)))))). 7.00/7.28 cnf(i_0_5925, 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),esk460_2(X2,X1))),hAPP(hAPP(c_List_Onth(X1),X2),esk459_2(X2,X1)))))). 7.00/7.28 cnf(i_0_6620, 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))). 7.00/7.28 cnf(i_0_2977, 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)))). 7.00/7.28 cnf(i_0_2205, plain, (c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))|~c_Wellfounded_OwfP(X1,X2))). 7.00/7.28 cnf(i_0_5582, 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),esk425_1(X1)),hAPP(c_List_Oset(tc_Nat_Onat),X1))))). 7.00/7.28 cnf(i_0_4087, 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))). 7.00/7.28 cnf(i_0_465, 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)))). 7.00/7.28 cnf(i_0_2175, 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)))). 7.00/7.28 cnf(i_0_949, plain, (c_Relation_Osym(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))|~c_Predicate_Osymp(X1,X2))). 7.00/7.28 cnf(i_0_7179, plain, (c_Relation_Otrans(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))|~c_Predicate_Otransp(X1,X2))). 7.00/7.28 cnf(i_0_5552, plain, (c_Wellfounded_Oacyclic(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))|~c_Wellfounded_OwfP(X1,X2))). 7.00/7.28 cnf(i_0_2737, 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)))). 7.00/7.28 cnf(i_0_2176, 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)))). 7.00/7.28 cnf(i_0_4137, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~c_Predicate_Otransp(X4,X1)|~hBOOL(hAPP(hAPP(X1,X5),X3))|~hBOOL(hAPP(hAPP(X1,X2),X5)))). 7.00/7.28 cnf(i_0_6944, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~c_Equiv__Relations_Opart__equivp(X4,X1)|~hBOOL(hAPP(hAPP(X1,X5),X3))|~hBOOL(hAPP(hAPP(X1,X2),X5)))). 7.00/7.28 cnf(i_0_3164, plain, (esk241_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)))). 7.00/7.28 cnf(i_0_6738, plain, (esk528_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)))). 7.00/7.28 cnf(i_0_1698, plain, (c_Fun_Oinj__on(X1,X2,X3,X4)|hBOOL(hAPP(hAPP(c_member(X1),esk143_4(X4,X3,X2,X1)),X4)))). 7.00/7.28 cnf(i_0_5455, 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))). 7.00/7.28 cnf(i_0_3589, 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))). 7.00/7.28 cnf(i_0_5730, 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))). 7.00/7.28 cnf(i_0_1697, plain, (c_Fun_Oinj__on(X1,X2,X3,X4)|hBOOL(hAPP(hAPP(c_member(X1),esk144_4(X4,X3,X2,X1)),X4)))). 7.00/7.28 cnf(i_0_3027, 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))))). 7.00/7.28 cnf(i_0_3531, 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))))). 7.00/7.28 cnf(i_0_7378, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X2,X3),X4),X5)))|~hBOOL(hAPP(X1,esk583_3(X3,X2,X1))))). 7.00/7.28 cnf(i_0_5484, 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))))). 7.00/7.28 cnf(i_0_944, plain, (hAPP(c_Fun_Ooverride__on(X1,X2,X3,X4,X5),X6)=hAPP(X3,X6)|hBOOL(hAPP(hAPP(c_member(X1),X6),X5)))). 7.00/7.28 cnf(i_0_6176, 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))). 7.00/7.28 cnf(i_0_7200, 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))). 7.00/7.28 cnf(i_0_3474, 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))))). 7.00/7.28 cnf(i_0_5508, 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))))). 7.00/7.28 cnf(i_0_6643, 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))))). 7.00/7.28 cnf(i_0_5668, 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))))). 7.00/7.28 cnf(i_0_6120, 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)))). 7.00/7.28 cnf(i_0_984, 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))))). 7.00/7.28 cnf(i_0_6627, plain, (hBOOL(hAPP(X1,esk516_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))))). 7.00/7.28 cnf(i_0_2545, 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)))). 7.00/7.28 cnf(i_0_5494, plain, (hAPP(X1,esk417_4(X2,X1,X3,X4))=X4|~hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(c_Set_Oimage(X3,X5,X1),X2))))). 7.00/7.28 cnf(i_0_7132, plain, (hAPP(X1,esk552_4(X2,X1,X3,X4))=X4|~hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(c_Set_Oimage(X3,X5,X1),X2))))). 7.00/7.28 cnf(i_0_6689, 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))))). 7.00/7.28 cnf(i_0_1315, 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))))). 7.00/7.28 cnf(i_0_4314, 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))))). 7.00/7.28 cnf(i_0_5191, 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))). 7.00/7.28 cnf(i_0_612, 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))). 7.00/7.28 cnf(i_0_5862, 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))))). 7.00/7.28 cnf(i_0_1737, 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))))). 7.00/7.28 cnf(i_0_4002, 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))))). 7.00/7.28 cnf(i_0_5188, 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))))). 7.00/7.28 cnf(i_0_6640, 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))). 7.00/7.28 cnf(i_0_1349, 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)))). 7.00/7.28 cnf(i_0_2679, 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)))). 7.00/7.28 cnf(i_0_5796, 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))))). 7.00/7.28 cnf(i_0_2298, 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))))). 7.00/7.28 cnf(i_0_7197, 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,esk557_5(X5,X4,X3,X2,X1)),X5)))). 7.00/7.28 cnf(i_0_3091, 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,esk237_5(X2,X5,X4,X3,X1)),X5)))). 7.00/7.28 cnf(i_0_7042, 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))))). 7.00/7.28 cnf(i_0_463, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~class_Int_Onumber__ring(X3)|~class_Rings_Olinordered__idom(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))))). 7.00/7.28 cnf(i_0_5407, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~class_Int_Onumber__ring(X3)|~class_Rings_Olinordered__idom(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))))). 7.00/7.28 cnf(i_0_7219, 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)))))). 7.00/7.28 cnf(i_0_6479, 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)))))). 7.00/7.28 cnf(i_0_1552, 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)))). 7.00/7.28 cnf(i_0_3831, plain, (X1=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)|X3=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X2,X3),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X4))))). 7.00/7.28 cnf(i_0_3908, 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)))))). 7.00/7.28 cnf(i_0_5329, 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))). 7.00/7.28 cnf(i_0_2238, 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))))). 7.00/7.28 cnf(i_0_5800, plain, (c_List_Oremove1(X1,X2,X3)=X3|hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 7.00/7.28 cnf(i_0_725, 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))). 7.00/7.28 cnf(i_0_51, 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_Ominus__class_Ominus(tc_Int_Oint),X2),c_Int_OMin))))). 7.00/7.28 cnf(i_0_7226, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Nat_OSuc,X2))|~class_Rings_Osemiring__1(X1))). 7.00/7.28 cnf(i_0_788, 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)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2)). 7.00/7.28 cnf(i_0_2314, 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))). 7.00/7.28 cnf(i_0_5502, 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))). 7.00/7.28 cnf(i_0_6933, 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)))). 7.00/7.28 cnf(i_0_4906, 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),esk377_2(X1,X2))))). 7.00/7.28 cnf(i_0_7331, plain, (c_Relation_Osym(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~c_Relation_Osym(X1,X3)|~c_Relation_Osym(X1,X2))). 7.00/7.28 cnf(i_0_5842, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),esk453_2(X2,X1)),esk452_2(X2,X1))=X2|X2=c_List_Olist_ONil(X1)|~c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1))). 7.00/7.28 cnf(i_0_3044, plain, (hAPP(X1,esk231_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)))). 7.00/7.28 cnf(i_0_4436, plain, (hBOOL(hAPP(X1,esk334_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)))). 7.00/7.28 cnf(i_0_3401, 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))))). 7.00/7.28 cnf(i_0_5558, 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))))). 7.00/7.28 cnf(i_0_473, plain, (c_Relation_Osym(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~c_Relation_Osym(X1,X3)|~c_Relation_Osym(X1,X2))). 7.00/7.28 cnf(i_0_1531, plain, (c_Relation_Otrans(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~c_Relation_Otrans(X1,X3)|~c_Relation_Otrans(X1,X2))). 7.00/7.28 cnf(i_0_4191, 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)))). 7.00/7.28 cnf(i_0_1720, 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)))). 7.00/7.28 cnf(i_0_6832, 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)))). 7.00/7.28 cnf(i_0_195, 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,esk13_2(X1,X3))))). 7.00/7.28 cnf(i_0_3585, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk271_2(X2,X1)))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 7.00/7.28 cnf(i_0_4185, 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)))). 7.00/7.28 cnf(i_0_6871, 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)))). 7.00/7.28 cnf(i_0_836, 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))))))). 7.00/7.28 cnf(i_0_3444, 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)))). 7.00/7.28 cnf(i_0_3191, 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,esk247_3(X2,X1,X3)),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(X1,X2)))). 7.00/7.28 cnf(i_0_6444, plain, (hAPP(c_Finite__Set_Ocard(X1),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_member(X1),esk504_2(X2,X1)),X2)))). 7.00/7.28 cnf(i_0_2661, 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)))). 7.00/7.28 cnf(i_0_2976, 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))). 7.00/7.28 cnf(i_0_5362, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),esk410_3(X3,X2,X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))))). 7.00/7.28 cnf(i_0_1604, plain, (hAPP(X1,esk132_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)))). 7.00/7.28 cnf(i_0_5753, 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))). 7.00/7.28 cnf(i_0_4923, plain, (c_List_Olist_ONil(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),c_List_Olist_ONil(X1))),c_List_Olistrel(X1,X3))))). 7.00/7.28 cnf(i_0_848, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk66_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|~c_List_Olist__ex(X1,X3,X2))). 7.00/7.28 cnf(i_0_2303, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk181_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|~c_List_Olist__ex(X1,X3,X2))). 7.00/7.28 cnf(i_0_3162, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk241_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|~c_List_Olist__ex1(X1,X3,X2))). 7.00/7.28 cnf(i_0_4442, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk335_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))|~c_List_Olist__ex(X1,X2,X3))). 7.00/7.28 cnf(i_0_6755, 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)))). 7.00/7.28 cnf(i_0_1770, 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))))). 7.00/7.28 cnf(i_0_1641, 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)))). 7.00/7.28 cnf(i_0_3055, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)!=c_List_Opartition(X1,X4,X5)|~hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X4,X6)))). 7.00/7.28 cnf(i_0_5231, 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)). 7.00/7.28 cnf(i_0_6739, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk528_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|~c_List_Olist__ex1(X1,X3,X2))). 7.00/7.28 cnf(i_0_2911, 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))))). 7.00/7.28 cnf(i_0_6344, 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))). 7.00/7.28 cnf(i_0_3600, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)))|~hBOOL(hAPP(X1,esk273_3(X3,X2,X1)))|~hBOOL(hAPP(X1,esk275_3(X3,X2,X1)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.00/7.28 cnf(i_0_5688, 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,esk434_4(X1,X3,X2,X4))))). 7.00/7.28 cnf(i_0_3150, 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),esk240_5(X5,X4,X3,X2,X1))))). 7.00/7.28 cnf(i_0_6574, 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),esk514_5(X3,X5,X4,X2,X1))))). 7.00/7.28 cnf(i_0_2004, 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)). 7.00/7.28 cnf(i_0_7131, 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))). 7.00/7.28 cnf(i_0_4450, 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))))). 7.00/7.28 cnf(i_0_2419, 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))))). 7.00/7.28 cnf(i_0_6705, 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)))). 7.00/7.28 cnf(i_0_1694, 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)))). 7.00/7.28 cnf(i_0_5146, 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)))). 7.00/7.28 cnf(i_0_145, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X3)=X2|X3=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 7.00/7.28 cnf(i_0_3064, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X2)=X3|X2=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 7.00/7.28 cnf(i_0_5163, 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)))). 7.00/7.28 cnf(i_0_5491, 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)))). 7.00/7.28 cnf(i_0_287, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)|~class_Int_Onumber__ring(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3))))). 7.00/7.28 cnf(i_0_132, 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))). 7.00/7.28 cnf(i_0_4457, plain, (c_List_Olist_ONil(X1)=X2|hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_List_Ohd(X1),X2)),hAPP(c_List_Oset(X1),X2))))). 7.00/7.28 cnf(i_0_5848, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk455_2(X2,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))))). 7.00/7.28 cnf(i_0_4211, 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)))). 7.00/7.28 cnf(i_0_1080, plain, (hAPP(c_List_Ofilter(X1,X2),esk88_5(X3,X4,X5,X2,X1))=X3|hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3)!=hAPP(c_List_Ofilter(X1,X2),X5))). 7.00/7.28 cnf(i_0_1588, plain, (hAPP(c_List_Ofilter(X1,X2),esk131_5(X3,X2,X4,X5,X1))=X4|hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4)!=hAPP(c_List_Ofilter(X1,X2),X3))). 7.00/7.28 cnf(i_0_6772, 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)))). 7.00/7.28 cnf(i_0_4738, 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_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1))). 7.00/7.28 cnf(i_0_3141, 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))))). 7.00/7.28 cnf(i_0_2503, 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)))). 7.00/7.28 cnf(i_0_1655, 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)))). 7.00/7.28 cnf(i_0_396, 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)))). 7.00/7.28 cnf(i_0_4311, 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)))). 7.00/7.28 cnf(i_0_3816, 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)))). 7.00/7.28 cnf(i_0_359, 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)))). 7.00/7.28 cnf(i_0_858, plain, (hBOOL(hAPP(X1,X2))|~c_Fun_Oinj__on(X3,X4,X5,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))|~hBOOL(hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)),X5),esk69_5(X2,X1,X5,X4,X3)))))). 7.00/7.28 cnf(i_0_1398, plain, (X1=hAPP(c_Groups_Ouminus__class_Ouminus(X2),X3)|X3=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)|~class_Rings_Oidom(X2))). 7.00/7.28 cnf(i_0_647, 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)))). 7.00/7.28 cnf(i_0_4867, 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)))). 7.00/7.28 cnf(i_0_3404, 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)))). 7.00/7.28 cnf(i_0_5655, plain, (hAPP(X1,esk431_1(X1))=hAPP(X1,esk432_1(X1))|c_Equiv__Relations_Oequivp(X2,X1)|hBOOL(hAPP(hAPP(X1,esk431_1(X1)),esk432_1(X1))))). 7.00/7.28 cnf(i_0_309, plain, (X1=X2|hAPP(hAPP(c_List_Oappend(X3),X4),hAPP(hAPP(c_List_Olist_OCons(X3),X2),c_List_Olist_ONil(X3)))!=hAPP(hAPP(c_List_Oappend(X3),X5),hAPP(hAPP(c_List_Olist_OCons(X3),X1),c_List_Olist_ONil(X3))))). 7.00/7.28 cnf(i_0_308, 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))))). 7.00/7.28 cnf(i_0_5852, plain, (X1=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))). 7.00/7.28 cnf(i_0_3171, plain, (hBOOL(hAPP(X1,esk244_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)))). 7.00/7.28 cnf(i_0_6599, 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)))). 7.00/7.28 cnf(i_0_4232, 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)))). 7.00/7.28 cnf(i_0_7294, 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))). 7.00/7.28 cnf(i_0_2905, 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))). 7.00/7.28 cnf(i_0_3937, 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)). 7.00/7.28 cnf(i_0_623, 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)))). 7.00/7.28 cnf(i_0_4608, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 7.00/7.28 cnf(i_0_1431, plain, (X1=X2|hAPP(hAPP(c_List_Onth(X3),X1),esk114_3(X3,X2,X1))!=hAPP(hAPP(c_List_Onth(X3),X2),esk114_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))). 7.00/7.28 cnf(i_0_2518, 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))))). 7.00/7.28 cnf(i_0_1197, 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(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.00/7.28 cnf(i_0_6146, 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)))). 7.00/7.28 cnf(i_0_4748, 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)))). 7.00/7.28 cnf(i_0_4492, 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))))). 7.00/7.28 cnf(i_0_2407, plain, (c_Groups_Osgn__class_Osgn(X1,X2)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(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_Osgn__if(X1))). 7.00/7.28 cnf(i_0_1845, 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)))). 7.00/7.28 cnf(i_0_695, 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),esk59_3(X3,X2,X1)),esk60_3(X3,X2,X1))))). 7.00/7.28 cnf(i_0_3717, 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))). 7.00/7.28 cnf(i_0_4982, 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)))). 7.00/7.28 cnf(i_0_6971, 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))))). 7.00/7.28 cnf(i_0_988, 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)))). 7.00/7.28 cnf(i_0_7020, 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)))). 7.00/7.28 cnf(i_0_852, plain, (hBOOL(hAPP(hAPP(X1,X2),esk68_5(X3,X4,X1,X5,X2)))|~c_Wellfounded_Omax__extp(X5,X1,X4,X3)|~hBOOL(hAPP(hAPP(c_member(X5),X2),X4)))). 7.00/7.28 cnf(i_0_3181, plain, (hBOOL(hAPP(hAPP(X1,X2),esk245_5(X3,X4,X1,X5,X2)))|~c_Wellfounded_Omax__extp(X5,X1,X4,X3)|~hBOOL(hAPP(hAPP(c_member(X5),X2),X4)))). 7.00/7.28 cnf(i_0_3917, plain, (hBOOL(hAPP(X1,esk298_3(X1,X2,X3)))|~c_Equiv__Relations_Oequivp(X3,X2)|~hBOOL(hAPP(hAPP(c_member(X3),X4),c_Quotient_ORespects(X3,X2)))|~hBOOL(hAPP(X1,X4)))). 7.00/7.28 cnf(i_0_2474, 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)))). 7.00/7.28 cnf(i_0_6237, 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)))). 7.00/7.28 cnf(i_0_7509, 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)))). 7.00/7.28 cnf(i_0_4040, 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)))). 7.00/7.28 cnf(i_0_2472, 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)))). 7.00/7.28 cnf(i_0_794, 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))). 7.00/7.28 cnf(i_0_5419, 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)))). 7.00/7.28 cnf(i_0_7372, 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)))). 7.00/7.28 cnf(i_0_2903, 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)))). 7.00/7.28 cnf(i_0_1041, 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)))). 7.00/7.28 cnf(i_0_4435, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X3),esk333_3(X1,X2,X3)),esk334_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)))). 7.00/7.28 cnf(i_0_479, 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)))). 7.00/7.28 cnf(i_0_3192, plain, (hBOOL(hAPP(X1,esk247_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)))). 7.00/7.28 cnf(i_0_3204, 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))). 7.00/7.28 cnf(i_0_2534, 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))). 7.00/7.28 cnf(i_0_1444, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),esk115_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))))). 7.00/7.28 cnf(i_0_1443, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk115_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))))). 7.00/7.28 cnf(i_0_5621, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk427_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)))). 7.00/7.28 cnf(i_0_5620, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk427_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)))). 7.00/7.28 cnf(i_0_3786, 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)))). 7.00/7.28 cnf(i_0_6956, 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,esk545_3(X3,X2,X1))))). 7.00/7.28 cnf(i_0_5105, 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,esk397_3(X3,X2,X1))))). 7.00/7.28 cnf(i_0_1052, 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)))). 7.00/7.28 cnf(i_0_5743, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X2))|~c_Nat__Transfer_Ois__nat(X1)|~c_Nat__Transfer_Onat__set(X2)|~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))))). 7.00/7.28 cnf(i_0_5585, plain, (hAPP(X1,esk426_3(X1,X2,X3))=X3|~hBOOL(hAPP(hAPP(c_member(X4),X3),hAPP(c_Set_Oimage(X2,X4,X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))))). 7.00/7.28 cnf(i_0_2380, 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))). 7.00/7.28 cnf(i_0_4468, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk341_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))). 7.00/7.28 cnf(i_0_572, 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))). 7.00/7.28 cnf(i_0_4819, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X3)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(X3,X2))))). 7.00/7.28 cnf(i_0_3590, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X2)),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),X3)))). 7.00/7.28 cnf(i_0_4499, 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))))). 7.00/7.28 cnf(i_0_2906, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X2),c_Big__Operators_Olinorder__class_OMin(X2,X1)),X1))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 7.00/7.28 cnf(i_0_6873, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|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)))). 7.00/7.28 cnf(i_0_6235, 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)))). 7.00/7.28 cnf(i_0_991, 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)))). 7.00/7.28 cnf(i_0_6277, plain, (hAPP(hAPP(c_List_Onth(X1),X2),esk491_2(X2,X1))=hAPP(hAPP(c_List_Onth(X1),X2),esk492_2(X2,X1))|hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 7.00/7.28 cnf(i_0_2255, 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))))). 7.00/7.28 cnf(i_0_471, 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))))). 7.00/7.28 cnf(i_0_7063, 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))))). 7.00/7.28 cnf(i_0_4935, 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,X1)))). 7.00/7.28 cnf(i_0_2291, 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))))). 7.00/7.28 cnf(i_0_6419, 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))))). 7.00/7.28 cnf(i_0_1020, 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)))). 7.00/7.28 cnf(i_0_3383, 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))))). 7.00/7.28 cnf(i_0_7122, plain, (hAPP(c_List_Ohd(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))=hAPP(X3,hAPP(c_List_Ohd(X2),X4))|X4=c_List_Olist_ONil(X2))). 7.00/7.28 cnf(i_0_4375, 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))))). 7.00/7.28 cnf(i_0_1242, 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))))). 7.00/7.28 cnf(i_0_916, 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)|c_Orderings_Otop__class_Otop(X2)!=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X3),X1)|~class_Lattices_Oboolean__algebra(X2))). 7.00/7.28 cnf(i_0_1965, 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))). 7.00/7.28 cnf(i_0_2915, 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))). 7.00/7.28 cnf(i_0_5818, 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))). 7.00/7.28 cnf(i_0_1706, 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))). 7.00/7.28 cnf(i_0_5503, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(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))). 7.00/7.28 cnf(i_0_4267, 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)))). 7.00/7.28 cnf(i_0_766, 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)))). 7.00/7.28 cnf(i_0_371, 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))). 7.00/7.28 cnf(i_0_4396, 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)|~class_Int_Onumber__ring(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))). 7.00/7.28 cnf(i_0_4114, 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)))). 7.00/7.28 cnf(i_0_4119, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X3,X2),esk310_3(X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 7.00/7.28 cnf(i_0_2917, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(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))). 7.00/7.28 cnf(i_0_6048, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk472_3(X2,X1,X3)),X3))|~c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3)))). 7.00/7.28 cnf(i_0_2996, plain, (hBOOL(hAPP(hAPP(X1,esk227_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)))). 7.00/7.28 cnf(i_0_5033, plain, (hBOOL(hAPP(hAPP(X1,esk393_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)))). 7.00/7.28 cnf(i_0_6843, 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,esk537_3(X3,X2,X1)))),hAPP(X3,esk537_3(X3,X2,X1)))),X2)))). 7.00/7.28 cnf(i_0_4316, 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))))). 7.00/7.28 cnf(i_0_7479, 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,esk593_3(X2,X1,X3)))),hAPP(X3,esk593_3(X2,X1,X3)))),X2)))). 7.00/7.28 cnf(i_0_3246, 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))). 7.00/7.28 cnf(i_0_3601, 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)))|~hBOOL(hAPP(X2,esk273_3(X1,X3,X2)))|~hBOOL(hAPP(X2,esk275_3(X1,X3,X2))))). 7.00/7.28 cnf(i_0_938, plain, (hAPP(hAPP(c_Set_Oinsert(X1),esk80_3(X2,X3,X1)),esk81_3(X2,X3,X1))=X3|hAPP(c_Finite__Set_Ocard(X1),X3)!=hAPP(c_Nat_OSuc,X2))). 7.00/7.28 cnf(i_0_5550, plain, (c_List_Olist__all(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk423_3(X3,X2,X1)),hAPP(c_List_Oset(X1),X3))))). 7.00/7.28 cnf(i_0_5936, plain, (c_List_Olist__all(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk461_3(X3,X2,X1)),hAPP(c_List_Oset(X1),X3))))). 7.00/7.28 cnf(i_0_7406, 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))). 7.00/7.28 cnf(i_0_5080, 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))))). 7.00/7.28 cnf(i_0_281, 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))))). 7.00/7.28 cnf(i_0_6567, plain, (c_List_Olist__all(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk513_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3))))). 7.00/7.28 cnf(i_0_7443, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk591_2(X1,X2)),c_Int_OInteg))|hBOOL(hAPP(X2,X1)))). 7.00/7.28 cnf(i_0_4604, plain, (c_List_Oall__interval__int(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk352_3(X3,X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X2,X3))))). 7.00/7.28 cnf(i_0_292, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X2)),hAPP(X2,c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X2))))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~c_Orderings_Oorder__class_Omono(X1,X1,X2))). 7.00/7.28 cnf(i_0_4836, 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)))). 7.00/7.28 cnf(i_0_3410, 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))))). 7.00/7.28 cnf(i_0_4014, 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))))). 7.00/7.28 cnf(i_0_6918, 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))|X3=X2)). 7.00/7.28 cnf(i_0_6208, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X2)),hAPP(X2,c_Inductive_Ocomplete__lattice__class_Olfp(X1,X2))))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~c_Orderings_Oorder__class_Omono(X1,X1,X2))). 7.00/7.28 cnf(i_0_2509, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X2))),c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X2)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~c_Orderings_Oorder__class_Omono(X1,X1,X2))). 7.00/7.28 cnf(i_0_5649, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,c_Inductive_Ocomplete__lattice__class_Olfp(X1,X2))),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X2)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~c_Orderings_Oorder__class_Omono(X1,X1,X2))). 7.00/7.28 cnf(i_0_520, 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)))). 7.00/7.28 cnf(i_0_3929, 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))))))). 7.00/7.28 cnf(i_0_7364, 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)))))). 7.00/7.28 cnf(i_0_4418, plain, (hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))|hBOOL(hAPP(X1,esk332_3(X1,X3,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(X1,X3)))). 7.00/7.28 cnf(i_0_1027, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk84_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X1)))|~c_List_Olist__ex(X3,X2,X1))). 7.00/7.28 cnf(i_0_4172, 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))). 7.00/7.28 cnf(i_0_2281, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk178_1(X1)))|hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))))). 7.00/7.28 cnf(i_0_3461, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk262_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)))). 7.00/7.28 cnf(i_0_7513, 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)))))). 7.00/7.28 cnf(i_0_210, 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)))))). 7.00/7.28 cnf(i_0_7388, 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))))). 7.00/7.28 cnf(i_0_6404, 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))). 7.00/7.28 cnf(i_0_4477, 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))). 7.00/7.28 cnf(i_0_5477, 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))))). 7.00/7.28 cnf(i_0_5478, 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))))). 7.00/7.28 cnf(i_0_3459, 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)|esk263_4(X2,X3,X1,X4)!=X4|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.00/7.28 cnf(i_0_5402, 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)))). 7.00/7.28 cnf(i_0_4358, 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))). 7.00/7.28 cnf(i_0_3241, 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)))). 7.00/7.28 cnf(i_0_5103, 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)))). 7.00/7.28 cnf(i_0_4663, 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))). 7.00/7.28 cnf(i_0_2483, 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)))). 7.00/7.28 cnf(i_0_539, 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)))). 7.00/7.28 cnf(i_0_2656, 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)))). 7.00/7.28 cnf(i_0_4588, plain, (hBOOL(hAPP(X1,esk351_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)))). 7.00/7.28 cnf(i_0_3245, 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)))))). 7.00/7.28 cnf(i_0_6328, 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))). 7.00/7.28 cnf(i_0_4278, 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)))). 7.00/7.28 cnf(i_0_2553, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OgreaterThanLessThan(X1,X3,X4,X5)))|~hBOOL(hAPP(hAPP(X3,X4),X2))|~hBOOL(hAPP(hAPP(X3,X2),X5)))). 7.00/7.28 cnf(i_0_6892, 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)))). 7.00/7.28 cnf(i_0_6836, 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)))). 7.00/7.28 cnf(i_0_68, plain, (c_List_Olinorder__class_Osorted(X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk5_2(X2,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|~class_Orderings_Olinorder(X1))). 7.00/7.28 cnf(i_0_5927, plain, (c_List_Olinorder__class_Osorted(X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk459_2(X2,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|~class_Orderings_Olinorder(X1))). 7.00/7.28 cnf(i_0_363, 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)))). 7.00/7.28 cnf(i_0_7466, 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))). 7.00/7.28 cnf(i_0_7399, 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)))). 7.00/7.28 cnf(i_0_2918, 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)))). 7.00/7.28 cnf(i_0_3206, plain, (c_Equiv__Relations_Ocongruent(X1,X2,X3,hAPP(X4,X5))|~c_Equiv__Relations_Ocongruent2(X6,X1,X2,X7,X3,X4)|~hBOOL(hAPP(hAPP(c_member(X6),X5),X8))|~c_Equiv__Relations_Oequiv(X6,X8,X7))). 7.00/7.28 cnf(i_0_565, plain, (hBOOL(hAPP(hAPP(X1,X2),esk44_4(X3,X2,X4,X1)))|~hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X5,X6,X7,X1,X4),X2),X3)))). 7.00/7.28 cnf(i_0_5345, 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))))). 7.00/7.28 cnf(i_0_7338, 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))))). 7.00/7.28 cnf(i_0_6757, 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)))). 7.00/7.28 cnf(i_0_6339, 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)))). 7.00/7.28 cnf(i_0_2031, 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))). 7.00/7.28 cnf(i_0_564, plain, (hBOOL(hAPP(hAPP(X1,esk44_4(X2,X3,X1,X4)),X2))|~hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X5,X6,X7,X4,X1),X3),X2)))). 7.00/7.28 cnf(i_0_5284, 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))))). 7.00/7.28 cnf(i_0_4438, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk334_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)))). 7.00/7.28 cnf(i_0_3918, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk297_3(X2,X3,X1)),c_Quotient_ORespects(X1,X3)))|~c_Equiv__Relations_Oequivp(X1,X3)|~hBOOL(hAPP(X2,X4)))). 7.00/7.28 cnf(i_0_2504, 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))). 7.00/7.28 cnf(i_0_3066, 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)))). 7.00/7.28 cnf(i_0_895, 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))). 7.00/7.28 cnf(i_0_7354, 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)))))). 7.00/7.28 cnf(i_0_629, 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)))))). 7.00/7.28 cnf(i_0_1750, 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))). 7.00/7.28 cnf(i_0_5293, 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)))). 7.00/7.28 cnf(i_0_1465, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk116_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))))). 7.00/7.28 cnf(i_0_4161, 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)),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))))). 7.00/7.28 cnf(i_0_77, 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))))). 7.00/7.28 cnf(i_0_6271, 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)))). 7.00/7.28 cnf(i_0_5022, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))))). 7.00/7.28 cnf(i_0_951, 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))). 7.00/7.28 cnf(i_0_5215, plain, (c_List_OtakeWhile(X1,X2,X3)=X3|hBOOL(hAPP(hAPP(c_member(X1),esk405_3(X3,X2,X1)),hAPP(c_List_Oset(X1),X3))))). 7.00/7.28 cnf(i_0_5294, 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)))). 7.00/7.28 cnf(i_0_4075, 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)))). 7.00/7.28 cnf(i_0_3828, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))))). 7.00/7.28 cnf(i_0_3965, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))))). 7.00/7.28 cnf(i_0_4750, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))))). 7.00/7.28 cnf(i_0_591, plain, (c_Fun_Obij__betw(X1,X2,X3,X4,hAPP(c_Set_Oimage(X1,X2,X3),X4))|~c_Fun_Obij__betw(X1,X2,X3,X5,X6)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5)))). 7.00/7.28 cnf(i_0_3661, 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)))). 7.00/7.28 cnf(i_0_4342, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))))). 7.00/7.28 cnf(i_0_729, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Int_OMin)))). 7.00/7.28 cnf(i_0_5588, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.00/7.28 cnf(i_0_2180, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.00/7.28 cnf(i_0_4196, 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)))). 7.00/7.28 cnf(i_0_7295, 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))))). 7.00/7.28 cnf(i_0_4624, 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))))). 7.00/7.28 cnf(i_0_4633, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk356_3(X3,X2,X1)),X2)))). 7.00/7.28 cnf(i_0_7345, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Int_OMin)))). 7.00/7.28 cnf(i_0_533, 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)))). 7.00/7.28 cnf(i_0_4617, 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))). 7.00/7.28 cnf(i_0_710, 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))))). 7.00/7.28 cnf(i_0_7438, 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))))). 7.00/7.28 cnf(i_0_6313, plain, (hBOOL(hAPP(X1,X2))|~c_Orderings_Oorder__class_Omono(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X4)|~hBOOL(hAPP(hAPP(c_member(X3),X2),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X3,tc_HOL_Obool),X4)))|~hBOOL(hAPP(X1,esk494_4(X1,X4,X2,X3))))). 7.00/7.28 cnf(i_0_619, 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)))). 7.00/7.28 cnf(i_0_3234, 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)))). 7.00/7.28 cnf(i_0_3101, 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))). 7.00/7.28 cnf(i_0_48, 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)))). 7.00/7.28 cnf(i_0_3045, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk231_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)))). 7.00/7.28 cnf(i_0_2398, plain, (c_Fun_Obij__betw(X1,X2,esk189_4(X3,X2,X4,X1),X4,X3)|hAPP(c_Finite__Set_Ocard(X2),X3)!=hAPP(c_Finite__Set_Ocard(X1),X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 7.00/7.28 cnf(i_0_615, 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,esk48_3(X1,X3,X2)),esk49_3(X1,X3,X2))))). 7.00/7.28 cnf(i_0_731, 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)))). 7.00/7.28 cnf(i_0_870, 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)))). 7.00/7.28 cnf(i_0_6400, 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))). 7.00/7.28 cnf(i_0_1488, 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,esk122_3(X1,X3,X2)),esk123_3(X1,X3,X2))))). 7.00/7.28 cnf(i_0_3261, 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,esk250_3(X1,X3,X2)),esk251_3(X1,X3,X2))))). 7.00/7.28 cnf(i_0_3890, 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,esk290_3(X1,X3,X2)),esk291_3(X1,X3,X2))))). 7.00/7.28 cnf(i_0_5715, 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,esk438_3(X1,X3,X2)),esk439_3(X1,X3,X2))))). 7.00/7.28 cnf(i_0_4042, 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)))). 7.00/7.28 cnf(i_0_4335, 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)))). 7.00/7.28 cnf(i_0_6345, 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,esk497_3(X1,X3,X2)),esk498_3(X1,X3,X2))))). 7.00/7.28 cnf(i_0_712, 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)))). 7.00/7.28 cnf(i_0_801, 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)))). 7.00/7.28 cnf(i_0_815, 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)))). 7.00/7.28 cnf(i_0_2533, 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)))). 7.00/7.28 cnf(i_0_2532, 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)))). 7.00/7.28 cnf(i_0_6209, 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))). 7.00/7.28 cnf(i_0_5945, 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))). 7.00/7.28 cnf(i_0_2147, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X3),X4),esk168_3(X1,X4,X3))))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X4))))). 7.00/7.28 cnf(i_0_4305, 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))). 7.00/7.28 cnf(i_0_2486, plain, (hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk200_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)))). 7.00/7.28 cnf(i_0_2658, 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))))). 7.00/7.28 cnf(i_0_1768, 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)))). 7.00/7.28 cnf(i_0_3406, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 7.00/7.28 cnf(i_0_3310, 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))). 7.00/7.28 cnf(i_0_7094, 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)))). 7.00/7.28 cnf(i_0_2345, 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)))))). 7.00/7.28 cnf(i_0_4884, 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))))). 7.00/7.28 cnf(i_0_4885, 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),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))),c_Groups_Ozero__class_Ozero(X1))))). 7.00/7.28 cnf(i_0_6280, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk491_2(X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)))|hBOOL(hAPP(c_List_Odistinct(X2),X1)))). 7.00/7.28 cnf(i_0_52, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 7.00/7.28 cnf(i_0_6223, 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)))). 7.00/7.28 cnf(i_0_2659, 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)))). 7.00/7.28 cnf(i_0_4084, 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))))))). 7.00/7.28 cnf(i_0_6279, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk492_2(X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)))|hBOOL(hAPP(c_List_Odistinct(X2),X1)))). 7.00/7.28 cnf(i_0_116, 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,esk8_4(X4,X3,X1,X2)))). 7.00/7.28 cnf(i_0_4556, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))|~hBOOL(hAPP(c_List_Olistsp(X1,X3),X2)))). 7.00/7.28 cnf(i_0_663, 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))). 7.00/7.28 cnf(i_0_2804, 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)))). 7.00/7.28 cnf(i_0_2034, 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)))). 7.00/7.28 cnf(i_0_556, 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))). 7.00/7.28 cnf(i_0_3922, 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))). 7.00/7.28 cnf(i_0_6743, 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))). 7.00/7.28 cnf(i_0_2788, 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))). 7.00/7.28 cnf(i_0_4784, plain, (c_Equiv__Relations_Ocongruent(X1,X2,X3,X4)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk368_4(X4,X3,X2,X1)),X3)))). 7.00/7.28 cnf(i_0_3676, 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)))). 7.00/7.28 cnf(i_0_2384, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 7.00/7.28 cnf(i_0_6408, 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,esk502_4(X4,X1,X2,hAPP(c_Set_Oimage(X1,X2,X3),X4)),hAPP(c_Set_Oimage(X1,X2,X3),X4)))). 7.00/7.28 cnf(i_0_3457, 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)))). 7.00/7.28 cnf(i_0_4669, 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)))). 7.00/7.28 cnf(i_0_6490, 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)))). 7.00/7.28 cnf(i_0_784, 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)))). 7.00/7.28 cnf(i_0_7367, 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)). 7.00/7.28 cnf(i_0_226, plain, (hAPP(c_Hilbert__Choice_Oinv__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))))). 7.00/7.28 cnf(i_0_6527, 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))))). 7.00/7.28 cnf(i_0_6924, plain, (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(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))). 7.00/7.28 cnf(i_0_5597, 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)))). 7.00/7.28 cnf(i_0_6845, 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)))). 7.00/7.28 cnf(i_0_6321, 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)))). 7.00/7.28 cnf(i_0_5564, 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)))). 7.00/7.28 cnf(i_0_1059, 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)))). 7.00/7.28 cnf(i_0_786, 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))). 7.00/7.28 cnf(i_0_6364, 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)))). 7.00/7.28 cnf(i_0_4585, 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))). 7.00/7.28 cnf(i_0_3880, 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))))). 7.00/7.28 cnf(i_0_6254, plain, (hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X2,X3,X4,X1),X5))=X5|~hBOOL(hAPP(hAPP(c_member(X3),X5),hAPP(c_Set_Oimage(X2,X3,X1),X4))))). 7.00/7.28 cnf(i_0_3757, 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))))). 7.00/7.28 cnf(i_0_2171, 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)))). 7.00/7.28 cnf(i_0_7167, 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_Int_Onumber__ring(X1)|~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)))). 7.00/7.28 cnf(i_0_1822, 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_Int_Onumber__ring(X1)|~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)))). 7.00/7.28 cnf(i_0_4551, 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_Int_Onumber__ring(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))))). 7.00/7.28 cnf(i_0_5826, 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)))). 7.00/7.28 cnf(i_0_5825, 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)))). 7.00/7.28 cnf(i_0_4540, 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)))). 7.00/7.28 cnf(i_0_1004, 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_Int_Onumber__ring(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))))). 7.00/7.28 cnf(i_0_2573, plain, (X1=c_List_Olist_ONil(X2)|hBOOL(hAPP(hAPP(c_member(X2),esk204_3(X3,X1,X2)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X1),c_List_Olists(X2,X3))))). 7.00/7.28 cnf(i_0_2952, 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)))). 7.00/7.28 cnf(i_0_1744, 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)))). 7.00/7.28 cnf(i_0_4541, 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)))). 7.00/7.28 cnf(i_0_1742, 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)))). 7.00/7.28 cnf(i_0_4394, 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))). 7.00/7.28 cnf(i_0_6087, 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)))). 7.00/7.28 cnf(i_0_5487, 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)))))). 7.00/7.28 cnf(i_0_851, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk68_5(X2,X3,X4,X1,X5)),X2))|~c_Wellfounded_Omax__extp(X1,X4,X3,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X5),X3)))). 7.00/7.28 cnf(i_0_3180, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk245_5(X2,X3,X4,X1,X5)),X2))|~c_Wellfounded_Omax__extp(X1,X4,X3,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X5),X3)))). 7.00/7.28 cnf(i_0_2758, 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)))). 7.00/7.28 cnf(i_0_1526, 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)))). 7.00/7.28 cnf(i_0_6951, 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)))). 7.00/7.28 cnf(i_0_1078, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~class_Rings_Ocomm__semiring__1(X1)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4)))). 7.00/7.28 cnf(i_0_582, 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))|c_Groups_Ozero__class_Ozero(X1)=X3|~class_Rings_Odivision__ring(X1))). 7.00/7.28 cnf(i_0_7348, plain, (hAPP(c_List_Ofilter(X1,X2),X3)=X3|hBOOL(hAPP(hAPP(c_member(X1),esk578_3(X3,X2,X1)),hAPP(c_List_Oset(X1),X3))))). 7.00/7.28 cnf(i_0_6677, 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)))). 7.00/7.28 cnf(i_0_7546, 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)))). 7.00/7.28 cnf(i_0_6607, 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)))). 7.00/7.28 cnf(i_0_2498, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~class_Rings_Ocomm__semiring__1(X1)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)))). 7.00/7.28 cnf(i_0_6480, 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)))). 7.00/7.28 cnf(i_0_5562, 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)))). 7.00/7.28 cnf(i_0_7118, 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)))). 7.00/7.28 cnf(i_0_4374, 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))))). 7.00/7.28 cnf(i_0_7062, 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))))). 7.00/7.28 cnf(i_0_5967, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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(X1,tc_HOL_Obool)),X2),esk468_3(X2,X3,X1))))). 7.00/7.28 cnf(i_0_4629, 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)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk355_3(X3,X2,X1)),X3)))). 7.00/7.28 cnf(i_0_7297, plain, (c_List_Olist__all(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk569_3(X3,X2,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 7.00/7.28 cnf(i_0_2370, 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)))). 7.00/7.28 cnf(i_0_4695, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk361_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 7.00/7.28 cnf(i_0_3334, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1)))|~hBOOL(hAPP(X2,esk255_3(X1,X3,X2)))|~hBOOL(hAPP(X2,X3)))). 7.00/7.28 cnf(i_0_3350, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1)))|~hBOOL(hAPP(X2,esk257_3(X1,X3,X2)))|~hBOOL(hAPP(X2,X3)))). 7.00/7.28 cnf(i_0_3147, plain, (c_List_Oall__interval__nat(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk239_3(X3,X2,X1)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3))))). 7.00/7.28 cnf(i_0_5038, 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))))). 7.00/7.28 cnf(i_0_3110, 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)))). 7.00/7.28 cnf(i_0_4699, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk361_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1))))). 7.00/7.28 cnf(i_0_4896, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,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(X2),X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 7.00/7.28 cnf(i_0_6442, 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)))). 7.00/7.28 cnf(i_0_4581, 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))). 7.00/7.28 cnf(i_0_5639, plain, (c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),X1),X2,X3)|c_List_Olist__ex(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))))). 7.00/7.28 cnf(i_0_6702, 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)))). 7.00/7.28 cnf(i_0_1164, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk94_3(X2,X3,X1)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X3),c_Relation_OId__on(X1,X2))))). 7.00/7.28 cnf(i_0_2890, plain, (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))|hAPP(c_Fun_Ocomp(X1,X2,X2,X3),c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3))!=c_Fun_Oid(X2))). 7.00/7.28 cnf(i_0_4160, 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)))). 7.00/7.28 cnf(i_0_213, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),hAPP(X2,hAPP(c_Nat_OSuc,X3))))|~c_Orderings_Oorder__class_Omono(tc_Nat_Onat,X1,X2)|~class_Orderings_Oorder(X1))). 7.00/7.28 cnf(i_0_5461, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),esk416_3(X2,X3,X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))|~class_Fields_Olinordered__field__inverse__zero(X1))). 7.00/7.28 cnf(i_0_6028, 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))). 7.00/7.28 cnf(i_0_6548, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OatLeastLessThan(X1,X3,X4,X5,X6)))|~hBOOL(hAPP(hAPP(X4,X2),X6))|~hBOOL(hAPP(hAPP(X3,X5),X2)))). 7.00/7.28 cnf(i_0_5718, 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)))). 7.00/7.28 cnf(i_0_4925, plain, (hAPP(X1,X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|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)))). 7.00/7.28 cnf(i_0_6249, 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)))). 7.00/7.28 cnf(i_0_6472, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),esk505_3(X2,X3,X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))|~class_Fields_Olinordered__field(X1))). 7.00/7.28 cnf(i_0_5460, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk416_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))). 7.00/7.28 cnf(i_0_1582, 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))))). 7.00/7.28 cnf(i_0_3799, 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))). 7.00/7.28 cnf(i_0_4744, 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)))). 7.00/7.28 cnf(i_0_431, 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)))))). 7.00/7.28 cnf(i_0_1583, 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))))). 7.00/7.28 cnf(i_0_3359, plain, (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)))|hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1)))|~hBOOL(hAPP(X2,esk255_3(X1,X3,X2))))). 7.00/7.28 cnf(i_0_3375, 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)),X1))|hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1)))|~hBOOL(hAPP(X2,esk257_3(X1,X3,X2))))). 7.00/7.28 cnf(i_0_2909, 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)))). 7.00/7.28 cnf(i_0_657, plain, (hBOOL(hAPP(X1,X2))|~c_Orderings_Oorder__class_Omono(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X4)|~hBOOL(hAPP(X1,esk53_5(X1,X2,X4,X3,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X3,tc_HOL_Obool),X4))))|~hBOOL(hAPP(hAPP(c_member(X3),X2),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X3,tc_HOL_Obool),X4))))). 7.00/7.28 cnf(i_0_7190, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|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)))))). 7.00/7.28 cnf(i_0_4951, plain, (c_Equiv__Relations_Ocongruent2(X1,X2,X3,X4,X5,X6)|hAPP(hAPP(X6,esk382_6(X3,X6,X5,X2,X4,X1)),esk384_6(X3,X6,X5,X2,X4,X1))!=hAPP(hAPP(X6,esk381_6(X3,X6,X5,X2,X4,X1)),esk383_6(X3,X6,X5,X2,X4,X1)))). 7.00/7.28 cnf(i_0_2936, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk224_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))))). 7.00/7.28 cnf(i_0_2995, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk227_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)))). 7.00/7.28 cnf(i_0_5034, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk393_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)))). 7.00/7.28 cnf(i_0_3737, 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)|X3=X5)). 7.00/7.28 cnf(i_0_79, 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,esk7_2(X2,X1))))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 7.00/7.28 cnf(i_0_4372, 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))). 7.00/7.28 cnf(i_0_5346, 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)))). 7.00/7.28 cnf(i_0_4823, 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)))). 7.00/7.28 cnf(i_0_4855, 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)))). 7.00/7.28 cnf(i_0_5572, 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)))). 7.00/7.28 cnf(i_0_4938, 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)))). 7.00/7.28 cnf(i_0_3732, 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)))). 7.00/7.28 cnf(i_0_1913, 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)))). 7.00/7.28 cnf(i_0_4420, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk332_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)))). 7.00/7.28 cnf(i_0_7519, 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)))). 7.00/7.28 cnf(i_0_7383, 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)))). 7.00/7.28 cnf(i_0_1881, 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)))). 7.00/7.28 cnf(i_0_6923, plain, (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)))|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))). 7.00/7.28 cnf(i_0_6926, plain, (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(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))). 7.00/7.28 cnf(i_0_6488, 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))). 7.00/7.28 cnf(i_0_4072, 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))))). 7.00/7.28 cnf(i_0_5801, 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)))). 7.00/7.28 cnf(i_0_5361, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk410_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))))). 7.00/7.28 cnf(i_0_1615, 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))). 7.00/7.28 cnf(i_0_2875, 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)))). 7.00/7.28 cnf(i_0_1945, 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|c_List_Olist_ONil(X1)=X2)). 7.00/7.28 cnf(i_0_6770, plain, (hAPP(c_Set_Oimage(X1,X2,X3),esk530_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))))). 7.00/7.28 cnf(i_0_2073, 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)))). 7.00/7.28 cnf(i_0_5253, 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))). 7.00/7.28 cnf(i_0_7424, 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))). 7.00/7.28 cnf(i_0_2630, 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)))). 7.00/7.28 cnf(i_0_880, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk72_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))). 7.00/7.28 cnf(i_0_550, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk42_3(X2,X3,X1)),X3))|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))). 7.00/7.28 cnf(i_0_2306, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk182_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))). 7.00/7.28 cnf(i_0_2623, 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))). 7.00/7.28 cnf(i_0_3054, plain, (hBOOL(hAPP(X1,X2))|hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X4),X5)!=c_List_Opartition(X3,X1,X6)|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X4))))). 7.00/7.28 cnf(i_0_6351, 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)))). 7.00/7.28 cnf(i_0_265, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~c_Orderings_Oorder__class_Ostrict__mono(X1,X4,X5)|~class_Orderings_Oorder(X4)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(X5,X2)),hAPP(X5,X3))))). 7.00/7.28 cnf(i_0_5750, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk443_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))). 7.00/7.28 cnf(i_0_6776, 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))). 7.00/7.28 cnf(i_0_6835, 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))). 7.00/7.28 cnf(i_0_5709, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~c_Orderings_Oorder__class_Ostrict__mono(X1,X4,X5)|~class_Orderings_Oorder(X4)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(X5,X2)),hAPP(X5,X3))))). 7.00/7.28 cnf(i_0_6049, plain, (~c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),esk472_3(X2,X1,X4))),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X4)))). 7.00/7.28 cnf(i_0_5276, 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,esk408_5(X4,X3,X5,X1,X2)))))). 7.00/7.28 cnf(i_0_1246, plain, (c_Wellfounded_Owf(tc_prod(X1,X2),c_Recdef_Osame__fst(X1,X2,X3,X4))|hBOOL(hAPP(X3,esk101_4(X1,X4,X2,X3))))). 7.00/7.28 cnf(i_0_3446, 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)))). 7.00/7.28 cnf(i_0_2994, 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)))). 7.00/7.28 cnf(i_0_3433, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk259_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|hBOOL(hAPP(c_List_Olistsp(X1,X3),X2)))). 7.00/7.28 cnf(i_0_2235, 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))). 7.00/7.28 cnf(i_0_4727, 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))). 7.00/7.28 cnf(i_0_260, 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)))). 7.00/7.28 cnf(i_0_1049, plain, (c_Fun_Obij__betw(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5),X6,X7)|~c_Fun_Obij__betw(X1,X3,X5,X6,X8)|~c_Fun_Obij__betw(X3,X2,X4,X8,X7))). 7.00/7.28 cnf(i_0_1672, 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,esk142_5(X1,X6,X5,X4,X3))))). 7.00/7.28 cnf(i_0_35, 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)))). 7.00/7.28 cnf(i_0_2206, 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)))). 7.00/7.28 cnf(i_0_3080, 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)))). 7.00/7.28 cnf(i_0_5982, 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)))). 7.00/7.28 cnf(i_0_1644, 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),esk137_3(X3,X2,X1)),X2)))). 7.00/7.28 cnf(i_0_5858, 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,esk456_4(X4,X3,X1,X2))),hAPP(X4,esk456_4(X4,X3,X1,X2)))))). 7.00/7.28 cnf(i_0_7569, 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,esk600_4(X1,X4,X3,X2))),hAPP(X4,esk600_4(X1,X4,X3,X2)))))). 7.00/7.28 cnf(i_0_1643, 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),esk138_3(X3,X2,X1)),X3)))). 7.00/7.28 cnf(i_0_1058, 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)))). 7.00/7.28 cnf(i_0_422, 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)))). 7.00/7.28 cnf(i_0_569, 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_Power_Opower(X1))). 7.00/7.28 cnf(i_0_878, 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)))). 7.00/7.28 cnf(i_0_2307, 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)))). 7.00/7.28 cnf(i_0_496, plain, (hAPP(c_List_Ofilter(X1,X2),X3)=c_List_Olist_ONil(X1)|hBOOL(hAPP(hAPP(c_member(X1),esk40_3(X3,X2,X1)),hAPP(c_List_Oset(X1),X3))))). 7.00/7.28 cnf(i_0_421, 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)))). 7.00/7.28 cnf(i_0_7456, 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))). 7.00/7.28 cnf(i_0_4213, 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))). 7.00/7.28 cnf(i_0_5738, plain, (c_Fun_Oinj__on(X1,X2,esk440_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)))). 7.00/7.28 cnf(i_0_2232, plain, (hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,c_Hilbert__Choice_Oinv__into(X2,X1,X4,X5)),X6)=hAPP(X5,X6)|~c_Fun_Obij__betw(X2,X1,X5,X4,X3)|~hBOOL(hAPP(hAPP(c_member(X2),X6),X4)))). 7.00/7.28 cnf(i_0_5197, plain, (c_List_Otranspose(X1,X2)=c_List_Olist_ONil(tc_List_Olist(X1))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk402_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))))). 7.00/7.28 cnf(i_0_2344, 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)))). 7.00/7.28 cnf(i_0_6276, 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)))). 7.00/7.28 cnf(i_0_3764, 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)))). 7.00/7.28 cnf(i_0_34, 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))). 7.00/7.28 cnf(i_0_3458, 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,esk263_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)))). 7.00/7.28 cnf(i_0_5844, plain, (X1=c_List_Olist_ONil(X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),esk453_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),esk452_2(X1,X2)))))). 7.00/7.28 cnf(i_0_3129, plain, (hBOOL(hAPP(X1,hAPP(c_Nat_OSuc,esk238_2(X2,X1))))|hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,X2)))). 7.00/7.28 cnf(i_0_2540, 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))). 7.00/7.28 cnf(i_0_774, 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))). 7.00/7.28 cnf(i_0_2603, 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))). 7.00/7.28 cnf(i_0_3396, 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))). 7.00/7.28 cnf(i_0_5421, 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)))). 7.00/7.28 cnf(i_0_1469, 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)))). 7.00/7.28 cnf(i_0_755, 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)))). 7.00/7.28 cnf(i_0_2394, 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))). 7.00/7.28 cnf(i_0_1559, 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))). 7.00/7.28 cnf(i_0_4011, plain, (c_Fun_Obij__betw(tc_Nat_Onat,X1,esk305_2(X2,X1),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 7.00/7.28 cnf(i_0_2718, 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))). 7.00/7.28 cnf(i_0_3769, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X3)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~c_Orderings_Oorder__class_Omono(X1,X1,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X3))))))). 7.00/7.28 cnf(i_0_5507, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X2)),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~c_Orderings_Oorder__class_Omono(X1,X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Inductive_Ocomplete__lattice__class_Olfp(X1,X2)),X3))),X3)))). 7.00/7.28 cnf(i_0_16, 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,esk1_4(X4,X1,X3,X2))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 7.00/7.28 cnf(i_0_5642, 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,esk430_4(X4,X1,X3,X2))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 7.00/7.28 cnf(i_0_2038, 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))). 7.00/7.28 cnf(i_0_1289, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|X3=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))|hAPP(hAPP(c_Product__Type_OSigma(X4,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X4),X2))!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X1),tc_HOL_Obool)))). 7.00/7.28 cnf(i_0_6078, 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))))). 7.00/7.28 cnf(i_0_372, 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,esk33_5(X5,X2,X4,X3,X1)))))). 7.00/7.28 cnf(i_0_6272, 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))))). 7.00/7.28 cnf(i_0_76, 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)))). 7.00/7.28 cnf(i_0_1281, 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__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)))). 7.00/7.28 cnf(i_0_4152, 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))))). 7.00/7.28 cnf(i_0_875, 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,esk71_5(X5,X4,X3,X2,X1)))))). 7.00/7.28 cnf(i_0_998, 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,esk83_5(X5,X4,X3,X2,X1))),X5)))). 7.00/7.28 cnf(i_0_5547, 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,esk422_5(X5,X4,X3,X2,X1))),X5)))). 7.00/7.28 cnf(i_0_3041, 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)|esk232_4(X2,X3,X1,X4)!=X4|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.00/7.28 cnf(i_0_4872, 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))). 7.00/7.28 cnf(i_0_4537, 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))). 7.00/7.28 cnf(i_0_6964, 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))). 7.00/7.28 cnf(i_0_5242, 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))). 7.00/7.28 cnf(i_0_1949, 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)))). 7.00/7.28 cnf(i_0_5020, plain, (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))|~c_Fun_Obij__betw(X1,X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))). 7.00/7.28 cnf(i_0_4889, 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))). 7.00/7.28 cnf(i_0_2386, 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))). 7.00/7.28 cnf(i_0_5940, 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))). 7.00/7.28 cnf(i_0_3313, 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))). 7.00/7.28 cnf(i_0_6598, 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))). 7.00/7.28 cnf(i_0_1299, 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))))). 7.00/7.28 cnf(i_0_1298, 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)),X2),X4)),hAPP(c_List_Olexn(X1,X5),X3))))). 7.00/7.28 cnf(i_0_1675, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(X4,X5)))|~hBOOL(hAPP(X1,esk140_5(X1,X4,X6,X7,X3)))|~hBOOL(hAPP(hAPP(c_member(X7),X5),X6)))). 7.00/7.28 cnf(i_0_566, 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)))). 7.00/7.28 cnf(i_0_3115, 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))). 7.00/7.28 cnf(i_0_844, 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))). 7.00/7.28 cnf(i_0_7147, 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))). 7.00/7.28 cnf(i_0_1928, 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))). 7.00/7.28 cnf(i_0_1774, 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))). 7.00/7.28 cnf(i_0_4076, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),X5))|~hBOOL(hAPP(hAPP(c_member(X1),hAPP(X3,esk309_5(X5,X3,X1,X4,X2))),X5)))). 7.00/7.28 cnf(i_0_7518, 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))). 7.00/7.28 cnf(i_0_3236, 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))))). 7.00/7.28 cnf(i_0_1044, 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)))). 7.00/7.28 cnf(i_0_2230, 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)))). 7.00/7.28 cnf(i_0_5451, 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))))). 7.00/7.28 cnf(i_0_4334, 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)))). 7.00/7.28 cnf(i_0_2531, 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)))). 7.00/7.28 cnf(i_0_435, 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))). 7.00/7.28 cnf(i_0_3568, 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)))). 7.00/7.28 cnf(i_0_90, 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))). 7.00/7.28 cnf(i_0_1877, 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)))). 7.00/7.28 cnf(i_0_7496, 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)))). 7.00/7.28 cnf(i_0_735, 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))))). 7.00/7.28 cnf(i_0_3161, plain, (c_List_Olist__ex1(X1,X2,X3)|hBOOL(hAPP(X2,esk242_4(X3,X2,X1,X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X2,X4)))). 7.00/7.28 cnf(i_0_6741, plain, (c_List_Olist__ex1(X1,X2,X3)|hBOOL(hAPP(X2,esk527_4(X3,X2,X1,X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X2,X4)))). 7.00/7.28 cnf(i_0_3025, 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))))). 7.00/7.28 cnf(i_0_2507, 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)))). 7.00/7.28 cnf(i_0_23, 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)))))). 7.00/7.28 cnf(i_0_4380, 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))))). 7.00/7.28 cnf(i_0_6878, 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)))). 7.00/7.28 cnf(i_0_5273, 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))))). 7.00/7.28 cnf(i_0_831, 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)))). 7.00/7.28 cnf(i_0_7547, 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)))). 7.00/7.28 cnf(i_0_4260, 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))))). 7.00/7.28 cnf(i_0_393, 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)))). 7.00/7.28 cnf(i_0_6476, 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))))). 7.00/7.28 cnf(i_0_7059, 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)))). 7.00/7.28 cnf(i_0_2629, 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)))). 7.00/7.28 cnf(i_0_6502, 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)))). 7.00/7.28 cnf(i_0_2145, 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,esk169_3(X1,X3,X2))))). 7.00/7.28 cnf(i_0_315, 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))))). 7.00/7.28 cnf(i_0_3548, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2))=X3|~class_Divides_Osemiring__div(X1)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)))). 7.00/7.28 cnf(i_0_4631, plain, (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)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X2)))). 7.00/7.28 cnf(i_0_2998, 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)))). 7.00/7.28 cnf(i_0_1347, 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)))). 7.00/7.28 cnf(i_0_1669, 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))). 7.00/7.28 cnf(i_0_1670, 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))). 7.00/7.28 cnf(i_0_4271, 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)))). 7.00/7.28 cnf(i_0_4270, 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)))). 7.00/7.28 cnf(i_0_934, 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)))). 7.00/7.28 cnf(i_0_165, plain, (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))|hAPP(X3,hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),esk10_3(X3,X2,X1)))!=esk10_3(X3,X2,X1))). 7.00/7.28 cnf(i_0_3493, 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)))). 7.00/7.28 cnf(i_0_5437, 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))). 7.00/7.28 cnf(i_0_4907, 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),esk377_2(X1,X2)),X2)))). 7.00/7.28 cnf(i_0_4861, 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)))). 7.00/7.28 cnf(i_0_7102, plain, (X1=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)),X4)|X4=c_Groups_Ozero__class_Ozero(X2)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X4)!=hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)|~class_Fields_Ofield__inverse__zero(X2)|~class_Int_Onumber(X2))). 7.00/7.28 cnf(i_0_1605, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk132_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)))). 7.00/7.28 cnf(i_0_6795, 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)))). 7.00/7.28 cnf(i_0_3157, 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)))). 7.00/7.28 cnf(i_0_3453, 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)))). 7.00/7.28 cnf(i_0_5468, 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))))). 7.00/7.28 cnf(i_0_139, 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))))). 7.00/7.28 cnf(i_0_758, 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))))). 7.00/7.28 cnf(i_0_1442, 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))))). 7.00/7.28 cnf(i_0_173, 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))))). 7.00/7.28 cnf(i_0_5918, 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)))). 7.00/7.28 cnf(i_0_924, plain, (hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X1),X4))=X4|hAPP(c_Set_Oimage(X2,X3,X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))). 7.00/7.28 cnf(i_0_4927, 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),esk379_3(X2,X3,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.00/7.28 cnf(i_0_3502, 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)))). 7.00/7.28 cnf(i_0_5857, 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)))). 7.00/7.28 cnf(i_0_6251, 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),esk487_3(X2,X3,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.00/7.28 cnf(i_0_3300, 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)))))). 7.00/7.28 cnf(i_0_5106, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk397_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))))). 7.00/7.28 cnf(i_0_4125, 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))))). 7.00/7.28 cnf(i_0_5248, 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))))). 7.00/7.28 cnf(i_0_5493, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk417_4(X2,X3,X1,X4)),X2))|~hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(c_Set_Oimage(X1,X5,X3),X2))))). 7.00/7.28 cnf(i_0_6959, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk545_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))))). 7.00/7.28 cnf(i_0_2223, 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)))). 7.00/7.28 cnf(i_0_3844, 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)))). 7.00/7.28 cnf(i_0_3028, 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)))). 7.00/7.28 cnf(i_0_7133, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk552_4(X2,X3,X1,X4)),X2))|~hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(c_Set_Oimage(X1,X5,X3),X2))))). 7.00/7.28 cnf(i_0_6338, 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))). 7.00/7.28 cnf(i_0_1610, 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))))). 7.00/7.28 cnf(i_0_4875, 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))))). 7.00/7.28 cnf(i_0_6169, 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)))). 7.00/7.28 cnf(i_0_2072, 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)))). 7.00/7.28 cnf(i_0_3530, 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)))). 7.00/7.28 cnf(i_0_4048, 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)))). 7.00/7.28 cnf(i_0_2310, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X4))|~class_Rings_Oidom(X1)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))))). 7.00/7.28 cnf(i_0_5338, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X4))|~class_Rings_Oidom(X1)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))))). 7.00/7.28 cnf(i_0_4482, 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))))). 7.00/7.28 cnf(i_0_5483, 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))))). 7.00/7.28 cnf(i_0_6644, 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))))). 7.00/7.28 cnf(i_0_5667, 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))))). 7.00/7.28 cnf(i_0_5904, 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))))). 7.00/7.28 cnf(i_0_7481, 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))))). 7.00/7.28 cnf(i_0_917, 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))))). 7.00/7.28 cnf(i_0_4365, 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)))). 7.00/7.28 cnf(i_0_6597, 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))). 7.00/7.28 cnf(i_0_1192, 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))). 7.00/7.28 cnf(i_0_6723, 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))))). 7.00/7.28 cnf(i_0_921, 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))))). 7.00/7.28 cnf(i_0_3465, 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))). 7.00/7.28 cnf(i_0_4625, 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))))). 7.00/7.28 cnf(i_0_4913, plain, (hAPP(hAPP(X1,X2),X3)=hAPP(hAPP(c_Finite__Set_Ofold(X4,X5,X6),X3),X2)|~c_Finite__Set_Ofolding(X4,X5,X6,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))). 7.00/7.28 cnf(i_0_6045, plain, (c_Wellfounded_Owf(X1,X2)|hBOOL(hAPP(hAPP(c_member(X1),esk475_3(X2,X1,X3)),esk473_2(X2,X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),esk473_2(X2,X1))))). 7.00/7.28 cnf(i_0_4099, 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)))). 7.00/7.28 cnf(i_0_6985, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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))))). 7.00/7.28 cnf(i_0_477, 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)))). 7.00/7.28 cnf(i_0_7477, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|X3=X4|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2))). 7.00/7.28 cnf(i_0_1471, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)=hAPP(hAPP(c_List_Omap(X1,X2),X5),X4)|hAPP(X3,esk117_5(X5,X4,X3,X2,X1))!=hAPP(X5,esk117_5(X5,X4,X3,X2,X1)))). 7.00/7.28 cnf(i_0_2939, 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)))). 7.00/7.28 cnf(i_0_793, 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))))). 7.00/7.28 cnf(i_0_3526, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk270_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1))))). 7.00/7.28 cnf(i_0_5811, 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)))). 7.00/7.28 cnf(i_0_6781, 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)))). 7.00/7.28 cnf(i_0_2657, 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))))). 7.00/7.28 cnf(i_0_3609, plain, (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)))|hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X1)))|~hBOOL(hAPP(X2,esk273_3(X1,X3,X2))))). 7.00/7.28 cnf(i_0_1659, 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))))). 7.00/7.28 cnf(i_0_1408, 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)))). 7.00/7.28 cnf(i_0_1163, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk94_3(X2,X3,X1)),esk94_3(X2,X3,X1))=X3|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X3),c_Relation_OId__on(X1,X2))))). 7.00/7.28 cnf(i_0_3641, plain, (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(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X1)))|~hBOOL(hAPP(X2,esk275_3(X1,X3,X2))))). 7.00/7.28 cnf(i_0_3510, 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)))). 7.00/7.28 cnf(i_0_2500, 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)))). 7.00/7.28 cnf(i_0_6412, 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)))). 7.00/7.28 cnf(i_0_3553, 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)))))). 7.00/7.28 cnf(i_0_2327, 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(X1,X3)),hAPP(hAPP(c_Product__Type_OSigma(X1,X3),X2),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X1),X4)))))). 7.00/7.28 cnf(i_0_6202, 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)))). 7.00/7.28 cnf(i_0_3470, 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)))). 7.00/7.28 cnf(i_0_6934, 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)))). 7.00/7.28 cnf(i_0_3299, 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)))). 7.00/7.28 cnf(i_0_7095, 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)))). 7.00/7.28 cnf(i_0_1304, 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,esk102_5(X5,X4,X3,X2,X1)))))). 7.00/7.28 cnf(i_0_4233, 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,esk322_5(X5,X2,X1,X4,X3)))))). 7.00/7.28 cnf(i_0_5087, 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))). 7.00/7.28 cnf(i_0_960, 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)))). 7.00/7.28 cnf(i_0_2893, plain, (c_Fun_Obij__betw(X1,tc_Nat_Onat,esk223_2(X2,X1),X2,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(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)))). 7.00/7.28 cnf(i_0_6057, plain, (c_Fun_Obij__betw(tc_Nat_Onat,X1,esk477_2(X2,X1),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),X2)),X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 7.00/7.28 cnf(i_0_6752, 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))))). 7.00/7.28 cnf(i_0_1981, 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)))). 7.00/7.28 cnf(i_0_1302, 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)))). 7.00/7.28 cnf(i_0_3522, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk270_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))))). 7.00/7.28 cnf(i_0_2405, 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)))). 7.00/7.28 cnf(i_0_5342, 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|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 7.00/7.28 cnf(i_0_2152, 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))). 7.00/7.28 cnf(i_0_1915, 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,esk156_4(X3,X4,X2,X1)))))). 7.00/7.28 cnf(i_0_6840, 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,esk536_4(X3,X4,X2,X1)))))). 7.00/7.28 cnf(i_0_1411, 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)))). 7.00/7.28 cnf(i_0_3608, 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(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X1)))|~hBOOL(hAPP(X2,esk273_3(X1,X3,X2)))|~hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.00/7.28 cnf(i_0_3640, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X1)))|~hBOOL(hAPP(X2,esk275_3(X1,X3,X2)))|~hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.00/7.28 cnf(i_0_6485, 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)))). 7.00/7.28 cnf(i_0_3193, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk247_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)))). 7.00/7.28 cnf(i_0_4765, 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)))). 7.00/7.28 cnf(i_0_5476, 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)))). 7.00/7.28 cnf(i_0_3680, 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))). 7.00/7.28 cnf(i_0_4421, 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)))). 7.00/7.28 cnf(i_0_1716, 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),esk145_4(X4,X3,X1,X2)),X3)))). 7.00/7.28 cnf(i_0_1941, 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)))))). 7.00/7.28 cnf(i_0_3760, 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))). 7.00/7.28 cnf(i_0_2318, 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),esk184_4(X4,X3,X2,X1)),X3)))). 7.00/7.28 cnf(i_0_1458, 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)))). 7.00/7.28 cnf(i_0_4292, 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))). 7.00/7.28 cnf(i_0_462, 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_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X3)))). 7.00/7.28 cnf(i_0_5408, 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_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3)))). 7.00/7.28 cnf(i_0_511, 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),esk41_4(X4,X3,X1,X2)),X3)))). 7.00/7.28 cnf(i_0_6565, 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))). 7.00/7.28 cnf(i_0_6084, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),esk480_4(X1,X4,X2,X3)),esk481_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)))). 7.00/7.28 cnf(i_0_7536, 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))). 7.00/7.28 cnf(i_0_2829, 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)))). 7.00/7.28 cnf(i_0_5229, 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),esk406_4(X4,X3,X2,X1)),X3)))). 7.00/7.28 cnf(i_0_4467, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X1,esk341_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))). 7.00/7.28 cnf(i_0_288, 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),X3)!=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|~class_Int_Onumber__ring(X1))). 7.00/7.28 cnf(i_0_6948, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk544_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))))). 7.00/7.28 cnf(i_0_3556, 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))). 7.00/7.28 cnf(i_0_664, 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)))). 7.00/7.28 cnf(i_0_1714, 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)))). 7.00/7.28 cnf(i_0_509, 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)))). 7.00/7.28 cnf(i_0_3105, 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))). 7.00/7.28 cnf(i_0_2539, 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))). 7.00/7.28 cnf(i_0_5630, 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))). 7.00/7.28 cnf(i_0_6390, 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)))). 7.00/7.28 cnf(i_0_3681, 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))). 7.00/7.28 cnf(i_0_6153, 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),esk485_3(X3,X2,X1))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 7.00/7.28 cnf(i_0_4332, 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)). 7.00/7.28 cnf(i_0_2749, 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))))). 7.00/7.28 cnf(i_0_6214, 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))))). 7.00/7.28 cnf(i_0_4639, 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))))). 7.00/7.28 cnf(i_0_4175, 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)))). 7.00/7.28 cnf(i_0_1094, 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)))). 7.00/7.28 cnf(i_0_676, 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))))). 7.00/7.28 cnf(i_0_7257, 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)))). 7.00/7.28 cnf(i_0_41, 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)))). 7.00/7.28 cnf(i_0_1847, 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)))). 7.00/7.28 cnf(i_0_7291, 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)))). 7.00/7.28 cnf(i_0_711, 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)))). 7.00/7.28 cnf(i_0_4946, 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)))). 7.00/7.28 cnf(i_0_2296, 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))))). 7.00/7.28 cnf(i_0_2759, 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)))). 7.00/7.28 cnf(i_0_4000, 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)))). 7.00/7.28 cnf(i_0_5828, 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)))). 7.00/7.28 cnf(i_0_792, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))))). 7.00/7.28 cnf(i_0_654, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))))). 7.00/7.28 cnf(i_0_2113, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))))). 7.00/7.28 cnf(i_0_3537, 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))). 7.00/7.28 cnf(i_0_2739, 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))). 7.00/7.28 cnf(i_0_4582, 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))). 7.00/7.28 cnf(i_0_1533, 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))). 7.00/7.28 cnf(i_0_5348, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2),X1)|c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 7.00/7.28 cnf(i_0_2253, 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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))))). 7.00/7.28 cnf(i_0_855, 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,esk67_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)))). 7.00/7.28 cnf(i_0_4023, 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))). 7.00/7.28 cnf(i_0_2085, 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))). 7.00/7.28 cnf(i_0_4732, 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)))). 7.00/7.28 cnf(i_0_6231, 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)))). 7.00/7.28 cnf(i_0_2374, 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))). 7.00/7.28 cnf(i_0_299, plain, (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,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))). 7.00/7.28 cnf(i_0_3744, 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,esk280_4(X3,X1,X4,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)))). 7.00/7.28 cnf(i_0_3177, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Wellfounded_Omax__extp(X1,X3,X4,X2)|~hBOOL(hAPP(hAPP(X3,esk246_4(X2,X4,X3,X1)),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 7.00/7.28 cnf(i_0_7109, 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),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))))). 7.00/7.28 cnf(i_0_1700, 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),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))))). 7.00/7.28 cnf(i_0_2848, 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)))). 7.00/7.28 cnf(i_0_3123, 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)))). 7.00/7.28 cnf(i_0_808, plain, (hAPP(c_Fun_Ocomp(X1,X2,X2,c_Hilbert__Choice_Oinv__into(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X3)),X3)=c_Fun_Oid(X2)|~c_Fun_Oinj__on(X2,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))). 7.00/7.28 cnf(i_0_6650, 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))). 7.00/7.28 cnf(i_0_611, 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))). 7.00/7.28 cnf(i_0_487, 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)))). 7.00/7.28 cnf(i_0_3026, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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_Oone__class_Oone(tc_Nat_Onat)),X3)))). 7.00/7.28 cnf(i_0_940, 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)))). 7.00/7.28 cnf(i_0_6259, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk490_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))). 7.00/7.28 cnf(i_0_2863, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk222_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))). 7.00/7.28 cnf(i_0_6261, plain, (hAPP(hAPP(c_List_Oappend(X1),esk490_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))). 7.00/7.28 cnf(i_0_2864, plain, (hAPP(hAPP(c_List_Oappend(X1),esk222_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))). 7.00/7.28 cnf(i_0_3473, 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(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.00/7.28 cnf(i_0_6611, 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)))). 7.00/7.28 cnf(i_0_3560, 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)))))). 7.00/7.28 cnf(i_0_6131, 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))). 7.00/7.28 cnf(i_0_3783, 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))))). 7.00/7.28 cnf(i_0_7250, 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)))). 7.00/7.28 cnf(i_0_6994, 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))))). 7.00/7.28 cnf(i_0_4665, plain, (X1=c_Big__Operators_Olinorder__class_OMin(X2,X3)|hBOOL(hAPP(hAPP(c_member(X2),esk359_3(X1,X3,X2)),X3))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(hAPP(c_member(X2),X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 7.00/7.28 cnf(i_0_6940, 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))). 7.00/7.28 cnf(i_0_1979, 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))). 7.00/7.28 cnf(i_0_6142, 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))). 7.00/7.28 cnf(i_0_1570, 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))). 7.00/7.28 cnf(i_0_4025, 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))))). 7.00/7.28 cnf(i_0_2624, 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))). 7.00/7.28 cnf(i_0_2088, plain, (c_Big__Operators_Olinorder__class_OMax(X1,X2)=X3|hBOOL(hAPP(hAPP(c_member(X1),esk162_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)))). 7.00/7.28 cnf(i_0_5744, 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)))). 7.00/7.28 cnf(i_0_316, 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,esk27_3(X3,X2,X1))))). 7.00/7.28 cnf(i_0_3810, 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)))). 7.00/7.28 cnf(i_0_4143, 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))). 7.00/7.28 cnf(i_0_1548, 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))). 7.00/7.28 cnf(i_0_4864, 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))). 7.00/7.28 cnf(i_0_973, 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))). 7.00/7.28 cnf(i_0_5795, 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)))). 7.00/7.28 cnf(i_0_4003, 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)))). 7.00/7.28 cnf(i_0_5187, 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)))). 7.00/7.28 cnf(i_0_1738, 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)))). 7.00/7.28 cnf(i_0_6022, 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))). 7.00/7.28 cnf(i_0_7016, 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))). 7.00/7.28 cnf(i_0_1834, 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,esk153_4(X4,X2,X3,X1))))). 7.00/7.28 cnf(i_0_4258, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk323_5(X2,X3,X1,X4,X5)),X2))|~hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(c_Relation_OImage(X1,X5,X3),X2))))). 7.00/7.28 cnf(i_0_5756, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk444_5(X2,X3,X1,X4,X5)),X2))|~hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(c_Relation_OImage(X1,X5,X3),X2))))). 7.00/7.28 cnf(i_0_892, 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))). 7.00/7.28 cnf(i_0_2299, 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)))). 7.00/7.28 cnf(i_0_5094, plain, (hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X1),c_List_Oupto(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin),X2))=c_List_Oupto(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 7.00/7.28 cnf(i_0_2575, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),esk204_3(X2,X3,X1)),esk205_3(X2,X3,X1))=X3|X3=c_List_Olist_ONil(X1)|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2))))). 7.00/7.28 cnf(i_0_3172, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk244_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)))). 7.00/7.28 cnf(i_0_2794, 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))). 7.00/7.28 cnf(i_0_4929, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk380_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))))). 7.00/7.28 cnf(i_0_376, 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))))). 7.00/7.28 cnf(i_0_1514, 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))))). 7.00/7.28 cnf(i_0_726, 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))))). 7.00/7.28 cnf(i_0_592, 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)))). 7.00/7.28 cnf(i_0_417, plain, (hAPP(c_Set_Oimage(X1,X2,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)))). 7.00/7.28 cnf(i_0_5268, 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)))). 7.00/7.28 cnf(i_0_1545, 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)))). 7.00/7.28 cnf(i_0_1445, 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)))). 7.00/7.28 cnf(i_0_5619, 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)))). 7.00/7.28 cnf(i_0_6083, plain, (hBOOL(hAPP(X1,esk481_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)))). 7.00/7.28 cnf(i_0_6824, 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,esk534_4(X1,X5,X4,X3)))|~hBOOL(hAPP(X1,esk535_4(X1,X5,X4,X3))))). 7.00/7.28 cnf(i_0_543, 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)))). 7.00/7.28 cnf(i_0_4950, 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)))). 7.00/7.28 cnf(i_0_5315, 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)))). 7.00/7.28 cnf(i_0_3097, 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)))). 7.00/7.28 cnf(i_0_3040, 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,esk232_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)))). 7.00/7.28 cnf(i_0_3060, 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)))). 7.00/7.28 cnf(i_0_6541, 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)))). 7.00/7.28 cnf(i_0_448, 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)))). 7.00/7.28 cnf(i_0_7000, 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)))))). 7.00/7.28 cnf(i_0_6928, 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(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)))))). 7.00/7.28 cnf(i_0_4006, 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)))). 7.00/7.28 cnf(i_0_1263, 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))). 7.00/7.28 cnf(i_0_5783, plain, (c_Equiv__Relations_Opart__equivp(X1,X2)|hAPP(X2,esk448_1(X2))!=hAPP(X2,esk449_1(X2))|~hBOOL(hAPP(hAPP(X2,esk448_1(X2)),esk448_1(X2)))|~hBOOL(hAPP(hAPP(X2,esk448_1(X2)),esk449_1(X2)))|~hBOOL(hAPP(hAPP(X2,esk449_1(X2)),esk449_1(X2)))|~hBOOL(hAPP(hAPP(X2,X3),X3)))). 7.00/7.28 cnf(i_0_374, 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)))). 7.00/7.28 cnf(i_0_4518, 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)))). 7.00/7.28 cnf(i_0_3034, 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)))). 7.00/7.28 cnf(i_0_6195, 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)))). 7.00/7.28 cnf(i_0_2831, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)|c_Groups_Ozero__class_Ozero(X1)=X5|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))). 7.00/7.28 cnf(i_0_3932, 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),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)))). 7.00/7.28 cnf(i_0_4651, plain, (hAPP(X1,esk358_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))))))). 7.00/7.28 cnf(i_0_3653, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),esk277_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)))). 7.00/7.28 cnf(i_0_2832, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X5)|c_Groups_Ozero__class_Ozero(X1)=X3|X5=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))). 7.00/7.28 cnf(i_0_266, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),hAPP(X2,X4)))|~c_Orderings_Oorder__class_Ostrict__mono(X5,X1,X2)|~class_Orderings_Oorder(X1)|~class_Orderings_Olinorder(X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X3),X4)))). 7.00/7.28 cnf(i_0_7350, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),hAPP(X2,X4)))|~c_Orderings_Oorder__class_Omono(X5,X1,X2)|~class_Orderings_Oorder(X1)|~class_Orderings_Oorder(X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X3),X4)))). 7.00/7.28 cnf(i_0_5708, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,X3)),hAPP(X2,X4)))|~c_Orderings_Oorder__class_Ostrict__mono(X5,X1,X2)|~class_Orderings_Oorder(X1)|~class_Orderings_Olinorder(X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X3),X4)))). 7.00/7.28 cnf(i_0_5793, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,X3)),hAPP(X2,X4)))|~c_Orderings_Oorder__class_Ostrict__mono(X5,X1,X2)|~class_Orderings_Oorder(X1)|~class_Orderings_Oorder(X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X3),X4)))). 7.00/7.28 cnf(i_0_5854, 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))))). 7.00/7.28 cnf(i_0_2750, 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)))). 7.00/7.28 cnf(i_0_403, 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)))). 7.00/7.28 cnf(i_0_7403, 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))). 7.00/7.28 cnf(i_0_3668, 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)|X2=c_List_Olist_ONil(X1))). 7.00/7.28 cnf(i_0_3569, 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)))). 7.00/7.28 cnf(i_0_6106, 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)))). 7.00/7.28 cnf(i_0_6303, 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)))). 7.00/7.28 cnf(i_0_1270, 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)))). 7.00/7.28 cnf(i_0_1426, 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))). 7.00/7.28 cnf(i_0_87, 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))). 7.00/7.28 cnf(i_0_2173, 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))). 7.00/7.28 cnf(i_0_6727, 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,esk526_7(X7,X6,X5,X4,X3,X2,X1)),X6),X7)))). 7.00/7.28 cnf(i_0_5303, 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,esk409_7(X3,X2,X7,X6,X5,X4,X1)),X6),X7)))). 7.00/7.28 cnf(i_0_7516, 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)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1)). 7.00/7.28 cnf(i_0_946, 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))). 7.00/7.28 cnf(i_0_4965, 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))). 7.00/7.28 cnf(i_0_3426, 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))). 7.00/7.28 cnf(i_0_927, 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),X5),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))). 7.00/7.28 cnf(i_0_928, 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),X2),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))). 7.00/7.28 cnf(i_0_4719, 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))))). 7.00/7.28 cnf(i_0_6894, 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)))). 7.00/7.28 cnf(i_0_2100, 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))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 7.00/7.28 cnf(i_0_2083, 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)))). 7.00/7.28 cnf(i_0_1491, plain, (X1=X2|~c_Relation_Oantisym(X3,X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X2),X1)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4)))). 7.00/7.28 cnf(i_0_2574, plain, (X1=c_List_Olist_ONil(X2)|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),esk205_3(X3,X1,X2)),c_List_Olists(X2,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X1),c_List_Olists(X2,X3))))). 7.00/7.28 cnf(i_0_2417, 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))))). 7.00/7.28 cnf(i_0_7352, 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)))). 7.00/7.28 cnf(i_0_7150, 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)))). 7.00/7.28 cnf(i_0_4921, 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)))). 7.00/7.28 cnf(i_0_1220, plain, (hBOOL(hAPP(X1,esk99_4(X1,X2,X3,X4)))|hBOOL(hAPP(X2,esk98_4(X1,X2,X3,X4)))|~c_Equiv__Relations_Oequivp(X4,X3)|~hBOOL(hAPP(X2,X5)))). 7.00/7.28 cnf(i_0_4514, 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))). 7.00/7.28 cnf(i_0_6177, 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)))). 7.00/7.28 cnf(i_0_44, 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)))). 7.00/7.28 cnf(i_0_5220, 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)))). 7.00/7.28 cnf(i_0_3486, 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),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 7.00/7.28 cnf(i_0_728, 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))))). 7.00/7.28 cnf(i_0_3766, 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))))). 7.00/7.28 cnf(i_0_339, 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)))). 7.00/7.28 cnf(i_0_4883, 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))))). 7.00/7.28 cnf(i_0_6178, 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)))). 7.00/7.28 cnf(i_0_2523, 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),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)))). 7.00/7.28 cnf(i_0_4830, 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))))). 7.00/7.28 cnf(i_0_2677, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~c_Fun_Obij__betw(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))))). 7.00/7.28 cnf(i_0_5199, 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))). 7.00/7.28 cnf(i_0_4735, 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,esk366_4(X4,X2,X3,X1))),hAPP(X4,esk366_4(X4,X2,X3,X1)))))). 7.00/7.28 cnf(i_0_6109, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|c_Fun_Oinj__on(X3,X4,X5,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),X6))|~c_Fun_Oinj__on(X3,X4,X5,hAPP(X6,esk482_6(X6,X5,X4,X3,X2,X1))))). 7.00/7.28 cnf(i_0_5954, plain, (hAPP(hAPP(X1,X2),esk463_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)))). 7.00/7.28 cnf(i_0_759, 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))))). 7.00/7.28 cnf(i_0_6539, 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)))). 7.00/7.28 cnf(i_0_5076, 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)))). 7.00/7.28 cnf(i_0_5781, plain, (hAPP(X1,esk448_1(X1))=hAPP(X1,esk449_1(X1))|c_Equiv__Relations_Opart__equivp(X2,X1)|hBOOL(hAPP(hAPP(X1,esk448_1(X1)),esk449_1(X1)))|~hBOOL(hAPP(hAPP(X1,X3),X3)))). 7.00/7.28 cnf(i_0_2676, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),X4)))|~c_Fun_Obij__betw(X1,X2,X4,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 7.00/7.28 cnf(i_0_983, 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))))). 7.00/7.28 cnf(i_0_1264, 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)))). 7.00/7.28 cnf(i_0_7184, 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))))). 7.00/7.28 cnf(i_0_6734, 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))))). 7.00/7.28 cnf(i_0_4027, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk306_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))))). 7.00/7.28 cnf(i_0_3354, 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)))|hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1)))|~hBOOL(hAPP(X2,X3)))). 7.00/7.28 cnf(i_0_989, 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)))). 7.00/7.28 cnf(i_0_5205, 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))=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 7.00/7.28 cnf(i_0_888, 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)))). 7.00/7.28 cnf(i_0_2940, 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)))). 7.00/7.28 cnf(i_0_5865, 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),esk457_2(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_List_Oset(tc_Nat_Onat),X1))))). 7.00/7.28 cnf(i_0_700, 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)))). 7.00/7.28 cnf(i_0_3862, 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)))). 7.00/7.28 cnf(i_0_5374, 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)))). 7.00/7.28 cnf(i_0_5061, 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)))). 7.00/7.28 cnf(i_0_6417, 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))). 7.00/7.28 cnf(i_0_4070, 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))). 7.00/7.28 cnf(i_0_3938, 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))). 7.00/7.28 cnf(i_0_3257, 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))). 7.00/7.28 cnf(i_0_7283, 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)))). 7.00/7.28 cnf(i_0_6617, 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))))). 7.00/7.28 cnf(i_0_7439, 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))))). 7.00/7.28 cnf(i_0_2353, plain, (c_Fun_Oinj__on(X1,X2,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))). 7.00/7.28 cnf(i_0_131, 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)))). 7.00/7.28 cnf(i_0_5721, 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))). 7.00/7.28 cnf(i_0_3002, 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))). 7.00/7.28 cnf(i_0_4224, 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)))). 7.00/7.28 cnf(i_0_5530, 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_Olistrel(X1,X4))))). 7.00/7.28 cnf(i_0_7249, 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))))). 7.00/7.28 cnf(i_0_897, 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))). 7.00/7.28 cnf(i_0_6007, 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))). 7.00/7.28 cnf(i_0_5501, 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))). 7.00/7.28 cnf(i_0_5908, 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)))). 7.00/7.28 cnf(i_0_6720, 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))))). 7.00/7.28 cnf(i_0_6082, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X3),esk480_4(X1,X4,X2,X3)),esk481_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)))). 7.00/7.28 cnf(i_0_7385, 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)))). 7.00/7.28 cnf(i_0_4650, plain, (esk358_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))))). 7.00/7.28 cnf(i_0_2447, 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))). 7.00/7.28 cnf(i_0_967, 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))). 7.00/7.28 cnf(i_0_7401, 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))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.00/7.28 cnf(i_0_7240, 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))). 7.00/7.28 cnf(i_0_4589, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk351_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)))). 7.00/7.28 cnf(i_0_2738, 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)))). 7.00/7.28 cnf(i_0_3408, 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)))). 7.00/7.28 cnf(i_0_6676, 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)))). 7.00/7.28 cnf(i_0_2308, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),c_Groups_Ozero__class_Ozero(X1))))|~class_Rings_Oidom(X1))). 7.00/7.28 cnf(i_0_1539, 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))). 7.00/7.28 cnf(i_0_1432, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk114_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))). 7.00/7.28 cnf(i_0_4275, 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))). 7.00/7.28 cnf(i_0_5337, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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)))|~class_Rings_Oidom(X1))). 7.00/7.28 cnf(i_0_5554, 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))))))))). 7.00/7.28 cnf(i_0_1470, 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))))). 7.00/7.28 cnf(i_0_5154, 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)))). 7.00/7.28 cnf(i_0_82, 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)))). 7.00/7.28 cnf(i_0_6483, plain, (c_Wellfounded_Owf(X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk506_2(X2,X1)),hAPP(c_Relation_OImage(X1,X1,X2),esk506_2(X2,X1)))))). 7.00/7.28 cnf(i_0_2821, 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))))). 7.00/7.28 cnf(i_0_5319, 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))))). 7.00/7.28 cnf(i_0_6970, 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)))). 7.00/7.28 cnf(i_0_3092, 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),esk237_5(X2,X5,X4,X3,X1)),X3)))). 7.00/7.28 cnf(i_0_600, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(c_COMBK(X2,X1),X3)),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),hAPP(c_Finite__Set_Ocard(X1),X4))),X3)|~class_Rings_Osemiring__1(X2))). 7.00/7.28 cnf(i_0_7006, 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)))). 7.00/7.28 cnf(i_0_3664, 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)))). 7.00/7.28 cnf(i_0_5221, 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)))). 7.00/7.28 cnf(i_0_7198, 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),esk557_5(X5,X4,X3,X2,X1)),X3)))). 7.00/7.28 cnf(i_0_6495, 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))))). 7.00/7.28 cnf(i_0_2796, 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))))). 7.00/7.28 cnf(i_0_6135, 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)))). 7.00/7.28 cnf(i_0_6808, 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)))). 7.00/7.28 cnf(i_0_2028, 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)))). 7.00/7.28 cnf(i_0_187, 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)))). 7.00/7.28 cnf(i_0_561, 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)))). 7.00/7.28 cnf(i_0_5306, 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)))). 7.00/7.28 cnf(i_0_3808, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 7.00/7.28 cnf(i_0_5053, 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))). 7.00/7.28 cnf(i_0_6137, 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))))). 7.00/7.28 cnf(i_0_2438, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(X2,X3)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1),X2),X5)!=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(X2,esk194_5(X3,X2,X5,X4,X1))))|~hBOOL(hAPP(hAPP(c_member(X4),X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X5)))). 7.00/7.28 cnf(i_0_2646, 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))))). 7.00/7.28 cnf(i_0_7449, 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)))). 7.00/7.28 cnf(i_0_7281, plain, (hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),X1),c_Nat_OSuc)))=c_Orderings_Oord__class_OLeast(tc_Nat_Onat,X1)|hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,X2)))). 7.00/7.28 cnf(i_0_3250, 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))))). 7.00/7.29 cnf(i_0_2649, 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))))). 7.00/7.29 cnf(i_0_2648, 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))))). 7.00/7.29 cnf(i_0_2647, 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))))). 7.00/7.29 cnf(i_0_1997, 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))))). 7.00/7.29 cnf(i_0_1022, 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))))). 7.00/7.29 cnf(i_0_1819, 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),X2)),X2))|~c_Relation_Otrans(X1,X2))). 7.00/7.29 cnf(i_0_6756, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Complete__Lattice_OInf__class_OInf(X1,X3))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X2),X3)|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.00/7.29 cnf(i_0_143, plain, (c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X2),X3)|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.00/7.29 cnf(i_0_7101, 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))). 7.00/7.29 cnf(i_0_1998, 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))))). 7.00/7.29 cnf(i_0_1999, 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))))). 7.00/7.29 cnf(i_0_1996, 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))))). 7.00/7.29 cnf(i_0_1074, 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),X2),X3)),c_Groups_Ozero__class_Ozero(X1))))). 7.00/7.29 cnf(i_0_6041, plain, (c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X2),X3)|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.00/7.29 cnf(i_0_485, 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)))). 7.00/7.29 cnf(i_0_941, 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)))). 7.00/7.29 cnf(i_0_1050, 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))). 7.00/7.29 cnf(i_0_5930, 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),X2),X3)),c_Groups_Ozero__class_Ozero(X1))))). 7.00/7.29 cnf(i_0_1073, 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))))). 7.00/7.29 cnf(i_0_1072, 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))))). 7.00/7.29 cnf(i_0_5929, 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))))). 7.00/7.29 cnf(i_0_4498, 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)))). 7.00/7.29 cnf(i_0_4566, 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)))). 7.00/7.29 cnf(i_0_1718, 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)))). 7.00/7.29 cnf(i_0_5932, 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))))). 7.00/7.29 cnf(i_0_1071, 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),X3),X2)),c_Groups_Ozero__class_Ozero(X1))))). 7.00/7.29 cnf(i_0_5931, 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),X3),X2)),c_Groups_Ozero__class_Ozero(X1))))). 7.00/7.29 cnf(i_0_3952, 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))))). 7.00/7.29 cnf(i_0_5107, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk397_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)))). 7.00/7.29 cnf(i_0_3655, 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)))). 7.00/7.29 cnf(i_0_5091, 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)))). 7.00/7.29 cnf(i_0_5517, 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)))). 7.00/7.29 cnf(i_0_2254, 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)))). 7.00/7.29 cnf(i_0_6957, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk545_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)))). 7.00/7.29 cnf(i_0_1132, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk90_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)))). 7.00/7.29 cnf(i_0_2469, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk196_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)))). 7.00/7.29 cnf(i_0_4831, 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)))). 7.00/7.29 cnf(i_0_6330, 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,esk495_3(X2,X1,X3)),esk496_3(X2,X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.00/7.29 cnf(i_0_5509, 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))))). 7.00/7.29 cnf(i_0_472, 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)))). 7.00/7.29 cnf(i_0_7261, 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)))). 7.00/7.29 cnf(i_0_2704, 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)))). 7.00/7.29 cnf(i_0_7455, 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)))). 7.00/7.29 cnf(i_0_3514, 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,esk267_3(X2,X1,X3)),esk268_3(X2,X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 7.00/7.29 cnf(i_0_705, 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)))). 7.00/7.29 cnf(i_0_1549, 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)))). 7.00/7.29 cnf(i_0_1944, plain, (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))|c_List_Olast(X2,hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X4))=c_List_Olast(X2,X3)|c_List_Olist_ONil(X2)=X3)). 7.00/7.29 cnf(i_0_1243, 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)))). 7.00/7.29 cnf(i_0_6987, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3)))). 7.00/7.29 cnf(i_0_5283, 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)))). 7.00/7.29 cnf(i_0_7379, 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))). 7.00/7.29 cnf(i_0_2304, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X5)),X3))|~hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Set_Oimage(X1,X2,X4),X3))))). 7.00/7.29 cnf(i_0_6395, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,esk500_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))))). 7.00/7.29 cnf(i_0_6784, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,esk531_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))))). 7.00/7.29 cnf(i_0_5021, 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_Ominus__class_Ominus(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),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 7.00/7.29 cnf(i_0_3964, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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),X1)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X1)))). 7.00/7.29 cnf(i_0_3829, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(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),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 7.00/7.29 cnf(i_0_4751, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(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),X1)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1)))). 7.00/7.29 cnf(i_0_656, 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))). 7.00/7.29 cnf(i_0_1666, 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_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_Ozero__class_Ozero(X1))))). 7.00/7.29 cnf(i_0_2715, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|~class_Int_Onumber__ring(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))))). 7.00/7.29 cnf(i_0_7232, 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)))). 7.00/7.29 cnf(i_0_4343, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 7.00/7.29 cnf(i_0_5587, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),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))))). 7.00/7.29 cnf(i_0_730, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)))). 7.00/7.29 cnf(i_0_1779, 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),c_Int_OMin))))). 7.00/7.29 cnf(i_0_4964, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))|~class_Enum_Oenum(X1)|~class_Orderings_Oorder(X2)|~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))))). 7.00/7.29 cnf(i_0_3388, 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)))). 7.00/7.29 cnf(i_0_2179, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),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))))). 7.00/7.29 cnf(i_0_7346, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OMin)))). 7.00/7.29 cnf(i_0_5274, 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))))). 7.00/7.29 cnf(i_0_2948, 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)))). 7.00/7.29 cnf(i_0_7078, 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))). 7.00/7.29 cnf(i_0_6012, 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))). 7.00/7.29 cnf(i_0_4731, 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))). 7.00/7.29 cnf(i_0_6086, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk481_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)))). 7.00/7.29 cnf(i_0_6240, 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))). 7.00/7.29 cnf(i_0_3108, 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)))). 7.00/7.29 cnf(i_0_337, 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)))). 7.00/7.29 cnf(i_0_830, 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)))). 7.00/7.29 cnf(i_0_4595, 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)))). 7.00/7.29 cnf(i_0_6893, 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))). 7.00/7.29 cnf(i_0_2551, 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))). 7.00/7.29 cnf(i_0_1986, 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))))). 7.00/7.29 cnf(i_0_1985, 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))))). 7.00/7.29 cnf(i_0_1746, 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)))). 7.00/7.29 cnf(i_0_1166, 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)))). 7.00/7.29 cnf(i_0_6475, 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)))). 7.00/7.29 cnf(i_0_444, 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)))). 7.00/7.29 cnf(i_0_1853, 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)). 7.00/7.29 cnf(i_0_7276, 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))). 7.00/7.29 cnf(i_0_1984, 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))))). 7.00/7.29 cnf(i_0_1987, 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))))). 7.00/7.29 cnf(i_0_456, plain, (X1=c_Big__Operators_Olattice__class_OInf__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)))). 7.00/7.29 cnf(i_0_3393, 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)))). 7.00/7.29 cnf(i_0_7194, 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))). 7.00/7.29 cnf(i_0_4985, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk386_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)))). 7.00/7.29 cnf(i_0_5203, 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))))). 7.00/7.29 cnf(i_0_2098, plain, (c_Fun_Oinj__on(X1,X2,c_Hilbert__Choice_Oinv__into(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X3),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(X1,tc_HOL_Obool)))). 7.00/7.29 cnf(i_0_1404, 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))). 7.00/7.29 cnf(i_0_4702, 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))). 7.00/7.29 cnf(i_0_7247, 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)))). 7.00/7.29 cnf(i_0_5271, plain, (c_Big__Operators_Olinorder__class_OMin(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)))). 7.00/7.29 cnf(i_0_2997, 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)))). 7.00/7.29 cnf(i_0_5968, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),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)),esk468_3(X2,X3,X1)),X3)))). 7.00/7.29 cnf(i_0_5223, 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)))). 7.00/7.29 cnf(i_0_6036, 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)))). 7.00/7.29 cnf(i_0_6903, 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)))). 7.00/7.29 cnf(i_0_190, 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))). 7.00/7.29 cnf(i_0_3284, 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),X2),X3)),c_Groups_Ozero__class_Ozero(X1))))). 7.00/7.29 cnf(i_0_3283, 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))))). 7.00/7.29 cnf(i_0_3282, 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))))). 7.00/7.29 cnf(i_0_3281, 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),X3),X2)),c_Groups_Ozero__class_Ozero(X1))))). 7.00/7.29 cnf(i_0_2182, 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,esk170_3(X2,X3,X1))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.00/7.29 cnf(i_0_4612, 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,esk353_3(X2,X3,X1))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.00/7.29 cnf(i_0_6992, 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))))). 7.00/7.29 cnf(i_0_4630, 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)),X3))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk355_3(X3,X2,X1)),X2)))). 7.00/7.29 cnf(i_0_1205, 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))). 7.00/7.29 cnf(i_0_3826, 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))))). 7.00/7.29 cnf(i_0_1752, 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))))). 7.00/7.29 cnf(i_0_102, 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))). 7.00/7.29 cnf(i_0_1457, 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)))). 7.00/7.29 cnf(i_0_1801, 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))). 7.00/7.29 cnf(i_0_5540, 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_Groups_Omonoid__mult(X1))). 7.00/7.29 cnf(i_0_6789, 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))). 7.00/7.29 cnf(i_0_883, 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))). 7.00/7.29 cnf(i_0_1293, 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))))). 7.00/7.29 cnf(i_0_1292, 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))))). 7.00/7.29 cnf(i_0_1473, plain, (c_Fun_Obij__betw(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)))|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))|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))). 7.00/7.29 cnf(i_0_3437, 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)))). 7.00/7.29 cnf(i_0_6638, plain, (c_Relation_Otrans(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_Relation_Otrans(X1,X2))). 7.00/7.29 cnf(i_0_4243, plain, (c_Relation_Oantisym(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_Relation_Oantisym(X1,X2))). 7.00/7.29 cnf(i_0_3266, 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)))). 7.00/7.29 cnf(i_0_5542, 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))). 7.00/7.29 cnf(i_0_6389, 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))). 7.00/7.29 cnf(i_0_5569, 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))). 7.00/7.29 cnf(i_0_3173, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk243_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)))). 7.00/7.29 cnf(i_0_4851, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk373_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))))). 7.00/7.29 cnf(i_0_2695, 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)))). 7.00/7.29 cnf(i_0_2891, plain, (hAPP(c_Fun_Ocomp(X1,X2,X2,X3),c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3))=c_Fun_Oid(X2)|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)))). 7.00/7.29 cnf(i_0_83, 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))). 7.00/7.29 cnf(i_0_3462, plain, (hAPP(X1,X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X2=esk262_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)))). 7.00/7.29 cnf(i_0_6382, 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),X3),X2)),hAPP(hAPP(c_List_Olist_OCons(X5),X4),X1))),c_List_Olistrel1(X5,X6))))). 7.00/7.29 cnf(i_0_6406, 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))))). 7.00/7.29 cnf(i_0_5726, 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)))). 7.00/7.29 cnf(i_0_521, 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)))). 7.00/7.29 cnf(i_0_4555, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2))))). 7.00/7.29 cnf(i_0_5780, plain, (c_Equiv__Relations_Opart__equivp(X1,X2)|hBOOL(hAPP(hAPP(X2,esk448_1(X2)),esk449_1(X2)))|hBOOL(hAPP(hAPP(X2,esk448_1(X2)),esk448_1(X2)))|~hBOOL(hAPP(hAPP(X2,X3),X3)))). 7.00/7.29 cnf(i_0_5782, plain, (c_Equiv__Relations_Opart__equivp(X1,X2)|hBOOL(hAPP(hAPP(X2,esk449_1(X2)),esk449_1(X2)))|hBOOL(hAPP(hAPP(X2,esk448_1(X2)),esk449_1(X2)))|~hBOOL(hAPP(hAPP(X2,X3),X3)))). 7.00/7.29 cnf(i_0_542, 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)))). 7.00/7.29 cnf(i_0_474, 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))). 7.00/7.29 cnf(i_0_425, 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))). 7.00/7.29 cnf(i_0_1291, 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)))). 7.00/7.29 cnf(i_0_1717, 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)))). 7.00/7.29 cnf(i_0_3539, 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)))). 7.00/7.29 cnf(i_0_2075, 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)))). 7.00/7.29 cnf(i_0_5302, 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)))). 7.00/7.29 cnf(i_0_4539, 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))). 7.00/7.29 cnf(i_0_2010, 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))). 7.00/7.29 cnf(i_0_2960, 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))). 7.00/7.29 cnf(i_0_1883, 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))). 7.00/7.29 cnf(i_0_795, 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))). 7.00/7.29 cnf(i_0_866, 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)))). 7.00/7.29 cnf(i_0_3912, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk295_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))))). 7.00/7.29 cnf(i_0_6519, 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))). 7.00/7.29 cnf(i_0_7505, 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)))). 7.00/7.29 cnf(i_0_2607, 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)))). 7.00/7.29 cnf(i_0_4496, 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)))). 7.00/7.29 cnf(i_0_6794, 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)))). 7.00/7.29 cnf(i_0_4837, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(c_List_Ofilter(X1,X3),X4))=hAPP(c_List_Ofilter(X1,X3),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4))|~hBOOL(hAPP(X3,X2)))). 7.00/7.29 cnf(i_0_6094, 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))). 7.00/7.29 cnf(i_0_5824, 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))))). 7.00/7.29 cnf(i_0_2338, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk187_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))))). 7.00/7.29 cnf(i_0_5644, 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)))). 7.00/7.29 cnf(i_0_3960, 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))). 7.00/7.29 cnf(i_0_597, 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)))). 7.00/7.29 cnf(i_0_1955, 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)))). 7.00/7.29 cnf(i_0_1661, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk139_3(X3,X2,X1)),hAPP(c_List_Oset(X1),X3)))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 7.00/7.29 cnf(i_0_6885, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk540_3(X3,X2,X1)),hAPP(c_List_Oset(X1),X3)))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 7.00/7.29 cnf(i_0_4165, 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))). 7.00/7.29 cnf(i_0_2719, plain, (hAPP(hAPP(X1,X2),X3)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X4,X5,X6),X2),X7),X3)|~c_Finite__Set_Ofolding__image(X4,X5,X6,X7,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3)))). 7.00/7.29 cnf(i_0_4785, 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)))). 7.00/7.29 cnf(i_0_1177, 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)))). 7.00/7.29 cnf(i_0_352, 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),esk32_4(X2,X3,X1,X4)))))). 7.00/7.29 cnf(i_0_4967, 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))). 7.00/7.29 cnf(i_0_4463, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk340_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 7.00/7.29 cnf(i_0_438, 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)))). 7.00/7.29 cnf(i_0_5553, 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))))). 7.00/7.29 cnf(i_0_7104, 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))). 7.00/7.29 cnf(i_0_2052, 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))). 7.00/7.29 cnf(i_0_1612, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(X3,esk133_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))))). 7.00/7.29 cnf(i_0_4579, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,esk349_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)))). 7.00/7.29 cnf(i_0_4691, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|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)))). 7.00/7.29 cnf(i_0_5385, 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))))). 7.00/7.29 cnf(i_0_955, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_member(X2),esk82_4(X3,X4,X1,X2)),hAPP(c_List_Oset(X2),c_List_Oreplicate(X2,X1,X4))))|~hBOOL(hAPP(X3,X4)))). 7.00/7.29 cnf(i_0_909, plain, (hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4))=hAPP(hAPP(c_Finite__Set_Ofold(X2,X2,X5),X3),X4)|~c_Finite__Set_Ofolding__one__idem(X2,X5,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 7.00/7.29 cnf(i_0_383, 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))))). 7.00/7.29 cnf(i_0_6904, 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)))). 7.00/7.29 cnf(i_0_4140, plain, (c_Relation_Osym(X1,X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk312_2(X2,X1)),esk313_2(X2,X1))),X2)))). 7.00/7.29 cnf(i_0_6068, 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))))). 7.00/7.29 cnf(i_0_2127, 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),X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))))). 7.00/7.29 cnf(i_0_7236, plain, (c_Relation_Otrans(X1,X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk562_2(X2,X1)),esk563_2(X2,X1))),X2)))). 7.00/7.29 cnf(i_0_718, plain, (c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X3))=X3|~c_Fun_Obij__betw(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))))). 7.00/7.29 cnf(i_0_1943, 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)))). 7.00/7.29 cnf(i_0_7235, plain, (c_Relation_Otrans(X1,X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk563_2(X2,X1)),esk564_2(X2,X1))),X2)))). 7.00/7.29 cnf(i_0_3449, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk261_4(X3,X4,X2,X1)),esk260_4(X3,X4,X2,X1))=X4|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),X4),hAPP(c_Relation_Oconverse(X2,X1),X3))))). 7.00/7.29 cnf(i_0_736, 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))))). 7.00/7.29 cnf(i_0_6396, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk500_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))))). 7.00/7.29 cnf(i_0_6785, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk531_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))))). 7.00/7.29 cnf(i_0_7522, plain, (c_Relation_Oantisym(X1,X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk596_2(X2,X1)),esk597_2(X2,X1))),X2)))). 7.00/7.29 cnf(i_0_3168, 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)))). 7.00/7.29 cnf(i_0_429, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk37_3(X2,X3,X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),X2)))). 7.00/7.29 cnf(i_0_6623, plain, (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),X1),esk516_3(X1,X2,X3))),X2))|~hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1))))). 7.00/7.29 cnf(i_0_7457, 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)))). 7.00/7.29 cnf(i_0_7521, plain, (c_Relation_Oantisym(X1,X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk597_2(X2,X1)),esk596_2(X2,X1))),X2)))). 7.00/7.29 cnf(i_0_7082, 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)))). 7.00/7.29 cnf(i_0_6686, 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,esk524_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)))). 7.00/7.29 cnf(i_0_2315, 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,esk183_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)))). 7.00/7.29 cnf(i_0_4154, 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,esk316_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)))). 7.00/7.29 cnf(i_0_5378, plain, (c_Relation_Oirrefl(X1,X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk412_2(X2,X1)),esk412_2(X2,X1))),X2)))). 7.00/7.29 cnf(i_0_1950, 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)))). 7.00/7.29 cnf(i_0_390, 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)))). 7.00/7.29 cnf(i_0_5727, 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))))). 7.00/7.29 cnf(i_0_2644, 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))))). 7.00/7.29 cnf(i_0_4753, 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,esk367_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)))). 7.00/7.29 cnf(i_0_1131, plain, (hBOOL(hAPP(hAPP(hAPP(X1,esk90_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)))). 7.00/7.29 cnf(i_0_2468, plain, (hBOOL(hAPP(hAPP(hAPP(X1,esk196_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)))). 7.00/7.29 cnf(i_0_3043, plain, (hAPP(X1,X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X2=esk231_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)))). 7.00/7.29 cnf(i_0_2001, 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),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))))). 7.00/7.29 cnf(i_0_2645, 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)))). 7.00/7.29 cnf(i_0_2000, 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)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 7.00/7.29 cnf(i_0_2956, 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))))). 7.00/7.29 cnf(i_0_4878, 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)))). 7.00/7.29 cnf(i_0_4681, 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)))). 7.00/7.29 cnf(i_0_1217, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk99_4(X2,X3,X4,X1)),c_Quotient_ORespects(X1,X4)))|~c_Equiv__Relations_Oequivp(X1,X4)|~hBOOL(hAPP(X2,esk98_4(X2,X3,X4,X1)))|~hBOOL(hAPP(X3,X5)))). 7.00/7.29 cnf(i_0_5285, 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))))). 7.00/7.29 cnf(i_0_3812, 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))))). 7.00/7.29 cnf(i_0_1876, 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))))). 7.00/7.29 cnf(i_0_5702, 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))))). 7.00/7.29 cnf(i_0_3881, 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))))). 7.00/7.29 cnf(i_0_1613, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk133_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))))). 7.00/7.29 cnf(i_0_4580, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk349_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)))). 7.00/7.29 cnf(i_0_4405, 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)))). 7.00/7.29 cnf(i_0_7178, plain, (hAPP(c_Set_Oimage(X1,X2,c_Hilbert__Choice_Oinv__into(X2,X1,X3,X4)),hAPP(c_Set_Oimage(X2,X1,X4),X5))=X5|~c_Fun_Oinj__on(X2,X1,X4,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X5),X3)))). 7.00/7.29 cnf(i_0_1076, 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)))). 7.00/7.29 cnf(i_0_1075, 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)))). 7.00/7.29 cnf(i_0_5934, 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)))). 7.00/7.29 cnf(i_0_5933, 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)))). 7.00/7.29 cnf(i_0_3381, plain, (hAPP(X1,hAPP(hAPP(c_Orderings_Oord__class_Omin(X2),X3),X4))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),hAPP(X1,X3)),hAPP(X1,X4))|~c_Orderings_Oorder__class_Omono(X2,X5,X1)|~class_Orderings_Olinorder(X5)|~class_Orderings_Olinorder(X2))). 7.00/7.29 cnf(i_0_1087, 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)))))). 7.00/7.29 cnf(i_0_6911, 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))). 7.00/7.29 cnf(i_0_2221, 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))))). 7.00/7.29 cnf(i_0_196, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk13_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))))). 7.00/7.29 cnf(i_0_753, 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)))). 7.00/7.29 cnf(i_0_3443, 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)))). 7.00/7.29 cnf(i_0_2947, 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)))). 7.00/7.29 cnf(i_0_6394, plain, (hAPP(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),X3),X4))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),hAPP(X1,X3)),hAPP(X1,X4))|~c_Orderings_Oorder__class_Omono(X2,X5,X1)|~class_Orderings_Olinorder(X5)|~class_Orderings_Olinorder(X2))). 7.00/7.29 cnf(i_0_1106, 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),esk89_5(X5,X4,X3,X2,X1))),hAPP(hAPP(c_List_Onth(X2),X5),esk89_5(X5,X4,X3,X2,X1)))))). 7.00/7.29 cnf(i_0_5705, 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),esk436_5(X3,X5,X2,X4,X1))),hAPP(hAPP(c_List_Onth(X2),X5),esk436_5(X3,X5,X2,X4,X1)))))). 7.00/7.29 cnf(i_0_894, 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)))). 7.00/7.29 cnf(i_0_910, 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_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin)))=c_Lazy__Sequence_Osmall__lazy_H(X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)))). 7.00/7.29 cnf(i_0_3331, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk257_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk255_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X2)))). 7.00/7.29 cnf(i_0_3345, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk257_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X2)))). 7.00/7.29 cnf(i_0_4895, 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)))). 7.00/7.29 cnf(i_0_5916, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk458_3(X1,X2,X3)))=X3|c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2)!=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3)))). 7.00/7.29 cnf(i_0_2404, 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)))). 7.00/7.29 cnf(i_0_1865, 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)))))). 7.00/7.29 cnf(i_0_6751, 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))))). 7.00/7.29 cnf(i_0_2081, 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)))). 7.00/7.29 cnf(i_0_6581, 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))). 7.00/7.29 cnf(i_0_3469, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(X2,X3)),hAPP(X4,X3))=hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,X1)),X2),X4),X3)|~class_Lattices_Olattice(X1))). 7.00/7.29 cnf(i_0_5840, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk454_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))). 7.00/7.29 cnf(i_0_2448, 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)). 7.00/7.29 cnf(i_0_5947, 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))). 7.00/7.29 cnf(i_0_3770, 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)))). 7.00/7.29 cnf(i_0_1574, plain, (hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,X2)),X3),X4),X5)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),hAPP(X3,X5)),hAPP(X4,X5))|~class_Lattices_Olattice(X2))). 7.00/7.29 cnf(i_0_5299, plain, (hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,X2)),X3),X4),X5)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),hAPP(X3,X5)),hAPP(X4,X5))|~class_Groups_Ominus(X2))). 7.00/7.29 cnf(i_0_407, 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))). 7.00/7.29 cnf(i_0_6295, 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)))). 7.00/7.29 cnf(i_0_1275, 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)))). 7.00/7.29 cnf(i_0_3580, 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)))). 7.00/7.29 cnf(i_0_6104, 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)))). 7.00/7.29 cnf(i_0_2102, plain, (X1=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))=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))). 7.00/7.29 cnf(i_0_2563, 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))). 7.00/7.29 cnf(i_0_1152, 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,esk93_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)))). 7.00/7.29 cnf(i_0_2816, 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))))). 7.00/7.29 cnf(i_0_1538, 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))). 7.00/7.29 cnf(i_0_5063, 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)))). 7.00/7.29 cnf(i_0_5710, 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)),esk437_3(X3,X2,X1)),X3)))). 7.00/7.29 cnf(i_0_2045, 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))))). 7.00/7.29 cnf(i_0_4100, 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))))). 7.00/7.29 cnf(i_0_6112, 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))))). 7.00/7.29 cnf(i_0_408, 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))). 7.00/7.29 cnf(i_0_1374, 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,esk107_5(X5,X2,X1,X4,X3)))))). 7.00/7.29 cnf(i_0_1860, 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,esk155_5(X5,X4,X3,X2,X1)))))). 7.00/7.29 cnf(i_0_3272, 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,esk252_5(X5,X4,X3,X2,X1))),X5)))). 7.00/7.29 cnf(i_0_1777, 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)))). 7.00/7.29 cnf(i_0_4972, 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)))). 7.00/7.29 cnf(i_0_2055, 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)))). 7.00/7.29 cnf(i_0_4587, 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))). 7.00/7.29 cnf(i_0_4344, 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,esk327_5(X5,X4,X1,X3,X2))),X5)))). 7.00/7.29 cnf(i_0_1259, 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)))). 7.00/7.29 cnf(i_0_3140, 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)))). 7.00/7.29 cnf(i_0_2177, 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(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.00/7.29 cnf(i_0_4591, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk350_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)))). 7.00/7.29 cnf(i_0_3356, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk257_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk255_3(X1,X2,X3))))). 7.00/7.29 cnf(i_0_2457, 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))). 7.00/7.29 cnf(i_0_6974, 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))). 7.00/7.29 cnf(i_0_3122, 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))). 7.00/7.29 cnf(i_0_6154, 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)),esk485_3(X3,X2,X1)),X2)))). 7.00/7.29 cnf(i_0_3370, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk257_3(X1,X2,X3))))). 7.00/7.29 cnf(i_0_5754, 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_Int_Onumber__ring(X1)|~class_Fields_Ofield(X1))). 7.00/7.29 cnf(i_0_1387, 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|~c_Finite__Set_Ofolding__one__idem(X2,X5,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 7.00/7.29 cnf(i_0_5423, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_member(X2),esk414_4(X3,X4,X1,X2)),hAPP(c_List_Oset(X2),c_List_Oreplicate(X2,X1,X4))))|hBOOL(hAPP(X3,X4)))). 7.00/7.29 cnf(i_0_1969, plain, (hAPP(X1,X2)=X3|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X3),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,X1)|~hBOOL(hAPP(hAPP(c_member(X4),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))). 7.00/7.29 cnf(i_0_5481, 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)))))). 7.00/7.29 cnf(i_0_6649, 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)))))). 7.00/7.29 cnf(i_0_796, 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_OInf__fin(X2,c_Orderings_Oord__class_Omin(X2),X1)),c_Big__Operators_Olattice_OSup__fin(X2,c_Orderings_Oord__class_Omax(X2),X1)))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 7.00/7.29 cnf(i_0_257, 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)))). 7.00/7.29 cnf(i_0_6774, 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)))). 7.00/7.29 cnf(i_0_4724, 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)))). 7.00/7.29 cnf(i_0_1665, 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_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1))). 7.00/7.29 cnf(i_0_7353, plain, (X1=X2|hAPP(c_Hilbert__Choice_Oinv__into(X3,X4,X5,X6),X1)!=hAPP(c_Hilbert__Choice_Oinv__into(X3,X4,X5,X6),X2)|~hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(c_Set_Oimage(X3,X4,X6),X5)))|~hBOOL(hAPP(hAPP(c_member(X4),X1),hAPP(c_Set_Oimage(X3,X4,X6),X5))))). 7.00/7.29 cnf(i_0_6227, 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))))). 7.00/7.29 cnf(i_0_280, 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)))). 7.00/7.29 cnf(i_0_295, 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)))). 7.00/7.29 cnf(i_0_3411, 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)))). 7.00/7.29 cnf(i_0_1079, 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)))). 7.00/7.29 cnf(i_0_3068, 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)))). 7.00/7.29 cnf(i_0_1948, 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))))). 7.00/7.29 cnf(i_0_6852, 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))))). 7.00/7.29 cnf(i_0_1989, 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),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 7.00/7.29 cnf(i_0_596, 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))))). 7.00/7.29 cnf(i_0_4362, 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)))))). 7.00/7.29 cnf(i_0_4015, 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)))). 7.00/7.29 cnf(i_0_5336, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~class_Rings_Oidom(X1)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X4)))). 7.00/7.29 cnf(i_0_2309, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~class_Rings_Oidom(X1)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4)))). 7.00/7.29 cnf(i_0_4479, 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)))). 7.00/7.29 cnf(i_0_3715, 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))))). 7.00/7.29 cnf(i_0_7024, 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)))). 7.00/7.29 cnf(i_0_6851, 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)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 7.00/7.29 cnf(i_0_1988, 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)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 7.00/7.29 cnf(i_0_7126, 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_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)))). 7.00/7.29 cnf(i_0_6596, 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)))). 7.00/7.29 cnf(i_0_6054, 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)))). 7.00/7.29 cnf(i_0_517, 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)|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 7.00/7.29 cnf(i_0_6113, 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)))). 7.00/7.29 cnf(i_0_2985, 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)))). 7.00/7.29 cnf(i_0_3029, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X1),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin),X2))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)))). 7.00/7.29 cnf(i_0_2925, 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)))). 7.00/7.29 cnf(i_0_3957, 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)))). 7.00/7.29 cnf(i_0_445, 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))))). 7.00/7.29 cnf(i_0_1033, 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))))). 7.00/7.29 cnf(i_0_1754, 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)|c_List_Olist_ONil(X1)=X2)). 7.00/7.29 cnf(i_0_6285, 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))))). 7.00/7.29 cnf(i_0_4263, 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))))). 7.00/7.29 cnf(i_0_2036, 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)))). 7.00/7.29 cnf(i_0_701, 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)))). 7.00/7.29 cnf(i_0_3286, 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)))). 7.00/7.29 cnf(i_0_4797, 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)))). 7.00/7.29 cnf(i_0_3285, 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)))). 7.00/7.29 cnf(i_0_5816, 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)))). 7.00/7.29 cnf(i_0_4798, 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)))). 7.00/7.29 cnf(i_0_1802, 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)))). 7.00/7.29 cnf(i_0_6171, 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))))). 7.00/7.29 cnf(i_0_2015, 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)))). 7.00/7.29 cnf(i_0_7359, 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)))). 7.00/7.29 cnf(i_0_7548, 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)))). 7.00/7.29 cnf(i_0_5470, 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))))). 7.00/7.29 cnf(i_0_2128, 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))))). 7.00/7.29 cnf(i_0_6070, 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))))). 7.00/7.29 cnf(i_0_6067, 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))))). 7.00/7.29 cnf(i_0_2125, 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))))). 7.00/7.29 cnf(i_0_6260, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk490_5(X3,X2,X4,X5,X1))=X5|X4=hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)|hAPP(hAPP(c_List_Oappend(X1),X5),X4)!=hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))). 7.00/7.29 cnf(i_0_2861, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk222_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))). 7.00/7.29 cnf(i_0_3666, 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))). 7.00/7.29 cnf(i_0_3003, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk229_2(X2,X1)),esk229_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))))))). 7.00/7.29 cnf(i_0_2548, 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)))). 7.00/7.29 cnf(i_0_7221, 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,esk561_5(X2,X4,X3,X3,X1))!=hAPP(X4,esk561_5(X2,X4,X3,X3,X1))|~class_Groups_Ocomm__monoid__mult(X1)|~class_Groups_Ocomm__monoid__add(X1)|~c_Nat__Transfer_Onat__set(X3))). 7.00/7.29 cnf(i_0_3376, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk257_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))))). 7.00/7.29 cnf(i_0_6262, plain, (hAPP(hAPP(c_List_Oappend(X1),esk490_5(X2,X3,X4,X5,X1)),X4)=X2|X4=hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2)|hAPP(hAPP(c_List_Oappend(X1),X5),X4)!=hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))). 7.00/7.29 cnf(i_0_2862, plain, (hAPP(hAPP(c_List_Oappend(X1),esk222_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))). 7.00/7.29 cnf(i_0_2183, 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),esk170_3(X2,X3,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.00/7.29 cnf(i_0_4214, plain, (hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=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))),X4)|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 7.00/7.29 cnf(i_0_3374, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X1,X2,X3)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))))). 7.00/7.29 cnf(i_0_6749, 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,esk529_5(X4,X2,X3,X3,X1))!=hAPP(X4,esk529_5(X4,X2,X3,X3,X1))|~class_Groups_Ocomm__monoid__mult(X1)|~class_Groups_Ocomm__monoid__add(X1)|~c_Nat__Transfer_Onat__set(X3))). 7.00/7.29 cnf(i_0_3969, plain, (hAPP(hAPP(X1,X2),X3)=hAPP(hAPP(X1,X4),X3)|hAPP(X2,esk300_7(X2,X4,X3,X1,X5,X6,X7))!=hAPP(X4,esk300_7(X2,X4,X3,X1,X5,X6,X7))|~c_Finite__Set_Ofolding__image(X8,X7,X6,X5,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X3)))). 7.00/7.29 cnf(i_0_6952, 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))). 7.00/7.29 cnf(i_0_942, 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)))). 7.00/7.29 cnf(i_0_4613, 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),esk353_3(X2,X3,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.00/7.29 cnf(i_0_626, 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)))). 7.00/7.29 cnf(i_0_2237, 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)))). 7.00/7.29 cnf(i_0_6586, plain, (c_Relation_Otrans(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_Relation_Oantisym(X1,X2)|~c_Relation_Otrans(X1,X2))). 7.00/7.29 cnf(i_0_486, 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)))). 7.00/7.29 cnf(i_0_1743, 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)))). 7.00/7.29 cnf(i_0_2454, 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))))). 7.00/7.29 cnf(i_0_3069, 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),esk233_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))))). 7.00/7.29 cnf(i_0_7185, 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))))). 7.00/7.29 cnf(i_0_317, 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),esk27_3(X3,X2,X1)),hAPP(c_List_Oset(X1),X3))))). 7.00/7.29 cnf(i_0_1035, 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)))). 7.00/7.29 cnf(i_0_4419, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk331_3(X2,X3,X1)),esk332_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)))). 7.00/7.29 cnf(i_0_4849, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk374_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)))). 7.00/7.29 cnf(i_0_506, 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))). 7.00/7.29 cnf(i_0_6733, 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))))). 7.00/7.29 cnf(i_0_966, 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)))). 7.00/7.29 cnf(i_0_6717, 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)))). 7.00/7.29 cnf(i_0_7489, 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))). 7.00/7.29 cnf(i_0_5249, 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)))). 7.00/7.29 cnf(i_0_620, 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)))). 7.00/7.29 cnf(i_0_5387, 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)))). 7.00/7.29 cnf(i_0_2506, 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)))). 7.00/7.29 cnf(i_0_977, 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)))). 7.00/7.29 cnf(i_0_1908, 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)))). 7.00/7.29 cnf(i_0_1318, 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)). 7.00/7.29 cnf(i_0_6618, 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))))). 7.00/7.29 cnf(i_0_7440, 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))))). 7.00/7.29 cnf(i_0_2991, plain, (hAPP(c_Set_Oimage(X1,X2,c_Hilbert__Choice_Oinv__into(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X3)),X4)=hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X4),X3)|~c_Fun_Obij__betw(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))))). 7.00/7.29 cnf(i_0_3186, 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)|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 7.00/7.29 cnf(i_0_5576, 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)))). 7.00/7.29 cnf(i_0_3351, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk257_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 7.00/7.29 cnf(i_0_3349, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X1,X2,X3)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 7.00/7.29 cnf(i_0_25, 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)))). 7.00/7.29 cnf(i_0_624, 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,esk50_4(X4,X2,X3,X1))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.00/7.29 cnf(i_0_3319, 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))))). 7.00/7.29 cnf(i_0_4615, 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))))). 7.00/7.29 cnf(i_0_6691, 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))))). 7.00/7.29 cnf(i_0_2017, 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)))). 7.00/7.29 cnf(i_0_2934, 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)))). 7.00/7.29 cnf(i_0_4654, 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)))). 7.00/7.29 cnf(i_0_833, 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)))). 7.00/7.29 cnf(i_0_2354, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),hAPP(c_List_Oset(X1),X4))=hAPP(c_List_Omonoid__add__class_Olistsum(X2),hAPP(hAPP(c_List_Omap(X1,X2),X3),X4))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_List_Odistinct(X1),X4)))). 7.00/7.29 cnf(i_0_5115, 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))). 7.00/7.29 cnf(i_0_874, 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)))). 7.00/7.29 cnf(i_0_6432, 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))). 7.00/7.29 cnf(i_0_3247, 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)))). 7.00/7.29 cnf(i_0_4503, 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)))). 7.00/7.29 cnf(i_0_3648, 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)))|hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X1)))|~hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.00/7.29 cnf(i_0_697, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk59_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))). 7.00/7.29 cnf(i_0_6693, 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)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X3)). 7.00/7.29 cnf(i_0_568, 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)))). 7.00/7.29 cnf(i_0_5546, 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)))). 7.00/7.29 cnf(i_0_1935, plain, (c_Fun_Obij__betw(X1,X2,X3,X4,X5)|~c_Fun_Obij__betw(X1,X6,hAPP(c_Fun_Ocomp(X2,X6,X1,X7),X3),X4,X8)|~c_Fun_Obij__betw(X2,X6,X7,X5,X8)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),X5)))). 7.00/7.29 cnf(i_0_3797, 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))). 7.00/7.29 cnf(i_0_6902, plain, (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,X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(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)),X3)))). 7.00/7.29 cnf(i_0_696, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk60_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))). 7.00/7.29 cnf(i_0_7169, 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)). 7.00/7.29 cnf(i_0_1356, 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))))). 7.00/7.29 cnf(i_0_1904, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))))). 7.00/7.29 cnf(i_0_1892, 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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))))). 7.00/7.29 cnf(i_0_2773, 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)))). 7.00/7.29 cnf(i_0_7171, 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)))). 7.00/7.29 cnf(i_0_6675, plain, (hAPP(hAPP(c_List_Oappend(X1),esk522_3(X2,X3,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),esk523_3(X2,X3,X1)))=X2|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2))))). 7.00/7.29 cnf(i_0_4323, 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))|X3=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)))). 7.00/7.29 cnf(i_0_1010, 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)))))))). 7.00/7.29 cnf(i_0_3518, 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)))). 7.00/7.29 cnf(i_0_2562, 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))). 7.00/7.29 cnf(i_0_2639, plain, (hAPP(hAPP(c_List_Oappend(X1),esk210_3(X2,X3,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),esk211_3(X2,X3,X1)))=X2|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2))))). 7.00/7.29 cnf(i_0_5626, plain, (hAPP(hAPP(c_List_Oappend(X1),esk428_3(X2,X3,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),esk429_3(X2,X3,X1)))=X2|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2))))). 7.00/7.29 cnf(i_0_347, 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)))). 7.00/7.29 cnf(i_0_7357, 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)))). 7.00/7.29 cnf(i_0_2172, 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)|X3=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 7.00/7.29 cnf(i_0_4019, 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))). 7.00/7.29 cnf(i_0_5235, 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))))). 7.00/7.29 cnf(i_0_6370, 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))). 7.00/7.29 cnf(i_0_453, 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))). 7.00/7.29 cnf(i_0_49, 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)))). 7.00/7.29 cnf(i_0_1303, 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)))). 7.00/7.29 cnf(i_0_2452, plain, (hAPP(c_Set_Oimage(X1,X2,c_Hilbert__Choice_Oinv__into(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X3)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))|~c_Fun_Oinj__on(X2,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))). 7.00/7.29 cnf(i_0_1794, plain, (hAPP(c_Set_Oimage(X1,X2,c_Hilbert__Choice_Oinv__into(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X3)),hAPP(c_Set_Oimage(X2,X1,X3),X4))=X4|~c_Fun_Oinj__on(X2,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))). 7.00/7.29 cnf(i_0_1529, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk126_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)))). 7.00/7.29 cnf(i_0_5521, 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))). 7.00/7.29 cnf(i_0_6349, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk499_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))))). 7.00/7.29 cnf(i_0_4538, 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)))). 7.00/7.29 cnf(i_0_3745, 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),esk280_4(X3,X1,X4,X2)),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 7.00/7.29 cnf(i_0_856, 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),esk67_4(X1,X4,X3,X2)),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 7.00/7.29 cnf(i_0_4460, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk339_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)))). 7.00/7.29 cnf(i_0_1480, plain, (hBOOL(hAPP(X1,esk120_2(X1,X2)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk118_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk119_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,esk118_2(X1,X2)))|~hBOOL(hAPP(X1,X3)))). 7.00/7.29 cnf(i_0_7538, 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)))). 7.00/7.29 cnf(i_0_2130, 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)))). 7.00/7.29 cnf(i_0_5074, 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))). 7.00/7.29 cnf(i_0_3178, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Wellfounded_Omax__extp(X1,X3,X4,X2)|hBOOL(hAPP(hAPP(c_member(X1),esk246_4(X2,X4,X3,X1)),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 7.00/7.29 cnf(i_0_3335, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk255_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk257_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X2)))). 7.00/7.29 cnf(i_0_3332, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk255_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X2)))). 7.00/7.29 cnf(i_0_3543, 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)))))). 7.00/7.29 cnf(i_0_4506, 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))). 7.00/7.29 cnf(i_0_2767, plain, (c_Relation_Orefl__on(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk216_3(X3,X2,X1)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk217_3(X3,X2,X1)),esk217_3(X3,X2,X1))),X3)))). 7.00/7.29 cnf(i_0_1728, 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),esk146_3(X3,X2,X1)),esk146_3(X3,X2,X1))),X3)))). 7.00/7.29 cnf(i_0_312, 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),esk26_3(X2,X3,X1)),esk26_3(X2,X3,X1))),X3)))). 7.00/7.29 cnf(i_0_3544, 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)))))). 7.00/7.29 cnf(i_0_3559, 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))))). 7.00/7.29 cnf(i_0_6626, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk516_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))))). 7.00/7.29 cnf(i_0_3360, 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)),esk255_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk257_3(X1,X2,X3))))). 7.00/7.29 cnf(i_0_2059, 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))). 7.00/7.29 cnf(i_0_6085, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk480_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)))). 7.00/7.29 cnf(i_0_562, 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)))). 7.00/7.29 cnf(i_0_5397, 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)))). 7.00/7.29 cnf(i_0_5758, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(X3,X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 7.00/7.29 cnf(i_0_3357, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk255_3(X1,X2,X3))))). 7.00/7.29 cnf(i_0_662, 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)))). 7.00/7.29 cnf(i_0_4840, 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))). 7.00/7.29 cnf(i_0_2126, 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))))). 7.00/7.29 cnf(i_0_6069, 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))))). 7.00/7.29 cnf(i_0_5821, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk451_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)))))). 7.00/7.29 cnf(i_0_1729, plain, (c_Relation_Orefl__on(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk146_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)))))). 7.00/7.29 cnf(i_0_6518, 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)))). 7.00/7.29 cnf(i_0_2868, 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)))). 7.00/7.29 cnf(i_0_2437, 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)))). 7.00/7.29 cnf(i_0_313, plain, (c_Relation_Orefl__on(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk26_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)))))). 7.00/7.29 cnf(i_0_4417, 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)),esk332_3(X1,X3,X2)),hAPP(hAPP(c_Set_Oinsert(X2),esk331_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)))). 7.00/7.29 cnf(i_0_4835, 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))))). 7.00/7.29 cnf(i_0_4705, 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))))). 7.00/7.29 cnf(i_0_175, 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)))). 7.00/7.29 cnf(i_0_5760, 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)|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)))). 7.00/7.29 cnf(i_0_6427, 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)))). 7.00/7.29 cnf(i_0_508, 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)))). 7.00/7.29 cnf(i_0_1500, 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)). 7.00/7.29 cnf(i_0_3160, plain, (c_List_Olist__ex1(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk242_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)))). 7.00/7.29 cnf(i_0_6742, plain, (c_List_Olist__ex1(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk527_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)))). 7.00/7.29 cnf(i_0_353, 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),esk32_4(X2,X3,X1,X4)))))). 7.00/7.29 cnf(i_0_7018, 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)))). 7.00/7.29 cnf(i_0_7462, 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)))). 7.00/7.29 cnf(i_0_4050, plain, (hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X1)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X1))=c_Random__Sequence_ORandom(X1,X2,X3,X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X3),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))). 7.00/7.29 cnf(i_0_1238, 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))|hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X4),X1)!=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3)))). 7.00/7.29 cnf(i_0_6769, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk530_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))))). 7.00/7.29 cnf(i_0_433, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,esk38_5(X3,X4,X5,X2,X1),esk39_5(X3,X4,X5,X2,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)),X3)))). 7.00/7.29 cnf(i_0_5210, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,esk403_5(X3,X4,X5,X2,X1),esk404_5(X3,X4,X5,X2,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)),X3)))). 7.00/7.29 cnf(i_0_2888, 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))). 7.00/7.29 cnf(i_0_7390, 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)))). 7.00/7.29 cnf(i_0_1468, 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))). 7.00/7.29 cnf(i_0_6993, 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)))))). 7.00/7.29 cnf(i_0_5469, 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))))). 7.00/7.29 cnf(i_0_418, 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))))). 7.00/7.29 cnf(i_0_6126, plain, (c_Fun_Ofun__upd(X1,X2,c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X6,X7)=c_Fun_Ofun__upd(X1,X2,c_Fun_Ofun__upd(X1,X2,X3,X6,X7),X4,X5)|X4=X6)). 7.00/7.29 cnf(i_0_588, 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)))). 7.00/7.29 cnf(i_0_744, 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)))). 7.00/7.29 cnf(i_0_3603, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk276_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk273_3(X1,X2,X3))))). 7.00/7.29 cnf(i_0_3611, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk275_3(X1,X2,X3))))). 7.00/7.29 cnf(i_0_1158, 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))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.00/7.29 cnf(i_0_5260, 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)))). 7.00/7.29 cnf(i_0_2243, 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)))). 7.00/7.29 cnf(i_0_5366, 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))). 7.00/7.29 cnf(i_0_3395, 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))))). 7.00/7.29 cnf(i_0_194, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk14_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)))). 7.00/7.29 cnf(i_0_4410, 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))|c_List_Olist_ONil(X1)=X2|~class_Lattices_Oab__semigroup__idem__mult(X1))). 7.00/7.29 cnf(i_0_2051, 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))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.00/7.29 cnf(i_0_1168, plain, (hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,X1))=c_Orderings_Oord__class_OLeast(tc_Nat_Onat,X2)|hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X2,hAPP(c_Nat_OSuc,esk95_4(X3,X1,X4,X2))))|~hBOOL(hAPP(X1,esk95_4(X3,X1,X4,X2)))|~hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(X2,X4)))). 7.00/7.29 cnf(i_0_2488, 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)))). 7.00/7.29 cnf(i_0_3006, plain, (hAPP(hAPP(c_List_Omap(X1,X2),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))))). 7.00/7.29 cnf(i_0_3339, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk255_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 7.00/7.29 cnf(i_0_3352, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_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)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 7.00/7.29 cnf(i_0_3815, 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))). 7.00/7.29 cnf(i_0_1417, 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)))). 7.00/7.29 cnf(i_0_2096, 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,esk165_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)))). 7.00/7.29 cnf(i_0_6984, 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)))). 7.00/7.29 cnf(i_0_3910, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk295_5(X3,X4,X5,X2,X1)),esk296_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))))). 7.00/7.29 cnf(i_0_3364, 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)),esk255_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))))). 7.00/7.29 cnf(i_0_5243, 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))). 7.00/7.29 cnf(i_0_3602, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk276_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk273_3(X1,X2,X3)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.00/7.29 cnf(i_0_3610, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk275_3(X1,X2,X3)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.00/7.29 cnf(i_0_734, 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)))))). 7.00/7.29 cnf(i_0_7304, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)|hAPP(X5,esk570_6(X2,X4,X5,X1,X3,X3))!=hAPP(X4,esk570_6(X2,X4,X5,X1,X3,X3)))). 7.00/7.29 cnf(i_0_3377, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_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)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))))). 7.00/7.29 cnf(i_0_3848, 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)))|esk289_2(X2,X1)!=esk288_2(X2,X1)|~hBOOL(hAPP(c_List_Odistinct(X1),esk287_2(X2,X1)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)))). 7.00/7.29 cnf(i_0_4222, 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,esk319_6(X5,X2,X1,X4,X3,X6)),esk320_6(X5,X2,X1,X4,X3,X6)))))). 7.00/7.29 cnf(i_0_1516, 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)))). 7.00/7.29 cnf(i_0_6671, 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)))). 7.00/7.29 cnf(i_0_5583, 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)))). 7.00/7.29 cnf(i_0_4124, 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)))). 7.00/7.29 cnf(i_0_6625, plain, (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),X1),hAPP(c_Nat_OSuc,esk516_3(X1,X2,X3)))))|~hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1))))). 7.00/7.29 cnf(i_0_7313, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),c_Groups_Oone__class_Oone(X1))),X2)|~class_Rings_Ocomm__semiring__1(X1))). 7.00/7.29 cnf(i_0_1308, 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)))). 7.00/7.29 cnf(i_0_7273, 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)))). 7.00/7.29 cnf(i_0_2107, 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)))|X2=c_List_Olist_ONil(tc_List_Olist(X1))|~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))))). 7.00/7.29 cnf(i_0_2332, plain, (hAPP(c_Nat_OSuc,esk186_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))))). 7.00/7.29 cnf(i_0_5799, 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)))). 7.00/7.29 cnf(i_0_7319, 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)))). 7.00/7.29 cnf(i_0_6595, 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)))). 7.00/7.29 cnf(i_0_6369, 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))))))). 7.00/7.29 cnf(i_0_5813, 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)))). 7.00/7.29 cnf(i_0_322, plain, (hAPP(c_Nat_OSuc,esk29_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))))). 7.00/7.29 cnf(i_0_5012, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,X4),X5),X6)))|~hBOOL(hAPP(X1,hAPP(hAPP(X5,esk389_7(X4,X5,X1,X6,X3,X2,X7)),esk390_7(X4,X5,X1,X6,X3,X2,X7))))|~hBOOL(hAPP(hAPP(X7,hAPP(c_Product__Type_Osnd(X2,X3),X6)),hAPP(c_Product__Type_Ofst(X2,X3),X6))))). 7.00/7.29 cnf(i_0_4186, 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)))). 7.00/7.29 cnf(i_0_5014, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X4))|~class_Divides_Osemiring__div(X1)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X4),X3)))). 7.00/7.29 cnf(i_0_2044, 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)))). 7.00/7.29 cnf(i_0_3346, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X1,X2,X3)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk257_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 7.00/7.29 cnf(i_0_4675, 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)))). 7.00/7.29 cnf(i_0_3061, 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)))). 7.00/7.29 cnf(i_0_2899, 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)))). 7.00/7.29 cnf(i_0_3472, 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)))). 7.00/7.29 cnf(i_0_3148, 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)))))). 7.00/7.29 cnf(i_0_1503, 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)))). 7.00/7.29 cnf(i_0_6268, 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)))). 7.00/7.29 cnf(i_0_4908, 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)))). 7.00/7.29 cnf(i_0_2084, 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)))). 7.00/7.29 cnf(i_0_5645, plain, (hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4))=hAPP(hAPP(X5,X3),hAPP(X1,X4))|X4=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X2),X3),X4))|~c_Finite__Set_Ofolding__one(X2,X5,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 7.00/7.29 cnf(i_0_3240, 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))). 7.00/7.29 cnf(i_0_7212, plain, (hBOOL(hAPP(X1,esk559_4(X1,X2,X3,X4)))|hBOOL(hAPP(X1,esk558_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)))). 7.00/7.29 cnf(i_0_2711, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X2),esk212_7(X3,X4,X1,X5,X6,X7,X2)),X1))|~c_Nitpick_Ofold__graph_H(X2,X7,X6,X5,X1,hAPP(hAPP(X6,X4),X3)))). 7.00/7.29 cnf(i_0_5589, 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))). 7.00/7.29 cnf(i_0_166, 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))). 7.00/7.29 cnf(i_0_3452, 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)))). 7.00/7.29 cnf(i_0_4621, 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)))))). 7.00/7.29 cnf(i_0_900, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),esk74_3(X3,X1,X2))))|~class_Rings_Osemiring__0(X2)|~class_Rings_Odvd(X2)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X4),c_Groups_Ozero__class_Ozero(X2))))|~hBOOL(hAPP(X1,X4)))). 7.00/7.29 cnf(i_0_1105, 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))))). 7.00/7.29 cnf(i_0_535, 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))))). 7.00/7.29 cnf(i_0_687, 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))). 7.00/7.29 cnf(i_0_3643, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk276_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1))))). 7.00/7.29 cnf(i_0_1619, 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))|hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ocomm__monoid__add(X1))). 7.00/7.29 cnf(i_0_3508, plain, (hAPP(hAPP(X1,hAPP(X2,X3)),hAPP(X4,X5))=hAPP(X4,hAPP(hAPP(c_Set_Oinsert(X6),X3),X5))|~c_Finite__Set_Ofolding__image__simple__idem(X7,X6,X1,X8,X2,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6),X5)))). 7.00/7.29 cnf(i_0_3619, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X1,X2,X3)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1))))). 7.00/7.29 cnf(i_0_3371, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X1,X2,X3)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk257_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))))). 7.00/7.29 cnf(i_0_2110, 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_Groups_Ocomm__monoid__mult(X2)|~class_Rings_Osemiring__1(X2))). 7.00/7.29 cnf(i_0_6610, 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_Groups_Ocomm__monoid__mult(X2)|~class_Rings_Oring__1(X2))). 7.00/7.29 cnf(i_0_1345, 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)))). 7.00/7.29 cnf(i_0_5969, 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))). 7.00/7.29 cnf(i_0_5330, 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))). 7.00/7.29 cnf(i_0_5492, 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))). 7.00/7.29 cnf(i_0_6672, 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))). 7.00/7.29 cnf(i_0_693, 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))))). 7.00/7.29 cnf(i_0_356, 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),esk32_4(X2,X3,X1,X4)),X4))|hBOOL(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),X4))))). 7.00/7.29 cnf(i_0_6997, 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)))). 7.00/7.29 cnf(i_0_2762, 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)))). 7.00/7.29 cnf(i_0_5565, 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))). 7.00/7.29 cnf(i_0_4545, 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))). 7.00/7.29 cnf(i_0_3011, 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))). 7.00/7.29 cnf(i_0_117, 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)),esk8_4(X4,X3,X1,X2)),X2)))). 7.00/7.29 cnf(i_0_947, 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)))). 7.00/7.29 cnf(i_0_902, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),esk73_3(X2,X3,X1)),c_Groups_Ozero__class_Ozero(X1))))|~class_Rings_Osemiring__0(X1)|~class_Rings_Odvd(X1)|~hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))))). 7.00/7.29 cnf(i_0_6657, 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),esk519_3(X3,X2,X1)),esk520_3(X3,X2,X1))),X3)))). 7.00/7.29 cnf(i_0_3017, 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)))). 7.00/7.29 cnf(i_0_5118, 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)))). 7.00/7.29 cnf(i_0_3642, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk276_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.00/7.29 cnf(i_0_3618, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X1,X2,X3)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.00/7.29 cnf(i_0_5827, 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))). 7.00/7.29 cnf(i_0_6656, 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),esk519_3(X3,X2,X1)),esk521_3(X3,X2,X1))),X3)))). 7.00/7.29 cnf(i_0_2712, plain, (X1=hAPP(hAPP(X2,X3),X4)|hBOOL(hAPP(hAPP(c_member(X5),esk212_7(X4,X3,X6,X1,X2,X7,X5)),X6))|~c_Nitpick_Ofold__graph_H(X5,X7,X2,X1,X6,hAPP(hAPP(X2,X3),X4)))). 7.00/7.29 cnf(i_0_2973, 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)))). 7.00/7.29 cnf(i_0_1092, 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)))). 7.00/7.29 cnf(i_0_1628, 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)))). 7.00/7.29 cnf(i_0_1155, 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)))). 7.00/7.29 cnf(i_0_364, 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))))). 7.00/7.29 cnf(i_0_434, plain, (hAPP(hAPP(c_Set_Oinsert(X1),esk38_5(X2,X3,X4,X5,X1)),esk39_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)))). 7.00/7.29 cnf(i_0_6157, 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)))). 7.00/7.29 cnf(i_0_4373, 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)))). 7.00/7.29 cnf(i_0_3317, 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)))). 7.00/7.29 cnf(i_0_5212, plain, (hAPP(hAPP(c_Set_Oinsert(X1),esk403_5(X2,X3,X4,X5,X1)),esk404_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)))). 7.00/7.29 cnf(i_0_4718, 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)))). 7.00/7.29 cnf(i_0_7153, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X2),esk553_3(X3,X1,X2)),X1))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Finite__Set_Ofold1(X2,c_Orderings_Oord__class_Omin(X2)),X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 7.00/7.29 cnf(i_0_7152, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),esk553_3(X3,X1,X2)),X3))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Finite__Set_Ofold1(X2,c_Orderings_Oord__class_Omin(X2)),X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 7.00/7.29 cnf(i_0_1835, 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),esk153_4(X4,X2,X3,X1)),hAPP(c_List_Oset(X1),X3))))). 7.00/7.29 cnf(i_0_37, 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)))). 7.00/7.29 cnf(i_0_3631, plain, (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)),esk274_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk275_3(X1,X2,X3))))). 7.00/7.29 cnf(i_0_3607, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk273_3(X1,X2,X3))))). 7.00/7.29 cnf(i_0_3830, 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)))). 7.00/7.29 cnf(i_0_2389, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_member(X1),esk188_3(X3,X2,X1)),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 7.00/7.29 cnf(i_0_2390, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk188_3(X3,X2,X1)),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 7.00/7.29 cnf(i_0_4145, 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))). 7.00/7.29 cnf(i_0_6092, 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)))). 7.00/7.29 cnf(i_0_3292, 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))). 7.00/7.29 cnf(i_0_1741, 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)))). 7.00/7.29 cnf(i_0_502, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),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)))). 7.00/7.29 cnf(i_0_3196, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk249_3(X3,X1,X2)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(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)))). 7.00/7.29 cnf(i_0_4150, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk315_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)))). 7.00/7.29 cnf(i_0_167, 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))). 7.00/7.29 cnf(i_0_4698, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk361_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk360_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))))). 7.00/7.29 cnf(i_0_6470, 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)))). 7.00/7.29 cnf(i_0_5479, 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)),X3),c_List_Olists(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X4))))). 7.00/7.29 cnf(i_0_1858, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),esk154_4(X4,X2,X3,X1))),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_Relation_ODomain(X1,X2),X4))))). 7.00/7.29 cnf(i_0_555, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk43_3(X2,X3,X1)),X3)),X2))|hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2))))). 7.00/7.29 cnf(i_0_3896, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,X1,esk293_2(X2,X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),esk292_2(X2,X1)))=X2|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 7.00/7.29 cnf(i_0_4427, 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))). 7.00/7.29 cnf(i_0_6501, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),esk507_4(X4,X2,X3,X1))),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_Relation_ODomain(X1,X2),X4))))). 7.00/7.29 cnf(i_0_704, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk61_4(X3,X1,X4,X2)),X4)),X3))|~hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_Relation_ORange(X1,X2),X3))))). 7.00/7.29 cnf(i_0_340, 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))). 7.00/7.29 cnf(i_0_2561, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk203_3(X2,X3,X1)),X3)),X2))|hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2))))). 7.00/7.29 cnf(i_0_3820, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk283_4(X3,X1,X4,X2)),X4)),X3))|~hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_Relation_ORange(X1,X2),X3))))). 7.00/7.29 cnf(i_0_964, 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))))). 7.00/7.29 cnf(i_0_6584, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk515_3(X2,X3,X1)),X3)),X2))|hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2))))). 7.00/7.29 cnf(i_0_5277, 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),esk408_5(X4,X3,X5,X1,X2)),hAPP(c_List_Oset(X1),X5)))|~class_Orderings_Olinorder(X2))). 7.00/7.29 cnf(i_0_1584, 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)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)))). 7.00/7.29 cnf(i_0_3131, 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)))). 7.00/7.29 cnf(i_0_6955, 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)))). 7.00/7.29 cnf(i_0_1365, 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))). 7.00/7.29 cnf(i_0_6409, plain, (hAPP(c_Set_Oimage(X1,X2,esk501_4(X3,X1,X2,X4)),X3)=X4|X4=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~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)))). 7.00/7.29 cnf(i_0_6080, 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)))). 7.00/7.29 cnf(i_0_2879, plain, (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))=X3|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X2),X1)))). 7.00/7.29 cnf(i_0_3630, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk274_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk275_3(X1,X2,X3)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.00/7.29 cnf(i_0_2980, 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))). 7.00/7.29 cnf(i_0_2439, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(X2,X3)|hBOOL(hAPP(hAPP(c_member(X4),esk194_5(X3,X2,X5,X4,X1)),X5))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1),X2),X5)!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_member(X4),X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X5)))). 7.00/7.29 cnf(i_0_3460, 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),esk263_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)))). 7.00/7.29 cnf(i_0_2866, plain, (hAPP(c_Fun_Ocomp(X1,X2,X3,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),c_Hilbert__Choice_Oinv__into(X3,X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)),X5))),X5)=X4|~c_Fun_Oinj__on(X3,X1,X5,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))). 7.00/7.29 cnf(i_0_3606, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk273_3(X1,X2,X3)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.00/7.29 cnf(i_0_2336, 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)))). 7.00/7.29 cnf(i_0_4887, 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)))). 7.00/7.29 cnf(i_0_6046, plain, (c_Wellfounded_Owf(X1,X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk475_3(X2,X1,X3)),X3)),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),esk473_2(X2,X1))))). 7.00/7.29 cnf(i_0_4029, 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))). 7.00/7.29 cnf(i_0_4548, 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)))). 7.00/7.29 cnf(i_0_2335, plain, (hAPP(c_Nat_OSuc,esk186_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))))). 7.00/7.29 cnf(i_0_1472, 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),esk117_5(X3,X4,X5,X2,X1)),hAPP(c_List_Oset(X1),X4))))). 7.00/7.29 cnf(i_0_4694, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk361_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk360_3(X1,X2,X3)))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 7.00/7.29 cnf(i_0_2257, 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)))). 7.00/7.29 cnf(i_0_2782, 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))). 7.00/7.29 cnf(i_0_251, 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))). 7.00/7.29 cnf(i_0_325, plain, (hAPP(c_Nat_OSuc,esk29_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))))). 7.00/7.29 cnf(i_0_4824, plain, (c_Fun_Obij__betw(X1,X2,esk372_6(X3,X4,X5,X6,X2,X1),X5,X4)|~c_Fun_Oinj__on(X2,X1,X3,X4)|~c_Fun_Oinj__on(X1,X2,X6,X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X6),X5)),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)))). 7.00/7.29 cnf(i_0_3327, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,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),X3),X4)),X2),X3)))|~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)))). 7.00/7.29 cnf(i_0_1088, 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))). 7.00/7.29 cnf(i_0_5907, 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))). 7.00/7.29 cnf(i_0_7031, 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))). 7.00/7.29 cnf(i_0_1942, 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)))). 7.00/7.29 cnf(i_0_5497, 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)))). 7.00/7.29 cnf(i_0_3328, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,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),X3),X4)),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(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)))). 7.00/7.29 cnf(i_0_2200, 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))). 7.00/7.29 cnf(i_0_6093, 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)))). 7.00/7.29 cnf(i_0_6560, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)))|~class_Rings_Ocomm__semiring__1(X1)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4)))). 7.00/7.29 cnf(i_0_5573, 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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X3)|~class_Rings_Ocomm__semiring__1(X1))). 7.00/7.29 cnf(i_0_2809, 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))). 7.00/7.29 cnf(i_0_6215, 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)))). 7.00/7.29 cnf(i_0_1611, 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)))). 7.00/7.29 cnf(i_0_4578, 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)))). 7.00/7.29 cnf(i_0_6628, 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,esk516_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))))). 7.00/7.29 cnf(i_0_3639, plain, (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)),esk274_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1))))). 7.00/7.29 cnf(i_0_3647, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_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)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1))))). 7.00/7.29 cnf(i_0_1107, plain, (c_List_Olist__all2(X1,X2,X3,X4,X5)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk89_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))). 7.00/7.29 cnf(i_0_4366, 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)))). 7.00/7.29 cnf(i_0_3911, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk296_5(X2,X3,X4,X1,X5)),hAPP(X2,esk295_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))))). 7.00/7.29 cnf(i_0_2853, 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))))). 7.00/7.29 cnf(i_0_5309, 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)))). 7.00/7.29 cnf(i_0_272, 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)))). 7.00/7.29 cnf(i_0_5706, plain, (c_List_Olist__all2(X1,X2,X3,X4,X5)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk436_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))). 7.00/7.29 cnf(i_0_3946, 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))))). 7.00/7.29 cnf(i_0_5659, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3)),c_Groups_Oone__class_Oone(X1))|X3=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 7.00/7.29 cnf(i_0_5304, 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),esk409_7(X3,X2,X7,X6,X5,X4,X1)),X4)))). 7.00/7.29 cnf(i_0_7506, 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))). 7.00/7.29 cnf(i_0_512, 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)))). 7.00/7.29 cnf(i_0_6728, 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),esk526_7(X7,X6,X5,X4,X3,X2,X1)),X4)))). 7.00/7.29 cnf(i_0_5518, 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))). 7.00/7.29 cnf(i_0_1594, 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))). 7.00/7.29 cnf(i_0_5287, 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))). 7.00/7.29 cnf(i_0_4012, 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))). 7.00/7.29 cnf(i_0_1346, 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))|c_Groups_Ozero__class_Ozero(X1)=X2|~class_Divides_Osemiring__div(X1))). 7.00/7.29 cnf(i_0_4287, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),X4))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),hAPP(c_Finite__Set_Ofold1(X2,c_Orderings_Oord__class_Omin(X2)),X1)))|~hBOOL(hAPP(hAPP(c_member(X2),X4),X1))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 7.00/7.29 cnf(i_0_240, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),X4))|~class_Lattices_Osemilattice__inf(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),hAPP(c_Finite__Set_Ofold1(X2,c_Lattices_Osemilattice__inf__class_Oinf(X2)),X1)))|~hBOOL(hAPP(hAPP(c_member(X2),X4),X1))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 7.00/7.29 cnf(i_0_6434, 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)))). 7.00/7.29 cnf(i_0_2349, 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))). 7.00/7.29 cnf(i_0_368, 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))). 7.00/7.29 cnf(i_0_1388, 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))). 7.00/7.29 cnf(i_0_7528, 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))). 7.00/7.29 cnf(i_0_4834, 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))). 7.00/7.29 cnf(i_0_6447, 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_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))). 7.00/7.29 cnf(i_0_1362, 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_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))). 7.00/7.29 cnf(i_0_1402, 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_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))). 7.00/7.29 cnf(i_0_378, 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_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))). 7.00/7.29 cnf(i_0_2892, 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))). 7.00/7.29 cnf(i_0_4289, 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))). 7.00/7.29 cnf(i_0_5035, 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)))). 7.00/7.29 cnf(i_0_4704, 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))). 7.00/7.29 cnf(i_0_4637, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3)),X5))=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))))). 7.00/7.29 cnf(i_0_1219, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk99_4(X2,X3,X4,X1)),c_Quotient_ORespects(X1,X4)))|hBOOL(hAPP(X3,esk98_4(X2,X3,X4,X1)))|~c_Equiv__Relations_Oequivp(X1,X4)|~hBOOL(hAPP(X3,X5)))). 7.00/7.29 cnf(i_0_4766, 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)))). 7.00/7.29 cnf(i_0_2792, 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)))). 7.00/7.29 cnf(i_0_5475, 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)))). 7.00/7.29 cnf(i_0_2460, 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|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)),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)))). 7.00/7.29 cnf(i_0_3983, 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)))). 7.00/7.29 cnf(i_0_2772, 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)))). 7.00/7.29 cnf(i_0_202, 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)))). 7.00/7.29 cnf(i_0_2549, 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)))). 7.00/7.29 cnf(i_0_2428, 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)))). 7.00/7.29 cnf(i_0_2013, 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)))). 7.00/7.29 cnf(i_0_4388, 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)))). 7.00/7.29 cnf(i_0_5474, 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)))). 7.00/7.29 cnf(i_0_3762, 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)))). 7.00/7.29 cnf(i_0_1919, 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)))). 7.00/7.29 cnf(i_0_756, 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))))). 7.00/7.29 cnf(i_0_3638, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk274_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.00/7.29 cnf(i_0_3646, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_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)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.00/7.29 cnf(i_0_3613, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X1,X2,X3)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk276_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1))))). 7.00/7.29 cnf(i_0_4368, plain, (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)=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)|~class_Int_Onumber__ring(X1))). 7.00/7.29 cnf(i_0_437, 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))). 7.00/7.29 cnf(i_0_3538, 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_Relation_Oconverse(X1,X1),X2)),X2)),X2))|~c_Relation_Otrans(X1,X2)|~c_Relation_Osym(X1,X2))). 7.00/7.29 cnf(i_0_3688, 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)))). 7.00/7.29 cnf(i_0_3838, 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)))). 7.00/7.29 cnf(i_0_3067, 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)))). 7.00/7.29 cnf(i_0_650, 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))). 7.00/7.29 cnf(i_0_1674, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk141_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))))). 7.00/7.29 cnf(i_0_2634, 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))). 7.00/7.29 cnf(i_0_4433, 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))))). 7.00/7.29 cnf(i_0_1911, 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)))))). 7.00/7.29 cnf(i_0_2768, plain, (c_Relation_Orefl__on(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk216_3(X3,X2,X1)),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk217_3(X3,X2,X1)),X2)))). 7.00/7.29 cnf(i_0_144, 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))))). 7.00/7.29 cnf(i_0_3598, 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)))). 7.00/7.29 cnf(i_0_2148, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk168_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))))). 7.00/7.29 cnf(i_0_5665, 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))). 7.00/7.29 cnf(i_0_4711, 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)))). 7.00/7.29 cnf(i_0_6609, 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)))). 7.00/7.29 cnf(i_0_3571, 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))))). 7.00/7.29 cnf(i_0_6107, 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))))). 7.00/7.29 cnf(i_0_357, 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),esk32_4(X2,X3,X1,X4)),X4)))). 7.00/7.29 cnf(i_0_38, 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))). 7.00/7.29 cnf(i_0_1727, 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))). 7.00/7.29 cnf(i_0_1295, 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))))). 7.00/7.29 cnf(i_0_6302, 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))))). 7.00/7.29 cnf(i_0_1268, 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))))). 7.00/7.29 cnf(i_0_2835, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk218_6(X3,X4,X5,X6,X2,X1)),esk220_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))))). 7.00/7.29 cnf(i_0_6185, 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))). 7.00/7.29 cnf(i_0_2937, plain, (hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),esk224_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))))). 7.00/7.29 cnf(i_0_1751, 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)))). 7.00/7.29 cnf(i_0_3337, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_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)),esk255_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 7.00/7.29 cnf(i_0_7176, 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)))). 7.00/7.29 cnf(i_0_5772, 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,esk446_3(X2,X3,X1))!=hAPP(X3,esk447_3(X2,X3,X1))|~c_Wellfounded_OwfP(X1,hAPP(X3,esk445_3(X2,X3,X1))))). 7.00/7.29 cnf(i_0_65, 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)))). 7.00/7.29 cnf(i_0_4257, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk323_5(X3,X4,X1,X5,X2)),X5)),X4))|~hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Relation_OImage(X1,X2,X4),X3))))). 7.00/7.29 cnf(i_0_5757, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk444_5(X3,X4,X1,X5,X2)),X5)),X4))|~hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Relation_OImage(X1,X2,X4),X3))))). 7.00/7.29 cnf(i_0_6077, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk479_3(X3,X2,X1)),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X3))))). 7.00/7.29 cnf(i_0_5173, 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))))). 7.00/7.29 cnf(i_0_5174, 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))))). 7.00/7.29 cnf(i_0_5948, 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))). 7.00/7.29 cnf(i_0_3570, 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))))). 7.00/7.29 cnf(i_0_6108, 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))))). 7.00/7.29 cnf(i_0_238, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),hAPP(c_Finite__Set_Ofold1(X2,c_Lattices_Osemilattice__inf__class_Oinf(X2)),X1)))|~class_Lattices_Osemilattice__inf(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),esk20_3(X3,X1,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 7.00/7.29 cnf(i_0_4285, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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(X2),X3),esk326_3(X3,X1,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 7.00/7.29 cnf(i_0_3362, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_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)),esk255_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))))). 7.00/7.29 cnf(i_0_5689, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk434_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))))). 7.00/7.29 cnf(i_0_3612, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X1,X2,X3)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk276_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.00/7.29 cnf(i_0_6301, 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)))). 7.00/7.29 cnf(i_0_1269, 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)))). 7.00/7.29 cnf(i_0_3525, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk270_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk269_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))))). 7.00/7.29 cnf(i_0_6435, 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),esk503_3(X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 7.00/7.29 cnf(i_0_6529, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk511_6(X3,X4,X2,X1,X5,X6)),esk512_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))))). 7.00/7.29 cnf(i_0_4376, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))|~class_Rings_Ocomm__ring(X1)|~class_Rings_Odvd(X1)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X6))),X4)))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X6)))). 7.00/7.29 cnf(i_0_5711, 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)),esk437_3(X3,X2,X1)),X2)))). 7.00/7.29 cnf(i_0_1021, 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)))). 7.00/7.29 cnf(i_0_1200, 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)))). 7.00/7.29 cnf(i_0_1553, 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),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),X3),X1)))). 7.00/7.29 cnf(i_0_2157, plain, (hAPP(c_List_Oset(X1),X2)=hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Oappend(X1),X3),X4))|c_List_Opartition(X1,X5,X2)!=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4))). 7.00/7.29 cnf(i_0_4169, 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)))). 7.00/7.29 cnf(i_0_6213, 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)))). 7.00/7.29 cnf(i_0_4416, 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)))). 7.00/7.29 cnf(i_0_2586, 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))|esk207_3(X3,X2,X1)!=esk206_3(X3,X2,X1))). 7.00/7.29 cnf(i_0_1806, 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)))). 7.00/7.29 cnf(i_0_6747, plain, (c_Divides_OposDivAlg(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))|~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)))). 7.00/7.29 cnf(i_0_1772, 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)))). 7.00/7.29 cnf(i_0_2550, 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)))). 7.00/7.29 cnf(i_0_2261, 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)))). 7.00/7.29 cnf(i_0_2123, 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)))). 7.00/7.29 cnf(i_0_7045, 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)))). 7.00/7.29 cnf(i_0_889, 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)))). 7.00/7.29 cnf(i_0_1095, 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)))). 7.00/7.29 cnf(i_0_610, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Int_OMin))=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))). 7.00/7.29 cnf(i_0_1359, 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)). 7.00/7.29 cnf(i_0_6853, 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)))). 7.00/7.29 cnf(i_0_974, 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)))). 7.00/7.29 cnf(i_0_3187, 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)))). 7.00/7.29 cnf(i_0_6398, 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)))). 7.00/7.29 cnf(i_0_1848, 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)))). 7.00/7.29 cnf(i_0_1957, 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)))). 7.00/7.29 cnf(i_0_1812, 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)))). 7.00/7.29 cnf(i_0_2124, 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)))). 7.00/7.29 cnf(i_0_6155, 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)))). 7.00/7.29 cnf(i_0_3541, 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)))). 7.00/7.29 cnf(i_0_791, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 7.00/7.29 cnf(i_0_655, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 7.00/7.29 cnf(i_0_6621, 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)))). 7.00/7.29 cnf(i_0_3427, 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))))). 7.00/7.29 cnf(i_0_5308, 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)))). 7.00/7.29 cnf(i_0_682, plain, (hAPP(X1,esk58_3(X2,X1,X3))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk57_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))))). 7.00/7.29 cnf(i_0_2112, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),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)))). 7.00/7.29 cnf(i_0_2252, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),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)))). 7.00/7.29 cnf(i_0_6818, plain, (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))))=hAPP(c_List_Oset(X1),c_List_Oremove1(X1,X3,X2))|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 7.00/7.29 cnf(i_0_4324, 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))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X3)). 7.00/7.29 cnf(i_0_1564, plain, (hAPP(X1,esk128_3(X2,X1,X3))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk127_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))))). 7.00/7.29 cnf(i_0_7121, 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)))). 7.00/7.29 cnf(i_0_4822, 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)))). 7.00/7.29 cnf(i_0_6855, 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)))). 7.00/7.29 cnf(i_0_683, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk57_3(X1,X2,X3)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk58_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))))). 7.00/7.29 cnf(i_0_1565, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk127_3(X1,X2,X3)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk128_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))))). 7.00/7.29 cnf(i_0_1830, 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)))). 7.00/7.29 cnf(i_0_4641, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)|X3=c_Groups_Ozero__class_Ozero(X1)|X4=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X5),X3)!=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X4)|~class_Divides_Osemiring__div(X1)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X4),X2))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X5)))). 7.00/7.29 cnf(i_0_5051, 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)))). 7.00/7.29 cnf(i_0_7210, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk560_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)))). 7.00/7.29 cnf(i_0_7208, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk560_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)))). 7.00/7.29 cnf(i_0_2470, 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)))). 7.00/7.29 cnf(i_0_6309, 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),esk493_2(X2,X1)),hAPP(X1,esk493_2(X2,X1)))))). 7.00/7.29 cnf(i_0_5975, 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)))). 7.00/7.29 cnf(i_0_4044, 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)))). 7.00/7.29 cnf(i_0_4640, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(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),X3),X4)|~class_Divides_Osemiring__div(X1)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X2))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X5),X4)))). 7.00/7.29 cnf(i_0_4306, 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)))). 7.00/7.29 cnf(i_0_3572, 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))))). 7.00/7.29 cnf(i_0_6732, 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)))). 7.00/7.29 cnf(i_0_1749, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),hAPP(c_List_Oset(X1),X5))=hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),X3),X4),X5)|~c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3))). 7.00/7.29 cnf(i_0_1962, 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)))). 7.00/7.29 cnf(i_0_3864, 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)))). 7.00/7.29 cnf(i_0_3574, 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))))). 7.00/7.29 cnf(i_0_6100, 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))))). 7.00/7.29 cnf(i_0_6096, 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))))). 7.00/7.29 cnf(i_0_6292, 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))))). 7.00/7.29 cnf(i_0_2222, 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)))). 7.00/7.29 cnf(i_0_4459, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk339_4(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3),X3,X2)),esk338_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)))). 7.00/7.29 cnf(i_0_1165, 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)))). 7.00/7.29 cnf(i_0_1273, 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))))). 7.00/7.29 cnf(i_0_6291, 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)))). 7.00/7.29 cnf(i_0_1271, 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)))). 7.00/7.29 cnf(i_0_3540, 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))). 7.00/7.29 cnf(i_0_3651, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(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),X3),X2)),X4)),X3)))|~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)))). 7.00/7.29 cnf(i_0_4280, 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),esk325_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)))). 7.00/7.29 cnf(i_0_4473, 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),esk343_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)))). 7.00/7.29 cnf(i_0_4219, 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),esk318_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)))). 7.00/7.29 cnf(i_0_1528, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk126_4(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3),X3,X2)),esk125_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)))). 7.00/7.29 cnf(i_0_2056, 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)))). 7.00/7.29 cnf(i_0_3652, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(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),X3),X2)),X4)),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),X3)))). 7.00/7.29 cnf(i_0_1172, 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),X3),c_Groups_Ozero__class_Ozero(X1))))). 7.00/7.29 cnf(i_0_1171, 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)))). 7.00/7.29 cnf(i_0_4709, 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),esk363_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)))). 7.00/7.29 cnf(i_0_7427, 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)))). 7.00/7.29 cnf(i_0_7305, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)|hBOOL(hAPP(hAPP(c_member(X1),esk570_6(X2,X4,X5,X1,X3,X3)),X3)))). 7.00/7.29 cnf(i_0_3993, 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|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)))). 7.00/7.29 cnf(i_0_1174, 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)))). 7.00/7.29 cnf(i_0_1173, 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)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 7.00/7.29 cnf(i_0_1862, 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)))). 7.00/7.29 cnf(i_0_4138, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|~c_Relation_Osym(X1,X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),X4)))). 7.00/7.29 cnf(i_0_3521, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk270_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk269_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))))). 7.00/7.29 cnf(i_0_3042, 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),esk232_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)))). 7.00/7.29 cnf(i_0_7222, 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)),esk561_5(X2,X4,X3,X3,X1)))|~class_Groups_Ocomm__monoid__mult(X1)|~class_Groups_Ocomm__monoid__add(X1)|~c_Nat__Transfer_Onat__set(X3))). 7.00/7.29 cnf(i_0_7425, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),esk588_3(X2,X3,X1)),esk589_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))))). 7.00/7.29 cnf(i_0_3271, 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)))). 7.00/7.29 cnf(i_0_4999, 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))))). 7.00/7.29 cnf(i_0_6750, 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)),esk529_5(X2,X4,X3,X3,X1)))|~class_Groups_Ocomm__monoid__mult(X1)|~class_Groups_Ocomm__monoid__add(X1)|~c_Nat__Transfer_Onat__set(X3))). 7.00/7.29 cnf(i_0_1916, 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),esk156_4(X3,X4,X2,X1)),X4))|~class_Rings_Olinordered__semidom(X1))). 7.00/7.29 cnf(i_0_6841, 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),esk536_4(X3,X4,X2,X1)),X4))|~class_Rings_Olinordered__semidom(X1))). 7.00/7.29 cnf(i_0_5430, 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))=X3|X2=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)))). 7.00/7.29 cnf(i_0_5944, 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)),esk462_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))))). 7.00/7.29 cnf(i_0_4611, 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)))). 7.00/7.29 cnf(i_0_3970, plain, (hAPP(hAPP(X1,X2),X3)=hAPP(hAPP(X1,X4),X3)|hBOOL(hAPP(hAPP(c_member(X5),esk300_7(X2,X4,X3,X1,X6,X7,X5)),X3))|~c_Finite__Set_Ofolding__image(X8,X5,X7,X6,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3)))). 7.00/7.29 cnf(i_0_4962, 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))). 7.00/7.29 cnf(i_0_6608, 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)))). 7.00/7.29 cnf(i_0_7437, 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)),esk590_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))))). 7.00/7.29 cnf(i_0_373, 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),esk33_5(X5,X2,X4,X3,X1)),X4))|~class_Complete__Lattice_Ocomplete__lattice(X1))). 7.00/7.29 cnf(i_0_876, 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),esk71_5(X5,X4,X3,X2,X1)),X4))|~class_Complete__Lattice_Ocomplete__lattice(X1))). 7.00/7.29 cnf(i_0_999, 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),esk83_5(X5,X4,X3,X2,X1)),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1))). 7.00/7.29 cnf(i_0_5548, 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),esk422_5(X5,X4,X3,X2,X1)),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1))). 7.00/7.29 cnf(i_0_7201, 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)))). 7.00/7.29 cnf(i_0_3551, 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))))))). 7.00/7.29 cnf(i_0_6052, 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,esk476_5(X3,X4,X5,X2,X1))))). 7.00/7.29 cnf(i_0_4077, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),X5))|hBOOL(hAPP(hAPP(c_member(X2),esk309_5(X5,X3,X1,X4,X2)),X4)))). 7.00/7.29 cnf(i_0_7123, 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))))). 7.00/7.29 cnf(i_0_532, 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)))). 7.00/7.29 cnf(i_0_6407, 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,esk502_4(X4,X1,X2,hAPP(c_Set_Oimage(X1,X2,X3),X4))),hAPP(c_Set_Oimage(X1,X2,X3),X4))),X4)))). 7.00/7.29 cnf(i_0_2011, 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)))). 7.00/7.29 cnf(i_0_7318, plain, (hAPP(hAPP(X1,X2),esk574_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)))). 7.00/7.29 cnf(i_0_1191, 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))). 7.00/7.29 cnf(i_0_6051, 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,esk476_5(X3,X4,X5,X2,X1))!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Omonoid__add(X1))). 7.00/7.29 cnf(i_0_4158, 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)|c_Groups_Ozero__class_Ozero(X1)=X4|~class_Fields_Ofield(X1))). 7.00/7.29 cnf(i_0_5185, 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)|c_List_Olist_ONil(X1)=X2|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 7.00/7.29 cnf(i_0_1530, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk125_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)))). 7.00/7.29 cnf(i_0_2734, 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))). 7.00/7.29 cnf(i_0_1083, plain, (hAPP(hAPP(c_List_Oappend(X1),esk87_5(X2,X3,X4,X5,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),esk88_5(X2,X3,X4,X5,X1)))=X4|hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2)!=hAPP(c_List_Ofilter(X1,X5),X4))). 7.00/7.29 cnf(i_0_1585, plain, (hAPP(hAPP(c_List_Oappend(X1),esk130_5(X2,X3,X4,X5,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),esk131_5(X2,X3,X4,X5,X1)))=X2|hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4)!=hAPP(c_List_Ofilter(X1,X3),X2))). 7.00/7.29 cnf(i_0_5881, 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)))). 7.00/7.29 cnf(i_0_859, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk69_5(X2,X3,X4,X1,X5)),hAPP(c_Set_Oimage(X5,X1,X4),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))|hBOOL(hAPP(X3,X2))|~c_Fun_Oinj__on(X5,X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))). 7.00/7.29 cnf(i_0_3939, 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)))). 7.00/7.29 cnf(i_0_1711, 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)))). 7.00/7.29 cnf(i_0_4461, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk338_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)))). 7.00/7.29 cnf(i_0_1839, 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)))). 7.00/7.29 cnf(i_0_5045, 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))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(X2,esk394_3(X3,X2,X1))),hAPP(X2,esk395_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),esk394_3(X3,X2,X1)),esk395_3(X3,X2,X1)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.00/7.29 cnf(i_0_176, 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,esk11_3(X3,X2,X1))),hAPP(X2,esk12_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),esk11_3(X3,X2,X1)),esk12_3(X3,X2,X1)))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.00/7.29 cnf(i_0_5506, 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))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(X2,esk418_3(X3,X2,X1))),hAPP(X2,esk419_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),esk418_3(X3,X2,X1)),esk419_3(X3,X2,X1)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.00/7.29 cnf(i_0_589, 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))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(X2,esk45_3(X3,X2,X1))),hAPP(X2,esk46_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),esk45_3(X3,X2,X1)),esk46_3(X3,X2,X1)))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.00/7.29 cnf(i_0_3836, plain, (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),esk285_4(X2,X4,X3,X1)),esk286_4(X2,X4,X3,X1))),X3)))). 7.00/7.29 cnf(i_0_7050, 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,esk546_3(X2,X3,X1))))). 7.00/7.29 cnf(i_0_5177, 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,esk398_3(X2,X3,X1))))). 7.00/7.29 cnf(i_0_3807, 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)))). 7.00/7.29 cnf(i_0_5834, 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)))). 7.00/7.29 cnf(i_0_5566, 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))). 7.00/7.29 cnf(i_0_1542, 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)))). 7.00/7.29 cnf(i_0_5089, 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))). 7.00/7.29 cnf(i_0_625, 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),esk50_4(X4,X2,X3,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.00/7.29 cnf(i_0_17, 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),esk1_4(X4,X1,X3,X2)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 7.00/7.29 cnf(i_0_5643, 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),esk430_4(X4,X1,X3,X2)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 7.00/7.29 cnf(i_0_721, 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)))). 7.00/7.29 cnf(i_0_1371, 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(X7,esk106_8(X3,X7,hAPP(c_Set_Oimage(X4,X1,X5),X6),X6,X5,X1,X4,X2))!=hAPP(X3,hAPP(X5,esk106_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))). 7.00/7.29 cnf(i_0_7526, 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)))). 7.00/7.29 cnf(i_0_3637, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_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)),esk274_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1))))). 7.00/7.29 cnf(i_0_4085, 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),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3))))|~class_Rings_Olinordered__ring__strict(X2))). 7.00/7.29 cnf(i_0_4086, 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),X3),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2))))|~class_Rings_Olinordered__ring__strict(X1))). 7.00/7.29 cnf(i_0_4992, 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))=X3|X2=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)))). 7.00/7.29 cnf(i_0_4113, 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)))). 7.00/7.29 cnf(i_0_7317, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),esk574_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)))). 7.00/7.29 cnf(i_0_3195, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk249_3(X1,X2,X3)),esk248_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_Ominus__class_Ominus(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)))). 7.00/7.29 cnf(i_0_4149, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk315_3(X1,X2,X3)),esk314_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)))). 7.00/7.29 cnf(i_0_3895, 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__mult(X1)|~class_Groups_Ocomm__monoid__add(X1))). 7.00/7.29 cnf(i_0_5351, 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__mult(X1)|~class_Groups_Ocomm__monoid__add(X1))). 7.00/7.29 cnf(i_0_2528, 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))). 7.00/7.29 cnf(i_0_2585, 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)),esk206_3(X3,X2,X1)),esk207_3(X3,X2,X1))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 7.00/7.29 cnf(i_0_4500, 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)))). 7.00/7.29 cnf(i_0_6577, 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)))). 7.00/7.29 cnf(i_0_468, 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)))). 7.00/7.29 cnf(i_0_4561, 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))|X3=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 7.00/7.29 cnf(i_0_6275, 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))|c_Groups_Ozero__class_Ozero(X1)=X4|~class_Fields_Ofield__inverse__zero(X1))). 7.00/7.29 cnf(i_0_1390, 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)))). 7.00/7.29 cnf(i_0_4171, 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)). 7.00/7.29 cnf(i_0_4322, 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)))). 7.00/7.29 cnf(i_0_3869, 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)))). 7.00/7.29 cnf(i_0_6029, 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))))). 7.00/7.29 cnf(i_0_4350, 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)))). 7.02/7.29 cnf(i_0_2133, 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))). 7.02/7.29 cnf(i_0_467, 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))). 7.02/7.29 cnf(i_0_2375, 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)|X3=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield(X1))). 7.02/7.29 cnf(i_0_4352, 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))). 7.02/7.29 cnf(i_0_1427, 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),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X1),X2),hAPP(hAPP(c_Set_Oinsert(X4),X3),X5))|hBOOL(hAPP(hAPP(c_member(X4),X3),X5))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X5)))). 7.02/7.29 cnf(i_0_483, 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))))))). 7.02/7.29 cnf(i_0_2672, 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))))))). 7.02/7.29 cnf(i_0_1740, 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)))). 7.02/7.29 cnf(i_0_39, 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))|c_Groups_Ozero__class_Ozero(X1)=X2|~class_Fields_Ofield(X1))). 7.02/7.29 cnf(i_0_2601, 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))|c_Groups_Ozero__class_Ozero(X1)=X2|~class_Fields_Ofield(X1))). 7.02/7.29 cnf(i_0_7422, 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)))). 7.02/7.29 cnf(i_0_5608, 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))). 7.02/7.29 cnf(i_0_1739, 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)))). 7.02/7.29 cnf(i_0_7416, 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),X3),hAPP(hAPP(c_List_Olist_OCons(X5),X2),c_List_Olist_ONil(X5)))),hAPP(hAPP(c_List_Oappend(X5),X4),hAPP(hAPP(c_List_Olist_OCons(X5),X1),c_List_Olist_ONil(X5))))),c_List_Olistrel1(X5,X6))))). 7.02/7.29 cnf(i_0_5267, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))|~class_Enum_Oenum(X1)|~class_Orderings_Oorder(X2)|~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)))). 7.02/7.29 cnf(i_0_3575, 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))))). 7.02/7.29 cnf(i_0_3636, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_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)),esk274_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.02/7.29 cnf(i_0_6448, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~class_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(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))))). 7.02/7.29 cnf(i_0_1361, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~class_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(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))))). 7.02/7.29 cnf(i_0_1401, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))|~class_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(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))))). 7.02/7.29 cnf(i_0_7480, plain, (c_Wellfounded_Owf(X1,X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(esk592_2(X2,X1),hAPP(c_Nat_OSuc,X3))),hAPP(esk592_2(X2,X1),X3))),X2)))). 7.02/7.29 cnf(i_0_3573, 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))))). 7.02/7.29 cnf(i_0_6097, 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))))). 7.02/7.29 cnf(i_0_6101, 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))))). 7.02/7.29 cnf(i_0_6293, 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)))). 7.02/7.29 cnf(i_0_377, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))|~class_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(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))))). 7.02/7.29 cnf(i_0_1011, 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)))). 7.02/7.29 cnf(i_0_1272, 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)))). 7.02/7.29 cnf(i_0_3576, 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))))). 7.02/7.29 cnf(i_0_6098, 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))))). 7.02/7.29 cnf(i_0_1278, 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))))). 7.02/7.29 cnf(i_0_749, 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)))). 7.02/7.29 cnf(i_0_6830, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk533_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)))). 7.02/7.29 cnf(i_0_6831, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk533_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)))). 7.02/7.29 cnf(i_0_3062, 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)))). 7.02/7.29 cnf(i_0_6297, 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))))). 7.02/7.29 cnf(i_0_6296, 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)))). 7.02/7.29 cnf(i_0_1276, 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)))). 7.02/7.29 cnf(i_0_2610, 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)))). 7.02/7.29 cnf(i_0_6696, 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))))). 7.02/7.29 cnf(i_0_6943, 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))). 7.02/7.29 cnf(i_0_7053, 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))). 7.02/7.29 cnf(i_0_7419, 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))). 7.02/7.29 cnf(i_0_4736, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk366_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))))). 7.02/7.29 cnf(i_0_242, 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),esk21_3(X3,X2,X1))!=X3|esk23_3(X3,X2,X1)!=esk22_3(X3,X2,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))))). 7.02/7.29 cnf(i_0_6719, 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))))). 7.02/7.29 cnf(i_0_1305, 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),esk102_5(X5,X4,X3,X2,X1)),X4)))). 7.02/7.29 cnf(i_0_406, 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))). 7.02/7.29 cnf(i_0_5866, 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))). 7.02/7.29 cnf(i_0_2146, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk169_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))))). 7.02/7.29 cnf(i_0_3582, 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,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_Osemiring__div(X1))). 7.02/7.29 cnf(i_0_4234, 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),esk322_5(X5,X2,X1,X4,X3)),X4)))). 7.02/7.29 cnf(i_0_5928, 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)))). 7.02/7.29 cnf(i_0_3847, 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),esk288_2(X2,X1))),hAPP(c_List_Oset(X1),esk289_2(X2,X1)))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_List_Odistinct(X1),esk287_2(X2,X1)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)))). 7.02/7.29 cnf(i_0_4055, 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))). 7.02/7.29 cnf(i_0_3824, 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)))). 7.02/7.29 cnf(i_0_343, 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)))). 7.02/7.29 cnf(i_0_1449, 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))). 7.02/7.29 cnf(i_0_7173, 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)))). 7.02/7.29 cnf(i_0_7151, 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)),X1)),X3))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(hAPP(c_member(X2),X4),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 7.02/7.29 cnf(i_0_2388, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(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(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 7.02/7.29 cnf(i_0_3392, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)))=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)))). 7.02/7.29 cnf(i_0_4078, 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)))). 7.02/7.29 cnf(i_0_5060, 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)))). 7.02/7.29 cnf(i_0_3980, plain, (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)))))=c_List_Oremove1(X1,X3,c_List_Olinorder__class_Osorted__list__of__set(X1,X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 7.02/7.29 cnf(i_0_2459, 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|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))|~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)))). 7.02/7.29 cnf(i_0_3858, 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))). 7.02/7.29 cnf(i_0_3577, 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))))). 7.02/7.29 cnf(i_0_6099, 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))))). 7.02/7.29 cnf(i_0_6298, 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)))). 7.02/7.29 cnf(i_0_4886, 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))). 7.02/7.29 cnf(i_0_5180, plain, (hAPP(hAPP(c_List_Olist__update(X1,X2),esk400_4(X3,X4,X2,X1)),esk399_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))))). 7.02/7.29 cnf(i_0_6825, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk535_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,esk534_4(X2,X3,X4,X1))))). 7.02/7.29 cnf(i_0_6826, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk534_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,esk535_4(X2,X3,X4,X1))))). 7.02/7.29 cnf(i_0_1277, 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)))). 7.02/7.29 cnf(i_0_3340, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk255_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk254_3(X1,X2,X3)))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk257_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X2)))). 7.02/7.29 cnf(i_0_3333, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk257_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3)))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk255_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X2)))). 7.02/7.29 cnf(i_0_1195, 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)))). 7.02/7.29 cnf(i_0_2458, 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|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__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)))). 7.02/7.29 cnf(i_0_4355, 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)))))). 7.02/7.29 cnf(i_0_6241, 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)))). 7.02/7.29 cnf(i_0_5528, 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)))). 7.02/7.29 cnf(i_0_2379, 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__mult(X1)|~class_Groups_Ocomm__monoid__add(X1)|~c_Nat__Transfer_Onat__set(X3))). 7.02/7.29 cnf(i_0_4769, 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__mult(X1)|~class_Groups_Ocomm__monoid__add(X1)|~c_Nat__Transfer_Onat__set(X3))). 7.02/7.29 cnf(i_0_2357, 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)))). 7.02/7.29 cnf(i_0_2552, 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)))). 7.02/7.29 cnf(i_0_5737, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,esk440_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)))). 7.02/7.29 cnf(i_0_6164, 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))))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|~c_Equiv__Relations_Oequiv(X1,X4,X3))). 7.02/7.29 cnf(i_0_750, 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)))). 7.02/7.29 cnf(i_0_3365, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk255_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk254_3(X1,X2,X3)))=X2|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk257_3(X1,X2,X3))))). 7.02/7.29 cnf(i_0_3358, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk257_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3)))=X2|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk255_3(X1,X2,X3))))). 7.02/7.29 cnf(i_0_2097, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk165_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)))). 7.02/7.29 cnf(i_0_4466, 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))). 7.02/7.29 cnf(i_0_513, 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)))). 7.02/7.29 cnf(i_0_1481, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk120_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),esk118_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk119_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,esk118_2(X1,X2)))|~hBOOL(hAPP(X1,X3)))). 7.02/7.29 cnf(i_0_1153, 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),esk93_4(X3,X4,X2,X1)),X4))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 7.02/7.29 cnf(i_0_4924, 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))). 7.02/7.29 cnf(i_0_5697, 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)),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)))). 7.02/7.29 cnf(i_0_2746, 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,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_Oring__div(X1))). 7.02/7.29 cnf(i_0_6557, 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)))). 7.02/7.29 cnf(i_0_4053, 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)))). 7.02/7.29 cnf(i_0_860, plain, (hAPP(hAPP(c_List_Otake(X1),X2),X3)=hAPP(hAPP(c_List_Otake(X1),X2),X4)|hAPP(hAPP(c_List_Onth(X1),X3),esk70_4(X4,X3,X1,X2))!=hAPP(hAPP(c_List_Onth(X1),X4),esk70_4(X4,X3,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))))). 7.02/7.29 cnf(i_0_4839, 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)))). 7.02/7.29 cnf(i_0_709, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3),X4),X5))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(X2,X4)),hAPP(X2,X5))))|~class_Lattices_Osemilattice__inf(X1)|~class_Lattices_Osemilattice__inf(X3)|~c_Orderings_Oorder__class_Omono(X3,X1,X2))). 7.02/7.29 cnf(i_0_6481, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X4),X5))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(X2,X4)),hAPP(X2,X5))))|~class_Lattices_Osemilattice__inf(X1)|~c_Orderings_Oorder__class_Omono(X3,X1,X2)|~class_Orderings_Olinorder(X3))). 7.02/7.29 cnf(i_0_3336, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk255_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk257_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 7.02/7.29 cnf(i_0_3347, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 7.02/7.29 cnf(i_0_7175, 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)))). 7.02/7.29 cnf(i_0_7271, 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)))). 7.02/7.29 cnf(i_0_7055, 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)))). 7.02/7.29 cnf(i_0_1912, 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))))). 7.02/7.29 cnf(i_0_5714, 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)))))). 7.02/7.29 cnf(i_0_354, 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),esk32_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))))). 7.02/7.29 cnf(i_0_1778, 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))). 7.02/7.29 cnf(i_0_2716, 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)))|c_Groups_Oone__class_Oone(X1)!=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|~class_Int_Onumber__ring(X1))). 7.02/7.29 cnf(i_0_4890, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X4)),X3)|~class_Divides_Osemiring__div(X1)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X4),X2)))). 7.02/7.29 cnf(i_0_7482, 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)))). 7.02/7.29 cnf(i_0_2426, 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)))). 7.02/7.29 cnf(i_0_2907, 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))). 7.02/7.29 cnf(i_0_6333, 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),esk496_3(X2,X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.02/7.29 cnf(i_0_3517, 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),esk268_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)))). 7.02/7.29 cnf(i_0_6001, 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)))). 7.02/7.29 cnf(i_0_2225, 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)))). 7.02/7.29 cnf(i_0_1954, 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)))). 7.02/7.29 cnf(i_0_3678, 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)))). 7.02/7.29 cnf(i_0_3258, 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)))). 7.02/7.29 cnf(i_0_3361, 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)),esk255_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk257_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))))). 7.02/7.29 cnf(i_0_3372, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))))). 7.02/7.29 cnf(i_0_4874, 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))). 7.02/7.29 cnf(i_0_1609, 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))). 7.02/7.29 cnf(i_0_3703, 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))=X3|X4=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~c_Finite__Set_Ofolding__one__idem(X2,X5,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 7.02/7.29 cnf(i_0_7186, 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))). 7.02/7.29 cnf(i_0_5179, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk400_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))))). 7.02/7.29 cnf(i_0_3671, 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)))). 7.02/7.29 cnf(i_0_3436, 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,X1)))). 7.02/7.29 cnf(i_0_3197, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk248_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_Ominus__class_Ominus(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)))). 7.02/7.29 cnf(i_0_4151, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk314_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)))). 7.02/7.29 cnf(i_0_5442, 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))))). 7.02/7.29 cnf(i_0_7269, 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(X3,hAPP(X5,esk568_8(X3,X7,hAPP(c_Set_Oimage(X4,X1,X5),X6),X6,X5,X1,X4,X2)))!=hAPP(X7,esk568_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))). 7.02/7.29 cnf(i_0_203, 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))). 7.02/7.29 cnf(i_0_205, 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))). 7.02/7.29 cnf(i_0_2635, 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)). 7.02/7.29 cnf(i_0_4963, 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_Enum_Oenum(X1)|~class_Orderings_Oorder(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4)))). 7.02/7.29 cnf(i_0_1664, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(X2,X3)),hAPP(X2,X4))),hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X3),X4))))|~class_Lattices_Osemilattice__sup(X1)|~c_Orderings_Oorder__class_Omono(X5,X1,X2)|~class_Orderings_Olinorder(X5))). 7.02/7.29 cnf(i_0_4475, 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)))). 7.02/7.29 cnf(i_0_3882, plain, (c_Lazy__Sequence_Ohb__bind(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(tc_Option_Ooption(X2))),X5),X4))=hAPP(c_New__DSequence_Oneg__decr__bind(X1,X2,X3,X5),X4)|X4=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). 7.02/7.29 cnf(i_0_3448, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk260_4(X3,X4,X1,X2)),esk261_4(X3,X4,X1,X2))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),X4),hAPP(c_Relation_Oconverse(X1,X2),X3))))). 7.02/7.29 cnf(i_0_1479, plain, (hBOOL(hAPP(X1,esk121_2(X1,X2)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk118_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk119_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,esk118_2(X1,X2)))|~hBOOL(hAPP(X1,X3)))). 7.02/7.30 cnf(i_0_7494, 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,esk594_5(X4,X3,X1,X5,X2))),hAPP(X3,esk595_5(X4,X3,X1,X5,X2)))!=hAPP(X3,hAPP(hAPP(X5,esk594_5(X4,X3,X1,X5,X2)),esk595_5(X4,X3,X1,X5,X2)))|~c_Finite__Set_Ofolding__one__idem(X2,X5,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 7.02/7.30 cnf(i_0_578, 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)))). 7.02/7.30 cnf(i_0_329, 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)))). 7.02/7.30 cnf(i_0_5797, 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)))). 7.02/7.30 cnf(i_0_7265, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))|~class_Int_Onumber__ring(X1))). 7.02/7.30 cnf(i_0_4464, 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))). 7.02/7.30 cnf(i_0_5771, 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,esk446_3(X2,X3,X1)))),c_Predicate_ORangeP(X1,X1,hAPP(X3,esk447_3(X2,X3,X1))))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~c_Wellfounded_OwfP(X1,hAPP(X3,esk445_3(X2,X3,X1))))). 7.02/7.30 cnf(i_0_2400, plain, (hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4))=hAPP(hAPP(X5,hAPP(X6,X3)),hAPP(X1,X4))|hBOOL(hAPP(hAPP(c_member(X2),X3),X4))|~c_Finite__Set_Ofolding__image__simple(X7,X2,X5,X8,X6,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 7.02/7.30 cnf(i_0_3086, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),esk236_5(X3,X4,X5,X2,X1))=X4|hAPP(hAPP(c_List_Oappend(X1),X4),esk235_5(X3,X4,X5,X2,X1))=X2|hAPP(hAPP(c_List_Oappend(X1),X4),X3)!=hAPP(hAPP(c_List_Oappend(X1),X2),X5))). 7.02/7.30 cnf(i_0_3085, plain, (hAPP(hAPP(c_List_Oappend(X1),esk236_5(X2,X3,X4,X5,X1)),X2)=X4|hAPP(hAPP(c_List_Oappend(X1),X3),esk235_5(X2,X3,X4,X5,X1))=X5|hAPP(hAPP(c_List_Oappend(X1),X3),X2)!=hAPP(hAPP(c_List_Oappend(X1),X5),X4))). 7.02/7.30 cnf(i_0_5006, 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))). 7.02/7.30 cnf(i_0_6579, 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)))). 7.02/7.30 cnf(i_0_965, 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))))). 7.02/7.30 cnf(i_0_3380, 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))). 7.02/7.30 cnf(i_0_3088, plain, (hAPP(hAPP(c_List_Oappend(X1),esk235_5(X2,X3,X4,X5,X1)),X4)=X2|hAPP(hAPP(c_List_Oappend(X1),X5),esk236_5(X2,X3,X4,X5,X1))=X3|hAPP(hAPP(c_List_Oappend(X1),X3),X2)!=hAPP(hAPP(c_List_Oappend(X1),X5),X4))). 7.02/7.30 cnf(i_0_3087, plain, (hAPP(hAPP(c_List_Oappend(X1),esk235_5(X2,X3,X4,X5,X1)),X4)=X2|hAPP(hAPP(c_List_Oappend(X1),esk236_5(X2,X3,X4,X5,X1)),X2)=X4|hAPP(hAPP(c_List_Oappend(X1),X3),X2)!=hAPP(hAPP(c_List_Oappend(X1),X5),X4))). 7.02/7.30 cnf(i_0_2707, plain, (hAPP(hAPP(X1,esk212_7(X2,X3,X4,X5,X1,X6,X7)),esk213_7(X2,X3,X4,X5,X1,X6,X7))=hAPP(hAPP(X1,X3),X2)|X4=c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))|~c_Nitpick_Ofold__graph_H(X7,X6,X1,X5,X4,hAPP(hAPP(X1,X3),X2)))). 7.02/7.30 cnf(i_0_386, 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)))). 7.02/7.30 cnf(i_0_2839, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(X2,X3)),hAPP(X2,X4))),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X3),X4))))|~class_Lattices_Osemilattice__sup(X5)|~class_Lattices_Osemilattice__sup(X1)|~c_Orderings_Oorder__class_Omono(X5,X1,X2))). 7.02/7.30 cnf(i_0_1115, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X3)))))|~c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X3))))). 7.02/7.30 cnf(i_0_1691, 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)))). 7.02/7.30 cnf(i_0_6446, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X3)),c_Int_OMin)))=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))). 7.02/7.30 cnf(i_0_3288, 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))). 7.02/7.30 cnf(i_0_6528, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(X3,esk511_6(X4,X3,X5,X6,X2,X1)),esk512_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))))). 7.02/7.30 cnf(i_0_4455, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(X4,X5),tc_HOL_Obool),tc_fun(tc_prod(X4,X5),tc_HOL_Obool),X6)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X5)),hAPP(hAPP(c_Product__Type_OPair(X4,X5),X2),X3)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(X4,X5),tc_HOL_Obool),X6)))|~hBOOL(hAPP(hAPP(X1,esk336_6(X1,X6,X3,X2,X5,X4)),esk337_6(X1,X6,X3,X2,X5,X4))))). 7.02/7.30 cnf(i_0_1037, 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))))))). 7.02/7.30 cnf(i_0_4046, 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)))). 7.02/7.30 cnf(i_0_239, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),hAPP(c_Finite__Set_Ofold1(X2,c_Lattices_Osemilattice__inf__class_Oinf(X2)),X1)))|hBOOL(hAPP(hAPP(c_member(X2),esk20_3(X3,X1,X2)),X1))|~class_Lattices_Osemilattice__inf(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 7.02/7.30 cnf(i_0_4286, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),hAPP(c_Finite__Set_Ofold1(X2,c_Orderings_Oord__class_Omin(X2)),X1)))|hBOOL(hAPP(hAPP(c_member(X2),esk326_3(X3,X1,X2)),X1))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 7.02/7.30 cnf(i_0_6436, 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),esk503_3(X3,X2,X1)),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 7.02/7.30 cnf(i_0_6362, 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))))). 7.02/7.30 cnf(i_0_2708, plain, (hAPP(hAPP(X1,esk212_7(X2,X3,X4,X5,X1,X6,X7)),esk213_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)))). 7.02/7.30 cnf(i_0_5209, 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)))). 7.02/7.30 cnf(i_0_2136, 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))). 7.02/7.30 cnf(i_0_2138, 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)))). 7.02/7.30 cnf(i_0_5522, 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))). 7.02/7.30 cnf(i_0_919, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk79_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)))). 7.02/7.30 cnf(i_0_7475, 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))). 7.02/7.30 cnf(i_0_5664, 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)|c_List_Olist_ONil(X1)=X3|~c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Orev(X1),X3))|~class_Orderings_Olinorder(X1))). 7.02/7.30 cnf(i_0_5204, 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))))). 7.02/7.30 cnf(i_0_5201, 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)))). 7.02/7.30 cnf(i_0_5202, 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)))). 7.02/7.30 cnf(i_0_1084, 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,esk86_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)))). 7.02/7.30 cnf(i_0_1225, 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)))). 7.02/7.30 cnf(i_0_3484, plain, (hAPP(X1,esk265_4(X2,X1,X3,X4))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),esk264_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)))). 7.02/7.30 cnf(i_0_3481, plain, (hAPP(X1,esk265_4(X2,X1,X3,X4))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk264_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)))). 7.02/7.30 cnf(i_0_2352, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X4))=hAPP(c_Set_Oimage(X1,X2,X4),X3)|~c_Fun_Obij__betw(X1,X2,X4,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))). 7.02/7.30 cnf(i_0_3482, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk265_4(X2,X3,X4,X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk264_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)))). 7.02/7.30 cnf(i_0_6494, 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))). 7.02/7.30 cnf(i_0_6988, 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)))). 7.02/7.30 cnf(i_0_1589, 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,esk129_7(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,X5)))|~hBOOL(hAPP(X2,X4)))). 7.02/7.30 cnf(i_0_355, 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),esk32_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))))). 7.02/7.30 cnf(i_0_962, 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)))). 7.02/7.30 cnf(i_0_861, 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),esk70_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))))). 7.02/7.30 cnf(i_0_3480, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk264_4(X1,X2,X3,X4)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk265_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)))). 7.02/7.30 cnf(i_0_4646, plain, (c_Fun_Obij__betw(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)),X6),X7))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X6),X7)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~c_Fun_Obij__betw(X1,X2,X3,X5,X7)|~c_Fun_Obij__betw(X1,X2,X3,X4,X6))). 7.02/7.30 cnf(i_0_3289, 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))). 7.02/7.30 cnf(i_0_2855, 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))). 7.02/7.30 cnf(i_0_3515, 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)),esk268_3(X2,X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 7.02/7.30 cnf(i_0_6331, 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),esk496_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))))). 7.02/7.30 cnf(i_0_6782, 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))). 7.02/7.30 cnf(i_0_1357, 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))))). 7.02/7.30 cnf(i_0_5660, plain, (hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4))=hAPP(c_Fun_Ocomp(X5,X5,X5,hAPP(X1,X4)),hAPP(X6,X3))|hBOOL(hAPP(hAPP(c_member(X2),X3),X4))|~c_Finite__Set_Ofolding(X2,X5,X6,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 7.02/7.30 cnf(i_0_3227, 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)))). 7.02/7.30 cnf(i_0_350, 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)))). 7.02/7.30 cnf(i_0_3399, 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))). 7.02/7.30 cnf(i_0_5560, 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))). 7.02/7.30 cnf(i_0_1939, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),esk157_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))). 7.02/7.30 cnf(i_0_4845, 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)|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X5)). 7.02/7.30 cnf(i_0_4832, 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)))). 7.02/7.30 cnf(i_0_6009, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X1,X2),X6)),hAPP(X4,hAPP(c_Set_Oimage(X5,X1,X2),X6))))|~hBOOL(hAPP(hAPP(c_member(X5),X3),X6)))). 7.02/7.30 cnf(i_0_7213, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk559_4(X2,X3,X4,X1)),X3))|hBOOL(hAPP(X2,esk558_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)))). 7.02/7.30 cnf(i_0_7214, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk558_4(X2,X3,X4,X1)),X4))|hBOOL(hAPP(X2,esk559_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)))). 7.02/7.30 cnf(i_0_1375, 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),esk107_5(X5,X2,X1,X4,X3)),X4)))). 7.02/7.30 cnf(i_0_3605, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk276_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk275_3(X1,X2,X3)))=X2|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk273_3(X1,X2,X3))))). 7.02/7.30 cnf(i_0_3621, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk274_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk273_3(X1,X2,X3)))=X2|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk275_3(X1,X2,X3))))). 7.02/7.30 cnf(i_0_2785, 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))))). 7.02/7.30 cnf(i_0_1861, 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),esk155_5(X5,X4,X3,X2,X1)),X4)))). 7.02/7.30 cnf(i_0_2978, 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_Obij__betw(X1,X2,X4,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),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)),X3),hAPP(c_Set_Oimage(X1,X2,X4),X5))))). 7.02/7.30 cnf(i_0_2979, 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)))|~c_Fun_Obij__betw(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)))). 7.02/7.30 cnf(i_0_6381, 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))))). 7.02/7.30 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_Olist_OCons(X3),X1),X5)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X6))),c_List_Olex(X3,X4))))). 7.02/7.30 cnf(i_0_3273, 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),esk252_5(X5,X4,X3,X2,X1)),X3)))). 7.02/7.30 cnf(i_0_1624, 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))))). 7.02/7.30 cnf(i_0_6906, 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),esk543_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)))). 7.02/7.30 cnf(i_0_7192, 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),esk556_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)))). 7.02/7.30 cnf(i_0_5320, 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))))). 7.02/7.30 cnf(i_0_4345, 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),esk327_5(X5,X4,X1,X3,X2)),X3)))). 7.02/7.30 cnf(i_0_1680, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X2),X1)),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),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X6))),c_List_Olexord(X3,X4))))). 7.02/7.30 cnf(i_0_972, 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))))). 7.02/7.30 cnf(i_0_3966, 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))))). 7.02/7.30 cnf(i_0_3633, plain, (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)),esk274_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk276_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1))))). 7.02/7.30 cnf(i_0_1176, 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)))). 7.02/7.30 cnf(i_0_3604, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk276_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk275_3(X1,X2,X3)))=X2|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk273_3(X1,X2,X3)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.02/7.30 cnf(i_0_3620, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk274_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk273_3(X1,X2,X3)))=X2|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk275_3(X1,X2,X3)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.02/7.30 cnf(i_0_342, 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)))). 7.02/7.30 cnf(i_0_3617, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1))))). 7.02/7.30 cnf(i_0_7258, 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)))). 7.02/7.30 cnf(i_0_5245, 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)))). 7.02/7.30 cnf(i_0_567, 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)))). 7.02/7.30 cnf(i_0_270, 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))))). 7.02/7.30 cnf(i_0_3899, 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)))). 7.02/7.30 cnf(i_0_204, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X3)))|~c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X3)))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 7.02/7.30 cnf(i_0_7230, 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)))). 7.02/7.30 cnf(i_0_3632, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk274_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk276_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.02/7.30 cnf(i_0_3616, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.02/7.30 cnf(i_0_4279, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk325_4(X1,X2,X3,X4)),esk324_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)))). 7.02/7.30 cnf(i_0_1372, 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),esk106_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))). 7.02/7.30 cnf(i_0_4993, 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)))). 7.02/7.30 cnf(i_0_3988, 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))|X2=c_List_Olist_ONil(X1))). 7.02/7.30 cnf(i_0_4472, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk343_4(X1,X2,X3,X4)),esk342_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)))). 7.02/7.30 cnf(i_0_4218, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk318_4(X1,X2,X3,X4)),esk317_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)))). 7.02/7.30 cnf(i_0_4708, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk363_4(X1,X2,X3,X4)),esk362_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)))). 7.02/7.30 cnf(i_0_6110, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|c_Fun_Oinj__on(X3,X4,X5,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),X6))|hBOOL(hAPP(hAPP(c_member(X2),esk482_6(X6,X5,X4,X3,X2,X1)),X1)))). 7.02/7.30 cnf(i_0_7270, 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),esk568_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))). 7.02/7.30 cnf(i_0_2871, plain, (hAPP(X1,X2)=hAPP(X1,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X3)),hAPP(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X3),X2)),c_List_Omeasures(X4,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat)),X1),X5)))))). 7.02/7.30 cnf(i_0_4919, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk378_3(X2,X3,X1)),esk378_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))))). 7.02/7.30 cnf(i_0_5567, 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),esk424_4(X3,X2,X4,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 7.02/7.30 cnf(i_0_3344, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk255_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk254_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 7.02/7.30 cnf(i_0_3353, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk257_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 7.02/7.30 cnf(i_0_2358, 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)))). 7.02/7.30 cnf(i_0_4400, 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),esk328_4(X3,X2,X4,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 7.02/7.30 cnf(i_0_2014, 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)))). 7.02/7.30 cnf(i_0_536, 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)))). 7.02/7.30 cnf(i_0_4900, 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),esk376_4(X2,X4,X3,X1)),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.02/7.30 cnf(i_0_3369, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk255_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk254_3(X1,X2,X3)))=X2|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)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))))). 7.02/7.30 cnf(i_0_3378, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk257_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3)))=X2|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))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))))). 7.02/7.30 cnf(i_0_6856, 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)))). 7.02/7.30 cnf(i_0_1226, 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)))). 7.02/7.30 cnf(i_0_3777, 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_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 7.02/7.30 cnf(i_0_4618, 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),esk354_4(X2,X4,X3,X1)),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.02/7.30 cnf(i_0_7038, 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)))). 7.02/7.30 cnf(i_0_627, 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)))). 7.02/7.30 cnf(i_0_4281, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk324_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)))). 7.02/7.30 cnf(i_0_4474, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk342_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)))). 7.02/7.30 cnf(i_0_4220, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk317_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)))). 7.02/7.30 cnf(i_0_4710, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk362_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)))). 7.02/7.30 cnf(i_0_341, 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)))). 7.02/7.30 cnf(i_0_3422, 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)))). 7.02/7.30 cnf(i_0_7125, 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)))). 7.02/7.30 cnf(i_0_4489, 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)))). 7.02/7.30 cnf(i_0_3565, 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))))). 7.02/7.30 cnf(i_0_2356, 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)))). 7.02/7.30 cnf(i_0_424, plain, (c_List_OtakeWhile(X1,X2,X3)=hAPP(c_List_Ofilter(X1,X2),X3)|hBOOL(hAPP(hAPP(c_member(X1),esk36_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)))))). 7.02/7.30 cnf(i_0_747, 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)))). 7.02/7.30 cnf(i_0_358, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),hAPP(hAPP(X3,X4),X5)),X6)=hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X5),hAPP(hAPP(c_Set_Oinsert(X1),X4),X6))|~c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 7.02/7.30 cnf(i_0_1313, 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))|~c_Finite__Set_Ofun__left__comm__idem(X3,X4,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X6)))). 7.02/7.30 cnf(i_0_742, 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)),esk63_3(X3,X2,X1))),X2)),X3)))). 7.02/7.30 cnf(i_0_896, 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),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1))|~class_Int_Onumber__ring(X1))). 7.02/7.30 cnf(i_0_3916, 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))). 7.02/7.30 cnf(i_0_4627, 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))). 7.02/7.30 cnf(i_0_470, plain, (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_Fun_Obij__betw(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))))). 7.02/7.30 cnf(i_0_3155, 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)))). 7.02/7.30 cnf(i_0_1068, 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)))). 7.02/7.30 cnf(i_0_5646, 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|~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)))|~c_Equiv__Relations_Oequiv(X1,X4,X5))). 7.02/7.30 cnf(i_0_7487, 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))). 7.02/7.30 cnf(i_0_3070, 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),esk233_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))))). 7.02/7.30 cnf(i_0_3710, 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)))). 7.02/7.30 cnf(i_0_1231, 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,esk100_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)))). 7.02/7.30 cnf(i_0_5435, 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,esk415_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)))). 7.02/7.30 cnf(i_0_405, 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)))). 7.02/7.30 cnf(i_0_628, plain, (c_Wellfounded_Oacyclic(X1,X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk51_2(X2,X1)),esk51_2(X2,X1))),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))))). 7.02/7.30 cnf(i_0_1229, 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))). 7.02/7.30 cnf(i_0_5498, 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)))). 7.02/7.30 cnf(i_0_2706, 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)))). 7.02/7.30 cnf(i_0_2854, 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))))). 7.02/7.30 cnf(i_0_4553, plain, (c_Wellfounded_Oacyclic(X1,X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk346_2(X2,X1)),esk346_2(X2,X1))),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))))). 7.02/7.30 cnf(i_0_2441, plain, (c_Relation_Orefl__on(X1,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(tc_prod(X1,X1),tc_HOL_Obool)),X3),X5))|hBOOL(hAPP(hAPP(c_member(X2),esk195_5(X5,X4,X1,X3,X2)),X3)))). 7.02/7.30 cnf(i_0_4860, 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),esk375_5(X5,X4,X1,X3,X2)),X3)))). 7.02/7.30 cnf(i_0_4434, 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)))). 7.02/7.30 cnf(i_0_1905, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 7.02/7.30 cnf(i_0_6111, 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))))). 7.02/7.30 cnf(i_0_4223, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk319_6(X3,X4,X5,X2,X1,X6)),esk320_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))))). 7.02/7.30 cnf(i_0_3776, 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)))). 7.02/7.30 cnf(i_0_1230, 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),esk100_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)))). 7.02/7.30 cnf(i_0_1893, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 7.02/7.30 cnf(i_0_4096, 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)))). 7.02/7.30 cnf(i_0_6334, 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)))). 7.02/7.30 cnf(i_0_6646, 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)),X5)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),X6)),X5)|hBOOL(hAPP(hAPP(c_member(X1),esk517_6(X3,X2,X4,X6,X5,X1)),X5)))). 7.02/7.30 cnf(i_0_5434, 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),esk415_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)))). 7.02/7.30 cnf(i_0_1785, 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))). 7.02/7.30 cnf(i_0_3494, 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))))). 7.02/7.30 cnf(i_0_5810, 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))). 7.02/7.30 cnf(i_0_3429, 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)))). 7.02/7.30 cnf(i_0_7241, 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)))). 7.02/7.30 cnf(i_0_737, 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)))). 7.02/7.30 cnf(i_0_1490, 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),esk122_3(X1,X2,X3)),esk123_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))))). 7.02/7.30 cnf(i_0_3513, 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)))). 7.02/7.30 cnf(i_0_7555, 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))). 7.02/7.30 cnf(i_0_1870, 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))). 7.02/7.30 cnf(i_0_680, plain, (hAPP(X1,esk58_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,esk57_3(X2,X1,X3)))),hAPP(X1,esk57_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))))). 7.02/7.30 cnf(i_0_1562, plain, (hAPP(X1,esk128_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,esk127_3(X2,X1,X3)))),hAPP(X1,esk127_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))))). 7.02/7.30 cnf(i_0_3263, 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),esk250_3(X1,X2,X3)),esk251_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))))). 7.02/7.30 cnf(i_0_617, 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),esk48_3(X1,X2,X3)),esk49_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))))). 7.02/7.30 cnf(i_0_6347, 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),esk497_3(X1,X2,X3)),esk498_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))))). 7.02/7.30 cnf(i_0_3892, 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),esk290_3(X1,X2,X3)),esk291_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))))). 7.02/7.30 cnf(i_0_6405, 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))|~class_Lattices_Oab__semigroup__idem__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 7.02/7.30 cnf(i_0_7533, 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)))). 7.02/7.30 cnf(i_0_5333, 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)))). 7.02/7.30 cnf(i_0_1626, 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)))). 7.02/7.30 cnf(i_0_1864, 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)))). 7.02/7.30 cnf(i_0_5717, 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),esk438_3(X1,X2,X3)),esk439_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))))). 7.02/7.30 cnf(i_0_1167, plain, (hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,X1))=c_Orderings_Oord__class_OLeast(tc_Nat_Onat,X2)|hBOOL(hAPP(X2,hAPP(c_Nat_OSuc,esk95_4(X3,X1,X4,X2))))|hBOOL(hAPP(X1,esk95_4(X3,X1,X4,X2)))|hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(X2,X4)))). 7.02/7.30 cnf(i_0_1575, 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))))). 7.02/7.30 cnf(i_0_108, 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))))). 7.02/7.30 cnf(i_0_7493, 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)))). 7.02/7.30 cnf(i_0_3904, 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)))). 7.02/7.30 cnf(i_0_4458, 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)))). 7.02/7.30 cnf(i_0_1339, 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)))). 7.02/7.30 cnf(i_0_6332, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk496_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk495_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))))). 7.02/7.30 cnf(i_0_3516, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk268_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk267_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)))). 7.02/7.30 cnf(i_0_5867, 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)))). 7.02/7.30 cnf(i_0_2602, 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)))). 7.02/7.30 cnf(i_0_1180, 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)))|esk97_5(X5,X4,X3,X2,X1)!=esk96_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)))))). 7.02/7.30 cnf(i_0_6522, 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)))|esk510_5(X5,X4,X3,X2,X1)!=esk509_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)))))). 7.02/7.30 cnf(i_0_3341, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk255_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk254_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk257_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 7.02/7.30 cnf(i_0_3348, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk257_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 7.02/7.30 cnf(i_0_1578, 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))). 7.02/7.30 cnf(i_0_1103, 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)))). 7.02/7.30 cnf(i_0_2783, 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)))). 7.02/7.30 cnf(i_0_4783, 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)),esk368_4(X4,X3,X2,X1))))). 7.02/7.30 cnf(i_0_7542, 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))))). 7.02/7.30 cnf(i_0_3629, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk274_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk273_3(X1,X2,X3)))=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)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1))))). 7.02/7.30 cnf(i_0_3645, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk276_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk275_3(X1,X2,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)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1))))). 7.02/7.30 cnf(i_0_3366, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk255_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk254_3(X1,X2,X3)))=X2|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk257_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))))). 7.02/7.30 cnf(i_0_3373, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk257_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3)))=X2|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk255_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))))). 7.02/7.30 cnf(i_0_3124, 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)))). 7.02/7.30 cnf(i_0_5820, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk451_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)))))). 7.02/7.30 cnf(i_0_328, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),esk30_5(X2,X3,X4,X5,X1)),esk31_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))))). 7.02/7.30 cnf(i_0_1422, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),esk112_5(X2,X3,X4,X5,X1)),esk113_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))))). 7.02/7.30 cnf(i_0_263, 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)))). 7.02/7.30 cnf(i_0_5386, 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)))). 7.02/7.30 cnf(i_0_5128, 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)))). 7.02/7.30 cnf(i_0_7499, 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)))). 7.02/7.30 cnf(i_0_5360, 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))). 7.02/7.30 cnf(i_0_3723, 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)))). 7.02/7.30 cnf(i_0_391, 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),esk34_2(X2,X1)),esk35_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk34_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk35_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 7.02/7.30 cnf(i_0_1086, 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))). 7.02/7.30 cnf(i_0_3628, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk274_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk273_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.02/7.30 cnf(i_0_3644, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk276_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk275_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.02/7.30 cnf(i_0_823, 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_Rings_Oring(X1)|~class_Int_Onumber(X1))). 7.02/7.30 cnf(i_0_4952, plain, (c_Equiv__Relations_Ocongruent2(X1,X2,X3,X4,X5,X6)|hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),esk383_6(X3,X6,X5,X2,X4,X1)),esk384_6(X3,X6,X5,X2,X4,X1))),X5)))). 7.02/7.30 cnf(i_0_4953, plain, (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),esk381_6(X3,X6,X5,X2,X4,X1)),esk382_6(X3,X6,X5,X2,X4,X1))),X4)))). 7.02/7.30 cnf(i_0_1576, 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))))). 7.02/7.30 cnf(i_0_1829, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk149_4(X2,X3,X4,X1)),esk150_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))))). 7.02/7.30 cnf(i_0_4079, 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)))). 7.02/7.30 cnf(i_0_2381, 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)))). 7.02/7.30 cnf(i_0_762, 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)))). 7.02/7.30 cnf(i_0_7362, 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))))). 7.02/7.30 cnf(i_0_1413, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X3),X4),X1)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X3),X5),X1)))|~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,esk111_5(X5,X4,X1,X2,X3))),hAPP(X5,esk111_5(X5,X4,X1,X2,X3))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 7.02/7.30 cnf(i_0_3842, 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))))). 7.02/7.30 cnf(i_0_1673, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk142_5(X2,X3,X4,X5,X1)),hAPP(X3,esk141_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))))). 7.02/7.30 cnf(i_0_779, 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))))). 7.02/7.30 cnf(i_0_5090, 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)). 7.02/7.30 cnf(i_0_3338, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk257_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk255_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 7.02/7.30 cnf(i_0_2797, 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))). 7.02/7.30 cnf(i_0_5819, 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)))). 7.02/7.30 cnf(i_0_5013, plain, (hBOOL(hAPP(hAPP(X1,esk390_7(X2,X3,X4,X5,X6,X7,X1)),esk389_7(X2,X3,X4,X5,X6,X7,X1)))|hBOOL(hAPP(X4,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X7,X6,X2),X3),X5)))|~hBOOL(hAPP(hAPP(X1,hAPP(c_Product__Type_Osnd(X7,X6),X5)),hAPP(c_Product__Type_Ofst(X7,X6),X5))))). 7.02/7.30 cnf(i_0_748, 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)))). 7.02/7.30 cnf(i_0_3342, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk255_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk254_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 7.02/7.30 cnf(i_0_2070, 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)))). 7.02/7.30 cnf(i_0_1639, 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),esk136_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)))). 7.02/7.30 cnf(i_0_4511, 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),esk345_4(X4,X3,X2,X1)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),c_Int_OMin)),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)))). 7.02/7.30 cnf(i_0_6457, 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))))). 7.02/7.30 cnf(i_0_7051, 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),esk546_3(X2,X3,X1)),X3)))). 7.02/7.30 cnf(i_0_5178, 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),esk398_3(X2,X3,X1)),X3)))). 7.02/7.30 cnf(i_0_7022, 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)))). 7.02/7.30 cnf(i_0_370, plain, (hAPP(c_List_Ofilter(X1,X2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X3,X4),X5),X6))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X3,X4),X5),hAPP(c_List_Ofilter(X1,X2),X6))|~c_List_Olinorder__class_Osorted(X3,hAPP(hAPP(c_List_Omap(X1,X3),X4),X6))|~class_Orderings_Olinorder(X3)|~hBOOL(hAPP(X2,X5)))). 7.02/7.30 cnf(i_0_3363, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk257_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3)))=X2|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)),esk255_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))))). 7.02/7.30 cnf(i_0_3367, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk255_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk254_3(X1,X2,X3)))=X2|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk257_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))))). 7.02/7.30 cnf(i_0_7398, 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)))). 7.02/7.30 cnf(i_0_1489, plain, (esk123_3(X1,X2,X3)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(X1,esk123_3(X1,X2,X3)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,esk122_3(X1,X2,X3),esk123_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))))). 7.02/7.30 cnf(i_0_2090, 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))=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)))). 7.02/7.30 cnf(i_0_6760, 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))). 7.02/7.30 cnf(i_0_4574, 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))|X3=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|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)!=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)))). 7.02/7.30 cnf(i_0_5995, 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))))). 7.02/7.30 cnf(i_0_1047, 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))))). 7.02/7.30 cnf(i_0_2104, 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))))). 7.02/7.30 cnf(i_0_7343, 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))))). 7.02/7.30 cnf(i_0_7174, 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)))). 7.02/7.30 cnf(i_0_3253, 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))))). 7.02/7.30 cnf(i_0_4425, plain, (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|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5)|~class_Rings_Oring(X1))). 7.02/7.30 cnf(i_0_1827, plain, (hAPP(hAPP(c_List_Oappend(X1),esk151_4(X2,X3,X4,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),esk150_4(X2,X3,X4,X1)),esk152_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))))). 7.02/7.30 cnf(i_0_1581, 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))))). 7.02/7.30 cnf(i_0_6486, 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))). 7.02/7.30 cnf(i_0_1828, plain, (hAPP(hAPP(c_List_Oappend(X1),esk151_4(X2,X3,X4,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),esk149_4(X2,X3,X4,X1)),esk152_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))))). 7.02/7.30 cnf(i_0_2851, 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))))). 7.02/7.30 cnf(i_0_4854, plain, (X1=X2|hAPP(c_List_Oset(X3),X1)!=hAPP(c_List_Oset(X3),X2)|~c_Fun_Oinj__on(X3,X4,X5,hAPP(c_List_Oset(X3),hAPP(hAPP(c_List_Oappend(X3),X1),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))|~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))))). 7.02/7.30 cnf(i_0_397, 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)))). 7.02/7.30 cnf(i_0_7420, 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)))). 7.02/7.30 cnf(i_0_3623, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk274_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk273_3(X1,X2,X3)))=X2|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk276_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1))))). 7.02/7.30 cnf(i_0_3615, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk276_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk275_3(X1,X2,X3)))=X2|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1))))). 7.02/7.30 cnf(i_0_1477, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk118_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk119_2(X1,X2)))))|hBOOL(hAPP(X1,esk120_2(X1,X2)))|hBOOL(hAPP(X1,esk118_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)))). 7.02/7.30 cnf(i_0_5610, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),hAPP(hAPP(X3,X4),X5)),X6)=hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X5),hAPP(hAPP(c_Set_Oinsert(X1),X4),X6))|hBOOL(hAPP(hAPP(c_member(X1),X4),X6))|~c_Finite__Set_Ofun__left__comm(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 7.02/7.30 cnf(i_0_428, 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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))))). 7.02/7.30 cnf(i_0_2440, plain, (c_Relation_Orefl__on(X1,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(tc_prod(X1,X1),tc_HOL_Obool)),X3),X5))|~c_Relation_Orefl__on(X1,hAPP(X4,esk195_5(X5,X4,X1,X3,X2)),hAPP(X5,esk195_5(X5,X4,X1,X3,X2))))). 7.02/7.30 cnf(i_0_2489, 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))))). 7.02/7.30 cnf(i_0_3711, 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)))). 7.02/7.30 cnf(i_0_4337, 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))). 7.02/7.30 cnf(i_0_4859, 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,esk375_5(X5,X4,X1,X3,X2)),hAPP(X5,esk375_5(X5,X4,X1,X3,X2))))). 7.02/7.30 cnf(i_0_4842, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X4),X5))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))|~class_Divides_Osemiring__div(X1)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X5),X4))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X2)))). 7.02/7.30 cnf(i_0_241, 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)),esk22_3(X3,X2,X1)),esk23_3(X3,X2,X1))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(c_Finite__Set_Ocard(X1),esk21_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))))). 7.02/7.30 cnf(i_0_3843, 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)))). 7.02/7.30 cnf(i_0_6905, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk543_4(X1,X2,X3,X4)),esk542_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)))). 7.02/7.30 cnf(i_0_7191, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk556_4(X1,X2,X3,X4)),esk555_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)))). 7.02/7.30 cnf(i_0_7410, 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))). 7.02/7.30 cnf(i_0_3991, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk302_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)))))). 7.02/7.30 cnf(i_0_4407, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk330_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)))))). 7.02/7.30 cnf(i_0_4094, 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))). 7.02/7.30 cnf(i_0_5239, 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))))). 7.02/7.30 cnf(i_0_6973, 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))))). 7.02/7.30 cnf(i_0_3622, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk274_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk273_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk276_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.02/7.30 cnf(i_0_3614, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk276_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk275_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk274_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.02/7.30 cnf(i_0_3802, 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))). 7.02/7.30 cnf(i_0_2988, 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))))). 7.02/7.30 cnf(i_0_5747, 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))))))). 7.02/7.30 cnf(i_0_2462, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X3))),hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X3)))))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~c_Orderings_Oorder__class_Omono(X1,X1,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Inductive_Ocomplete__lattice__class_Ogfp(X1,X3))))))). 7.02/7.30 cnf(i_0_904, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X2),c_Big__Operators_Olattice_OSup__fin(X2,c_Orderings_Oord__class_Omax(X2),X1)),X1))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(hAPP(c_member(X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),esk75_2(X1,X2)),esk76_2(X1,X2))),hAPP(hAPP(c_Set_Oinsert(X2),esk75_2(X1,X2)),hAPP(hAPP(c_Set_Oinsert(X2),esk76_2(X1,X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 7.02/7.30 cnf(i_0_579, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|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)))))). 7.02/7.30 cnf(i_0_4399, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))=X2|X2=c_Groups_Oone__class_Oone(X1)|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),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))). 7.02/7.30 cnf(i_0_4377, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6)))|~class_Rings_Ocomm__ring(X1)|~class_Rings_Odvd(X1)|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X6)))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X5)))). 7.02/7.30 cnf(i_0_5499, 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)))). 7.02/7.30 cnf(i_0_2436, 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),esk192_2(X2,X1)),esk193_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk192_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk193_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 7.02/7.30 cnf(i_0_2834, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk218_6(X3,X4,X2,X5,X6,X1)),esk219_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))))). 7.02/7.30 cnf(i_0_2833, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk219_6(X3,X4,X1,X5,X2,X6)),esk220_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))))). 7.02/7.30 cnf(i_0_7215, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk559_4(X2,X3,X4,X1)),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk558_4(X2,X3,X4,X1)),X4))|~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)))). 7.02/7.30 cnf(i_0_6725, 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))). 7.02/7.30 cnf(i_0_5113, 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))). 7.02/7.30 cnf(i_0_4936, 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)))). 7.02/7.30 cnf(i_0_6907, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk542_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)))). 7.02/7.30 cnf(i_0_274, 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)))). 7.02/7.30 cnf(i_0_7299, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X2),X1)),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),X2),X6)),hAPP(hAPP(c_Product__Type_OPair(X3,X5),X1),X7))),c_Wellfounded_Olex__prod(X3,X5,X4,X8))))). 7.02/7.30 cnf(i_0_804, 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)))). 7.02/7.30 cnf(i_0_92, 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)))). 7.02/7.30 cnf(i_0_7193, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk555_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)))). 7.02/7.30 cnf(i_0_1579, 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))). 7.02/7.30 cnf(i_0_3207, 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))). 7.02/7.30 cnf(i_0_1451, 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))). 7.02/7.30 cnf(i_0_5519, 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))))))). 7.02/7.30 cnf(i_0_3442, 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))). 7.02/7.30 cnf(i_0_2959, 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))))). 7.02/7.30 cnf(i_0_4308, 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))))). 7.02/7.30 cnf(i_0_3635, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk276_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk275_3(X1,X2,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)),esk274_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1))))). 7.02/7.30 cnf(i_0_6899, 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(X6,esk541_7(X4,X3,X1,X6,X7,X5,X2))!=X7|~c_Finite__Set_Ofolding__image__simple(X8,X2,X5,X7,X6,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 7.02/7.30 cnf(i_0_3627, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk274_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk273_3(X1,X2,X3)))=X2|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1))))). 7.02/7.30 cnf(i_0_7515, 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))). 7.02/7.30 cnf(i_0_616, plain, (hBOOL(hAPP(hAPP(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk48_3(X1,X2,X3))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk49_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),esk49_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.02/7.30 cnf(i_0_3483, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk265_4(X1,X2,X3,X4)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),esk264_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)))). 7.02/7.30 cnf(i_0_3479, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk264_4(X1,X2,X3,X4)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),esk265_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)))). 7.02/7.30 cnf(i_0_3634, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk276_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk275_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk274_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.02/7.30 cnf(i_0_6305, 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))). 7.02/7.30 cnf(i_0_5591, 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)))))). 7.02/7.30 cnf(i_0_3626, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk274_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk273_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk276_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.02/7.30 cnf(i_0_2627, 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),esk209_8(X3,X6,X5,X5,X4,X4,X1,X2)))|~class_Orderings_Oord(X1)|~class_Groups_Ocomm__monoid__add(X2))). 7.02/7.30 cnf(i_0_2626, 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),esk209_8(X3,X6,X5,X5,X4,X4,X1,X2)),X5))|~class_Orderings_Oord(X1)|~class_Groups_Ocomm__monoid__add(X2))). 7.02/7.30 cnf(i_0_5741, 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))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(X2,esk441_3(X3,X2,X1))),hAPP(X2,esk442_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),esk441_3(X3,X2,X1)),esk442_3(X3,X2,X1)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.02/7.30 cnf(i_0_3784, 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))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(X2,esk281_3(X3,X2,X1))),hAPP(X2,esk282_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),esk281_3(X3,X2,X1)),esk282_3(X3,X2,X1)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.02/7.30 cnf(i_0_681, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk58_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,esk57_3(X1,X2,X3)))),hAPP(X2,esk57_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))))). 7.02/7.30 cnf(i_0_1563, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk128_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,esk127_3(X1,X2,X3)))),hAPP(X2,esk127_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))))). 7.02/7.30 cnf(i_0_5244, 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)))). 7.02/7.30 cnf(i_0_4931, 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))))). 7.02/7.30 cnf(i_0_4346, 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)))). 7.02/7.30 cnf(i_0_4331, 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)))). 7.02/7.30 cnf(i_0_3151, plain, (c_List_Olist__all2(X1,X2,X3,X4,X5)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),esk240_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))). 7.02/7.30 cnf(i_0_3758, plain, (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)))=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)))|~class_Rings_Ocomm__semiring__1(X1))). 7.02/7.30 cnf(i_0_6575, plain, (c_List_Olist__all2(X1,X2,X3,X4,X5)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),esk514_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))). 7.02/7.30 cnf(i_0_5056, 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))))). 7.02/7.30 cnf(i_0_688, 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)))). 7.02/7.30 cnf(i_0_590, 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)))). 7.02/7.30 cnf(i_0_3554, 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)))). 7.02/7.30 cnf(i_0_4866, 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))). 7.02/7.30 cnf(i_0_5266, 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_Enum_Oenum(X1)|~class_Orderings_Oorder(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X3),X4)))). 7.02/7.30 cnf(i_0_7336, 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),esk577_5(X5,X3,X4,X2,X1)),X4))|~class_Groups_Oordered__ab__semigroup__add(X1)|~class_Rings_Osemiring__1(X1))). 7.02/7.30 cnf(i_0_2856, 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)),X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))|hAPP(hAPP(c_List_Oappend(X2),X3),X1)!=hAPP(hAPP(c_List_Oappend(X2),X4),X5))). 7.02/7.30 cnf(i_0_2993, 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))|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)))). 7.02/7.30 cnf(i_0_7310, 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)|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(X4,esk572_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)))|~c_Equiv__Relations_Oequiv(X2,X7,X6))). 7.02/7.30 cnf(i_0_1958, 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)))). 7.02/7.30 cnf(i_0_3852, 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)),esk287_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|esk289_2(X2,X1)!=esk288_2(X2,X1)|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)))). 7.02/7.30 cnf(i_0_1601, 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)))). 7.02/7.30 cnf(i_0_3262, plain, (hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk250_3(X1,X2,X3)),c_Int_OMin)),esk251_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),esk250_3(X1,X2,X3)),esk251_3(X1,X2,X3))))). 7.02/7.30 cnf(i_0_252, 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)))). 7.02/7.30 cnf(i_0_1085, 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),esk86_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)))). 7.02/7.30 cnf(i_0_2287, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|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(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),esk179_2(X2,X1)),esk180_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk179_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk180_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 7.02/7.30 cnf(i_0_6715, 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)),X3)),X4)=hAPP(c_Finite__Set_Ocard(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),hAPP(X3,esk525_4(X3,X2,X4,X1))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 7.02/7.30 cnf(i_0_4504, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|~c_Relation_Otrans(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)))). 7.02/7.30 cnf(i_0_4401, 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),esk328_4(X3,X2,X4,X1)),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 7.02/7.30 cnf(i_0_5568, 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),esk424_4(X3,X2,X4,X1)),X4))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 7.02/7.30 cnf(i_0_4619, 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),esk354_4(X2,X4,X3,X1)),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.02/7.30 cnf(i_0_4901, 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),esk376_4(X2,X4,X3,X1)),X3))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.02/7.30 cnf(i_0_1590, 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),esk129_7(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,X5)),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X2,X4)))). 7.02/7.30 cnf(i_0_2724, 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))|esk215_6(X3,X4,X5,X6,X1,X2)!=esk214_6(X3,X4,X5,X6,X1,X2)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 7.02/7.30 cnf(i_0_218, 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(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X3),X4)!=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))|~c_Finite__Set_Ofolding__image__simple(X6,X5,X1,X7,X8,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3)))). 7.02/7.30 cnf(i_0_2885, 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)))). 7.02/7.30 cnf(i_0_2872, 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,X3)!=hAPP(X4,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,X5))))). 7.02/7.30 cnf(i_0_3552, 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)))). 7.02/7.30 cnf(i_0_6538, 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)),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_Oorder__class_Omono(tc_fun(X5,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2))). 7.02/7.30 cnf(i_0_2884, 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)))). 7.02/7.30 cnf(i_0_1676, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk140_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)))). 7.02/7.30 cnf(i_0_5376, 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,esk411_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)))). 7.02/7.30 cnf(i_0_7289, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),X5))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,X4)),hAPP(X2,X5))))|~c_Orderings_Oorder__class_Omono(tc_fun(X3,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2))). 7.02/7.30 cnf(i_0_1773, 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),esk148_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)))). 7.02/7.30 cnf(i_0_5040, 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)))). 7.02/7.30 cnf(i_0_2588, 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)),esk206_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)))). 7.02/7.30 cnf(i_0_366, 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)))). 7.02/7.30 cnf(i_0_3478, plain, (hAPP(X1,esk265_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,esk264_4(X2,X1,X3,X4)))),hAPP(X1,esk264_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)))). 7.02/7.30 cnf(i_0_6384, 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))))). 7.02/7.30 cnf(i_0_5440, 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)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X6))|~c_Equiv__Relations_Oequiv(X1,X6,X3))). 7.02/7.30 cnf(i_0_2587, 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)),esk207_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)))). 7.02/7.30 cnf(i_0_6030, 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))). 7.02/7.30 cnf(i_0_4069, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk308_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))))). 7.02/7.30 cnf(i_0_5392, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk413_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))))). 7.02/7.30 cnf(i_0_2961, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk225_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))))). 7.02/7.30 cnf(i_0_6122, 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)))). 7.02/7.30 cnf(i_0_5657, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1))),c_Int_OMin)),X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 7.02/7.30 cnf(i_0_2095, 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,esk163_4(X2,X3,X4,X1)),esk164_4(X2,X3,X4,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk163_4(X2,X3,X4,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk164_4(X2,X3,X4,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 7.02/7.30 cnf(i_0_4856, 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)))). 7.02/7.30 cnf(i_0_4406, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk330_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)))))). 7.02/7.30 cnf(i_0_3990, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk302_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)))))). 7.02/7.30 cnf(i_0_4390, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))),c_Int_OMin)),X3))),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 7.02/7.30 cnf(i_0_4424, 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))). 7.02/7.30 cnf(i_0_2722, 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))|hAPP(X4,hAPP(X5,esk214_6(X3,X4,X5,X6,X1,X2)))!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 7.02/7.30 cnf(i_0_6143, 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)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X5),X6)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(X4,esk484_6(X6,X4,X1,X5,X3,X2))),hAPP(X6,esk484_6(X6,X4,X1,X5,X3,X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X3),X5)))). 7.02/7.30 cnf(i_0_4820, 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(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(X4,esk371_6(X5,X4,X1,X3,X6,X2))),hAPP(X5,esk371_6(X5,X4,X1,X3,X6,X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X6),X3)))). 7.02/7.30 cnf(i_0_3424, 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,esk258_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)))). 7.02/7.30 cnf(i_0_5393, 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)))). 7.02/7.30 cnf(i_0_7421, 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)))). 7.02/7.30 cnf(i_0_246, 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)),esk21_3(X3,X2,X1)),X2))|esk23_3(X3,X2,X1)!=esk22_3(X3,X2,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))))). 7.02/7.30 cnf(i_0_2331, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),esk185_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))))). 7.02/7.30 cnf(i_0_320, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),esk28_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))))). 7.02/7.30 cnf(i_0_652, 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,esk52_6(X4,X3,X6,X5,X2,X1))!=hAPP(X6,esk52_6(X4,X3,X6,X5,X2,X1))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 7.02/7.30 cnf(i_0_2822, 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)))). 7.02/7.30 cnf(i_0_6718, 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)),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))))). 7.02/7.30 cnf(i_0_2140, 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)))). 7.02/7.30 cnf(i_0_6207, 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))). 7.02/7.30 cnf(i_0_2776, 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))). 7.02/7.30 cnf(i_0_2728, 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))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 7.02/7.30 cnf(i_0_4805, 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(X1),X5),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)))))))|~c_Equiv__Relations_Oequiv(X1,X6,X4))). 7.02/7.30 cnf(i_0_7335, 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,esk577_5(X5,X3,X4,X2,X1))),X5)))). 7.02/7.30 cnf(i_0_2054, plain, (X1=X2|~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),X1))|~hBOOL(hAPP(hAPP(c_member(X3),X6),X2))|~c_Equiv__Relations_Oequiv(X3,X4,X5))). 7.02/7.30 cnf(i_0_3850, 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)),esk288_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),esk287_2(X2,X1)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)))). 7.02/7.30 cnf(i_0_3849, 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)),esk289_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),esk287_2(X2,X1)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)))). 7.02/7.30 cnf(i_0_1625, 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),X3)))=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)))|~class_Int_Onumber__ring(X1))). 7.02/7.30 cnf(i_0_6827, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk535_4(X2,X3,X4,X1)),X4))|hBOOL(hAPP(hAPP(c_member(X1),esk534_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))))). 7.02/7.30 cnf(i_0_4794, plain, (hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk370_3(X2,X1,X3)),X4))=hAPP(X1,esk370_3(X2,X1,X3))|~c_Wellfounded_Owf(X3,hAPP(hAPP(c_Relation_Orel__comp(X3,X3,X3),X2),c_Transitive__Closure_Ortrancl(X3,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),hAPP(X1,hAPP(c_Nat_OSuc,esk369_3(X2,X1,X3)))),hAPP(X1,esk369_3(X2,X1,X3)))),c_Transitive__Closure_Ortrancl(X3,X2))))). 7.02/7.30 cnf(i_0_6027, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),hAPP(X3,esk470_8(X4,X5,X3,X6,X7,X8,X2,X1))),hAPP(X5,esk471_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))))). 7.02/7.30 cnf(i_0_3994, 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))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X2,esk303_3(X3,X2,X1))),hAPP(X2,esk304_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),esk303_3(X3,X2,X1)),esk304_3(X3,X2,X1)))|~class_Lattices_Oab__semigroup__idem__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.02/7.30 cnf(i_0_1638, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk136_4(X1,X2,X3,X4)),esk135_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)))). 7.02/7.30 cnf(i_0_4510, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk345_4(X1,X2,X3,X4)),esk344_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_Ominus__class_Ominus(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),X4),X2)))). 7.02/7.30 cnf(i_0_5545, 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))))). 7.02/7.30 cnf(i_0_1162, 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(X2)),X6)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X5)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))). 7.02/7.30 cnf(i_0_3851, 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)),esk287_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),esk288_2(X2,X1))),hAPP(c_List_Oset(X1),esk289_2(X2,X1)))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)))). 7.02/7.30 cnf(i_0_1421, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk112_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))))). 7.02/7.30 cnf(i_0_327, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk30_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))))). 7.02/7.30 cnf(i_0_6239, 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)))). 7.02/7.30 cnf(i_0_3001, 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)))). 7.02/7.30 cnf(i_0_3311, 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)))). 7.02/7.30 cnf(i_0_2455, 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))))). 7.02/7.30 cnf(i_0_2316, 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),esk183_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)))). 7.02/7.30 cnf(i_0_264, 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)))). 7.02/7.30 cnf(i_0_3269, 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)))). 7.02/7.30 cnf(i_0_6056, 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)))). 7.02/7.30 cnf(i_0_6197, 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)))). 7.02/7.30 cnf(i_0_4155, 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),esk316_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)))). 7.02/7.30 cnf(i_0_4754, 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),esk367_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)))). 7.02/7.30 cnf(i_0_6687, 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),esk524_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)))). 7.02/7.30 cnf(i_0_1640, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk135_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)))). 7.02/7.30 cnf(i_0_3024, 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)))). 7.02/7.30 cnf(i_0_4512, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk344_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_Ominus__class_Ominus(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),X4),X2)))). 7.02/7.30 cnf(i_0_4429, 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)))). 7.02/7.30 cnf(i_0_3667, 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)))). 7.02/7.30 cnf(i_0_1608, 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)))). 7.02/7.30 cnf(i_0_3694, 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)))). 7.02/7.30 cnf(i_0_4764, 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)))). 7.02/7.30 cnf(i_0_537, 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)))). 7.02/7.30 cnf(i_0_5317, 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)))). 7.02/7.30 cnf(i_0_3967, 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))|X2=c_Groups_Oone__class_Oone(X1)|~class_Fields_Ofield(X1))). 7.02/7.30 cnf(i_0_3343, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk257_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3)))=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk255_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk254_3(X1,X2,X3)))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 7.02/7.30 cnf(i_0_5404, 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_Rings_Oring(X2)|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 7.02/7.30 cnf(i_0_268, 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_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))|~c_Equiv__Relations_Oequiv(X1,X5,X4))). 7.02/7.30 cnf(i_0_2334, 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),esk185_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))))). 7.02/7.30 cnf(i_0_323, 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),esk28_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))))). 7.02/7.30 cnf(i_0_3803, 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))))))). 7.02/7.30 cnf(i_0_3368, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk257_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk256_3(X1,X2,X3)))=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk255_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk254_3(X1,X2,X3)))=X2|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))))). 7.02/7.30 cnf(i_0_5500, 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)))). 7.02/7.30 cnf(i_0_4403, 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,esk329_5(X4,X3,X5,X2,X1)))),hAPP(X2,esk329_5(X4,X3,X5,X2,X1)))),c_Transitive__Closure_Ortrancl(X1,X5))))). 7.02/7.30 cnf(i_0_7418, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X2),X1)),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),X2),c_List_Olist_ONil(X3)))),hAPP(hAPP(c_List_Oappend(X3),X6),hAPP(hAPP(c_List_Olist_OCons(X3),X1),c_List_Olist_ONil(X3))))),c_List_Olistrel1(X3,X4))))). 7.02/7.30 cnf(i_0_1039, 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,esk85_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)))). 7.02/7.30 cnf(i_0_2076, 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,esk161_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)))). 7.02/7.30 cnf(i_0_659, 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)))). 7.02/7.30 cnf(i_0_3709, 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_SetInterval_Oord__class_OatLeastLessThan(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))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)))). 7.02/7.30 cnf(i_0_4265, 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)))). 7.02/7.30 cnf(i_0_658, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk53_5(X2,X3,X4,X1,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),X4))),hAPP(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),X4)),X2))))|hBOOL(hAPP(X2,X3))|~c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X4)|~hBOOL(hAPP(hAPP(c_member(X1),X3),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),X4))))). 7.02/7.30 cnf(i_0_2114, 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,esk166_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)))). 7.02/7.30 cnf(i_0_7056, 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,esk547_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)))). 7.02/7.30 cnf(i_0_7117, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(X3),esk550_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)|~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))). 7.02/7.30 cnf(i_0_7116, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(X3),esk551_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)|~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))). 7.02/7.30 cnf(i_0_5837, 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))))). 7.02/7.30 cnf(i_0_5394, 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)))). 7.02/7.30 cnf(i_0_273, 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_Rings_Oinverse__class_Odivide(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),X4)),hAPP(X3,X5))|hAPP(X3,X5)=c_Groups_Ozero__class_Ozero(X2)|~class_Fields_Ofield(X2)|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 7.02/7.30 cnf(i_0_5636, 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))))). 7.02/7.30 cnf(i_0_3015, 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,esk230_4(X4,X2,X3,X1))))). 7.02/7.30 cnf(i_0_5532, 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),esk421_4(X4,X3,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X3),esk421_4(X4,X3,X2,X1)))),X4)))). 7.02/7.30 cnf(i_0_1154, 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))))). 7.02/7.30 cnf(i_0_6053, 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),esk476_5(X3,X4,X5,X2,X1)),hAPP(c_List_Oset(X2),X5)))|~class_Groups_Omonoid__add(X1))). 7.02/7.30 cnf(i_0_7114, 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)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),esk550_7(X1,X2,X5,X4,X6,X7,X3)),esk551_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)))|~c_Equiv__Relations_Oequiv(X3,X7,X6))). 7.02/7.30 cnf(i_0_5651, 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))). 7.02/7.30 cnf(i_0_3476, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk265_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,esk264_4(X2,X3,X4,X1)))),hAPP(X3,esk264_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)))). 7.02/7.30 cnf(i_0_3477, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk265_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,esk264_4(X1,X2,X3,X4)))),hAPP(X2,esk264_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)))). 7.02/7.30 cnf(i_0_244, 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)),esk22_3(X3,X2,X1)),X2))|hAPP(c_Finite__Set_Ocard(X1),esk21_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))))). 7.02/7.30 cnf(i_0_243, 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)),esk23_3(X3,X2,X1)),X2))|hAPP(c_Finite__Set_Ocard(X1),esk21_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))))). 7.02/7.30 cnf(i_0_7386, 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)))). 7.02/7.30 cnf(i_0_7476, 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))))). 7.02/7.30 cnf(i_0_2625, 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,esk209_8(X6,X3,X5,X5,X4,X4,X1,X2))!=hAPP(X6,esk209_8(X6,X3,X5,X5,X4,X4,X1,X2))|~class_Orderings_Oord(X1)|~class_Groups_Ocomm__monoid__add(X2))). 7.02/7.30 cnf(i_0_5181, 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),esk400_4(X3,X4,X2,X1))),esk399_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))))). 7.02/7.30 cnf(i_0_2882, 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))))). 7.02/7.30 cnf(i_0_5958, 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)|esk466_4(X3,X4,X1,X2)!=esk465_4(X3,X4,X1,X2)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk464_4(X3,X4,X1,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X4)))). 7.02/7.30 cnf(i_0_1799, 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))))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~c_Equiv__Relations_Oequiv(X1,X5,X4))). 7.02/7.30 cnf(i_0_6645, 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)),X5)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),X6)),X5)|hAPP(X4,esk517_6(X3,X2,X6,X4,X5,X1))!=hAPP(X6,esk517_6(X3,X2,X6,X4,X5,X1)))). 7.02/7.30 cnf(i_0_920, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk79_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)))). 7.02/7.30 cnf(i_0_7368, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X4,X5),tc_prod(X4,X5))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X4,X5),tc_prod(X4,X5)),hAPP(hAPP(c_Product__Type_OPair(X4,X5),X2),X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X5),X6),X7))),c_Transitive__Closure_Ortrancl(tc_prod(X4,X5),X8)))|~hBOOL(hAPP(hAPP(X1,esk579_8(X1,X8,X7,X6,X3,X2,X5,X4)),esk580_8(X1,X8,X7,X6,X3,X2,X5,X4)))|~hBOOL(hAPP(hAPP(X1,X6),X7)))). 7.02/7.30 cnf(i_0_2265, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X4,X5),tc_prod(X4,X5))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X4,X5),tc_prod(X4,X5)),hAPP(hAPP(c_Product__Type_OPair(X4,X5),X6),X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X5),X2),X3))),c_Transitive__Closure_Ortrancl(tc_prod(X4,X5),X8)))|~hBOOL(hAPP(hAPP(X1,esk175_8(X1,X8,X3,X2,X7,X6,X5,X4)),esk176_8(X1,X8,X3,X2,X7,X6,X5,X4)))|~hBOOL(hAPP(hAPP(X1,X6),X7)))). 7.02/7.30 cnf(i_0_741, 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))). 7.02/7.30 cnf(i_0_3625, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk274_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk273_3(X1,X2,X3)))=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk276_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk275_3(X1,X2,X3)))=X2|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1))))). 7.02/7.30 cnf(i_0_6346, plain, (hBOOL(hAPP(hAPP(X1,esk497_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk498_3(X1,X2,X3)),c_Int_OMin)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk497_3(X1,X2,X3)),esk498_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))))). 7.02/7.30 cnf(i_0_1478, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk118_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk119_2(X1,X2)))))|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk120_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|hBOOL(hAPP(X1,esk118_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)))). 7.02/7.30 cnf(i_0_6648, 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))). 7.02/7.30 cnf(i_0_5052, 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))). 7.02/7.30 cnf(i_0_5237, 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))). 7.02/7.30 cnf(i_0_2870, 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)))))). 7.02/7.30 cnf(i_0_4932, 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)))). 7.02/7.30 cnf(i_0_1420, 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),esk113_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))))). 7.02/7.30 cnf(i_0_7264, 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)))))). 7.02/7.30 cnf(i_0_2850, 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)). 7.02/7.30 cnf(i_0_785, 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))))). 7.02/7.30 cnf(i_0_326, 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)),esk31_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))))). 7.02/7.30 cnf(i_0_2535, 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))). 7.02/7.30 cnf(i_0_2965, 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))). 7.02/7.30 cnf(i_0_4398, 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))). 7.02/7.30 cnf(i_0_6931, 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)))). 7.02/7.30 cnf(i_0_7290, 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))))). 7.02/7.30 cnf(i_0_245, 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)),esk21_3(X3,X2,X1)),X2))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),esk22_3(X3,X2,X1)),esk23_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))))). 7.02/7.30 cnf(i_0_7019, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),hAPP(c_Fun_Ocomp(X3,X1,X2,X4),X5)),X6),X7)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X3,c_Groups_Otimes__class_Otimes(X1)),X4),X6),hAPP(c_Set_Oimage(X2,X3,X5),X7))|~class_Groups_Oab__semigroup__mult(X1)|~c_Fun_Oinj__on(X2,X3,X5,X7)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7)))). 7.02/7.30 cnf(i_0_3624, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk274_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk273_3(X1,X2,X3)))=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk276_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk275_3(X1,X2,X3)))=X2|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.02/7.30 cnf(i_0_1678, 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)))). 7.02/7.30 cnf(i_0_1832, 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)))). 7.02/7.30 cnf(i_0_6927, 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)),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))). 7.02/7.30 cnf(i_0_2297, 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)))). 7.02/7.30 cnf(i_0_3804, plain, (hAPP(c_Fun_Ocomp(X1,X2,X3,c_Hilbert__Choice_Oinv__into(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X4)),c_Hilbert__Choice_Oinv__into(X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X5))=c_Hilbert__Choice_Oinv__into(X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(X1,X3,X2,X5),X4))|~c_Fun_Obij__betw(X2,X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~c_Fun_Obij__betw(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))))). 7.02/7.30 cnf(i_0_5955, 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,esk467_4(X3,X4,X1,X2))!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk464_4(X3,X4,X1,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X4)))). 7.02/7.30 cnf(i_0_5994, 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))))). 7.02/7.30 cnf(i_0_1046, 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))))). 7.02/7.30 cnf(i_0_5556, 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))). 7.02/7.30 cnf(i_0_6074, 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)))). 7.02/7.30 cnf(i_0_2103, 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)))). 7.02/7.30 cnf(i_0_7344, 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)))). 7.02/7.30 cnf(i_0_2337, 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,esk187_4(X4,X3,X2,X1))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Oimage(X1,X3,X4),X2))))). 7.02/7.30 cnf(i_0_2962, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk225_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))))). 7.02/7.30 cnf(i_0_757, 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)))). 7.02/7.30 cnf(i_0_7187, 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)))). 7.02/7.30 cnf(i_0_6969, 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)=X5|X3=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield(X1))). 7.02/7.30 cnf(i_0_4068, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk308_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))))). 7.02/7.30 cnf(i_0_5391, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk413_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))))). 7.02/7.30 cnf(i_0_7333, 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,esk576_5(X5,X3,X4,X2,X1))),hAPP(X5,esk576_5(X5,X3,X4,X2,X1)))))). 7.02/7.30 cnf(i_0_5557, 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)))). 7.02/7.30 cnf(i_0_3561, 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)))). 7.02/7.30 cnf(i_0_653, 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),esk52_6(X4,X3,X6,X5,X2,X1)),X5))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 7.02/7.30 cnf(i_0_6314, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk494_4(X2,X3,X4,X1)),hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),X3)),X2))))|hBOOL(hAPP(X2,X4))|~c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3)|~hBOOL(hAPP(hAPP(c_member(X1),X4),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),X3))))). 7.02/7.30 cnf(i_0_6716, 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)),X3)),X4)=hAPP(c_Finite__Set_Ocard(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk525_4(X3,X2,X4,X1)),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 7.02/7.30 cnf(i_0_5078, 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)=X5|c_Groups_Ozero__class_Ozero(X1)=X3|~class_Fields_Ofield(X1))). 7.02/7.30 cnf(i_0_621, 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)))). 7.02/7.30 cnf(i_0_2593, 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)))). 7.02/7.30 cnf(i_0_6220, 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)))). 7.02/7.30 cnf(i_0_3663, 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)))). 7.02/7.30 cnf(i_0_893, 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)))). 7.02/7.30 cnf(i_0_1414, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X3),X4),X1)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X3),X5),X1)))|hBOOL(hAPP(hAPP(c_member(X2),esk111_5(X5,X4,X1,X2,X3)),X1))|~class_Groups_Oordered__cancel__ab__semigroup__add(X3)|~class_Groups_Ocomm__monoid__add(X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 7.02/7.30 cnf(i_0_1635, plain, (hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),hAPP(c_Hilbert__Choice_Oinv__into(X2,X5,hAPP(c_Set_Oimage(X1,X2,X4),X3),X6),X7))=hAPP(c_Hilbert__Choice_Oinv__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)))))). 7.02/7.30 cnf(i_0_392, 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)))))). 7.02/7.30 cnf(i_0_4310, 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)))). 7.02/7.30 cnf(i_0_1820, 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)))). 7.02/7.30 cnf(i_0_5763, 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)))). 7.02/7.30 cnf(i_0_1875, 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))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3)). 7.02/7.30 cnf(i_0_2849, 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)). 7.02/7.30 cnf(i_0_5957, 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),esk467_4(X3,X4,X1,X2)),esk465_4(X3,X4,X1,X2)))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk464_4(X3,X4,X1,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X4)))). 7.02/7.30 cnf(i_0_5956, 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),esk467_4(X3,X4,X1,X2)),esk466_4(X3,X4,X1,X2)))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk464_4(X3,X4,X1,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X4)))). 7.02/7.30 cnf(i_0_5953, 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))))),esk463_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)))). 7.02/7.30 cnf(i_0_872, 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)))). 7.02/7.30 cnf(i_0_1377, 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,esk108_5(X5,X3,X4,X2,X1))))). 7.02/7.30 cnf(i_0_1723, 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)))). 7.02/7.30 cnf(i_0_74, 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)))). 7.02/7.30 cnf(i_0_6152, 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))|X3=X2)). 7.02/7.30 cnf(i_0_5399, 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_Obij__betw(X4,X2,X5,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))). 7.02/7.30 cnf(i_0_2271, 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)))). 7.02/7.30 cnf(i_0_825, 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)))))). 7.02/7.30 cnf(i_0_2949, 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)))). 7.02/7.30 cnf(i_0_7088, 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)))). 7.02/7.30 cnf(i_0_2880, 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)))). 7.02/7.30 cnf(i_0_3046, 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)))). 7.02/7.30 cnf(i_0_1060, 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),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2))),c_List_Olex(X1,X6))))). 7.02/7.30 cnf(i_0_6242, 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)))). 7.02/7.30 cnf(i_0_2491, plain, (hAPP(hAPP(c_List_Otake(X1),esk202_4(X2,X3,X4,X1)),X4)=hAPP(hAPP(c_List_Otake(X1),esk202_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))))). 7.02/7.30 cnf(i_0_1476, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk118_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk119_2(X1,X2)))))|hBOOL(hAPP(X1,esk121_2(X1,X2)))|hBOOL(hAPP(X1,esk118_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)))). 7.02/7.30 cnf(i_0_222, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),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)))). 7.02/7.30 cnf(i_0_248, 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)),esk22_3(X3,X2,X1)),X2))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk21_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))))). 7.02/7.30 cnf(i_0_247, 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)),esk23_3(X3,X2,X1)),X2))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk21_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))))). 7.02/7.30 cnf(i_0_7415, 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))))). 7.02/7.30 cnf(i_0_1, 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))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))|~c_Equiv__Relations_Oequiv(X1,X5,X2))). 7.02/7.30 cnf(i_0_5286, 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)))). 7.02/7.30 cnf(i_0_1607, 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)))). 7.02/7.30 cnf(i_0_743, 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)))). 7.02/7.30 cnf(i_0_198, 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,esk15_6(X6,X4,X2,X5,X3,X1))),hAPP(X6,esk15_6(X6,X4,X2,X5,X3,X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X5)))). 7.02/7.30 cnf(i_0_7540, 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)))). 7.02/7.30 cnf(i_0_3693, 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)))). 7.02/7.30 cnf(i_0_4763, 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)))). 7.02/7.30 cnf(i_0_538, 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)))). 7.02/7.30 cnf(i_0_7557, 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)))). 7.02/7.30 cnf(i_0_5261, 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)))). 7.02/7.30 cnf(i_0_2527, 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)))). 7.02/7.30 cnf(i_0_1101, 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))))). 7.02/7.30 cnf(i_0_455, 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)))). 7.02/7.30 cnf(i_0_7120, 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)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict)))). 7.02/7.30 cnf(i_0_416, plain, (hAPP(c_Set_Oimage(X1,X2,c_Fun_Ofun__upd(X1,X2,X3,X4,X5)),X6)=hAPP(hAPP(c_Set_Oinsert(X2),X5),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X6),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X6)))). 7.02/7.30 cnf(i_0_199, 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),esk15_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)))). 7.02/7.30 cnf(i_0_4397, 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))). 7.02/7.30 cnf(i_0_4976, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),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)),X3))))|~c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),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)),X3))|~hBOOL(hAPP(hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),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)),X3)))),esk385_5(X4,X2,X3,X1,c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),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)),X3)))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 7.02/7.30 cnf(i_0_1056, 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),X2),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),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X4)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X5))|~c_Equiv__Relations_Oequiv(X1,X5,X4))). 7.02/7.30 cnf(i_0_2726, 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))|hBOOL(hAPP(hAPP(c_member(X1),esk214_6(X3,X4,X5,X6,X1,X2)),X6))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 7.02/7.30 cnf(i_0_2725, 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))|hBOOL(hAPP(hAPP(c_member(X1),esk215_6(X3,X4,X5,X6,X1,X2)),X6))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 7.02/7.30 cnf(i_0_2053, 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_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X6),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X5))|~c_Equiv__Relations_Oequiv(X1,X6,X4))). 7.02/7.30 cnf(i_0_2784, 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),X1),X4)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))). 7.02/7.30 cnf(i_0_5871, 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))))). 7.02/7.30 cnf(i_0_1196, 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))))). 7.02/7.30 cnf(i_0_2242, 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)))). 7.02/7.30 cnf(i_0_3016, 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),esk230_4(X4,X2,X3,X1)),hAPP(c_List_Oset(X1),X3))))). 7.02/7.30 cnf(i_0_2723, 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))|hAPP(X5,esk215_6(X3,X4,X5,X6,X1,X2))=hAPP(X5,esk214_6(X3,X4,X5,X6,X1,X2))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 7.02/7.30 cnf(i_0_7311, 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),esk572_7(X5,X3,X4,X1,X6,X7,X2)),X7))|~c_Equiv__Relations_Ocongruent(X2,tc_fun(X1,tc_HOL_Obool),X6,X4)|~hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X7),X6)))|~c_Equiv__Relations_Oequiv(X2,X7,X6))). 7.02/7.30 cnf(i_0_7300, 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))))). 7.02/7.30 cnf(i_0_4356, 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)))). 7.02/7.30 cnf(i_0_5533, 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),esk421_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))). 7.02/7.30 cnf(i_0_1001, 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)))). 7.02/7.30 cnf(i_0_1175, 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))). 7.02/7.30 cnf(i_0_7541, 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))). 7.02/7.30 cnf(i_0_587, 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)))). 7.02/7.30 cnf(i_0_7115, plain, (hAPP(X1,esk551_7(X2,X3,X1,X4,X5,X6,X7))=hAPP(X1,esk550_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)|~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)))|~c_Equiv__Relations_Oequiv(X7,X6,X5))). 7.02/7.30 cnf(i_0_4810, 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)))). 7.02/7.30 cnf(i_0_6881, 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)))). 7.02/7.30 cnf(i_0_6468, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),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)),c_Int_OMin)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)|~class_Int_Onumber__ring(X1))). 7.02/7.30 cnf(i_0_1099, 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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))),X2)|~class_Int_Onumber__ring(X1))). 7.02/7.30 cnf(i_0_3854, 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)),esk288_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk287_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)))). 7.02/7.30 cnf(i_0_3853, 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)),esk289_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk287_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)))). 7.02/7.30 cnf(i_0_1065, 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))))). 7.02/7.30 cnf(i_0_5182, 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))))). 7.02/7.30 cnf(i_0_6026, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk470_8(X3,X4,X5,X2,X1,X6,X7,X8)),esk471_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))))). 7.02/7.30 cnf(i_0_7412, 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))))). 7.02/7.30 cnf(i_0_1679, 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))))). 7.02/7.30 cnf(i_0_7411, 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))))). 7.02/7.30 cnf(i_0_5531, 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))))). 7.02/7.30 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_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)))))). 7.02/7.30 cnf(i_0_835, 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))))))). 7.02/7.30 cnf(i_0_1170, 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)))). 7.02/7.30 cnf(i_0_2061, 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)))). 7.02/7.30 cnf(i_0_4530, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),X4),hAPP(hAPP(c_Set_Oinsert(X2),X5),X6))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X3,X5)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),X4),X6))|hBOOL(hAPP(hAPP(c_member(X2),X5),X6))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6)))). 7.02/7.30 cnf(i_0_7334, 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),esk576_5(X5,X3,X4,X2,X1)),hAPP(c_List_Oset(X2),X4)))|~class_Groups_Omonoid__add(X1)|~class_Groups_Oordered__ab__semigroup__add(X1))). 7.02/7.30 cnf(i_0_5272, 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)))). 7.02/7.30 cnf(i_0_1837, 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))). 7.02/7.30 cnf(i_0_6060, 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)),esk478_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),esk478_4(X2,X4,X3,X1)))),X2))). 7.02/7.30 cnf(i_0_1146, 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)))). 7.02/7.30 cnf(i_0_402, 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))))). 7.02/7.30 cnf(i_0_482, 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)))). 7.02/7.30 cnf(i_0_2671, 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)))). 7.02/7.30 cnf(i_0_803, 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))))). 7.02/7.30 cnf(i_0_3394, 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)))). 7.02/7.30 cnf(i_0_3759, 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),X5),X4))=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)),X5)),X4)|~class_Groups_Ocomm__monoid__mult(X1))). 7.02/7.30 cnf(i_0_1681, 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))))). 7.02/7.30 cnf(i_0_6383, 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))))). 7.02/7.30 cnf(i_0_1061, 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))))). 7.02/7.30 cnf(i_0_1064, 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)),X5)!=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),X2),X4)),X6)))). 7.02/7.30 cnf(i_0_1145, 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),X5),X4))=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)),X5)),X4)|~class_Groups_Oab__group__add(X1))). 7.02/7.30 cnf(i_0_93, 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))))). 7.02/7.30 cnf(i_0_1378, 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,esk108_5(X5,X3,X4,X2,X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 7.02/7.30 cnf(i_0_4821, 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(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X5)))|hBOOL(hAPP(hAPP(c_member(X2),esk371_6(X5,X4,X1,X3,X6,X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X6),X3)))). 7.02/7.30 cnf(i_0_6144, 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)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X5),X6)))|hBOOL(hAPP(hAPP(c_member(X2),esk484_6(X6,X4,X1,X5,X3,X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X3),X5)))). 7.02/7.30 cnf(i_0_457, 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)))). 7.02/7.30 cnf(i_0_284, 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))). 7.02/7.30 cnf(i_0_2709, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|c_Nitpick_Ofold__graph_H(X2,X3,X4,X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(hAPP(c_Set_Oinsert(X2),esk212_7(X6,X7,X1,X5,X4,X3,X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),esk213_7(X6,X7,X1,X5,X4,X3,X2))|~c_Nitpick_Ofold__graph_H(X2,X3,X4,X5,X1,hAPP(hAPP(X4,X7),X6)))). 7.02/7.30 cnf(i_0_1577, 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))). 7.02/7.30 cnf(i_0_7327, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk575_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))). 7.02/7.30 cnf(i_0_4977, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk385_5(X2,X3,X4,X1,c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),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)),X4)))),X2))|hBOOL(hAPP(hAPP(c_member(X1),X3),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),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)),X4))))|~c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),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)),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2)))). 7.02/7.30 cnf(i_0_5368, 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)))). 7.02/7.30 cnf(i_0_2492, plain, (hAPP(hAPP(c_List_Otake(X1),esk202_4(X2,X3,X4,X1)),X4)=hAPP(hAPP(c_List_Otake(X1),esk202_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))))). 7.02/7.30 cnf(i_0_321, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),esk28_5(X4,X5,X2,X1,X3))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X3,X3),tc_HOL_Obool),esk29_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))))). 7.02/7.30 cnf(i_0_2330, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),esk185_5(X4,X5,X1,X2,X3)),X1)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X3,X3),tc_HOL_Obool),esk186_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))))). 7.02/7.30 cnf(i_0_6762, plain, (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),X3))),c_Groups_Oone__class_Oone(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),X4),X3)))|hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 7.02/7.30 cnf(i_0_1055, 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)))). 7.02/7.30 cnf(i_0_1338, 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)))). 7.02/7.30 cnf(i_0_2710, 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),esk212_7(X4,X3,X7,X1,X2,X6,X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),esk213_7(X4,X3,X7,X1,X2,X6,X5))|~c_Nitpick_Ofold__graph_H(X5,X6,X2,X1,X7,hAPP(hAPP(X2,X3),X4)))). 7.02/7.30 cnf(i_0_4573, 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),esk347_4(X1,X2,X4,X3)),esk348_4(X1,X2,X4,X3))),X4)))). 7.02/7.30 cnf(i_0_4571, 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),esk348_4(X1,X2,X4,X3)),esk347_4(X1,X2,X4,X3))),X4)))). 7.02/7.30 cnf(i_0_4678, 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)))). 7.02/7.30 cnf(i_0_4642, 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)))). 7.02/7.30 cnf(i_0_334, 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)))). 7.02/7.30 cnf(i_0_7332, 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)))). 7.02/7.30 cnf(i_0_3940, 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)))). 7.02/7.30 cnf(i_0_6282, 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)))). 7.02/7.30 cnf(i_0_6982, 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))))))). 7.02/7.30 cnf(i_0_3504, 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))))))). 7.02/7.30 cnf(i_0_2844, 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,esk221_8(X5,X8,X4,X3,X7,X1,X6,X2)))!=hAPP(c_Fun_Ocomp(X1,X1,X7,hAPP(X3,esk221_8(X5,X8,X4,X3,X7,X1,X6,X2))),X4))). 7.02/7.30 cnf(i_0_7248, 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)))). 7.02/7.30 cnf(i_0_7037, 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)))). 7.02/7.30 cnf(i_0_5963, 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),esk467_4(X3,X4,X1,X2)),esk465_4(X3,X4,X1,X2)))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk464_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)))). 7.02/7.30 cnf(i_0_5962, 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),esk467_4(X3,X4,X1,X2)),esk466_4(X3,X4,X1,X2)))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk464_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)))). 7.02/7.30 cnf(i_0_6469, 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)))). 7.02/7.30 cnf(i_0_7397, 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),X2)),X4)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X1)),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),X3),X2)),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6))|~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),X4),X3)))). 7.02/7.30 cnf(i_0_1194, 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)))). 7.02/7.30 cnf(i_0_1932, 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))))). 7.02/7.30 cnf(i_0_6603, 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)))). 7.02/7.30 cnf(i_0_3053, 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)))). 7.02/7.30 cnf(i_0_923, 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),esk78_4(X4,X1,X3,X2)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 7.02/7.30 cnf(i_0_4230, 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),esk321_4(X4,X2,X3,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 7.02/7.30 cnf(i_0_5746, 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))). 7.02/7.30 cnf(i_0_3809, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 7.02/7.30 cnf(i_0_324, 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),esk28_5(X4,X1,X5,X3,X2))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X2,X2),tc_HOL_Obool),esk29_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))))). 7.02/7.30 cnf(i_0_2333, 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),esk185_5(X3,X1,X4,X5,X2)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X2,X2),tc_HOL_Obool),esk186_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))))). 7.02/7.30 cnf(i_0_2283, 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)))). 7.02/7.30 cnf(i_0_7409, 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))). 7.02/7.30 cnf(i_0_2908, 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))))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))|~c_Equiv__Relations_Oequiv(X1,X5,X2))). 7.02/7.30 cnf(i_0_1970, 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)))). 7.02/7.30 cnf(i_0_3402, 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)))). 7.02/7.30 cnf(i_0_913, 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)))))). 7.02/7.30 cnf(i_0_1260, 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)))). 7.02/7.30 cnf(i_0_3230, 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)))). 7.02/7.30 cnf(i_0_5964, 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)),esk464_4(X3,X4,X1,X2)),X4))|esk466_4(X3,X4,X1,X2)!=esk465_4(X3,X4,X1,X2)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X4)))). 7.02/7.30 cnf(i_0_1405, 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)))). 7.02/7.30 cnf(i_0_7301, 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)))). 7.02/7.30 cnf(i_0_5960, 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)),esk465_4(X3,X4,X1,X2)),X4))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk464_4(X3,X4,X1,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X4)))). 7.02/7.30 cnf(i_0_5959, 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)),esk466_4(X3,X4,X1,X2)),X4))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk464_4(X3,X4,X1,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X4)))). 7.02/7.30 cnf(i_0_1379, 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),esk108_5(X5,X3,X4,X2,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 7.02/7.30 cnf(i_0_3763, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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),X5),X4))=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)),X3)),X5)),X4)|~class_Fields_Ofield__inverse__zero(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 7.02/7.30 cnf(i_0_3139, 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)))). 7.02/7.30 cnf(i_0_7550, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),esk598_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))). 7.02/7.30 cnf(i_0_7564, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),esk599_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))). 7.02/7.30 cnf(i_0_5377, 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),esk411_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)))). 7.02/7.30 cnf(i_0_2495, 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),esk202_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))))). 7.02/7.30 cnf(i_0_1054, 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)))). 7.02/7.30 cnf(i_0_1902, 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))). 7.02/7.30 cnf(i_0_2845, 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),esk221_8(X5,X8,X4,X3,X7,X1,X6,X2)),hAPP(c_List_Oset(X2),X6))))). 7.02/7.30 cnf(i_0_1982, 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,esk158_8(X8,X6,X3,X1,X7,X5,X2,X4))),X7))|~hBOOL(hAPP(hAPP(c_member(X1),X8),X3)))). 7.02/7.30 cnf(i_0_5765, 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))))). 7.02/7.30 cnf(i_0_5593, 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))))). 7.02/7.30 cnf(i_0_2578, 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))))). 7.02/7.30 cnf(i_0_4606, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,X4))),X5))=hAPP(c_List_Ofilter(X2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_fequal,hAPP(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))))). 7.02/7.30 cnf(i_0_3665, 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),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X3))),c_SetInterval_Oord__class_OatLeastAtMost(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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),X3)))|~class_Groups_Ocomm__monoid__add(X1))). 7.02/7.30 cnf(i_0_6454, plain, (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)))))=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))|~class_Rings_Oring__1(X1))). 7.02/7.30 cnf(i_0_5398, 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)))). 7.02/7.30 cnf(i_0_7302, 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)))). 7.02/7.30 cnf(i_0_3425, 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),esk258_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)))). 7.02/7.30 cnf(i_0_6639, 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)))). 7.02/7.30 cnf(i_0_1089, 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)))). 7.02/7.30 cnf(i_0_563, 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)))). 7.02/7.30 cnf(i_0_221, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),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_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin)),X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 7.02/7.30 cnf(i_0_7498, 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)))). 7.02/7.30 cnf(i_0_1038, 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)))|~c_Relation_Otrans(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),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),X5)),c_List_Olexord(X1,X4))))). 7.02/7.30 cnf(i_0_4177, 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)))). 7.02/7.30 cnf(i_0_7369, plain, (hBOOL(hAPP(hAPP(X1,esk581_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk582_8(X1,X2,X3,X4,X5,X6,X7,X8)))|hBOOL(hAPP(hAPP(X1,X6),X5))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X8,X7),tc_prod(X8,X7))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X8,X7),tc_prod(X8,X7)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X6),X5)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X4),X3))),c_Transitive__Closure_Ortrancl(tc_prod(X8,X7),X2)))|~hBOOL(hAPP(hAPP(X1,X4),X3)))). 7.02/7.30 cnf(i_0_163, 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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),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)))). 7.02/7.30 cnf(i_0_5961, 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)),esk464_4(X3,X4,X1,X2)),X4))|hAPP(X3,esk467_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)))). 7.02/7.30 cnf(i_0_1840, 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))). 7.02/7.30 cnf(i_0_2266, plain, (hBOOL(hAPP(hAPP(X1,esk173_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk174_8(X1,X2,X3,X4,X5,X6,X7,X8)))|hBOOL(hAPP(hAPP(X1,X4),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X8,X7),tc_prod(X8,X7))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X8,X7),tc_prod(X8,X7)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X6),X5)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X4),X3))),c_Transitive__Closure_Ortrancl(tc_prod(X8,X7),X2)))|~hBOOL(hAPP(hAPP(X1,X6),X5)))). 7.02/7.30 cnf(i_0_5911, 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)))). 7.02/7.30 cnf(i_0_7181, plain, (c_Orderings_Oord__class_OLeast(X1,hAPP(c_Set_Oimage(X2,X1,X3),X4))=hAPP(X3,c_Orderings_Oord__class_OLeast(X2,X4))|~c_Orderings_Oorder__class_Omono(X2,X1,X3)|~class_Orderings_Oorder(X1)|~class_Orderings_Oorder(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X5),esk554_5(X4,X3,X2,X1,X5)))|~hBOOL(hAPP(hAPP(c_member(X2),X5),X4)))). 7.02/7.30 cnf(i_0_5880, 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)))). 7.02/7.30 cnf(i_0_3226, 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))). 7.02/7.30 cnf(i_0_4572, 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)))|esk347_4(X1,X2,X4,X3)!=esk348_4(X1,X2,X4,X3))). 7.02/7.30 cnf(i_0_1090, 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))). 7.02/7.30 cnf(i_0_4178, 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))). 7.02/7.30 cnf(i_0_5194, 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))). 7.02/7.30 cnf(i_0_6945, 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)))). 7.02/7.30 cnf(i_0_1766, 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,esk147_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)))). 7.02/7.30 cnf(i_0_5457, 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)))). 7.02/7.30 cnf(i_0_922, 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),esk78_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)))). 7.02/7.30 cnf(i_0_7559, 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),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X3))),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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),X3)))|~class_Groups_Ocomm__monoid__add(X1))). 7.02/7.30 cnf(i_0_3924, 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)))))). 7.02/7.30 cnf(i_0_1866, 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)))). 7.02/7.30 cnf(i_0_1825, 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)))). 7.02/7.30 cnf(i_0_3138, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,X4))),X5))=hAPP(c_List_Ofilter(X2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_fequal,hAPP(X3,X4)))),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5))|~c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Set_Oinsert(X1),X4),hAPP(c_List_Oset(X1),X5))))). 7.02/7.30 cnf(i_0_2016, 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))))). 7.02/7.30 cnf(i_0_4229, 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),esk321_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)))). 7.02/7.30 cnf(i_0_6387, 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))). 7.02/7.30 cnf(i_0_6388, 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))). 7.02/7.30 cnf(i_0_2490, 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)))))). 7.02/7.30 cnf(i_0_2496, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk202_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))))). 7.02/7.30 cnf(i_0_1256, 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))))))). 7.02/7.30 cnf(i_0_4706, 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)))). 7.02/7.30 cnf(i_0_6524, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk509_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)))))). 7.02/7.30 cnf(i_0_1182, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk96_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)))))). 7.02/7.30 cnf(i_0_4428, 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)))). 7.02/7.30 cnf(i_0_6877, 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))))). 7.02/7.30 cnf(i_0_5116, 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))). 7.02/7.30 cnf(i_0_6900, 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))|hBOOL(hAPP(hAPP(c_member(X2),esk541_7(X4,X3,X1,X6,X7,X5,X2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4)))|~c_Finite__Set_Ofolding__image__simple(X8,X2,X5,X7,X6,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 7.02/7.30 cnf(i_0_1709, 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)))). 7.02/7.30 cnf(i_0_1057, 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)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),X3))|~c_Equiv__Relations_Oequiv(X1,X5,X3))). 7.02/7.30 cnf(i_0_4505, 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)))). 7.02/7.30 cnf(i_0_5883, plain, (hAPP(c_Divides_Oadjust(X1),c_Divides_OposDivAlg(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),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)))). 7.02/7.30 cnf(i_0_3845, 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)))). 7.02/7.30 cnf(i_0_2493, 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),esk202_4(X4,X3,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X3),esk202_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))))). 7.02/7.30 cnf(i_0_2270, 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)))). 7.02/7.30 cnf(i_0_1504, 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)))). 7.02/7.30 cnf(i_0_7417, 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))))). 7.02/7.30 cnf(i_0_1976, 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)))))). 7.02/7.30 cnf(i_0_5966, 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)),esk465_4(X3,X4,X1,X2)),X4))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk464_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)))). 7.02/7.30 cnf(i_0_5965, 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)),esk466_4(X3,X4,X1,X2)),X4))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk464_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)))). 7.02/7.30 cnf(i_0_6658, 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))). 7.02/7.30 cnf(i_0_5592, 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(X1)),X2)),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(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(X3)),X4)))|hBOOL(hAPP(X5,hAPP(hAPP(c_List_Ozip(X1,X3),X2),X4))))). 7.02/7.30 cnf(i_0_1042, 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)))). 7.02/7.30 cnf(i_0_1097, 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)))). 7.02/7.30 cnf(i_0_1181, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk97_5(X2,X3,X4,X5,X1)),esk96_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)))))). 7.02/7.30 cnf(i_0_6523, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk509_5(X2,X3,X4,X5,X1)),esk510_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)))))). 7.02/7.30 cnf(i_0_2752, 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)))). 7.02/7.30 cnf(i_0_2431, 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)))))))). 7.02/7.30 cnf(i_0_2665, 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))))). 7.02/7.30 cnf(i_0_2664, 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))))). 7.02/7.30 cnf(i_0_7320, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),X2)=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))))|~class_Groups_Omonoid__mult(X1))). 7.02/7.30 cnf(i_0_1850, plain, (hAPP(c_Divides_Oadjust(X1),c_Divides_OposDivAlg(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),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)))). 7.02/7.30 cnf(i_0_1492, 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)))). 7.02/7.30 cnf(i_0_2756, 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)))). 7.02/7.30 cnf(i_0_3391, plain, (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)))=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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 7.02/7.30 cnf(i_0_4133, 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)))). 7.02/7.30 cnf(i_0_7549, 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)))),esk598_3(X1,X2,X3))))). 7.02/7.30 cnf(i_0_7562, 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)))),esk599_3(X1,X2,X3))))). 7.02/7.30 cnf(i_0_1983, 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),esk158_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)))). 7.02/7.30 cnf(i_0_1040, 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),esk85_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)))). 7.02/7.30 cnf(i_0_6460, 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)))). 7.02/7.30 cnf(i_0_6232, 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)))). 7.02/7.30 cnf(i_0_2582, 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))))). 7.02/7.30 cnf(i_0_2077, 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),esk161_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)))). 7.02/7.30 cnf(i_0_2115, 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),esk166_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)))). 7.02/7.30 cnf(i_0_152, 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)))). 7.02/7.30 cnf(i_0_1366, 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)))). 7.02/7.30 cnf(i_0_7057, 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),esk547_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)))). 7.02/7.30 cnf(i_0_6880, 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)),esk539_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),esk539_4(X3,X4,X2,X1)))),X3))))). 7.02/7.30 cnf(i_0_5208, 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))))). 7.02/7.30 cnf(i_0_706, 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(hAPP(c_member(X2),X4),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 7.02/7.30 cnf(i_0_7182, plain, (c_Orderings_Oord__class_OLeast(X1,hAPP(c_Set_Oimage(X2,X1,X3),X4))=hAPP(X3,c_Orderings_Oord__class_OLeast(X2,X4))|hBOOL(hAPP(hAPP(c_member(X2),esk554_5(X4,X3,X2,X1,X5)),X4))|~c_Orderings_Oorder__class_Omono(X2,X1,X3)|~class_Orderings_Oorder(X1)|~class_Orderings_Oorder(X2)|~hBOOL(hAPP(hAPP(c_member(X2),X5),X4)))). 7.02/7.30 cnf(i_0_1722, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Oplus__class_Oplus(X1)),X3)),X5)),X4))|~class_Groups_Ocomm__monoid__add(X1))). 7.02/7.30 cnf(i_0_760, 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_Ominus__class_Ominus(X1)),X3)),X4)),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(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_Oab__group__add(X1))). 7.02/7.30 cnf(i_0_6445, 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_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X3)),c_Int_OMin)))|~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)))). 7.02/7.30 cnf(i_0_3591, 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,esk272_6(X4,X5,X3,X6,X1,X2))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 7.02/7.30 cnf(i_0_2910, 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)|~hBOOL(hAPP(hAPP(c_member(X4),X6),X8))|~c_Equiv__Relations_Oequiv(X4,X8,X5)|~c_Equiv__Relations_Oequiv(X1,X9,X3))). 7.02/7.30 cnf(i_0_1764, 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)))))))). 7.02/7.30 cnf(i_0_1493, 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))). 7.02/7.30 cnf(i_0_2755, 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))). 7.02/7.31 cnf(i_0_7015, 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)))). 7.02/7.31 cnf(i_0_4315, 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))))). 7.02/7.31 cnf(i_0_1960, 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)))))))). 7.02/7.31 cnf(i_0_2494, 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),esk202_4(X3,X4,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X4),esk202_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))))). 7.02/7.31 cnf(i_0_4971, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|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))))). 7.02/7.31 cnf(i_0_3733, 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)))). 7.02/7.31 cnf(i_0_1294, 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))))). 7.02/7.31 cnf(i_0_3734, 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)))). 7.02/7.31 cnf(i_0_216, 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)))). 7.02/7.31 cnf(i_0_698, 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)))))). 7.02/7.31 cnf(i_0_6869, 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))))))). 7.02/7.31 cnf(i_0_5332, plain, (hAPP(c_Divides_Oadjust(X1),c_Divides_OnegDivAlg(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),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)))). 7.02/7.31 cnf(i_0_4806, 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))))). 7.02/7.31 cnf(i_0_3659, 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))))))). 7.02/7.31 cnf(i_0_3962, 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))))))). 7.02/7.31 cnf(i_0_1507, 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,esk124_3(X2,X1,X3))),hAPP(X1,esk124_3(X2,X1,X3)))))). 7.02/7.31 cnf(i_0_7384, 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))))). 7.02/7.31 cnf(i_0_4153, 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)))). 7.02/7.31 cnf(i_0_1255, 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))). 7.02/7.31 cnf(i_0_153, 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)))). 7.02/7.31 cnf(i_0_6357, 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))). 7.02/7.31 cnf(i_0_4439, 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)))). 7.02/7.31 cnf(i_0_5922, 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)))). 7.02/7.31 cnf(i_0_2476, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),X1,X2),hAPP(hAPP(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,X3,c_Groups_Otimes__class_Otimes(X1)),X4),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X6),X5))|esk199_6(X4,X5,X3,X6,X2,X1)!=esk198_6(X4,X5,X3,X6,X2,X1)|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(X5,esk197_6(X4,X5,X3,X6,X2,X1))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6)))). 7.02/7.31 cnf(i_0_1112, 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)))). 7.02/7.31 cnf(i_0_3499, 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,esk266_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)))). 7.02/7.31 cnf(i_0_148, 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)))))). 7.02/7.31 cnf(i_0_3233, 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)))). 7.02/7.31 cnf(i_0_2975, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk226_5(X2,X3,X4,X5,X1)),esk226_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))))). 7.02/7.31 cnf(i_0_3736, 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)))). 7.02/7.31 cnf(i_0_1407, 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,esk110_4(X4,X1,X3,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 7.02/7.31 cnf(i_0_4623, plain, (hAPP(c_Divides_Oadjust(X1),c_Divides_OnegDivAlg(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),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))))). 7.02/7.31 cnf(i_0_4782, 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)))). 7.02/7.31 cnf(i_0_3592, 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),esk272_6(X4,X5,X3,X6,X1,X2)),X6))|~class_Groups_Ocomm__monoid__mult(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 7.02/7.31 cnf(i_0_3735, 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)))). 7.02/7.31 cnf(i_0_2276, 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)))). 7.02/7.31 cnf(i_0_787, 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))). 7.02/7.31 cnf(i_0_2840, 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))). 7.02/7.31 cnf(i_0_4129, 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,esk311_2(X2,X1)))|~hBOOL(hAPP(X1,esk311_2(X2,X1))))). 7.02/7.31 cnf(i_0_6402, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_Hilbert__Choice_Oinv__into(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),c_List_Odistinct(X1),c_List_Oset(X1)),X2))=c_Nitpick_Ocard_H(X1,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 7.02/7.31 cnf(i_0_3211, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))|c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2,X1)!=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)))). 7.02/7.31 cnf(i_0_544, plain, (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))|c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2,X1)!=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)))). 7.02/7.31 cnf(i_0_3423, 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))). 7.02/7.31 cnf(i_0_6659, 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)))). 7.02/7.31 cnf(i_0_4130, 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)),esk311_2(X1,X2))))). 7.02/7.31 cnf(i_0_4560, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(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__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),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X1),X5)))|~class_Groups_Ocomm__monoid__mult(X2))). 7.02/7.31 cnf(i_0_574, 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))). 7.02/7.31 cnf(i_0_4313, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|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))))). 7.02/7.31 cnf(i_0_4128, 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,esk311_2(X2,X1)))|hBOOL(hAPP(X2,esk311_2(X2,X1))))). 7.02/7.31 cnf(i_0_1406, 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),esk110_4(X4,X1,X3,X2))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 7.02/7.31 cnf(i_0_2480, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),X1,X2),hAPP(hAPP(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,X3,c_Groups_Otimes__class_Otimes(X1)),X4),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X6),X5))|hBOOL(hAPP(hAPP(c_member(X2),esk197_6(X4,X5,X3,X6,X2,X1)),X6))|esk199_6(X4,X5,X3,X6,X2,X1)!=esk198_6(X4,X5,X3,X6,X2,X1)|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6)))). 7.02/7.31 cnf(i_0_2321, 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)))). 7.02/7.31 cnf(i_0_3232, 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)))). 7.02/7.31 cnf(i_0_138, 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))))). 7.02/7.31 cnf(i_0_5156, 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)))). 7.02/7.31 cnf(i_0_3270, plain, (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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),X2)))=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)))|~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)))). 7.02/7.31 cnf(i_0_1351, 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))))). 7.02/7.31 cnf(i_0_827, 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,esk65_6(X4,X6,X2,X5,X1,X3))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 7.02/7.31 cnf(i_0_481, plain, (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)),X4)),c_Groups_Oone__class_Oone(X1)),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)),X5)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X4),c_Groups_Oone__class_Oone(X1)),X5))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 7.02/7.31 cnf(i_0_6709, 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))). 7.02/7.31 cnf(i_0_4370, 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))). 7.02/7.31 cnf(i_0_1161, 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))). 7.02/7.31 cnf(i_0_7128, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X3)))|~c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(X3,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),X3)),X4))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X3))))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 7.02/7.31 cnf(i_0_2475, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),X1,X2),hAPP(hAPP(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,X3,c_Groups_Otimes__class_Otimes(X1)),X4),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X6),X5))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),hAPP(X5,esk198_6(X4,X5,X3,X6,X2,X1))),hAPP(X5,esk199_6(X4,X5,X3,X6,X2,X1)))!=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(X5,esk197_6(X4,X5,X3,X6,X2,X1))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6)))). 7.02/7.31 cnf(i_0_3500, 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),esk266_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)))). 7.02/7.31 cnf(i_0_2766, plain, (c_Relation_Orefl__on(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk217_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)),esk216_3(X3,X2,X1))))). 7.02/7.31 cnf(i_0_2765, 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),esk217_3(X3,X2,X1)),esk217_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)),esk216_3(X3,X2,X1))))). 7.02/7.31 cnf(i_0_5263, 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))). 7.02/7.31 cnf(i_0_1767, 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),esk147_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)))). 7.02/7.31 cnf(i_0_6981, 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))))). 7.02/7.31 cnf(i_0_3505, 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))))). 7.02/7.31 cnf(i_0_2559, 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)))). 7.02/7.31 cnf(i_0_500, 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)))). 7.02/7.31 cnf(i_0_2478, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),X1,X2),hAPP(hAPP(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,X3,c_Groups_Otimes__class_Otimes(X1)),X4),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X6),X5))|hBOOL(hAPP(hAPP(c_member(X2),esk198_6(X4,X5,X3,X6,X2,X1)),X6))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(X5,esk197_6(X4,X5,X3,X6,X2,X1))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6)))). 7.02/7.31 cnf(i_0_2477, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),X1,X2),hAPP(hAPP(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,X3,c_Groups_Otimes__class_Otimes(X1)),X4),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X6),X5))|hBOOL(hAPP(hAPP(c_member(X2),esk199_6(X4,X5,X3,X6,X2,X1)),X6))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(X5,esk197_6(X4,X5,X3,X6,X2,X1))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6)))). 7.02/7.31 cnf(i_0_4917, 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_Ominus__class_Ominus(tc_Int_Oint),X4),c_Int_OMin)))),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))))). 7.02/7.31 cnf(i_0_3051, 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_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)))=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)))|~class_Rings_Ocomm__semiring__1(X1))). 7.02/7.31 cnf(i_0_2288, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(c_Hilbert__Choice_Oinv__into(tc_List_Olist(X2),tc_fun(X2,tc_HOL_Obool),c_List_Odistinct(X2),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)))). 7.02/7.31 cnf(i_0_2482, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),X1,X2),hAPP(hAPP(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,X3,c_Groups_Otimes__class_Otimes(X1)),X4),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X6),X5))|hBOOL(hAPP(hAPP(c_member(X2),esk198_6(X4,X5,X3,X6,X2,X1)),X6))|hBOOL(hAPP(hAPP(c_member(X2),esk197_6(X4,X5,X3,X6,X2,X1)),X6))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6)))). 7.02/7.31 cnf(i_0_2481, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),X1,X2),hAPP(hAPP(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,X3,c_Groups_Otimes__class_Otimes(X1)),X4),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X6),X5))|hBOOL(hAPP(hAPP(c_member(X2),esk199_6(X4,X5,X3,X6,X2,X1)),X6))|hBOOL(hAPP(hAPP(c_member(X2),esk197_6(X4,X5,X3,X6,X2,X1)),X6))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6)))). 7.02/7.31 cnf(i_0_2479, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),X1,X2),hAPP(hAPP(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,X3,c_Groups_Otimes__class_Otimes(X1)),X4),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X6),X5))|hBOOL(hAPP(hAPP(c_member(X2),esk197_6(X4,X5,X3,X6,X2,X1)),X6))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),hAPP(X5,esk198_6(X4,X5,X3,X6,X2,X1))),hAPP(X5,esk199_6(X4,X5,X3,X6,X2,X1)))!=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6)))). 7.02/7.31 cnf(i_0_3023, 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)))). 7.02/7.31 cnf(i_0_2132, 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))). 7.02/7.31 cnf(i_0_708, 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(hAPP(c_member(X2),esk62_4(X4,X1,X3,X2)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 7.02/7.31 cnf(i_0_828, 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),esk65_6(X4,X6,X2,X5,X1,X3)),X5))|~class_Groups_Ocomm__monoid__add(X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 7.02/7.31 cnf(i_0_7326, 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)),esk575_4(X4,X3,X2,X1))))). 7.02/7.31 cnf(i_0_707, 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),esk62_4(X4,X1,X3,X2))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 7.02/7.31 cnf(i_0_135, plain, (c_Orderings_Oorder__class_Omono(X1,tc_fun(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(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))),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))),X5))|~c_Orderings_Oorder__class_Omono(X1,tc_fun(X2,tc_HOL_Obool),X3)|~class_Orderings_Oorder(X1))). 7.02/7.31 cnf(i_0_2423, 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)|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(X6,esk190_11(X7,X5,X3,X6,X1,X9,X10,X4,X8,X11,X2)),esk191_11(X7,X5,X3,X6,X1,X9,X10,X4,X8,X11,X2))),X7))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X11),X8)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X10),X9)))|~c_Equiv__Relations_Oequiv(X2,X11,X8)|~c_Equiv__Relations_Oequiv(X4,X10,X9))). 7.02/7.31 cnf(i_0_4456, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk336_6(X3,X4,X5,X6,X2,X1)),esk337_6(X3,X4,X5,X6,X2,X1))),hAPP(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3)))))|hBOOL(hAPP(hAPP(X3,X6),X5))|~c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X5)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X4))))). 7.02/7.31 cnf(i_0_4995, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)=hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)|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),esk387_7(X7,X6,X5,X4,X3,X2,X1)),esk388_7(X7,X6,X5,X4,X3,X2,X1)))),X7))|~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_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X7))))). 7.02/7.31 cnf(i_0_4067, 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)))). 7.02/7.31 cnf(i_0_4978, 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))). 7.02/7.31 cnf(i_0_2268, 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),esk173_8(X5,X6,X7,X8,X4,X3,X2,X1)),esk174_8(X5,X6,X7,X8,X4,X3,X2,X1)))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X6)))|hBOOL(hAPP(hAPP(X5,X8),X7))|~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),X8),X7))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X6)))|~hBOOL(hAPP(hAPP(X5,X3),X4)))). 7.02/7.31 cnf(i_0_7370, 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),esk581_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk582_8(X3,X4,X5,X6,X7,X8,X2,X1))),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X5))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X4)))|hBOOL(hAPP(hAPP(X3,X8),X7))|~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),X8),X7)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X5))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X4)))|~hBOOL(hAPP(hAPP(X3,X6),X5)))). 7.02/7.31 cnf(i_0_2425, 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),esk190_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)|~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)))|~c_Equiv__Relations_Oequiv(X4,X9,X8)|~c_Equiv__Relations_Oequiv(X2,X11,X10))). 7.02/7.31 cnf(i_0_2424, 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),esk191_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)|~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)))|~c_Equiv__Relations_Oequiv(X2,X11,X10)|~c_Equiv__Relations_Oequiv(X4,X9,X8))). 7.02/7.31 cnf(i_0_1385, 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))). 7.02/7.31 cnf(i_0_6540, 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)))))). 7.02/7.31 cnf(i_0_3891, plain, (hBOOL(hAPP(hAPP(X1,esk290_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),esk291_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk290_3(X1,X2,X3)),esk291_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk291_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))))). 7.02/7.31 cnf(i_0_1765, 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))))). 7.02/7.31 cnf(i_0_1370, 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)|~hBOOL(hAPP(hAPP(c_member(X5),X7),X9))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X10))|~c_Equiv__Relations_Oequiv(X5,X9,X6)|~c_Equiv__Relations_Oequiv(X1,X10,X3))). 7.02/7.31 cnf(i_0_4994, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)=hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)|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),esk387_7(X7,X4,X3,X6,X5,X2,X1)),esk388_7(X7,X4,X3,X6,X5,X2,X1))),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X7)))|~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),X5),X6)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X7))))). 7.02/7.31 cnf(i_0_140, 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,esk9_6(X4,X5,X3,X6,X2,X1))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6)))). 7.02/7.31 cnf(i_0_7461, 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)))). 7.02/7.31 cnf(i_0_1959, 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))))). 7.02/7.31 cnf(i_0_2382, 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)))). 7.02/7.31 cnf(i_0_1127, 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)))). 7.02/7.31 cnf(i_0_2675, 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)))). 7.02/7.31 cnf(i_0_1849, 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)))). 7.02/7.31 cnf(i_0_236, 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)))). 7.02/7.31 cnf(i_0_180, 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)))). 7.02/7.31 cnf(i_0_5157, 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))). 7.02/7.31 cnf(i_0_7203, 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))). 7.02/7.31 cnf(i_0_7245, 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,esk565_4(X1,X3,X4,X2))))). 7.02/7.31 cnf(i_0_2764, 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)))). 7.02/7.31 cnf(i_0_4559, 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))). 7.02/7.31 cnf(i_0_141, 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),esk9_6(X4,X5,X3,X6,X2,X1)),X6))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6)))). 7.02/7.31 cnf(i_0_7371, 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),esk579_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk580_8(X3,X4,X5,X6,X7,X8,X2,X1))),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk581_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk582_8(X3,X4,X5,X6,X7,X8,X2,X1)))),X4))|hBOOL(hAPP(hAPP(X3,X8),X7))|~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),X8),X7)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X5))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X4)))|~hBOOL(hAPP(hAPP(X3,X6),X5)))). 7.02/7.31 cnf(i_0_6386, 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))). 7.02/7.31 cnf(i_0_5716, plain, (hBOOL(hAPP(hAPP(X1,esk438_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),esk439_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),esk439_3(X1,X2,X3)),esk438_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk439_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))))). 7.02/7.31 cnf(i_0_6870, 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))))). 7.02/7.31 cnf(i_0_3658, 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))))). 7.02/7.31 cnf(i_0_4626, plain, (c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2)=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)))). 7.02/7.31 cnf(i_0_2267, 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),esk173_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk174_8(X3,X4,X5,X6,X7,X8,X2,X1))),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk175_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk176_8(X3,X4,X5,X6,X7,X8,X2,X1)))),X4))|hBOOL(hAPP(hAPP(X3,X6),X5))|~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),X8),X7)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X5))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X4)))|~hBOOL(hAPP(hAPP(X3,X8),X7)))). 7.02/7.31 cnf(i_0_7244, 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,esk565_4(X1,X3,X4,X2)))),hAPP(X4,esk565_4(X1,X3,X4,X2)))))). 7.02/7.31 cnf(i_0_6356, 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__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),X5)))=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)),X5)),X3)),X6)),X4)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 7.02/7.31 cnf(i_0_4369, 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)))). 7.02/7.31 cnf(i_0_6812, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))),c_Int_OMin)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin),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)))). 7.02/7.31 cnf(i_0_3563, 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)))). 7.02/7.31 cnf(i_0_3209, plain, (c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2)=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)))). 7.02/7.31 cnf(i_0_6516, 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))). 7.02/7.31 cnf(i_0_4227, 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))). 7.02/7.31 cnf(i_0_5912, 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))). 7.02/7.31 cnf(i_0_2430, 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))). 7.02/7.31 cnf(i_0_2187, 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),esk171_3(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2)))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 7.02/7.31 cnf(i_0_3963, 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))). 7.02/7.31 cnf(i_0_2429, 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),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))). 7.02/7.31 cnf(i_0_546, plain, (c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2)=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)))). 7.02/7.31 cnf(i_0_1098, 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))). 7.02/7.31 cnf(i_0_2279, 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))). 7.02/7.31 cnf(i_0_2189, 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),esk171_3(X3,X1,X2)))!=X3)). 7.02/7.31 cnf(i_0_2666, 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))). 7.02/7.31 cnf(i_0_2188, 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),esk171_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))))). 7.02/7.31 cnf(i_0_6589, 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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),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)))). 7.02/7.31 cnf(i_0_2190, 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),esk171_3(X3,X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2))))). 7.02/7.31 cnf(i_0_278, 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),esk25_6(X6,X4,X3,X2,X5,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 7.02/7.31 cnf(i_0_2215, 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)))). 7.02/7.31 cnf(i_0_217, 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))))). 7.02/7.31 cnf(i_0_3022, 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)))). 7.02/7.31 cnf(i_0_6811, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin),X2)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 7.02/7.31 cnf(i_0_3210, plain, (c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2)=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)))). 7.02/7.31 cnf(i_0_107, plain, (c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2)=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)))). 7.02/7.31 cnf(i_0_5370, 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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin)),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.02/7.31 cnf(i_0_5923, 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))))). 7.02/7.31 cnf(i_0_4440, 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))))). 7.02/7.31 cnf(i_0_604, 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),esk47_6(X6,X4,X3,X2,X5,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 7.02/7.31 cnf(i_0_575, 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))))). 7.02/7.31 cnf(i_0_6799, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))=hAPP(c_Code__Numeral_Oint__of,X1)|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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). 7.02/7.31 cnf(i_0_6450, 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)))). 7.02/7.31 cnf(i_0_993, 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)))). 7.02/7.31 cnf(i_0_2846, 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)))). 7.02/7.31 cnf(i_0_5264, 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))))). 7.02/7.31 cnf(i_0_2530, 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))))). 7.02/7.31 cnf(i_0_2320, 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))))). 7.02/7.31 cnf(i_0_4248, 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)))). 7.02/7.31 cnf(i_0_5658, 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))). 7.02/7.31 cnf(i_0_6515, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk508_2(X2,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),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_COMBS(X1,X1,tc_HOL_Obool),X2),c_COMBI(X1))))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),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_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1)),c_fequal)),X2)))))|~c_Equiv__Relations_Opart__equivp(X1,X2))). 7.02/7.31 cnf(i_0_6800, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))),c_Int_OMin)=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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|X1=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). 7.02/7.31 cnf(i_0_603, 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),esk47_6(X6,X4,X3,X2,X5,X1))))!=X6|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 7.02/7.31 cnf(i_0_6183, 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)))). 7.02/7.31 cnf(i_0_7032, 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)))). 7.02/7.31 cnf(i_0_1903, 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)))). 7.02/7.31 cnf(i_0_2600, 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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),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)))). 7.02/7.31 cnf(i_0_277, 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),esk25_6(X6,X4,X3,X2,X5,X1))))!=hAPP(X6,esk25_6(X6,X4,X3,X2,X5,X1))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 7.02/7.31 cnf(i_0_4066, 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)))))))). 7.02/7.31 cnf(i_0_7329, 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)))))). 7.02/7.31 cnf(i_0_4513, 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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 7.02/7.31 cnf(i_0_6441, 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))|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)))). 7.02/7.31 cnf(i_0_6165, 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)))). 7.02/7.31 cnf(i_0_2808, 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)))). 7.02/7.31 cnf(i_0_237, 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))))). 7.02/7.31 cnf(i_0_181, 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))))). 7.02/7.31 cnf(i_0_4141, 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)))). 7.02/7.31 cnf(i_0_5949, 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))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.02/7.31 cnf(i_0_6290, 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))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 7.02/7.31 cnf(i_0_1159, plain, (c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_fun(X2,X1))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_HOL_Obool),X1),hAPP(c_COMBS(tc_fun(X2,X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X2,X1)),c_fconj),X3))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_fun(X2,X1),X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X2,X1),X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_fun(X2,X1))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X2,X1),X2,X1),c_COMBI(tc_fun(X2,X1))),X4)))))=hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,X1),X3),X4)|~class_Complete__Lattice_Ocomplete__lattice(X1))). 7.02/7.31 cnf(i_0_4521, plain, (c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_fun(X2,X1))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_HOL_Obool),X1),hAPP(c_COMBS(tc_fun(X2,X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X2,X1)),c_fconj),X3))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_fun(X2,X1),X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X2,X1),X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_fun(X2,X1))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X2,X1),X2,X1),c_COMBI(tc_fun(X2,X1))),X4)))))=hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,X1),X3),X4)|~class_Complete__Lattice_Ocomplete__lattice(X1))). 7.02/7.31 cnf(i_0_4049, plain, (hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X1,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X1)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(X2,X3)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X1)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X1)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X1)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(X1,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X1)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X1)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(X1,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X4),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X3))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X1)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X1))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X1)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X1)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(X1,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X1)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X1)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X1))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X1)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X1)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X1)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X1))))),tc_prod(X1,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(X1)),hAPP(hAPP(c_COMBB(X1,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X1)))),tc_prod(X1,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(X1)),c_Product__Type_Ofst(X1,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)))))))=c_Random__Sequence_ORandom(X1,X2,X4,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X4),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))). 7.02/7.31 cnf(i_0_5046, 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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))),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))). 7.02/7.31 cnf(i_0_6919, 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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),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_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Int_Onumber__ring(X1))). 7.02/7.31 cnf(i_0_3902, plain, (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)|X5=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). 7.02/7.31 cnf(i_0_5941, 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)),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))),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)),hAPP(c_COMBC(X1,X3,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))),hAPP(c_COMBC(X1,X3,tc_HOL_Obool),X6))))),X5)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X7)))). 7.02/7.31 cnf(i_0_2529, 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)))). 7.02/7.31 cnf(i_0_4249, 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))))). 7.02/7.31 cnf(i_0_6182, 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))))). 7.02/7.31 cnf(i_0_7033, 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))))). 7.02/7.31 cnf(i_0_5687, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),X2)),X3))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X2)))),hAPP(X2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),X2)),X3))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X2))))))|~c_Orderings_Oorder__class_Omono(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(X2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),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)),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),X2)),X3))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(X1,tc_HOL_Obool),X2)))))))). 7.02/7.31 cnf(i_0_1513, 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(c_fequal,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))=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))). 7.02/7.31 cnf(i_0_1557, 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(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)=X1|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 7.02/7.31 cnf(i_0_1005, 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(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)|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 7.02/7.31 cnf(i_0_6788, 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)))). 7.02/7.31 cnf(i_0_5240, 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))|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_Odistrib__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 7.02/7.31 cnf(i_0_6680, 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|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)))). 7.02/7.31 cnf(i_0_3071, 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|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)))). 7.02/7.31 cnf(i_0_2159, 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))))). 7.02/7.31 # End listing active clauses. There is an equivalent clause to each of these in the clausification! 7.02/7.31 # Begin printing tableau 7.02/7.31 # 2,0,0,1 x c 7.02/7.31 cnf(i_0_8544, plain, (c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts))). 7.02/7.31 # 1,3,5234,0 7.02/7.31 cnf(i_0_8147, plain, (~c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts))). 7.02/7.31 # 0,1,540,0 7.02/7.31 cnf(i_0_540, watchlist, (~c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts))). 7.02/7.31 7.02/7.31 # 2,0,0,0 c 7.02/7.31 cnf(i_0_8545, plain, (~c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))). 7.02/7.31 # 1,3,5234,0 7.02/7.31 cnf(i_0_8147, plain, (~c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts))). 7.02/7.31 # 0,1,540,0 7.02/7.31 cnf(i_0_540, watchlist, (~c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts))). 7.02/7.31 7.02/7.31 # 2,0,0,0 c s 7.02/7.31 cnf(i_0_8546, plain, (~c_Hoare__Mirabelle_Ohoare__derivs(t_a,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts))). 7.02/7.31 # 1,3,5234,0 7.02/7.31 cnf(i_0_8147, plain, (~c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts))). 7.02/7.31 # 0,1,540,0 7.02/7.31 cnf(i_0_540, watchlist, (~c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts))). 7.02/7.31 7.02/7.31 # End printing tableau 7.02/7.31 # SZS output end CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 7.02/7.31 # Branches closed with saturation will be marked with an "s" 7.02/7.31 # Proof search success! 7.02/7.31 # Exiting... 7.04/7.32 EOF